1. (a) 180 for Sara 1

212 for Zenta 1

108 for Huw 1 Accept figures written elsewhere on the page so long as it is clear which number belongs to which house.

(b) States four numbers in ascending order, eg: 1 • 92. 108, 180, 212

Accept correct numbers stated in words for (b). Accept correct ordering of own responses to (a) only if three different, non-consecutive, 3-figure numbers have been given. Award 3m for (a) if this has been left completely blank but(b) has been completed correctly. Do not accept numbers in descending order Do not accept names in place of numbers

[4]

2. (a) Indicates vertical line of symmetry only. 1

(b) Indicates vertical, horizontal and two diagonal lines of symmetry only. 1

(c) Indicates vertical and horizontal lines of symmetry only. 1

(d) Indicates diagonal line of symmetry only. 1

(e) Indicates horizontal line of symmetry only. 1

For each mark all lines of symmetry, and no extra lines, must be indicated. Lines need not be accurately drawn, so long as the general position is indicated correctly.

[5]

3. (a) Indicates 30 zebras 1

(b) Indicates a number of elephants between 23 and 27 inclusive. 1

2

(c) Indicates that the fifth symbol is not a half square eg: 1 • Its not half a bird. • Its only a bit. • She thought it was a half. • For 45 it should be half a box. • Its 42 birds.

Accept responses indicating that there are between 41 and 44 whole birds inclusive. Do not accept responses which imply that there are parts of a bird in the park. eg Its 42½ birds

(d) Indicates 2 symbols for snakes and less than half of another symbol. 1 Accept symbols for snakes indicated elsewhere on the question. Accept written descriptions of the pictogram required eg 2 whole ones and less than a half. Symbols may be any shape, but the third symbol must have less than half the area of the whole symbol Do not accept more than three symbols or parts of symbols.

4. (a) For 2m indicates – 75. 2

For only 1m shows – in any position, eg: • 75 – • – 15 • - –

Accept + – 75 Do not accept correct number with wrong sign eg + 75

(b) For 2m indicates ÷ 6. 2

For only 1m shows ÷ in any position, eg: • 6 ÷ • ÷ 15 • ÷ ÷

Accept x 16

Do not accept correct number with wrong sign eg 6 x Accept responses to parts (a) and (b) in reverse order, if otherwise correct for 1 or 2 marks.

[4]

3

5. (a) a bird 1

(b) diver 1

(c) fish 1 Accept any indication of the correct responses eg states the object draws an arrow to the object draws the object. Accept ♦ – 20m for the fish. Do not accept ♦ 20m for the fish

[3]

6. (a) Reflects complete figure correctly 1

mirror If the shape is drawn freehand, it must go from dot to dot.

(b) Reflects L shape correctly. 1 mirror

Reflects remaining shape correctly 1

mirror

Award 2m for:

mirror

If the shape is drawn freehand, it must go from dot to dot.

(c) Reflects the complete pattern in the vertical mirror 1 mirror

mirror

4

Reflects the complete pattern in the horizontal mirror 1

mirror

mirror

Reflects the complete pattern in both mirrors 1

mirror

mirror

Award 3m for:

mirror

mirror

eg for 2m:

mirror

mirror

Do not accept follow through.

If the shape is drawn freehand, it must go from dot to dot. [6]

7. (a) Indicates fraction in the range 13/20 to 17/20 exclusive for Lena, eg: 1 • 3/4 • 3 quarters 2/3 7/10 8/10

Accept decimals in the range 0.65 to 0.85 exclusive. Do not accept percentages.

5

Indicates fraction in the range 7/30 to 13/30 exclusive for John, eg: 1 • 1/3 third

1/4

3/10

3/8

2/5

Accept decimals in the range 0.23 to 0.43 exclusive. Do not accept percentages.

(b) Indicates a percentage in the range 15% to 35% exclusive for Mindu. 1

Indicates a percentage in the range 30% to 50% exclusive for Mary. 1 Do not accept fractions or decimals

(c) Indicates a position between 3.8cm and 6.2cm inclusive up the rope. 1 Accept any mark on the line whose vertical midpoint is within the range given.

[5]

8. (a) Lists the six shoe sizes in order. 1 Ignore references to other sizes.

Uses a tallying method to show number sold in each size or number sold each day. 1

Accept errors or omissions if there is evidence that a tallying method was used. Accept ⏐⏐ , ⏐⏐⏐ or for tally of 5.

A single symbol, used consistently, is required for this mark.

Indicates how many of each size were sold, eg: 1 • Makes an accurate tally. Draws an accurate bar chart. States the correct number of each size sold

The numbers of each size sold need not be stated if the information is indicated in any other way. The correct numbers are Size Number Sold

4 55 66 57 88 39 2

The 3 marks for part (a) are independent

(b) Indicates most frequently sold size, eg: 1 • 7

Accept follow through from results in(a)

6

(c) Uses own table to compare the sales of sizes 7, 8 and 9 with the sales of sizes 1

4, 5 and 6, eg: • They sold more of other sizes. • That is what they sold less of. • The smaller sizes were more popular. • That was only 13 pairs. There were 16 smaller ones. There are more | on the 4, 5, 6. Add up all the 4,5,6 then add up all the 7, 8, 9.

Accept valid explanations based on the pupils own table that Lisa is right or wrong. Award this mark only for explanations which could be based on the pupils own table. Do not accept explanations which refer only to some larger or some smaller sizes. eg ♦ Only 5 were sold in sizes 8 and 9 but 5 were sold in

size 4. ♦ Compare the number below size 6 with the number

above size 6. [5]

9. (a) Indicates 19 matchsticks, without drawing the matchsticks in a pattern 1 Do not accept incomplete calculation eg ♦ 2 × 9 + 1 Accept responses accompanied by a table of results. Do not accept responses accompanied by drawings of matchsticks in a pattern.

(b) Expresses the rule symbolically, eg: 1 • M = 2T +1

M = 1 + 2 × T

T + T + 1 = M

T → × 2 → + 1 → M

T2 = M – 1

T = ½ M – ½

T = ½ (M – 1)

Accept use of lower case letters, eg ♦ m = 2t + 1 Do not accept expressions which do not indicate the relationship between M and T, eg: ♦ 2T + 1 ♦ 2T + 1M. Do not accept use of words as well as symbols, eg: ♦ × T by 2 + 1 = M Do not accept incorrect equations, eg: ♦ M – 1 ÷ 2 = T

(c) Indicates 5 triangles, without drawing the matchsticks in a pattern 1

7

(d) Indicates 17 triangles, without drawing the matchsticks in a pattern 1

Do not accept incomplete calculations Accept responses accompanied by a table of results. Do not accept responses accompanied by drawings of matchsticks in a pattern.

[4]

10. (a) Indicates correct probability, eg: 1 • ½ • 50% • 0.5

Accept equivalent fractions eg: ♦ 2/4 ♦ 2 out of 4 Do not accept answers in ratio form, eg: ♦ 1:1 ♦ 1 to 1 ♦ fifty fifty ♦ events Do not accept 1 in 2 Accept responses which relate the half to the area of the sector, eg: ♦ 3 is half of the circle. Do not accept incorrect number eg ♦ 50

(b) Shades in two thirds of the diagram, eg: 1 • Shades in any eight sectors

(c) Shades in 40% of the diagram, eg: 1 • Shades in any eight sectors

[3]

11. 3a 1

3b + 2c 1

2d + 7 1 Accept alternative orders or use of multiplication sign, eg: ♦ a × 3 ♦ c × 2 + b3 ♦ 2 × d + 1× 7

ccept use of capA ital letters, eg: ♦ 3A ♦ 2c + B3 Accept use of extra zeros, eg: ♦ 3a + 00 ♦ 2d + 07

8

Do not accept use of repeated addition instead of multiplication, eg: ♦ a + a + a ♦ b + 2b + c + c Do not accept multiplication by 1 without use of a multiplication sign, eg: ♦ 2d + 17 ♦ 2d + 1.7 Do not accept missing addition signs, eg: ♦ 3b, 2c Do not accept use of s to indicate plurality, eg: ♦ 3as ♦ 3bs + 2cs Do not accept incorrect use of indices, eg: ♦ b³ + 2c

4c + 4f + 8 1 Accept factorisation, eg: ♦ 4(e + f) + 8 ♦ 4(e + f + 2) Accept ♦ 5 + 3 for 8

[4]

12. (a) Labels correct sections 1

badminton

squash

football

Accept correct sections labelled 40% and 5%.

(b) Estimates between 25% and 35% inclusive went swimming 1

Estimates between 10% and 20% inclusive played tennis 1

The estimates given for swimming and tennis total 45%. 1

eg for 3m • 30, 15 • 35, 10

9

eg for 2m • 30, 10 • 35, 15

Labels for swimming and tennis are not required. Accept follow through from(a). Acceptable estimates for each sector are:

25%-35%

3%-10%

35%-45%

Do not accept a percentage for tennis which is greater than that given for swimming

(c) Indicates 104 for football 1

Indicates 13 for squash 1

(d) Shows evidence of calculating 20% of 700 1 or indicates that the total number of people affects the calculation, eg: • More people there on Saturday. • It matters what it is a percentage of. • 20% of 700 is more than on Friday. • A different number of people makes it different. On Friday it was only 260 people and on Saturday it was 700. It was 20% of a different day. There were 700 people on Saturday so 20% would be more. 260 came on Friday but 700 came on Saturday. The percentage doesnt say how many people went.

Accept 140 as evidence. Do not accept responses which add nothing to the information provided eg: ♦ Because 260 people came on Friday and 700 came

on Saturday. Do not accept false statements, eg: ♦ On Saturday 700 people played football. ♦ 20% is a larger percentage on Saturday, and 40% is a

smaller, percentage on Friday. [7]

13. (a) Draws the base of the triangle as 9cm ±2mm 1

Draws 51° angle accurately to ±2° and extends edge to intersect 1

Draws 74° angle accurate to ±2°, and extends edge to intersect 1 Award only 2m for base and two angles drawn accurately, but sloping edges not extended to intersect. Award only 1m for base and one angle, or two angles only, drawn accurately, but sloping edges not extended to intersect.

10

(b) Draws 121° angle accurately to ±2° 1

Draws edge from end of given base as 2.5cm ±2mm, and completes the diagram. 1 Accept correct trapezium drawn in (a)

Award second mark for (b) only if trapezium is complete. [5]

11

1. (a) Indicates 20 points. 1 Do not accept incomplete calculation, eg: ♦ 8 + 12

(b) Indicates 2 hoops on the 8 peg and 1 hoop on the 6 peg 1 Accept any indication eg correct number of hoops drawn onto the diagram.

(c) Indicates 4 hoops 1 Accept 32 (points). Accept indication of 4 hoops in a valid calculation to total 30 or 32, eg: ♦ 3 × 8 + 6 = 30 ♦ 3 and 1 ♦ 4 × 8 Do not accept 30 or 31.

[3]

2. (a) Indicates that belongs in set A. 1

Indicates that belongs in set B. 1

Indicates that belongs in set A. 1

Accept shapes drawn in correct sets.

(b) Indicates that the shape has four edges, eg: 1 • 4 sides. • 4 corners. • 4 points.

Do not accept false statements, eg: ♦ Because they are squares.

(c) Indicates that the shape is symmetrical, eg: 1 • Its got symmetry. • Same on both sides. • Its got a mirror line. • You can fold it. • It balances.

[5]

3. (a) Row 5. 1

(b) Row 1. 1

(c) Row 4. 1 Accept any indication of the correct responses.

12

(d) Indicates 3 more numbers ending in 3 or 8, eg: 1

• 18, 23, 28 • 43, 18, 38 • 18, 28, 38

Do not accept any of 3, 8 or 13.

(e) Completes the first column as 35 1 34 33

Completes the third column as 45 1 44 43

Award only 1m if 2 rows are correct but no column is correct, eg for ♦ 35 (40) 45 ♦ 33 (39) 43 ♦ 33 (38) 43

[6]

4. (a) 177 1

(b) Carl 1

(c) Carl 1

Deri 1

(d) Deri 1

(e) Akira 1 Accept any indication of the correct responses. Do not accept additional incorrect responses. Accept 324 for Carl. Accept Carl and Deri in either order. Accept ♦ 411 for Carl and 212 for Deri

[6]

5. (a) Indicates a circle, square and triangle, eg: 1 • Round, square, triangle. Draws: Circles one of each shape on the diagram.

Do not accept a listing of all the counters in the bag. eg: 1 2 4 Triangle : 1 Circle : 2 Square : 4

13

(b) Explains that there are more squares than circles or triangles, eg: 1

• More

4 squares, but only 2 round and 1 triangle. Not as many s and s Squares because there are a lot of them.

Accept responses which do not specify that the square is the most likely shape if it is clear from the explanation that the square is intended. Accept explanations which refer to squares and only one other shape, eg: ♦ More squares than circles. Accept sophisticated responses related to the probability eg ♦ because its 4/7. Do not accept explanations which add nothing to the information provided eg ♦ There are 4 , 2 and 1 .

(c) Indicates a greater number of circles than squares. 1 Ignore any reference to triangular counters.

Accept use of more counters than are illustrated at the start of the question, eg: ♦ 20 round, 10 square. Accept one or more circles with no squares. Accept descriptions of the process eg ♦ She puts in more circles.

(d) For 2m indicates a number of circles, squares and triangles which will make the number of each shape equal., eg 2 • ‘1 square, 2 round. • Draws: • 1 2 3

• ‘He must make

For only 1m indicates numbers to make the number of two of the shapes equal. Accept responses drawn on the diagram given. Accept descriptions of the process. eg ♦ You need to make it so there are the same number of

each shape. Do not accept responses which could imply that an equal number of each shape are added to the bag eg: ♦ You need to have the same number of each shape.

You need

[5]

6. (a) 2 1

(b) 3 1

(c) 4 1

14

(d) 3, eg: 1

Accept any indication of the correct responses.

[4]

7. (a) Indicates that 0 is the last digit, eg: 1 • Writes 0 in the third box. • 0 at the end.

Ignore any digit, or no digit, suggested for the middle number eg: ♦ 700 7 0 Accept responses written elsewhere than on the screen. Do not accept insertion of a decimal point eg ♦ 7.40

(b) Indicates that the first digit is 7, eg: 1 • 74

Indicates the last two digits are both 0, eg: 1 • 0400.

eg for 2m • 7400

Accept responses written elsewhere than on the screen. Do not accept insertion of a decimal point eg ♦ 74.00

[3]

8. (a) For 2m indicates 2

4, 2 6, 2 8, 2 10, 2 12, 2

Accept any five co-ordinate pairs, given in any order from: (4,2);(6,2); (8,2); (10,2); (12, 2); (14,2); (16,2) Award only 1m for four acceptable co-ordinate pairs, or for five acceptable co-ordinate pairs but with positions reversed eg (2,6); (2,8); (2,10); (2,12); (2,14)

15

(b) Indicates awareness of the sameness of one co-ordinate, eg: 1 • All 2s. • It stays the same. • Its 2 2 2 2 2. • They are all on the line for 2. • The height stays at 2.

Indicates awareness of the increment of 2 in the other co-ordinate, eg: 1 • Even numbers. • Its the 2 times (table). • Goes up 2. • Its add 2.

Do not accept responses which do not refer to the co-ordinate numbers eg ♦ all the squares are the same height. Accept awareness indicated in (c). Allow follow through for both marks if co-ordinates are reversed in (a), but not for other errors. Do not accept responses which could imply that the series is geometric eg ♦ Times by 2.

(c) Indicates that 17 is not a multiple of 2, eg: 1 • Its not even. • Because it should go up in 2s. • 2 × 8 = 16

2 × 9 = 18 • The squares are 2cm across. • Its 1 out. • It should be (18,2). • That would mean half a square.

Do not accept follow through from positions reversed in (a) eg ♦ It should be 2, something not something, 2. Do not accept irrelevant explanations eg ♦ 17 does not go in to 2 ♦ The graph doesnt go up to 17.

(d) 3, 3 1

6, 3 1 Accept Co-ordinate pairs with the structure (3n, 3), (3n + 1, 3) eg for 2m ♦ (9,3) and (12,3) Award only 1m for two acceptable co-ordinate pairs but with positions reversed.

[7]

16

9. (a) Indicates why 9 × 19 must be less than 2000, eg: 1

• Thats enough for 10 stamps. • For stamps 1p more its still less than £2. • Make them 20p each.. • 9 × 20 = 180 • 10 × 19 = 190 • 20 × 10 = 200 • 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 = 180 • All the 10s in 19 is only 90p, and all the 9s is less than that. • 9 × 10 = 90 and 9 × 9 = 81, both less than £1.

Accept working with rounded numbers even if there is a numerical error, eg 20 × 9 = 189 Do not accept partial working with no explanation eg 9 × 10 = 90, 9 × 9 = 81

Ignore any reference to units

(b) States 171(p) and indicates use of a correct non-calculator method, eg: 1

20 9 = 180180 – 9 = 171

2 19 = 384 19 = 768 19 = 1529 19 = 171

199

1.718

9 10 = 909 9 = 81

1.71

191919191919191919

1.71819 19 = 38

19571976199519

11419

13319

15219

171 Units are not required.

Accept 171 or 1.71 with any units. Do not accept 17.1 Do not accept responses accompanied by no working or spurious working Do not accept 19 9 1.17 with no carried 8.

17

Do not accept 19 19 19 19 19 19 19 19 19 171 with no carried 8.

[2]

10. (a) For 3m indicates nets (A), (B), (E) and (F), and no others 3 Award only 2m for one error or omission eg (A), (B), (E), (F), (D) (A), (B), (E) Award only 1m for two errors or omissions eg (A), (B), (E), (F), (C), (D) (A), (B), (E), (C) (A), (B)

(b) Explains why net (C) cannot be folded into a cuboid, eg: 1 • draws: or: or:

differentlengths

swap

• One side is too big. • It cant reach to join up. • The top square and rectangle are the wrong way round. • Because a long side would be opposite a short side when you fold it. • Bends in the wrong place. • There is an end where the side should be.

(c) Explains why net (D) cannot be folded into a cuboid, eg: 1 • draws: or: or:

• Its got no top. • One square is on the wrong side. • It would have a hole.

18

• • 2 ends on one side. • One end missing. • it would overlap itself.

Accept responses in which nets (C) and (D) are not marked if it is clear that they are being referred to. Accept explanations relating to nets (C) and (D) in either order. Do not accept false statements eg There are not enough faces to make a cuboid. In net (C) the faces overlap. Do not accept responses which give no reason why the net cannot be folded.

[5]

11. (a) For 2m indicates use of a suitable no-calculator method, obtaining 52920g for the weight, eg: 2

84063

1202400

002400

4800052920

840× 63

25205040052920

840 4 = 210210

6313230

452920

:

×

×

×

6 is 5040; 60 is 50400 3 is 2520 so 63 is 52920

50400 2520 52920

Award only 1m if there is an error in multiplication or addition of one pair of digits, eg:

84063

25205040051920

84063

508002520

53320

× ×

Award 1m for 2520 and 50400 shown in working.

Do not accept failure to multiply by 10 or 100, eg:

84063

252050407550

Do not accept responses accompanied by no working or spurious working.

19

(b) Correctly compares 50kg and 52920g., eg: 1 • 52920g is more than 50kg. • 50kg is only 50000g. • The tins are 2920 too heavy. • About 2kg over.

Accept follow through from(a) provided the units have been converted correctly. Do not accept responses based on incorrect conversions eg ♦ 529.2kg is 29.2kg too heavy. ♦ 292 grams over. Do not accept responses which do not involve relevant conversions eg ♦ No because 1000g = 1kg. ♦ Its too heavy.

(c) Correctly converts between metres and centimetres before or after calculation, eg: 1.24m to 124m, 14cm to (0).14m or 112cm to 1.12m 1

For 2m indicates use of a suitable non-calculator method, obtaining 8 for the number of layers of tins, eg: • states 8 and shows: 2

2 14 = 284 14 = 568 14 = 122

10 14 = 140–14

9 14 = 126–14

8 14 = 112

14 = 14+ 14 = 28+ 14 = 42+ 14 = 56+ 14 = 70+ 14 = 84+ 14 = 98+ 14 = 112

814 124

11212

14 1248 r. 12

124 14 = 62 762 7 = 8

and a bit

×××

×

×

×

Accept implied conversation eg shows 1.24 ÷ 14 = 0.08, but states 8 tins (high). Award only 1m for 2/5a if an acceptable non-calculator method is shown but the answer is not rounded down correctly eg shows correct method and 8.857 or 9 tins (high). For 2/5a accept correct calculation of equivalent difficulty based on incorrectly converted units eg for 2m

12

‘

40 1410 14 = 14020 14 = 28040 14 = 56080 14 = 1120

8 14 = 11288 14 = 1232It's 88 laye rs .

××××××

’

20

Do not accept responses accompanied by no working or spurious working. Do not accept 14 ÷ 1.24 = 11 Do not accept division shown with incorrect remainder

eg 8 r 8

14 124 [6]

12. (a) Indicates a value between 30% and 47% inclusive. 1 Accept ranges within the given range eg ♦ About 40 to 45%.

(b) Indicates a value between 15% and 24% inclusive 1 Accept ranges within the given range eg: ♦ 15% – 20%

(c) for 2m draws a line on pie chart to give angle between 96° and 116° inclusive for land 2

For only 1m draws a line to give an angle between 70° and 142° inclusive for land.

Marking overlay provided. Both sectors must be correctly labelled, or one correct and the other unlabelled. Accept correctly labelled diagram with water to the right and land to the left of given line. Accept sectors split into northern and southern hemispheres so long as total angle for land is correct. Accept lines sketched by hand provided the whole of the line falls within the boundaries indicated.

[4]

13. (a) n 1 Accept equivalent expressions eg: ♦ 1n n × 1 Accept use of capital letter Accept consistent use of a single alternative term equivalent to n eg: ♦ c cherry trees, c plum trees, 2c apples trees etc.

(b) 2n 1 Accept equivalent expressions eg: ♦ 2 × n n2 Do not accept repeated addition instead of multiplication eg : n + n Do not accept the use of s to indicate plurality. eg: 2ns

(c) n + 7 1 Accept equivalent expression eg 7 + n

21

(d) For 2m indicates simplified total, eg: 2

• 5n + 7 • 7 + n × 5

For only 1m indicates an equivalent expression in which the ‘n’s have not been collected eg • n + n + 2n + n + 7 • 7 + n + n + n + n + n

Award only 1m for correctly simplified expression in which the number of cherry trees has been overlooked eg ♦ 4n + 7 7 + n × 4 Do not accept follow through from incorrect responses to earlier parts of the question. Do not accept incorrect use of indices eg: ♦ n5 + 7 Do not accept use of s to indicate plurality eg: ♦ 5ns + 7

[5]

22

1. (a) Indicates 45 buttons 1 Working need not be shown for the award of this mark. Do not accept incorrect or incomplete computation, eg: ♦ 5 × 9 = 48

(b) Indicates 84 buttons 1 Working need not be shown for the award of this mark. Do not accept incorrect or incomplete computation, eg: ♦ 8 × 10 + 2 × 2

(c) Indicates flower buttons, eg: 1 • Flower • The last sort. • The 2 ones. • Draws a flower

Working need not be shown for the award of this mark. Accept indication of the correct relevant calculation, eg: ♦ 8 × 2 ♦ She bought 8 cards Do not accept ambiguous descriptions, eg: ♦ She bought buttons with holes in the middle.

(d) Indicates star buttons, eg: 1 • The cards with five on. • Draws arrow to star buttons.

Working need not be shown for the award of this mark. Indication of the correct relevant calculations, eg: ♦ 5 × 3 ♦ 3 lots Ambiguous descriptions.

(e) Indicates 4 cards of star buttons 1 Working need not be shown for the award of any marks.

Accept any indication, eg ♦ 4 cards of buttons.

Indicates 10 cards of flower buttons 1 Accept any indication, eg: ♦ 10 cards of 2 buttons. Accept responses in either order.

[6]

2. (a) Indicates 60 cold drinks, eg: 1 • 60 • 6 × 10

(b) Indicates 45 ice creams, eg: 1 • 45 • four and a half tens

Do not accept other numbers of ice creams, eg: ♦ 44

Ignore percentage signs.

23

(c) Indicates a whole number of hot drinks between 26 and 29 inclusive 1 Do not accept parts of a hot drink, eg: ♦ 27½

Ignore percentage signs.

(d) Indicates 4 symbols for hot drinks 1 Accept symbols indicated elsewhere on the question. Accept any shape for the four symbols. These must resemble one another, but need not be identical in size or shape. Do not accept more than four symbols.

(e) Indicates 1 whole symbol and less than half a symbol for cold drinks. 1 Accept symbols indicated elsewhere. Accept any consistent shapes for the two symbols. For two cold drinks, accept an incomplete symbol, open on one side, with an area less than half the area of the symbol for 10 cold drinks. Do not accept more than two symbols.

(f) Draws a reasonable conclusion about the weather on one or both days, or 1 explains that it was different on the two days, or that the types of food sold depended on the weather, eg: • It rained on Tuesday. • The first day was quite sunny. • On Monday it was summer. • The first pictogram was hot. • It changed. • More people came when it was warm. • It got colder. • Monday hot, Tuesday warm. Only one nice day. Lots of tea when its cold. Not many ice creams sold means its cold.

Do not accept statements about the pictograms, with no conclusion about the weather drawn eg: ♦ They sold more ice-creams on Monday. ♦ People bought more cold drinks on Monday and more

hot drinks on Tuesday. ♦ More people came to the cafe on Monday. Do not accept explanations which relate to only one day without specifying which day it was eg: ♦ It was fine on one day. ♦ It was cold. Do not accept incorrect explanations eg: ♦ Lots of hot drinks means it was a hot day.

[6]

24

3. (a) Indicates correct point 1

Accept any indication of the correct response.

(b) For 3m indicates remaining six points 3

For only 2m make only one or two errors or only one or two omissions or one

error and one omission.

For only 1m makes a total of three errors or omissions. Any indication of the correct response eg: ♦ Draws lines joining the four corners of the square

formed by the correct points. Ignore additional points, arrows or other marks inside the square formed by the correct points A point misplaced outside the square formed by the correct points counts as one error and one omission eg

♦

(c) Indicates West 1 West South

25

Indicates West 1

South West

Accept responses in either order. Award only 1m for two horizontal lines of the table completed as S W W or S W W W W S W S W

[6]

4. (a) Explains that Kim puts the cubes back in the bag 1 or explains that she could have taken the same cube out more than once or explains that the chart relates only to the cubes taken out on this occasion, eg: • Because she put the cubes back. • She puts them in and out. • If she didnt put it back then it wouldnt come up again. • It could be the same one again. • The table is just what she got. • She might not get 7 next time. • 7 is what she got this time, there could be more.

Do not accept explanations which simply repeat that the statement made is wrong, eg: ♦ There could be a different number of reds in the bag. Do not accept false statements, eg: ♦ There is a 7% chance of a red cube. ♦ There cannot be 7 red cubes. ♦ All the colours had an equal chance. Do not accept responses which only describe what happens, without explaining that she puts the cubes back in the bag, or that she could have taken the same cube out more than once, or that the chart relates only to the cubes taken out on this occasion, eg: ♦ 7 is what she got, there could be more. ♦ Its all up to chance. ♦ She would have to take them all out to be sure. ♦ She does not look inside the bag.

(b) Indicates 1 cube, eg: 1 • 1 • The green one.

Accept any indication, eg:

♦

130

♦ 1 out of 30 ♦ 1 in 30

26

(c) Explains that Kim puts the cubes back in the bag 1

or explains that she could have taken the same cube out more than once or explains that she may not have happened to take out a blue one or explains that the chart refers only to the number of cubes taken out on this occasion, eg: • She put them back. • She just picked the same one out twice. • She just didnt pick a blue. • She could have kept missing the blue ones. • She could have been unlucky with the blues. • She may have got a white instead. • The way she picks the cubes means she might not get the blue. • Thats just what happened this time. • Another time she might get one. • There might be only one blue in the bag, and the others had a better

chance. • The chart just gives the probability.

Accept explanations which imply that the chart, rather than the statement, is wrong eg: ♦ Her chart is wrong because its just what happened

this time. Do not accept explanations which simply repeat that the statement made is wrong eg ♦ There could be some blue cubes in the bag. Do not accept explanations which imply that Kim did pick out a blue cube, eg: ♦ She might have put a blue one back. Do not accept explanations which imply that there are more than 30 cubes in total, eg: ♦ There could be more cubes. Do not accept responses which only describe what happens, without explaining that she puts the cubes back in the bag, or that she could have taken the same cube out more than once, or that she may not have happened to take out a blue one, or that the chart relates only to the cubes taken out on this occasion, eg: ♦ She just takes out the first one she touches. ♦ Its the way she picks the cubes. ♦ Because its selected at random.

(d) Indicates that white is the most probable. 1 Accept any indication, eg: ♦ 11 ♦ White: first; Red: second. ♦ White then red.

[4]

27

5. (a) For cabbages estimates a percentage between 26% and 35% inclusive 1

which is greater than any percentage estimated for lettuces.

For lettuces estimates a percentage between 15% and 24% inclusive 1 which is less than any percentage estimated for cabbages.

Do not accept values given as fractions or decimals. Ignore fractions or decimals, whether or not correct, given in addition to a correct percentage.

(b) For broad beans estimates a fraction between 25

and 35

inclusive 1

which is greater than any fraction estimated for peas, eg: 48

• • 4 eighths • Half

For peas estimates a fraction between 1140

and 1940

inclusive which is 1

less than any fraction estimated for broad beans., eg: 38

• • Three eighths 13

25

Accept decimals in the range 0.4 and 0.6 inclusive for broad beans. Accept decimals in the range 0.275 to 0.475 inclusive for peas. Award only 1m for (b) if both estimates are within range, but the estimate for peas is not less than the estimate for broad beans. Do not accept values given as percentages. Ignore percentages, whether or not correct, given in addition to correct fractions or decimals. Do not accept incorrect or ambiguous fraction notation eg

2 12

82 58

4 18

18

; . ; ;s Four s ♦

(c) Draws a straight line from one long edge to the other passing through the 1 horizontal line shown on the overlay and shades in the larger section or draws a straight line from one short edge to the other passing through the vertical line shown on the overlay, and shades in the larger section

28

Indicates 1/5, eg: 1 • About 1/5 turnips. Labels smaller area on diagram 1/5

A ruler need not be used, but the line must be within 2mm of being straight. Accept unambiguous labelling of either or both parts instead of shading, eg: ♦ Labels smaller area turnips Labels larger area 4/5 Accept other dissections of the rectangle giving correct proportions, ± 10% of the total area eg:

(ie 70% – 90% of total shaded) ♦ Do not accept dissections with more than one area indicated for turnips. Accept equivalent fractions, decimals or percentages, eg: ♦ 2/10; 20%; 0.2

[6]

6. (a) Draws an acceptable shape made of three tiles congruent to those shown. 1

(b) Draws a different acceptable shape made of three tiles congruent to those shown. 1 Accept any lines drawn inside shapes. Ignore additional incorrect shapes. The marks for parts (a) and (b) may be awarded for acceptable shapes drawn in any part of the question. Drawings do not need to be accurate, as long as the pupils intention is clear. The shapes must be able to be made out of three tiles congruent to those show in the question. Do not accept rotations or reflections of the shape given in the question, or of a shape already credited.

(c) Indicates 11 1

(d) Draws 1

or

oror or a rotation or reflection of one of these.

Accept shape drawn in part (a) or (b) repeated in part (d) Accept any lines drawn inside the shape. Ignore additional incorrect shapes.

29

Drawings do not need to be accurate, as long as the pupils intention is clear. The shapes must be able to be made out of three tiles congruent to those shown in the question.

[4]

7. (a) Indicates 134 or 143 1

(b) Indicates 431 1

(c) Indicates 0 1 Working need not be shown for the award of any marks.

Accept 0 written outside the card, but not as part of a multi-digit number.

Indicates 3140 1 Accept description of how to make the number 3140 eg ♦ Put the card at the end of 314, where 0 has been

indicated. Accept the use of a comma after the thousands digit eg: ♦ 3,140 Do not accept the use of a point after the thousands digit eg: ♦ 3.140

(d) Indicates 425 or 425·0 1 Working need not be shown for the award of any marks.

Use of decimal point without the 0 eg: ♦ 425• Accept a description of how to make the number 425 with the cards eg: ♦ Remove the decimal point. Subtract the •. Move the • up one place right.

Indicates 4250 1 Accept indication of the correct use of the cards, eg: ♦ 4, 2, 5 4 2 5

Accept alternative uses of the decimal point or 0, eg: ♦ 4250• 4250•0 Accept a description of how to make the number 4250 with the cards, eg: ♦ Put 0 on the end and take away the dot. ♦ Move the numbers 2 to the left. Accept indication of the correct use of the cards, eg:

4 2♦ 5 0+ + + 4 2 5 0

[6]

8. (a) Shows evidence of correctly subtracting 32 from 320, eg: 1 • Shows 288 in working.

30

Shows evidence of correctly multiplying the result of their subtraction by 5 1

or of correctly dividing the result of their subtraction by 9, eg: • Shows 1440 in working. • Shows 288 ÷ 9 = 32 in working.

Allow follow through, including with numbers rounded or truncated. Do not accept 32 seen in working as evidence, unless it is clear that this is the result of a relevant computation. If the second mark is awarded for a calculation involving 1440 or 288, then also award the previous mark for a correct subtraction.

Indicates 160° as temperature, with no working or appropriate working. 1 Allow follow through, including with numbers rounded or truncated. Do not accept 160 as the result of an inappropriate calculation, eg: ♦ 32 × 5 = 160 Do not accept Incorrect calculations, eg: ♦ 320 – 32 × 5 ÷ 9 = 302.2 If the third mark is awarded for a temperature of 160°, then also award the previous two marks.

(b) Indicates litres for milk 1

For 2m indicates width of bowl in the range 15 to 25 centimetres 2 inclusive, as a whole number of centimetres, eg: • 20

For only 1m indicates width of bowl not as above, but in the range 10 to 30 centimetres inclusive, as a whole, mixed or decimal number of centimetres, eg: • 28 • 14.5 • 20.32 • 20½ • 20.0

Accept abbreviations for litre, eg: ♦ l ♦ li. Accept re-statement of given quantities or units eg: ♦ half a litre ♦ 20cm

[6]

9. Draws the large wheel with radius 4cm ± 2mm. 1 Accept wheel drawn as a semi-circle below the engine. Ignore radial lines drawn as spokes on the wheel. If more than one circle is drawn, mark the outer circle only and ignore additional circles drawn inside. The whole of the circle must be within 2mm of the correct position even if the centre has been placed inaccurately or no compasses have been used.

ely to ± 2°. Draws 45° angle accurat 1

31

Draws 106° angle accurately to ± 2°. 1

op edge of length 4.5cm ± 2mm at angle of 90° ±

in the boundaries indicated even if a

[4]

0. (a) For 2m draws a line on the pie chart to give an angle between 2

angle outside the range as given above, but

le between 54° and 66° inclusive, but

r 2m both sectors must be correctly labelled, or one

(b) For 2m sta 2

rect values.

(c) d by the total number of pupils 1

one class.

upils there are.

.

spread out more than hers.

a person.

Completes the trapezium by drawing t2° 1 to line given, and drawing left hand edge to within 2mm of each end.

The position from which an angle is drawn must be accurate to ± 2mm. All lines must be withruler has not been used.

154° and 66° inclusive for the sector labelled train. The line must start within 2mm of the centre of the pie chart.

For only 1m draws a line to give anbetween 48° and 72° inclusive, for the sector labelled train. The line must start within 2mm of the centre of the pie chart. or draws a line on the pie chart to give an angdoes not label correctly and / or does not start the line within 2mm of the centre ofthe pie chart.

Focorrect and the other unlabelled. Accept sketched lines completely within the tolerances given. Award 1m if the correct value of 60° is seen, even if the line drawn is incorrect or omitted.

tes all 3 correct values, eg: • Train 3; Bicycle 9; Car 3.

For only 1m states any 2 cor

Indicates that the representation is affectein each class, eg: • More people in • Its out of more pupils. • It depends how many p• Its 12 out of 24, not out of 36. • 36 in Saras, but only 24 in Jims• 15 out of 36 is less than half. • Jims got 24 fractions, so his is• Its a different percentage. • Its a different proportion. • He has more degrees for

32

or

Explains why the 150° used for Sara’s chart must be correct, eg: • 360 ÷ 36 = 10 so there are 10° for each person. 15 × 10 = 150° and

thats what the chart measures so Sara must be right. Accept responses which refer to possible rather than actual totals eg: ♦ There might be less people in Jims class. Overlook incorrect statements accompanying a correct statement eg: accept ♦ It might be a different percentage or they might live

further away. Do not accept explanations which do not compare the total number of pupils in each class, unless 150° has been shown to be correct, eg: ♦ Shes got 36 in her class. ♦ They are from different classes. ♦ Shes got more people travelling by bus. ♦ Its 12 out of 24. ♦ 12 out of 24 for Jim, 15 out of 36 for Sara. ♦ 36 in Saras class, 24 in Jims. Do not accept explanations which could refer to the total number of people travelling by bus, eg: ♦ The amounts vary from class to class. ♦ Its a different number of people.

[5]

11. Indicates a correct expression for Cal, eg: 1 • m – 2 • m + –2 • 1m – 2 • 1 × m – 2

Do not accept a correct expression which has then been evaluated or incorrectly simplified eg: ♦ 1m – 2 = –1

For 2m indicates a correct simplified expression for Fiona, eg: 2 • 4m + 4 • 4 + 4 × m • 4 + m4

For 2m accept an unsimplified expression followed by a correctly simplified expression eg ♦ 4m + 6 – 2 ♦ (4m + 4) A correctly simplified expression that uses letters other than m or M, or redundant words, should be awarded only 1 mark eg: ♦ 4p + 4

of m

♦ 4ms + 4♦ 4 + 4 lots

33

For only 1m indicates a correct expression not simplified, eg:

• 4m + 6 – 2 • m + m + m + m + 4

For only 1m accept a correct non-simplified expression followed by an incorrectly simplified expression eg: ♦ 4m + 6 – 2 = + 4 ♦ 4m – 2 + 6 = 4m – 4

[3]

12. (a) for 2m indicates the correct use of a non-calculator method, obtaining 2 (£)123.50(p) or (£)123 50(p)

4.7526

28509500

£123 50

4.7526

28.5095

123.50

264.751 3

18 2104123 5 = £123 50p

26 × £5 = 130, 26 × 25p = £6.50, so £123.50

4 × 26 = £104, 75p × 20 = £15,

75p × 6 = £4.50 total is £123.50p 475 8 = 3800x

16 = 7600x475 10 = 4750x475 26 =12350x

123.50

40070

5

80001400100

240042030

20 6

123 50 4 7 50 1 1

8 4 02 4 3

6 4 2 0

1 2 3 5 0 = £123.50

4 7 52 6

£ 1 2 3 . 5 019 13

34

Acceptable evidence of non-calculator working would include any of the following sets of numbers (note that units must be consistent in £ or pence, hence 950 with 2850 would not be acceptable).... 95(.00), 28.5(0) 9500, 2850 04(.00) 18.2(0), 1.3(0) 0400, 1820, 130 Acceptable any single digit multiplication done without supported working (eg 475 × 6) but not an unsupported double digit multiplication other than by a multiple of 10 or by 25 (eg unsupported 75 × 26) Award only 1m for all working shown correctly but with the answer given as 12.35, 123.5, (£)12350(p) or other error in the final stage (for example in the final addition, eg:

♦

40070

5

80001400100

240042030

20 6

124 00

4 .7526

28509500

£113.50 Award only 1m if the only error throughout is in the multiplication of one pair of digits eg:

♦

4 .7526

28559500

£123 55

4 7 50 1 1

82

6

6 02 4 3

4 2 01 2 5 5 0 = £125.50

Do not accept responses accompanied by no working or spurious working.

(b) For 2m shows in working the correct use of a non-calculator method, 2 indicating 15 as the number of kites that can be made, eg:

16 25015 r 10

16 25 0

159

enough for 15 kites

35

16 25 0159

r 2

16 25 0

159

.625

so 15 of them 15 kites

250 16125 862 431 2

15

÷÷÷÷

=

16 250160

908010

15

16 16 15 16 80 96 160 160 240, so 15 256, 15 kites

Acceptable evidence of non-calculator working would include the carry digit 9 shown, or the remainder 10 shown, or both even if 625 or a different incorrect remainder is also shown. For 2m accept, with correct non-calculator method, indication of 15 elsewhere on the page, provided it is clear that 15 has been chosen as the number of kites that can be made. Award only 1m if a suitable non-calculator method is shown, but the correct number of kites is not given eg

♦ 16 25 0 0

1 5 69 10.

.

16 15 80 160 240

16 25015

rem 10, 16 kites

Do not accept responses accompanied by no working or spurious working, eg

♦ 16 250

15

16 25015 r 6

16 25015 .625

[4]

36

1. (a) for 2m states correct amount in figures, eg: 2 • 103.50 • 103.50p • 103 50 • 103 50p • 103 50 pence • 103-50 • 103;50pence • 103,50p • 103:50

For only 1m states correct number of pounds, followed by incorrect indication, or not indication, of pence, eg: • 103 • 1035 • 10350 • 103 5 • 103.5

Accept correct responses in pounds and pence written in figures in answer space or elsewhere eg: ♦ £103.50 ♦ £103 50p Do not accept incorrect placement of decimal points, spaces, hyphens, etc. eg: ♦ 10.3 50 ♦ 1 03 50 ♦ 10-3-50 Do not accept incorrect pounds followed by correct indication of pence eg ♦ 130.50

(b) For 2m states correct amount in figures, eg: 2 • 130.50 • 130;05p • 130 05 • 130 05p • 130-05 pence

For only 1m states correct number of pounds, followed by incorrect indication, or no indication, of pence, eg: • 130 • 13005 • 1305 • 130-50

37

or States incorrect number of pounds, followed by correct indication of pence, eg:

• 150.05 Accept correct response in pounds and pence written in figures in answer space or elsewhere eg: ♦ £130 05 ♦ £130.05 pence Do not accept incorrect placement of decimal points, spaces, hyphens, etc. eg: ♦ 13 0.05 ♦ 1:3:0 5

[4]

2. (a) Draws 3 rows of 8 1 Accept 8 rows of 3, and other orientations. Accept alternative correct diagrams eg:

Drawings do not need to be accurate, as long as the pupils intention is clear. Ignore other arrangements drawn.

(b) Draws a different acceptable arrangement, eg: 1 • 1 row of 24. • 4 rows of 6. • 6 rows of 4. • 8 rows of 3. • 12 rows of 2. • 24 rows of 1.

Accept 3 rows of 8 only if this orientation was not given in part (a). Ignore other arrangements drawn. Do not accept an arrangement in part (b) which has already been awarded a mark in part (a). Do not accept 2 rows of 12, as shown in the question.

(c) 3 rows 8 seeds. 1

4 rows 6 seeds. 1

6 rows 4 seeds. 1 Working need not be shown for the award of any of these marks. Accept responses in any order.

(d) Explains that 24 is not a multiple of 5, eg: 1 • It goes 20, 25. • It must have 0 or 5. • Because 5 fours are 20.

38

• 5 × 5 = 25 • She needs 25 seeds. • You would get four seeds left over. • You need one more seed. • She could only plant 4 rows. • 24 doesnt divide by 5. • It doesnt go into 24. • 5 does not fit into 24. • You cant make 24 out of fives. • 24 is not in the 5 times table. • You would have to cut up some seeds. • You cant share them equally between 5. • Going up in fives goes past the number. • 24 ÷ 5 = 4.8 • Draws 4 rows of 5 and 1 row of 4, indicating the gap.

Ignore incorrect responses if an acceptable explanation is also given eg ♦ It will be an odd number because you need another

seed. Do not accept false or irrelevant statements eg: ♦ You would get 1 seed left over. ♦ 24 wont go into 5. ♦ You cant get twenty four out of five. ♦ 5 is odd and 24 is even. ♦ It must end in a 5. ♦ There is no 5 in the rows column in the table. ♦ You would have to cut up one seed. Do not accept explanations which add nothing to the information given eg: ♦ She is wrong because the rows must be equal. ♦ The rows would not be all the same. ♦ There would be too many or too few seeds. ♦ They wouldnt divide into the same amount in each

row. [6]

3. (a) Indicates Wednesday 1

Explains that less money was raised or that few cakes were sold, eg: 1 • It has not got much money. •• Its a low amoun Less money.

t. Wednesday has lo• wer numbers. • On other days they go more. • They sold less cakes.

Do not accept responses which imply that the pupils were absent from only one class eg ♦ Class 1 on Wednesday. Do not award the second mark for the explanation in (a) unless the first mark for indicating Wednesday is awarded.

39

class eg: ♦ Class 1 only got £2.40 and its usually more. Do not accept explanations which imply that the prices changes eg: ♦ The prices were low on Wednesday.

(b) Indicates £13.50, eg: 1 • 13.50 • 13.50 • £13.50p • 13.50 pence • 13 pounds 50 • 13;50p • 13,50 • 13:50 pence • 13-50

Working need not be shown for the award of this mark. Correct answer given in pence written elsewhere on the page eg: 1350 p; 1350 pence Sum of four amounts taken from any other day of the week eg: ♦ £19.90 (Tuesday) ♦ £9.85 (Wednesday) ♦ £20.70 (Thursday) ♦ £13.95 (Friday) Do not accept incorrect or ambiguous use of pounds or pence eg: £1350; £1350 pence; 1350 Do not accept incorrect placement of decimal points, spaces, etc. or incorrect use of 0 eg: 1.350; 13.500; 13-5-0

(c) Rounds up to the nearest pound, ten pounds or hundred pounds, eg: 1 • 977 • 980 • 1000

Accept correct indication of pence after pounds eg: ♦ 1000.00 Accept correct answer in words eg: ♦ a thousand pounds ♦ nine hundred and 80 Accept comma after thousand digit eg: ♦ 1,000 Do not accept point after thousand digit eg: ♦ 1.000

[4]

Do not accept responses which clearly relate to only one

40

4. (a) Indicates co 1

• 09:30 • 9.30 • 930 • 9-30

t nine

o not accept incorrect use of points, colons, commas g: 9.30 930

incorrect use of pm eg: ♦ 9.30 pm

(b) ength of time in minutes, eg: 1

• 00.4

hour.

(c) Indicates co 1 • 08 25 • 8;25 • 0825 am• 08,25 • Twenty f• Eight twe

etc. eg: ♦ 0:8:2:5 ♦ 0.825 ♦ 82-5

(d) Indicates th 1 • 8:30; 8.45; 9• 08.30; 9• The first• 1; 2; 3 • 9.15; 93• Draws arrows to the first three buses.

Accept correct three buses in any order. Accept any unambiguous indication eg: ♦ 0.9.1.5; 84-5; 1;00-5

rrect time, eg:

• 9 thirty • Half pas• 9.30 am

Detc. e♦ 0.♦ 0.Do not accept

Indicates correct l• 45

5 Accept correct time given in hours eg: Three quarters of anDo not accept incorrect use of hours eg: 0.45 0045 hours

rrect time, eg:

ive past 8 nty five Do not accept incorrect use of points, colons, commas

Do not accept incorrect use of pm eg: ♦ 8:25pm

e correct three buses, eg: 20

20; 845 3

0; 10-05

41

ime, eg:

tes

incorrect use of hours eg: hours

20 hours [5]

5. (a) Draws a 3 by 3 square in correct orientation. 1 not need to be accurate, as long as the

, or no lines, drawn inside correct square.

Do not accept squares drawn in the wrong orientation eg:

(e) Indicates correct length of t 1 • 20 minu• 20 • 0020 • 00.20

Do not accept♦ 20

0.♦

Drawings do pupils intention is clear. Accept any linesIgnore additional incorrect diagrams.

Do not accept responses to this part gpart

ber of tiles greater th

iven in the next (Tier 3-5 only).

(b) States num an 9 in own correctly drawn and oriented square 1 t need to be accurate, as long as the is clear.

Accept any lines, or no lines, drawn inside correct square. Ignore additional incorrect diagrams.

cept correct number stated in the next part for a correct diagram drawn in this part if incorrect or no number is

is part. ra tiles clearly added after the response to this

been made.

(c) States one square number greater than 9 and different from any square 1 number for which a mark has been awarded in the previous part.

States a second square number greater than 9 and different from any 1 square number for which a mark has been awarded in the previous part.

es in any order. ded for two square numbers

than 9 for which marks have not been awarded in ous part. Once two marks for this part have been , any responses in the remaining answer space or

ewhere in the question should be ignored. [4]

Drawings do nopupils intention

Ac

stated in thtIgnore ex

part has Do not accept squares drawn in the wrong orientation.

Accept responsThese two marks are awargreater the previawardedels

42

6. (a) Explains th 0 1

• Most people spent that. • Thats the most common one. • There were less of the others. • More people buy a drink. • 6 people spent 40p and less people spent the other amounts. • 40p is used more often. • Its most popular. • Most of them are 40p • 40p is the amount most spent.

Accept incorrect number of people given eg: Because 3 people is more than spent the other amounts. Accept definitions of the mode eg: ♦ The mode is the most common one. Do not accept explanations that do not indicate that 40p has the highest frequency eg: ♦ They often spend 40p on a drink. ♦ 6 people spent 40p but only 4 spent 60p. ♦ 40p is the average amount spent. ♦ A lot of people spent that. Do not accept explanations which could imply that 40p is the greatest amount of money spent eg: ♦ 40p is the most spent. ♦ 40p is the most amount spent. Do not accept definitions of the median eg: ♦ 40p is the middle amount. Do not accept irrelevant or false explanations eg: ♦ Most people spent 40p between 5-6 and 6-7.

(b) Completes tallies correctly as: 1 7pm to 8pm

Under 50p 50p to 99p | | £1.00 to £1.49 | | | Over £1.49 | | | with no additional tallies.

Correctly totals own tallies and those given, eg for tallies correct as above 1 • 7

10 4 3

Accept use of 0 in empty cells. Accept any tally marks, used consistently eg ♦ √ √

√ √ √ √ √ √

For the mark to be awarded for the total of the tallies, some tally marks for 7pm to 8pm must have been added to the chart. Ignore any total given for the first row, whether or not it is amended to fit pupils incorrect tallies.

at 4 p is the amount most frequently spent, eg:

43

Do not accept tallies instead of numbers in the totals n.

(c) to 99p than any other amount, eg: 1 cause that was the most common.

spent the other amounts. o

• He is rig• 10 peop nly 7 spent the next amount. • Its most popular. • Most spend 50p to 99p.

rt, arks are added, that the

ions eg:

pt definitions of the mode. explanations that do not indicate that the

to 99p has the highest frequency eg:

Lots of people spent money in that interval.

nations which could imply that 50p to

(d) Observes a 1 • Spent m• It rises. • 5 to 6 pe• More mo

t , eg: 1 • Older pe• People g• They ge• People e• They fille• They sold out of cheap stuff.

eg for 2m • Older people with money go there later. • They get hungry at 7. • They have more to spend in the evening.

columExplains that more people spent 50p Yes b• e• Less people• Most pe ple spent that.

art has more lines there. ht because the chle spent that, and o

• 50p to 99p has the most amount of tallies. Accept explanations based on the pupils own tally chaor on chart given if no tally mstatement is right or wrong. Accept more sophisticated responses or definit♦ 50p to 99p is the modal group. Acce

♦

Do not acceptinterval 50p

♦ 10 people spent that, and only 7 spent under 50p. Do not accept expla99p is the highest amount spent eg: ♦ Thats the most they spent. Do not accept irrelevant or false explanations eg ♦ Most things cost 50p to 99p. Do not accept responses in which no explanation is given.

difference in the amounts spent, eg: ore at night.

ople spent under 99p, but 7 to 8 people spent around £1.49. ney at 7-8.

• Nobody spends less than 50p after 7pm. • More big amount tallies in last column.

Makes a hypothesis which could explain the difference in the amounts sta edople go there. o there for dinner.

t hungry. ar rolls. d the machine up.

44

•

e a sandwich. er on. hich imply that the data cover the

2m tea. r in

spend more. fferent explanations relating to the amounts

ould be based on the pupils own tally chart, no tally marks are added.

f it could explain pupil.

nce is observed and

[6]

7. (a) Indicates 4. 1

(b) States and r (6,0). 1

• People saved their cash for later. • At dinner time people hav• They sold out of cheap stuff lat

Accept explanations wwhole day eg for People spend less in the morning when they just haveThen they have a snack for lunch but they have dinnethe evening andAccept dispent which cor on the chart given if Award second mark for a hypothesis only ia difference in the amounts stated or implied by the Ignore additional incorrect or unacceptable differences or hypotheses if an acceptable differehypothesis made. Do not accept explanations that more people were there,or that more people spent money, at any particular time. eg: ♦ More people came later and spent their money.

Accept 22 for 4

cor ectly plots the points (0,0); (3,3);

0 1 2 3 4 5 6 7 8 9 10 11 12

123456

Points need nocorrect intersecti

t be accurately place, but must be closer to ons than to other intersections.

t p ints plotted but not joined up to make a triangle, d h an inaccurately drawn line.

up, in addition to the pupils own response.

(c) Indicates area of triangle formed by own three points plotted in (b), 1 eg: for points correc

• 9 r 9.

Do not accept area of a plotted triangle congruent to either of the triangles given in the question.

Accep oor joine witAccept intersections of edges of triangle drawn instead of points plotted. Ignore the points given in the question, plotted or joined

tly plotted as above

Accept 32 fo

Do not accept area of a non-triangular shape.

45

(d) Plots the po 1 int (5,5)

0

123456

1 2 3 4 5 6 7 8 9 10 11 12 The point need not be accurately placed, but mcloser to the correct intersection than to oth

ust be er

tersection of edges of triangle drawn instead of

(e) 1

[5]

8. (a) Explains that the perimeter must be more than twice the len 1 or explains tha e greater than the len he third side

either or both of the other two sides, eg: 4

36.

. hly the same.

es are too long.

-

y are about 10 and 14.

intersections. Accept inpoint plotted.

Indicates 5 Accept correct answer to one or more decimal places. Accept any indication of multiplication by 5 eg: ♦ 5 × ♦ 1 × 5 ♦ 5 cm ♦ ×5 = (5,5) ♦ 5,5 times by 5 Do not accept responses which could merely indicate theco-ordinates of the missing point eg ♦ (5,5) ♦ 5,5 ♦ 5.5 Do not accept 25.

gth of one side

t the sum of the lengths of the other two sides must bgth of t

or estimates the lengths of • 2 × 17 = 3• 2 × 18 = 36 • It must be more than• 17.5 + 17.5 is more than 30. • 30 – 17.5 = 12.5 thats too short. • The other two sides would make more than the one given.

doesnt leave enough. • The longest side alone is 17.5, which• One side is over half already

nd another is roug• One side is 17.5 a• The other two sid

• They add up to more than 12.• Because the

46

•eet up.

• The other two sides would have to be too small. • The long side must be less than 15 to get 30. • The others cant be only 6 each. • One side is nearly two thirds of that.

Accept valid explanations based on relevant computations, even if the calculation is incorrect eg ♦ 30 – 17.5 = 13.5 thats too short. Do not accept the statement that the perimeter is greater than 30cm, or that 17.5 is too long, with no explanation eg ♦ With the other two sides it must be more than 30cm. ♦ You can see by looking that it must be over 30cm. Do not accept explanations which imply that two or three sides of the triangle are equal eg ♦ Two sides are the same size. ♦ 3 × 17 = 51 too much. Do not accept false or irrelevant explanations eg ♦ The longest side alone is 17.5cm. ♦ The other two sides are more than double the 17.5 Do not accept explanations which imply that the triangle could have a perimeter of 30cm eg ♦ The other two sides would have to be very small.

(b) Indicates a length in the range 14.2cm to 14.6cm inclusive. 1

Indicates a length in the range 9.4cm to 9.8cm inclusive. 1 Accept responses in either order. Accept correct responses written on the diagram or used in part (c), even if an alternative incorrect response is given in part (b). Accept lengths in correct range given to two or more decimal places. Accept equivalent fractions Do not accept the use of commas for decimal points

(c) For 2m indicates the use of a suitable non-calculator method to find the 2 sum of the two lengths correctly measured in (b) and 17.5cm, eg:

• 14.5 • 14 + 9 = 23 • 14.2 9.5 17 + 23 = 40 9.4 17.5

• The other two sides would be too short to m

7 + 4 + 5 = 16 17.5 41.5 41.6 41.1 2 1

• 9.7 + 14.3 = 24 • 17.5 + 14.5 9.8 24 + 17.5 = 41.5 18 + 14 +10 = 42 42 – .2 = 41.8

47

calculation, eg:

14.6

For only 1m makes one error in the

• 17.5 • 17 + 14 + 9 = 40 9.7 0.5 + 0.6 + 0.8 = 1.8

40.8

• 146 97 175

41.8

418

om

r correct use of carried digits, as

o acceptable lengths and 17.5, even if the answer

Accept correct sum of lengths involving fractions given with a fraction.

ot accept result calculated with incorrect place es eg

(The decimal points are omitted.) For 2m or 1m allow follow through for sum of two incorrectly measure lengths, or lengths different frthose given in(b), and 17.5 only if neither length is a whole number of centimetres and both are given to at least one decimal place. Accept arrangement of three lengths with decimal pointscorrectly aligned, oevidence of the use of a non-calculator method. Accept correct calculation to one or more decimal places of twgiven in the question space is rounded or truncated.

Do nvalu

17 514 4

817

940 Answer: 40.17

17.514.49.8

122.71 1

[5]

9. (a) Indicates co 1 rrect square, and no other square(s).

48

(b) Indicates correct squ 1 are, and no other square(s).

Shading does not need to be accurate, as longpupils intention

as the

uares marked with crosses.

is clear. Accept any indication eg ♦ Correct sq

(c) Indicates corre 1 ct squares, and no other square(s)

(d) Indicates co 1 rrect squares, and no other square(s).

Shading does not need to be accurate, as long as the pupils intention is clear. Accept any indication eg ♦ Correct squares marked with crosses.

[4]

10. (a) t probability, eg: 1 Indicates correc3 5•

• 60% • 0.6 60

100Accept correct probability written in words

e is given, alleg: 3 in 5; 3 out of 5 If more than one respons must be correct to gain the mark.

g

Do not accept 60 without a percentage sign. (b) Indicates correct probability, eg: 1

Do not accept ratios e♦ 3:5; 3 to 5, 3:2, 3 to 2

49

• 1 • 100% 5 5100 100

Accept correct probability written in words eg ♦ certain; whole;. definite; ♦ 1 in 1; 5 out of 5 Accept any fraction equivalent to 1. If more than one response is given, all must be correct to gain the mark. Do not accept ratios eg ♦ 1 to 0, 1 to 1 Do not accept A probability not quantified eg

(c) Indicates co 1 • Draws an arrow pointing to the mark 0.6 of the way along the scale.

(d) Indicates co 1 • Draws a rr

ating the position.

(e) Indicates th o colours of sweet, eg: 1 • She cou• I dont lik eets. • There are only two colours she likes. • Yellow, p

e she doesn

ates purAccep sophis ated responses which correctly state the probability eg

likes two f

Do not accept re p ied eg ♦ She likes less than half of them. Do not accept responses which imply there are colours other than those specified in the machine eg ♦ She likes blue sweets and red sweets.

[5]

11. (a) Indicates the correct number of tiles, eg: 1

• 4

♦ Great. Do not accept 100 without a percentage sign

rrect position, eg:

rrect position, eg: n a ow pointing to 1 on the scale. Accepty follow through from values given earlier (including ratios) or correct position. Accept alternative methods of indicThe position of the arrow need not be accurate, as long asthe pupils intention is clear.

at Mandy likes twld like red and green ones. e red or orange or green sw

urple. • She likes a couple. • Theres thre t want. • She quite likes the reds but loves greens. • She h ples, yellows and oranges.

t more tic

♦ She fi ths. ♦ 0.4

s onses which are not quantif

50

• He adds 4 putting 1 on each line. • He adds 1 on each end, so the tota

t ccept responses whinumber of tiles added e

l is 4. Do no a ch do not state the total

g ♦ He adds one more to each arm.

not accept responses which indicate that 4 new tiles re added to each arm eg

♦ He adds 4 grey tiles on each side.

(b) on: 1

Explains th• The grey• All the o• The arm• The tiles• 4 rows o

or Explains th

• 4 rows w

or Explains N xplain the 4 , eg: • •

or not fully, explain N, eg:

• • The 4 is the f and N is the number of the pattern.

urs such as white,

Do not accept direct substitution eg ♦ 4 × the pattern number.

ttern. explanations which could refer to only the

ded to make a new pattern eg The 4 grey tiles. The ones you add on each time.

explanations which could refer to more that are in the pattern eg

4 × number of grey. Do not accept explanations which could refer to a single tile eg ♦ The grey tile.

(c) Indicates 1 black and 60 grey tiles. 1

(d) Indicates pattern number 10 1 (e) Indicates pattern number 20 1

[5]

Doa

Gives one of the following types of correct explanati

at 4 × N represents all the grey tiles, eg: .

ther tiles. s coming out. around the shape. f grey tiles.

e 4 and the N, eg: ith N squares in each row.

as the number of squares on each arm but does not e4 × number squares on each line. There are n tiles in one of the lines.

Explains the 4 but does not, or does Its 4 because there are 4 arms.

number of lines going ofAccept grey referred to as other cololightly shaded or not black. Accept N written as n.

♦ 4 grey tiles × the number of the paDo not acceptfour tiles ad♦ ♦

Do not acceptgrey tiles ♦

51

12. (a) 1 ed not be shown for the award of this mark.

f cubed sign eg 3

incorrect attempt to convert to different

(b) For 2m ind 2

For only 1m en 60 as volume of the box.

of any marks. allow follow through from part (a), with

ding or truncation. 1m for correct calculation indicated but not incorrectly evaluated eg

12 × 6 × 5 = 432 1.2 × 300 300 × 20 ÷ 100 + 300

with no further t to find the volume.

(c) 1 ed not be shown for the award of this mark.

Allow follow through from part (a) or (b) with correct truncation.

Accept any indication eg

Do not accept♦ 2 salt pots.

[4]

13. (a) es a correct expression, eg: 1 • 14n

Accept equivalent expression eg ♦ 3n + 2n + 3n + n + 3n + 2n ♦ 14 × n

Indicates 300 Working ne

Ignore use o♦ 300Do not acceptunits eg ♦ 3 ♦ 30

icates 360.

shows 60 as 20% of 300 in working or giv

Working need not be shown for the award For 2m or 1mcorrect rounAward onlyevaluated or♦ ♦ ♦

Do not accept height calculated as 12 attemp

Indicates 12 salt pots.Working ne

rounding or

♦ 2 more salt pots drawn on diagram given. Accept correct description eg ♦ 2 more salt pots. Do not accept fractions of a salt pot.

fewer than 10 salt pots eg

Ind tica

• 14n cm

♦ n14

52

Accept use of an alternative variable eg ♦ 14e The mark may be awarded for a correct expression even if correct or incorrect further working is given eg ♦ 14 × n = 28 Do not accept non-algebraic expressions eg ♦ 14ns

(b) Formulates o : 1 • 14n = 28• n = 28 ÷• 28 = 14 • n14 = 28

). warded for a formal response, hence the

sign. s that are embedded within true

in the equation eg

1 he first mark in part (b) and

warded for n = 2 seen anywhere in the question, edded.

rom own incorrect equation, form n = k where k is a unded or truncated

[3]

♦ 14 lots of n ♦ n times 14

a c rrect equation, eg

14 × n Accept follow through from response to part (aThis mark is aequation must contain n, 14, 28 and an equalsAccept correct equationstatements eg ♦ Perimeter = 14 × n = 28 Accept units given ♦ 14n cm = 28 cm Do not accept equations that are continued, embedded within false statements, use redundant variables or are non-algebraic eg ♦ Perimeter = 14 × n = 28 = n = 2 ♦ 14n = 28 ÷ 14 = n = 2 ♦ n = × 14 =14n = 28 ♦ 14n = a, a = 28 ♦ n = ? 14 × ? = 28 ♦ 28 is equal to 14n

Indicates 2 This mark is independent of tmay be aeven if embAccept follow through fprovided the equation is not of theconstant other than 2, including roresponses.

53

1. (a) Indicates 8 for first floor. 1 Accept correct number of tiles drawn in a correct arrangement if no numerical answer is given.

Indicates 9 for second floor. 1 Accept any indication eg: ♦ 2 × 4 ♦ 3 by 3

(b) Indicates 80 1

Indicates the correct number of packs for the number of tiles indicated, 1 provided the number of tiles indicated was over 10, eg: • 8 for 80 tiles. • 9 for 81 tiles.

If no number of tiles is given, then accept 8 packs but do not award the previous mark.

(c) Indicates 56 1

Indicates the correct number of packs for the number of tiles indicated, 1 provided the number of tiles indicated was over 10 and not a multiple of 10., eg: • 6 for 56 tiles. • 7 for 64 tiles.

If the pupil has already demonstrated, in part (b), the ability to find the correct number of packs for a number of tiles that is over 10 and not a multiple of 10, then allow follow through in part (c) for a number of tiles which is over 10 and is a multiple of 10, eg: ♦ If 4 was accepted for 36 tiles in part (b), then accept 7

for 70 tiles for the second mark in part (c). If no number of tiles is given, then accept 6 packs, but do not award the previous mark. Ignore references to any number of tiles left over if the number of packs is correct eg, for 56 tiles ♦ 6 boxes hell have to chuck out 6. Do not accept more or fewer than the correct number of packs eg: ♦ 5 packs plus 6 more tiles. ♦ If she buys a dozen packs shell be sure to have

enough. ♦ 60

[6]

2. (a) Correctly indicates 24°C on the thermometer. 1

(b) Correctly indicates – 4°C on the thermometer 1 Drawings need not be accurate, as long as the pupils intention is clear. Accept unlabelled or incorrectly labelled arrows or marks.

(c) Indicates 5 1 Accept any unambiguous indication eg: ♦ 5 marked on the diagram

54

(d) Indicates the correct order for the temperatures, eg: 1

• –10, –1,0,3,20 Accept any indication, as long as the order is correct eg: ♦ 10–, –1 , 0 , 3C, 20 ♦ –10, –1, 0, 3, 20 ♦ –10 , –1, –0, 3, 20 ♦ Arrows drawn from the temperatures to the correct

positions. Accept a list of the correct positions for each temperature eg: ♦ 3 should be fourth, –10 should be first, 0 should be

third, 20 should be fifth, and –1 should be second. ♦ 4, 1, 3, 5, 2 Accept temperatures identified by their positions in the list given eg: ♦ Second one should come first, then fifth, then third,

then first and the fourth one is the hottest. ♦ 2, 5, 3, 1, 4

[4]

3. (a) Draws a 9 by 2 rectangle. 1 Accept any indication of the correct rectangle eg: ♦ Corner pegs only shaded.

Lines drawn around the peg♦ s. ♦ Line drawn through the pegs.

Indicates 9 and indicates 2. 1 Accept length and width in either order. Accept responses based on rectangles formed with 18 pegs around the perimeter eg, for 2m

and 8 pegs long 3 pegs wide

(b) Draws a row with a prime number of pegs greater than 5 1 and identifies the prime number of pegs drawn.

Acceptable numbers of pegs are: 7, 11, 13

(c) Explains why 9 is not a prime number, eg: 1 • 3 threes. You can ma• ke a rectangle. • Three, three, three. • 3 + 3 + 3 • 3 goes into 9. • Its the three times table. • A prime number only divides by itself.

55

• • 9 splits into 3. • Its a square. • Draws a 3 by 3 square. • You can have 8 around the sides and one in the middle.

Do not accept explanations which imply that only even numbers are not prime eg: ♦ If it were even you could make a rectangle.

[4]

4. (a) Indicates 3 1 Accept any indication eg: ♦ 9 left. ♦ Three out of the twelve. 3

12

Do not accept incorrect number of biscuits eaten eg: ♦ 9

(b) Indicates 12

1

Accept equivalent fractions, decimals, percentages, or correct fractions written as words eg:

612

♦♦ 0.5 ♦ 50% ♦ Half of them. ♦ Its half and half. ♦ 2 quarters. Do not accept fractions described by words eg: ♦ 6 out of 12

1 over 2 ♦

(c) Indicates 15 1 Allow follow through from part (a), ie accept the difference between 18 and the number given in part (a). Do not accept incomplete or incorrect computations eg: ♦ 9 + 6 ♦ 9 + 6 = 14

[3]

5. (a) Indicates, for the correct computation,

97 1

90 1

10 1

180 1 Do not accept 90%. the correct order, ÷ th(b) Indicates, in en + 1

56

Ignore partial working shown. [5]

6. (a) Indicates 50, eg: 1 • 50 • fifties • 50s

(b) Indicates 80, 100, 120 in the correct order. 1

(c) Indicates –10 in the correct position. 1

Indicates 0 and 10 in the correct positions. 1 Accept use of positive and negative signs with the 0 eg: ♦ + 0 ♦ – 0

(d) Indicates –3 in the correct position. 1

Indicates 13 in the correct position 1 and indicates steps of 4.

(e) Indicates 7.9, 8(.0), 8.1 in the correct positions. 1

Indicates steps of 0.1, eg: 1 • 0.1 1

10

0.1s tenths point 1

Do not accept incorrect or ambiguous responses eg: ♦ 1 decimal place ♦ one decimal point ♦ 1 point ♦ 1 mm

[8]

7. (a) Indicates the correct pegs, eg: 1 •

57

Indicates the correct pegs, eg: 1 •

Shading need not be accurate as long as the pupil’s intention is clear. Accept any indication of the correct pegs eg: ♦ Pegs circled. ♦ Line drawn around the pegs. ♦ Line drawn through the pegs. Do not accept more than the correct number of pegs indicated.

(b) For 2m indicates the correct pegs, eg: 2 •

For only 1m indicates the correct pegs in any two of the three sections, eg: •

Shading need not be accurate as long as the pupil’s intention is clear. Accept any indication of the correct pegs eg: ♦ Pegs circled. ♦ Line drawn around the pegs. ♦ Line drawn through the pegs.

[4]

8. (a) Indicates the fraction is 310

1

Accept equivalent fractions or decimal fractions, or correct fractions written as words eg: ♦ ‘Three tenths.’

58

Indicates the percentage is 30 1

Allow follow through from an incorrect fraction, including rounding or truncation to the nearest integer. Award only 1m if both answers are correctly given but interchanged.

(b) Shades, or otherwise indicates, a total of 4 triangles. 1 Shading need not be accurate as long as the pupil’s intention is clear.

Indicates 40 1 Allow follow through from any incorrect shading other than 30%, 0% or 100%, or a value already credited in part (a).

[4]

9. (a) Indicates a correct expression, eg: 1 • n + 2 2 + n

(b) Indicates a correct expression, eg: 1 • n – 1 –1 + n

(c) Indicates a correct expression, eg: 1 • 2n 2 × n n × 2 n + n

Accept letters other than n used. Accept multiplication by 1 or reversed notation for variables multiplied by a constant eg: ♦ ‘2 + 1n’ for 2 + n’ ♦ ‘n2 for 2n’ ♦ Accept the word ‘cubes’ at the end of correct

expressions. Do not accept other expressions with words. Ignore a numerical substitution for n if a correct expression has been given. Otherwise, do not accept the inappropriate use of an = sign or incorrect attempts at simplification eg: ♦ ‘n = n + 2’ ♦ ‘n + 2 = 2n’

(d) For 2m explains there is a difference of one cube, eg: 2 • One hand has one more cube than the other. • One has one cube off. The other has two. • In one hand its –1, but the other is –2. • One more in one hand. • Draws a correct picture for each hand showing what is being held.

or Indicates one is odd and one is even.

59

or

Indicates 2(n – 1) = 2n – 2, eg: • In one hand its 2n – 2. No 2(n – 1) means n – 1 then multiply by 2, so its –2.

For only 1m explains the difference in structure of the expressions without explaining the outcome, eg: • No, 2(n – 1) means n – 1 then multiply by 2. • You do the brackets first so theyre different. 2n – 1 means 2 × n – 1, (2(n – 1) means times everything by 2.

or Evaluates correctly both hands for one or more values of n.

Award only 1m if a correct explanation is followed by incorrect algebra eg: ♦ ‘No, 2(n – 1 ) = 2n – 2 but 2n – 1 = 1n.’ For 2m or 1m accept explanations where operations are given sequentially but without brackets eg, for 1m ♦ ‘No because 2(n – 1) means n – 1 × 2.’ For 2m or 1m do not accept explanations which conclude that the expressions are the same. Do not accept a statement that they are different without justification. eg: ♦ ‘2n – 1 is not the same as 2(n – 1)’ ♦ ‘One of them has brackets.’ ♦ ‘More in first hand.’ ♦ ‘Brackets means times.’

[5]

10. (a) Indicates 59

1

Accept a correct probability written as an equivalent fraction, a decimal between 0.55 and 0.56 inclusive or a percentage between 55% and 56% inclusive. Accept a correct probability accompanied by that

probability written as words eg ‘ 59

that’s 5 in 9

Otherwise do not accept probability written as words or as a ratio.

(b) Indicates 13

1

Accept a correct probability written as an equivalent fraction, a decimal between 0.33 and 0.335 inclusive, or a percentage between 33% and 33.5% inclusive. Accept a correct probability accompanied by that probability written as words eg ‘1 out of 3 = 1 in 3 = 33%

60

If answers to both parts (a) and (b) use the correct digits but are expressed as words, this mark may be awarded eg: ♦ ‘5 in 9’ given in part (a) and ‘1 out of 3’ given in part

(b) is awarded 0 marks in part (a) and 1 mark in part (b).

If answers to both parts (a) and (b) are expressed as correct percentages but the percentage signs are omitted, then award only the mark for part (b). Do not accept a probability written as a ratio

(c) Shows all nine possible outcomes, eg: 1 •

+

2

3

4

4

6

8

6

9

12

8

12

16

2 3 4

Outcomes need not be in a table or be ordered in size.

Completes the sentence correctly, eg: 1 • Indicates a number greater than 12 but less than or equal to 16.

Allow follow through from incorrect outcomes.

Completes the sentence correctly, eg: 1 • Indicates a number that is 4 or less.

Allow follow through from incorrect outcomes. [5]

11. (a) Indicates the card n ÷ 2 1 Throughout, do not accept letters other than n or N.

(b) Indicates the card n2 1

(c) Indicates the card 2n 1

Indicates the card n + n 1 Do not accept cards not available eg: ♦ n × 2 ♦ n2

61

(d) Indicates an expression equivalent to 3n + 2n, eg: 1

• 5n n × 5 8n – 3n n + n + n + n + n 2n + 3n 3 × n + 2 × n

Accept multiplication by 1 or reversed notation for variables multiplied by a constant eg: ♦ n5 ♦ n2 + n3 ♦ 4n + 1n

[5]

12. (a) Indicates 7 or + 7 1

(b) Indicates –8 as the card chosen. 1

Give a correct answer for their negative card, eg: 1 • –10 if –8 chosen

Allow follow through from a negative number card, even if it is not one of the cards available. Do not allow follow through from a positive card. Do not allow follow through from 0, + 0 or –0. If –10 is given as the answer but no card has been indicated, award only this second mark.

[3]

13. (a) For 2m indicates £33.25’, eg: 2 • 33.25 • 33.25p on answer line.

For only 1m shows a correct method with only one computational error, eg: • Shows 3325 with the decimal point omitted or incorrectly placed, or with

units incorrectly stated. • Evaluates 35 × 5p and subtracts the answer from £35 making only one

error throughout. • Shows in working 2850 and 475 (or 3150 and 175) incorrectly totalled

with their answer correctly converted to pounds.

or Shows a complete correct method with no errors but the total amount not found, eg: • Shows in working 2850 and 475 (or 3150 and 175) with the intention to

add. • Shows in working 35 × £1 and 35 × 5p with the intention to subtract.

For 2m accept 3325p elsewhere on page. For 2m do not accept 33.25p other than on the answer line. For 1m do not accept inconsistent units eg: ♦ ‘285 and 475’

62

♦ ‘315 and 175’

63

(b) For 2m indicates 14 2

For only 1m shows a complete correct method with no errors other than in the remainder, but the total number of trees is not stated, eg: • Shows 14 r 12 or 14.7 ... • Shows 14 and 238 • Shows 15 and 255 • Shows 17 × 10 = 170 and 17 × 4 = 68, with no ambiguity that these are

the values chosen. Ignore reference to amount left over eg: ♦ ‘14, £12 left.’ Ignore incorrect amount left over eg: ♦ ‘14, £7 left.’ For 2m do not accept a remainder not given as an amount eg: ♦ ‘14 r 12’

[4]

64

1. (a) Draws a bar to 25° for Friday 1

Draws a bar to 19° for Saturday, eg: 1 30

20

10

0Sun Mon Tues Wed Thurs Fri Sat

Indicates a temperature between 26° and 28° inclusive. 1 Bars need not be shaded, and drawings need not be accurate, as long as the pupil’s intention is clear. The bar for Saturday must cover more than half of the 15° to 20° cell, but it must not touch the 20° line.

(b) For 3m makes all four correct connections, eg: 3

Sun

Sun

Sun

Sun

Sun

Mon

Mon

Mon

Mon

Mon

Tues

Tues

Tues

Tues

Tues

Wed

Wed

Wed

Wed

Wed

Thurs

Thurs

Thurs

Thurs

Thurs

Fri

Fri

Fri

Fri

Fri

Sat

Sat

Sat

Sat

Sat

30

30

30

30

30

20

20

20

20

20

10

10

10

10

10

0

0

0

0

0

Each day was colderthan the day before.

The temperature wasabout the same all week.

Each day was hotterthan the day before.

There were5 warm days and2 cold days.

For 2m makes two or three correct connections.

65

For only 1m makes one correct connection.

Connecting lines need not touch either the speech bubble or the bar chart, as long as the pupil’s intention is clear. Do not accept more than one pupil connected to a bar chart, or more than one bar chart connected to a pupil eg, for 2m showing two correct connections

Sun

Sun

Sun

Sun

Sun

Mon

Mon

Mon

Mon

Mon

Tues

Tues

Tues

Tues

Tues

Wed

Wed

Wed

Wed

Wed

Thurs

Thurs

Thurs

Thurs

Thurs

Fri

Fri

Fri

Fri

Fri

Sat

Sat

Sat

Sat

Sat

30

30

30

30

30

20

20

20

20

20

10

10

10

10

10

0

0

0

0

0

Each day was colderthan the day before.

The temperature wasabout the same all week.

Each day was hotterthan the day before.

There were5 warm days and2 cold days.

[6]

2. (a) Indicates 1

or (b) Indicates the correct shape not shaded in part (a). 1

Throughout, shading or drawing need not be accurate, as long as the pupil’s intention is clear. Accept correct shapes drawn on any grid. Ignore the shape given in the example, or individual single triangles, shaded or drawn on any grid. Ignore a correct shape repeated on any grid.

(c) Indicates 4 triangles which form a bigger triangle similar to those 1 forming the grid, eg:

66

(d) Indicates 9 or more triangles which form a bigger triangle similar to 1

those forming the grid, eg:

[4]

3. (a) Indicates £6.60, eg: 1 • 6.60 • 6-60

Alternative unambiguous indications of the correct amount eg: ♦ 6.60 ♦ £6.60p ♦ 6 pounds 60 ♦ 6.60 pence Accept correct answer given in pence written elsewhere on the page, and not contradicted eg 660 pence Do not accept incorrect or ambiguous use of pounds or pence eg: ♦ £660 pence ♦ 660 Do not accept incorrect placement of decimal points, spaces, etc, or incorrect use of 0 eg: ♦ 6.600 ♦ 6.6 ♦ 66 0 ♦ 6-6-0

(b) Indicates £89.60, eg: 1 • 89.60 • 89-60

Accept alternative unambiguous indications of the correct amount eg:

£89.60 p♦ ence ♦ 89,60 A t answer given in pence written elsewhere on the page, and not contradicted eg: ♦ 8960 p

ccept correc

Do not accept incorrect or ambiguous use of pounds or pence eg: ♦ £8960

67

Do not accept incorrect placement of decimal points spaces, etc, or incorrect use of 0 eg: ♦ 8.960 ♦ 89.600 ♦ 89-6-0

Indicates 5 1 [3]

4. (a) Indicates both Bangor and Hull. 1 Accept any indication of the two towns eg: ♦ ‘H and B’ Arrows drawn to the two place names. Do not accept responses which mention only the distance, with no indication of the two towns eg: 199

(b) Indicates 289 1

Indicates 248 1

Indicates 537 1 Allow follow through from the first two responses only if both numbers have at least three digits.

[4]

5. (a) Draws the next 4 lines correctly. 1 The fourth line must have an intended length of six units.

Ignore any continuation of the spiral beyond the four lines required. Lines need not be completely accurate, nor drawn with a ruler, as long as the pupil’s intention is clear.

(b) Indicates 12 1

(c) Indicates the correct rule, eg: 1 • ÷2 • Divide by 2 • Half of it. • × ½

Do not accept the value 2 or 12

without the correct

operation indicated.

(d) Indicates 9 1 Allow follow through from a incorrect rule given in part (c).

[4]

6. (a) Indicates 20 1

Indicates 120 1 Allow follow through for previous response correctly multiplied by 6. (b) Indicates 90 1

68

(c) Indicates any tw 1 o positive integers which multiply together to make 12. [4]

. (a) Indicates a correct rule, eg: 1

es. number youre at.

n 8

rect statement eg:

ined as a progression, do not

(b) 1m for each ff mpanied by the correctly continued 3

1

rm to term rule, eg:

ackward 4

eg:

ch time.

2, then the next 2 efore.

mation to enable the

nores the value 1 and uses

7• × 2 • Doubl• Add on the • 2 + 2, 4 + 4, 8 + 8 • Go up 2, then 4, the• Its 2, then 2 × 2, then 2 × 2 × 2

Do not accept an incor♦ ‘Go up in twos.’

eWh re a rule is explaaccept fewer than 3 differences specified eg: ♦ ‘+ 2, + 4’

di erent stated rule accochain. Examples of correct chains and rules include:

those with a constant term to term rule, eg: • 1, 5, 9, 13, 17 ... add 4 • 1, 5, 25, 125, 625 ... × 5• 1, 5, 21, 85, 341 ... × 4 + 1 • 1, 5, 17, 53, 161 ... × 3 + 2 • 1, 5, 13, 29, 61 ... × 2 + 3 • 1, 5, 29, 173, 1037 ... × 6 –

those with a constant multi-part te• 1, 5, 8, 12, 15 ... + 4, + 3 • 1, 5, 1, 5, 1 ... forward 4, b

those described by changing differences,• 1, 5, 11, 19, 29 ... + 4, + 6, + 8, + 10 • 1, 5, 8, 10, 11 ... + 4, + 3, + 2 • 1, 5, 10, 16, 23 ... its 1 more ea

those with a Fibonacci-type pattern, eg: • 1, 5, 6, 11, 17 ... add first 2, then next • 1, 5, 5, 25, 125 ... multiply each number by the number b

those which describe the numbers in the chain, eg: • 1, 5, 9, 13, 17 ... every other odd number.

Each rule must give sufficient inforchain to be continued. Accept more sophisticated rules such as the nth term given eg: ♦ ‘1, 5, 9, 13, 17 ... 4n – 3’ Do not accept a rule which ig

e 5 as the first number in theth chain. Do not accept errors or omissions in generating the numbers; a calculator is available.

69

ar to one already

credited eg: ♦ ‘+ 4’ and ‘ + 5 – 1’ Do not accept a rule which is not quantified eg: ♦ ‘1, 5, 10, 16, 23 ... add more each time.’ ♦ ‘1, 5, 1, 5, 1 ... go forwards then backwards.’ Where a rule is explained by listing changing differences, Fewer than 3 differences specified eg: ♦ ‘1, 5, 8, 10, 11 ... + 4, + 3’ Do not accept rules which reach a particular term and then remain constant eg: ♦ ‘1, 5, 5, 5, 5 ... don’t go higher than 5’

[4]

8. (a) Gives a correct explanation, eg: 1 • 4 of each. • Equal chances. • Half are triangles. • Just as likely. • Fifty fifty. • Evens. Not more

Do not accept a rule which is simil

.

Indicates certain. 1

Indicates likely. 1 Throughout, accept unconventional names for and as long as the pupil’s intention is clear. Do not accept explanations which imply the likelihood cannot be found eg: ♦ ‘No-one knows what she’ll get – he’s just guessing.’ Accept equivalent words or phrases. Accept equivalent words or phrases.

(b) Completes the sentence correctly, eg: 1 • (any number) than (any number) than

than (any number other than 9) than 9 Even than odd. White than black. Lower number than higher number.

70

Ticks the “h 1

and justifies the decision, eg: • 4 higher, 3 lower. • 8, 9, 7 and 9• Only 3 s• More hig .• Not man• Its 4 out • 4 in 7 higher

e ry may refer to cards which are not

makes it clear that “higher than 5” is intended. Do not accept responses which do not give a justification

‘It’s a higher change.’ than 5 is more.’

cept justifications which do not refer, explicitly y, to all the cards eg:

gher, there are two 9s.’ stifications are quantified, then do not accept

antification eg: ‘5 cards higher, 3 lower.’

igher than 5” box

are bigger ma r. lleher y lower. of 7.

, 3 in 7 lower. The second entry must be true for the cards shown in thquestion. The first entshown in the question. Accept no box ticked only if the justification

eg: ♦ ♦ ‘The probability of higherDo not acor implicitl♦ ‘HiIf juincorrect qu♦

‘It’s 48

not 38

’

[5]

9. (a) Indicates 48 1 ted

(b) Indicates 3. 1

ided correct units are indicated

(c) Indicates 1 lete or incorrect computations eg:

[3]

10. (a) Indicates 20 1

Indicates 40 1 Do not accept a value given as a percentage. Allow follow through from an incorrect number of girls, provided the percentage given is greater than 0 and less than 50.

Accept change of units provided correct units are indicaeg: 0.48m

8 ions. Accept equivalent decimals or fract

Accept change of units proveg: 3kg 800g

103 Do not accept incomp♦ 100 + 3

71

(b For 2m draws all 3 sections c 2 ) orrectly, eg:

• 3 sections totalling 100% and draws correctly one section

ons the same size.

on correctly with the ages, eg: 1

the ages. [5]

11. (a) 1m for indic 3

For only 1m sbut with no two secti

show

Labels each secti• 4, 3, 2

For 2m accept incorrect or omitted labels. Allow follow through from an incorrect drawing only if no sections are the same size, and 4 years is the largest labelled section and 2 years is the smallest labelled section. Accept additional correct information given as long as there are correct labels for

ating each correct position, eg:

Accept any unambiguous indication of where the square

t accept more than one square indicated on any

should be.Do nodiagram unless it is clearly shown that multiple responsesare intended eg, accept

here or

or

♦

72

(b) Draws a rectangle which fits along the upp 1 er horizontal edge given

ctly oriented right-angled triangles which fit along vertical edges and draws two corregiven, eg:, one of

e accurate as long as he rectangle drawn

as a square. t extra

Draws a 5.7 by the overlay. 1

Draws two cy as specified by the overlay. 1 This mark is available for two accurately drawn triangles anywhere on the page.

[6]

12. (a) 1

(b) value between 53 and 57 inclusive. 1

(c) value between 14 and 16 inclusive. 1

(d) 2

e value 60 [5]

13. mm. 1

of 8.5cm ± 2mm 1

1

radius 8.5cm ± 2mm, with the centre at the 1

nd of a line defined by the intersection of the

w through from a incorrect angle. Ignore

[4]

14. (a) Indicates 10 1 r non-ambiguous indication of

cost su an on the given

(b) Indicates 40 1

For this mark the drawing need not bthe pupil’s intention is clear. Accept t

Accept tabs drawn, otherwise do not accepshapes.

cm by 4cm rectangle within the accuracy as specified This mark is available for an accurately drawn rectangle anywhere on the page.

right-angled triangles within the accura

Indicates 80

Indicates a

Indicates a

For 2m indicates 10

For only 1m shows th

Draws one edge of 8.5cm ± 2

Draws the second edge

Draws an angle of 74° ± 2°

Draws a correct arc, withapex of the drawing.

Accept the eline with the arc or the other line. Allow follocontinuation of the arc beyond the lines.

6.25 Accept £106.25p or othe

ch as 10625p written other thanswer line.

73

(c) Indicates excellent and not boxed, eg: 1

• Excellent. No. • Best but isnt.

Accept unambiguous responses eg:♦ 65% Do not accept partial responses eg♦ Excellent.

:

[3]

74

1. (a) Indicates 09:15 1 Throughout the question ignore any reference to am or pm. Accept any indication eg: ♦ ‘Quarter past nine.’ ♦ ‘915’ ♦ ‘9-15’ Accept any indication eg: ♦ ‘Three quarters of an hour.’ ♦ ‘00:45’

Indicates 45 1

(b) Indicates the correct bus eg: 1 • 09:30 • 10-15 • The third bus. • Half past 9 • 930 • Arrow drawn to correct bus.

(c) Indicates £11 eg: 1 • 11 in answer space. • 11.00 in answer space, • £11.

[4]

2. (a) Indicates the two correct angles, and no other angles eg: 1

Accept any indication eg: Angle sizes marked, with correct pair equal or within four degrees of each other.

(b) Draws an angle which is greater than 90°. 1 Angles need not be accurately drawn provided the pupil’s intention is clear. Accept a reflex angle which is clearly indicated. Accept a straight line in which the 180° angle is clearly indicated.

Ignore any attempt to label the angle size.

75

(c) Indicates South eg: 1

• S • Draws an arrow down the page.

(d) Indicates South 1 Do not accept ambiguous or incorrect indications eg: ♦ ‘Down’

[4]

3.(a) Indicates 20 miles eg: 1 • 20 miles • 20 m

(b) Indicates 53 miles. 1

(c) Indicates 9 miles. 1 The correct units must be given at least once within this question. If they are not given anywhere in the question, do not accept the last response which is otherwise correct and would have been awarded the mark.

[3]

4. Draws the correct line, and no other lines eg: 1

Draws the four correct lines, and no other lines eg: 1

76

Draws the three correct lines, and no other lines eg: 1

Drawings need not be accurate and lines of symmetry need not extend to the edge of the pattern, provided the pupil’s intention is clear.

[3]

5. (a) Indicates 10 1

Indicates 16 1

Indicates 30 1

(b) Indicates 24 1 [4]

6. (a) Indicates a pair of numbers with a sum of 34 1

Indicates a pair of numbers with a product of 10 1

(b) Indicates 12 1 Do not accept remainders other than 0.

(c) Indicates 275 1

Indicates 368 1

Indicates 16 1 Do not accept remainders other than 0.

[6]

7. (a) Indicates £40 1

(b) Indicates £5.96 1

(c) Indicates 8 1

(d) Indicates 3 1 Accept 9 (cassettes).

77

(e) Indicates 11 eg: 1

• 11 • Three packs (of three) and two singles. • 3 × 3 + 2 • 3 at £3.99 and 2 at £1.49

Accept indication of the total cost eg: ♦ ‘£14.95’ ♦ ‘£11.97 + £2.98’ Ignore references to five items bought if it is clear from the working that three of these are packs (at £3.99) and two are cassettes (at £ 1.49) Throughout the question, ignore any reference to money left over, even if it is incorrect.

[5]

8. Indicates 63 as total. 1 For each cell, allow follow through from an incorrect total found, provided the two relevant values given in the square have been used.

Indicates 21 in centre cell. 1 Accept the difference between the pupil’s total and 42

Indicates 40 in centre right cell. 1 Accept the difference between the pupil’s total and 23

Indicates 8 in bottom centre cell. 1

eg for 4m

21 40

8

63

Accept the difference between the pupil’s total and 55 •

[4]

9. (a) Indicates the correct mass in grams for all three items eg: 1 • 1000 g caster sugar • 1500 g margarine • 1250 g mixed fruit

For 2m indicates the correct mass in kilograms of all three items eg: 2 • 1 kg caster sugar

1.5 kg margarine 1¼ kg mixed fruit

Accept unrounded masses in kilograms given to any number of decimal places eg: ♦ ‘1.000 kg; 1.50 kg; 1.25 kg’ Correct masses in kilograms and grams, with units indicated correctly eg: ♦ ‘1 kg 500’ ♦ ‘1 kilo 250g’

For only 1m indicates the correct mass in kilograms of any two items.

78

For 2m or only 1m , allow follow through from their number of grams provided three different masses have been given, not more than one of which is a whole number of kilograms, and at least one of which has three or more non-zero digits.

(b) Indicates £3.50 1 [4]

10. (a) Indicates 4 corner 1

12 edge

8 middle

(b) For 2m indicates 4 corner 2

18 edge

20 middle

For only 1m indicates two of the three numbers correctly. or Indicates the correct numbers in the wrong order.

(c) For 2m indicates 4 corner 2

32 edge

100 total

For only 1m indicates two of the three numbers correctly. [5]

11. (a) For 2m completes the chart correctly eg: 2 • 10% of 240 is 24

5% of 240 is 12 2½ % of 240is 6 so 17½ % of 240 is 42

For 2m also accept alternative methods leading to a total of 17½ % of 240 eg: 5% of 240 is 12 15% of 240 is 36 2½ % of 240 is 6 so 17½ % of 240 is 42 20% of 240 is 48 10% of 240 is 24 5% of 240 is 12 Halve it. So 17½ % of 240 is 42

79

10% of 240 is 24 7% of 240 is 16.8 0.5% of 240 is 1.2 so 17½ % of 240 is 42 20% of 240 is 48 2½ % of 240 is 6 so 17½ % of 240 is 42

For only 1m shows a complete method for finding 17½ % eg: • Shows 10%, 5% and 2½ % • Shows (5%), 15% and 2½ % • Shows 10%, 20% and 5% totalled, then halves. • Shows 10%, 7% and ½ % • Shows (10%), 20%, then subtracts 2½ %

or Indicates that the total percentage of 240 is 42, without showing a complete

method. For 2m or only 1m accept the rows of the chart showing the method in any order eg: 5% of 240 is 12 10% of 240 is 24 2½ % of 240 is 6 so 17½ % of 240 is 42 For 2m or 1m only Methods which do not show how 17½ % of 240 is to be found eg: Percentages summing to 35% shown, with no indication that the result must be halved. 10%, 5% and 15% shown, with no indication that 2½ % is also required. For only 1m also accept the chart completed correctly but the percentage sign incorrectly used in the second column.

(b) For 2m indicates 182 2

For only 1m shows in working a valid method to find 35% of 520 eg: • Attempts to find 50% and 15% and subtract. • Attempts to find 10%, multiply by 3, and add 5%. • Attempts to find 10%, double to 20%, double to 40% , and subtract 5%. • Attempts to find 17½ % as in part (a), and then to double. • Shows 35 ÷ 100 × 520 • Shows 0.35 × 520

For only 1m the attempt to find the relevant percentages of 520 need not produce correct figures eg: for 1m ♦ ‘10% = 52 ♦ 30% = 3 × 10% = 159 5% = 16 35% = ’

[4]

80

12. (a) For 2m indicates 14 2

For 2m accept any number under 16 given or implied as the number of extra booklets eg: ♦ ‘14, 3 booklets left over.’ ♦ ‘14 r 4’

For only 1m uses a correct method with only one error, and states the correct number of packs for their result eg:

• 10 is 160, 5 is 80, 160 + 80 = 230, so it’s 15

• ‘220/16 = 110/8 = 50/4 > 12, she needs 13

4016

1222016

Answer: 13

• •

10 160+ +5 80

240– –1 16 16 224 16 packs

or Shows a complete correct method with no error other than in the remainder, but

indicates an incorrect, or no, number of packs required eg: • Shows 13.75, 13¾ or 13 remainder 12 • Shows 13 and 208 • Shows 224 • 13 • 13 packs, and you need some more booklets. • 13 +

(b) For 2m shows the correct number of grams eg: 2 • 10560 (g)

For 3m accept the correct total in kilograms eg: ♦ ‘10.56’ in the answer space. ♦ ‘10.560 kg’ elsewhere.

For only 1m, uses a correct method to multiply 220 by 48, with only one computational error eg: • 48 × 220 = 12 × 880

2 × 880 = 1660, 8800 + 1660 = 10460 • Shows 8800and 1760 • Shows 960and 9600

Do not accept incorrect place values in the calculation eg: ♦ ‘1760’ and ‘880’ ♦ ‘960’ and ‘960’

81

or Shows a number with the digits 1056(00...) eg • 1.056 • 10.5.6 • 105600

Correctly converts 10560 grams to kilograms eg 1 • 10.56

Allow follow through from an incorrect number of grams provided the incorrect number of grams is over 1000 and is not a multiple of 1000 Accept rounding or truncation in the conversion to kilograms provided acceptable digits have been shown in working eg: ♦ ‘10.5’ with 1056(0) shown in working. ♦ ‘10 ½’ with 1056(0) shown in working. Accept the continental practice of using a comma for a decimal point eg: ♦ ‘10,560’ in the answer space. ♦ ‘10,56 kg’ elsewhere.

[5]

13. (a) Indicates n + 5 1 Ignore a numerical substitution for n or t if a correct expression has been given eg: ♦ ‘n + 5 = 17’ Accept unambiguous use of the equality sign eg: ♦ ‘n + 5 = n + 5’ ♦ ‘= t – 2’

(b) Indicates t – 2 1

(c) For 2m indicates the second, fourth and fifth statements only eg: 2

•

For only 1m indicates two correct and no incorrect statements.

or Indicates all three correct and one incorrect statements.

Any indication provided the pupil’s intention is clear. If a mixture of ticks, crosses and blanks are used, assume that only the ticks indicate selections.

[4]

82

14. (a) For 2m indicates classes Q, R and T only. 2

Accept any indication. Accept the correct classes indicated in any order.

For only 1m indicates two correct classes, and not more than one incorrect class.

or Indicates three correct classes and one incorrect class.

(b) For 2m indicates the second and fourth statements only eg: 2

Allow follow through from part (a) provided exactly three graphs were selected. The only valid follow through is for the second statement to be taken as false, so if the pupil has selected three classes including class P or class S, then for 2m accept: For only 1m accept:

•

For only 1m indicates one correct statement and no incorrect statements.

or Indicates both correct statements and one incorrect statement.

Accept any indication provided the pupil’s intention is clear. If a mixture of ticks, crosses and blanks are used, assume that only the ticks indicate selections.

(c) Completes the graph to show a mean score of 6, eg: 1 100

80

60

40

20

0

%of

Pupils

Score0 1 2 3 4 5 6 7 8 9 10 11 12

100

80

60

40

20

0

%of

Pupils

Score0 1 2 3 4 5 6 7 8 9 10 11 12

83

Drawings need not be accurate provided the pupil’s intention is clear. The total sum of the products of each score drawn with its percentage must equal 70. Do not accept a graph in which more or less than 100% of pupils are shown.

[5]

84

1. (a) For 2m completes the table correctly eg 2 • Ben 20p

Cal 25p Jan 30p Kim 15p Wyn 20p

Do not accept failure to specify the units eg: ♦ ‘25’

For only 1m completes three out of the four entries correctly.

(b) Indicates £1.10 1 Allow follow through from part (a) provided an entry has been made for Cal in the ‘Amount for each length’ column.

(c) Indicates £20.25 1

(d) Indicates £18 1

Indicates £4.50 1 Allow follow through from an incorrect total, rounded or truncated to a whole number of pence eg: for £1800 given as the total, accept £450

[6]

2. (a) Indicates 240 1

(b) Indicates 302 1

(c) Indicates 2513 1

(d) Indicates 3052 1 Throughout the question, ignore decimal points or indications of the thousands digit eg: ♦ ‘2.40’ ♦ ‘2,513’ ♦ ‘3:052’

[4]

3. (a) Indicates 4 1 Throughout the question, accept any indication of the correct response, provided the pupil’s intention is clear eg: ♦ Correct objects drawn

(b) Indicates 5 1

(c) Indicates 6 1 Throughout the question, ignore objects drawn if numbers are given.

85

(d) Correctly indicates the bottle on one side, and the boxes and can on the

other eg: 1

boxescan bottle

• box, box, can = bottle • bottle = the rest

Do not accept extra objects drawn or indicated. Do not accept responses which refer to only one box eg: ♦ ‘box, can = bottle’

[4]

4. (a) Indicates 18(th). 1 Accept correct month and correct or incorrect eg: ♦ ‘18 Jan’ ♦ ‘1.18.99’

(b) Indicates 4 1

Indicates 5 1

(c) Completes the sentence correctly, indicating that there are 1

more than Wednesdays or Sundays Thursdays Mondays Tuesdays Fridays or Saturdays

(d) Indicates February 11 eg: 1 • Feb 11th • 2/11

Accept correct or incorrect year or day of the week eg: ♦ ‘11 2 97’ ♦ ‘Tues, 11 Feb’ Do not accept responses which do not indicate both the date and the month.

(e) Indicates 3 1 Accept responses indicating one day less eg: ♦ ‘2 weeks and 6 days.’ Do not accept the answer given only in days eg: ♦ ‘21 days’

86

(f) Indicates Saturday, 1

Accept any indication eg: ♦ ‘7, 14, 21, 28’ Ignore further multiples of 7 Do not accept fewer than the first four dates.

[7]

5. (a) Indicates 4 eg: 1 • 4 • He adds one tile on each corner. • Diagram drawn showing that a tile is added to each corner.

Do not accept the total numbers of tiles in each pattern eg: ♦ ‘4, 8, 12’

(b) Indicates 24 1

(c) Indicates 36 1

(d) Indicates 10 1 [4]

6.(a) Indicates S. 1 Throughout the question, drawing and shading need not be accurate provided the pupil’s intention is clear.

(b) Indicates R. 1

(c) Shades the whole spinner. 1

(d) Shades half the spinner, using a diameter or radius to distinguish the sectors eg: 1

Accept any surface for the area which is not shaded eg: ♦ ‘plain’ ♦ ‘striped’ ♦ ‘coloured’ Do not accept shading in which there is no intention to divide the surface into sectors eg:

♦

[4]

7. (a) Indicates Liz. 1 Accept the name written in the table,

(b) Indicates Jim. 1

87

(c) Gives a valid advantage of Meg’s table. This may relate to: 1

The ready availability of summary information eg: • You can see who won overall. • It tells you how many games each person won. • Megs way is much better because its easy to see each persons total. • You can see who won the most. • Everything is all in one table. • You dont have to count names. • It gives you a running total all the way through the competition. • Its easy to keep count. • You can see who is winning. • It is less confusing. • Its easier to count the tallies.

Ease of recording eg: • Its quick to fill in. • You just have to put lines • You can count in fives. • It takes up less space.

Accept a correct response which is accompanied by an irrelevant reason or a reason which applies to both. Do not accept responses which simply state that one or the other method is better eg: ♦ ‘Jim’s way is much better.’ ♦ ‘Tally charts are better.’ Do not accept vague responses which could apply equally well to either record eg: ♦ ‘You can see the total number of games they played.’ ♦ ‘This chart is easy to use.’ Do not accept false statements, even if they are accompanied by a valid advantage eg: ♦ ‘Meg’s way is quick to fill in and it tells you who won each game.’ ‘Jim’s table shows the order in which the games were played and how often they won.’

(d) Gives a valid advantage of Jim’s table. This may relate to: 1

The detail of the information eg: • You can see who won each game. • You can tell who won the Ludo. • You know what games each person won. • You can see who won what. • It tells how many of each game each person won. • Jims way is more detailed. • It shows in what order people won.

88

Security/Accuracy eg: • You cant cheat with Jims way. • You are less likely to make mistakes.

Do not accept a description of the method used with no indication of its advantages eg: ♦ ‘Meg’s is good because she uses a tally chart.’ ♦ ‘Jim gives all the names.’ ♦ ‘Jim sorted the results out into columns.’ ♦ ‘Jim did each game separately.’

[4]

8. (a) Completes the column of lengths to the nearest 100 correctly eg: 1 • 400

300 300 200 100

Indicates Thames and Trent. 1 Accept rivers in either order.

(b) Completes the column of lengths to the nearest 10 correctly eg: 1 • 350

350 300 220 110

Indicates Severn and Thames. 1 Allow follow through from an incorrect table provided all the numbers in the table are of three digits. Accept 215 rounded down to 210. Accept any unambiguous indication of the correct rivers eg: ♦ ‘297’ for Trent and 346 for Thames. ♦ ‘350’ for Severn and Thames.

(c) Indicates a number greater than or equal to 150 and less than or equal to 155 1 (150 ≤ n ≤ 155) eg: • 150 • 151 • 152 • 153 • 154 • 155

89

(d) For 2m indicates one whole number greater than or equal to 245 and less 2

than or equal to 250 (245 ≤ n ≤ 250) eg: • 245 • 246 • 247 • 248 • 249 • 250

Accept numbers in either order.

and

indicates one different whole number greater than or equal to 250 and less than or equal to 255 (250 ≤ n ≤ 255) eg: • 250 • 251 • 252 • 253 • 254 • 255

For only 1m indicates one correct number but with the other number missing or incorrect eg: • 253 and 252 • 250 and 250 • 245 • 247 and 252.5

or

Indicates two different whole numbers which have the same value to the nearest 10 (but not 250), but are different to the nearest 100 eg: • 146 and 153

or

Indicates two numbers which fit the criteria but are not both whole numbers eg: • 249.999...and 250.1

For 2m do not accept 250 indicated twice. [7]

90

9. (a) Draws another triangle to form a 2 by 3 rectangle eg: 1

Throughout the question, drawings need not he accurate provided the pupil’s intention to draw a congruent triangle in the correct position is clear. Do not accept responses to part (a) given in part (b), or responses to part (b) given in part (a).

(b) Draws another congruent triangle to form a bigger triangle eg: 1

•

• (c) Draws another congruent triangle to form the other bigger triangle 1

[3]

91

10. (a) For 2m indicates 6 red and 14 blue. 2

Accept correct answers given in other metric units, provided the units are shown eg: ♦ ‘6000 millilitres’

For only 1m indicates one correct value in the correct position.

or

Indicates both values, but in the wrong order.

or

Indicates another pair of numbers, other than 3 and 7, which are in the ratio 3 to 7 eg: • 30and 70 • 60and 140

(b) For 2m indicates 6.5 yellow and 3.5 red eg 2 • 6½ and 3½

For only 1m indicates one correct value in the correct position.

or

Indicates both values, but in the wrong order. or

Indicates another pair of numbers, other than 13 and 7, which are in the ratio 13 to 7 eg: • 130and 70 • 0.65and 0.35

[4]

11. (a) Draws a shape different from that given made with 1 two L-triominoes with only one line of symmetry eg:

Throughout the question drawings need not be accurate provided the pupil’s intention is clear. Accept any or no internal lines showing individual squares forming triominoes, Throughout the question ignore attempts to draw lines of symmetry. Throughout the question accept enlargements of acceptable responses eg, for part (a)

92

Throughout the question ignore copies, rotations, reflections or enlargements of the examples given in the question given in addition to acceptable shapes. Throughout the question do not accept responses in the wrong answer spaces, unless the pupil’s intentions are clear. Throughout the question do not accept shapes which are not composed of two triominoes. Accept arrangements of two triominoes which have the correct symmetries but do not touch or touch only at a vertex or vertices eg, for part (a)

(b) Draws a shape made with two L-triominoes with two lines of symmetry eg: 1

(c) Draws a shape different from that given made with two 1

L-triominoes with rotational symmetry of order two eg:

(d) Draws a shape made with two L-triominoes with two lines of symmetry and 1

rotational symmetry of order two eg:

Accept arrangements of two triominoes which have the correct symmetries but do not touch or touch only at a vertex or vertices eg, for part (b)

93

eg, for part (c)

eg, for part (d)

[4]

12. (a) Indicates a value in the range 20 to 30% inclusive. 1 Accept equivalent fractions or decimals written outside the answer space.

(b) Indicates a number in the range 2 to 3 inclusive. 1 Accept a correct number of people which is not given in the answer space eg: ♦ ‘2,500,000’ Allow follow through from a percentage given in part (a).

(c) Indicates that the total number of people in each country needs to be taken 1 into account eg: • Greece has more people. • Ireland has 3.5 and Greece has 10. • Its out of more people. Ireland has only 3.5 million people. The total populations are not the same. 20% of 10 is more than 25% of 3.5 2 > 0.875

Accept explanations which indicate that the pie charts give only the proportions, or that they do not give the numbers of people eg: ♦ ‘The charts only show the percentages.’ ♦ ‘It doesn’t give the actual numbers of people.’ ♦ ‘One per cent in Greece is worth more than one per cent

in Ireland’ ♦ ‘The chart for Ireland is on a bigger scale.’ ♦ ‘1 % for Greece is about 3 % for Ireland.’ ♦ ‘It’s only the proportion of people under 15 which is

greater in Ireland.’ ♦ ‘The charts are drawn to different scales.’ ♦ ‘There are 10 million people in Greece so there is a bigger

pie for Greece.’

94

Ignore irrelevant statements which accompany a valid reason eg: ♦ ‘The charts are not dead accurate, and there are more

people in Greece.’ Do not accept explanations which could relate to the size of the countries and not to the populations eg: ♦ ‘Ireland is smaller.’ Do not accept explanations which state only one of the populations, without indicating that this is less or greater than the other eg: ♦ ‘Ireland has a population of 3.5 million.’ Do not accept false statements eg: ♦ ‘There are more people in Greece so 10% would look

larger on Ireland than on Greece.’ ♦ The chart for Ireland is on a smaller scale.’ ♦ ‘The chart for Ireland is bigger.’

(d) For 2m draws a correct pie chart, showing sectors with 2, 3½, 2½ and 2 2 of the 10% sectors given in the question eg:

Drawings need not be accurate provided the pupil’s intention is clear. Do not accept pie charts which have fewer than 4 or more than 4 sectors.

For only 1m draws a pie chart with four sectors, two of which are the correct size.

Labels their 4-sector pie chart, with the largest of their four sectors labelled 1 ‘15 – 39’, the second largest labelled ‘40 – 59’, and the remaining two labelled ‘under 15’ and ‘over 59’.

The two smallest sectors may be taken in either order for the purpose of labeling. Accept the use of a key to indicate the age ranges covered by each sector.

95

Accept correct percentages given in addition to age ranges, but do not accept percentages instead of age ranges. Do not accept incorrect labels eg: ♦ ‘15’ for ‘under 15’ Do not accept labels on two sectors which are the same size, unless they are smaller than the other two. Do not accept labels on three or four sectors which are the same size.

[6]

13. (a) Indicates the correct net, and no other nets eg: 1

Accept any indication.

(b) For 2m draws a semi-circle, radius 4 cm ± 2 mm, and its diameter. 2

For only1m draws a semi-circle, radius 8 cm ± 2 mm, and its diameter. For 2m or 1m accept more than a semi-circle drawn, provided at least one acceptable semi-circle and its diameter are drawn eg: ♦ Attempts to draw a complete net of the box ♦ Draws a whole circle with a diameter. ♦ Draws a part of a circle greater than a semi- circle, with

a diameter. [3]

96

1. Joining

This circle has the numbers 0 to 11 around it.

01

2

3

4

56

7

9

10

11

8

You can make a triangle by joining up the numbers in the 4 times table with straight lines.

01

2

3

4

56

7

9

10

11

8

(a) Join up the numbers in the 3 times table on the circle below.

Start and finish at 0. Use straight lines.

01

2

3

4

56

7

9

10

11

8

1 mark

97

What is the name of the shape you have drawn?

1 mark

(b) Join up some numbers in the circle below to make a shape with 6 equal sides.

Start and finish at 0. Use straight lines.

01

2

3

4

56

7

9

10

11

8

1 mark

Which times table makes this shape?

The ………………………. times table

1 mark

Total 4 marks

98

2. Eyes

Liam did a survey of the eye colour of all the children in his class.

This table shows his results:

Number of Boys Number of Girls

Brown eyes 11 12

Blue eyes 4 3

(a) How many children are there in Liam's class?

1 mark

(b) How many children in Liam's class have brown eyes?

1 mark

(c) Two new children join Liam's class.

They are both boys.

One has brown eyes and the other has blue eyes.

Liam changes the numbers in his table.

Fill in this table for Liam's class now:

Number of Boys Number of Girls

Brown eyes

Blue eyes

2 marks

99

(d) Julie does a survey of 10 children in her class.

She records her results like this:

Boy or girl Boy Girl Boy Girl Girl Boy Girl Boy Girl Boy

Colour of eyes Brown Brown Blue Blue Brown Brown Brown Brown Blue Brown

Fill in this table to show Julie's results:

Number of Boys Number of Girls

Brown eyes

Blue eyes

2 marks

(e) There are 14 boys and 17 girls in Mari's class.

10 boys and 13 girls have brown eyes. The others have blue eyes.

Use the information to complete this table for Mari's class:

Number of Boys Number of Girls

Brown eyes

Blue eyes

2 marks

Total 8 marks

3. Missing Numbers

Write one number at the end of each equation to make it correct.

Example

26 + 34 = 16 + .....44....

100

(a) 400 + 150 = 500 + …………..……….…….. 1 mark

(b) 14 + 6 = 4 + …………..……….…….. 1 mark

(c) 37 – 20 = 27 – …………..……….…….. 1 mark

(d) 6 × 5 = 3 × …………..……….…….. 1 mark

(e) 38 + 17 = 28 + …………..……….…….. 1 mark

(f) 38 – 17 = 28 – …………..……….…….. 1 mark

(g) 40 × 10 = 4 × …………..……….…….. 1 mark

(h) 7000 ÷ 100 = 700 ÷ …………..……….…….. 1 mark

Total 8 marks

101

4. Triangles

This is a right-angled You can fit 8 of the tiles into triangular tile: a 4cm by a 4cm square like this:

2cm

2cm

4cm

4cm

Write how many of the tiles you can fit into each of these shapes.

4cm

4cm

6cm

2cm

2cm

Number of tiles: …………………….. Number of tiles: ……………………..

2 marks

102

4cm

4cm

2cm

2cm

6cm

2cm

2cm

2cm

4cm

Number of tiles: …………………….. Number of tiles: ……………………..

2 marks

Total 4 marks

5. Tiles

Daniel has some parallelogram tiles.

He puts them on a grid, in a continuing pattern.

He numbers each tile.

The diagram shows part of the pattern of tiles on the grid.

1

2

3

x

x

x

y

x2 4 6 8

6

4

2

0

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Daniel marks the top right corner of each tile with a •

The co-ordinates of the corner with a • on tile number 3 are (6, 6)

(a) What are the co-ordinates of the corner with a • on tile number 4?

(…………… , ……………)

1 mark

(b) What are the co-ordinates of the corner with a • on tile number 20?

(…………… , ……………)

1 mark

Explain how you worked out your answer.

1 mark

104

(c) Daniel says:

One tile in the pattern has ain the corner at ( , )25 25

Explain why Daniel is wrong.

1 mark

(d) Daniel marks the bottom right corner of each tile with a X

Fill in the table to show the co-ordinates of each corner with a X

tile number co-ordinates of the corner with a X

1 (...2..., ...1...)

2 (……, ……)

3 (……, ……)

4 (……, ……)

105

1 mark

Fill in the missing numbers below.

(e) Tile number 7 has a X in the corner at (………… , …………) 1 mark

(f) Tile number ……………….. has a X in the corner at (20, 19) 1 mark

Total 7 marks

6. Relations

Look at these three signs:

is thanless

< is toequal

= is thangreater

>

Examples:

4 – 3 = 2 – 14 – 3 is to 2 – 1equal

5 < 65 is than 6less

6 – 2 > 9 – 66 – 2 is than 9 – 6greater

Put the correct sign, < or = or >, into each number sentence.

(a) 8 + 2 ........ 7 + 6 1 mark

(b) 6 – 3 ........ 1 + 2 1 mark

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(c) 0 ........ –3 1 mark

(d) –7 ........ –2 1 mark

(e) 3 – 2 ........ –5 1 mark

(f) 5 – 5 ........ 4 – 6 1 mark

Total 6 marks

7. Coins

A coin has two sides, heads and tails.

(a) Chris is going to toss a coin.

What is the probability that Chris will get heads?

Write your answer as a fraction.

1 mark

107

(b) Sion is going to toss 2 coins.

Fill in the table to show the different results he could get.

First coin

heads

Second coin

heads

1 mark

(c) Sion is going to toss 2 coins.

What is the probability that he will get tails with both his coins?

Write your answer as a fraction.

1 mark

(d) Dianne tossed one coin.

She got tails.

Dianne is going to toss another coin.

What is the probability that she will get tails again with her next coin?

Write your answer as a fraction.

1 mark

Total 4 marks

8. Numbers

108

Here is a list of numbers:

–7 –5 –3 –1 0 2 4 6

You can choose some of the numbers from the list and add them to find their total.

For example,

…6… + …–1… = 5 (a) Choose two of the numbers from the list which have a total of 3

.... + .... = 3 1 mark

(b) Choose two of the numbers from the list which have a total of –1

.... + .... = –1 1 mark

Choose two other numbers from the list which have a total of –1

.... + .... = –1 1 mark

109

–7 –5 –3 –1 0 2 4 6 (c) What is the total of all eight of the numbers on the list?

1 mark

(d) Choose the three numbers from the list which have the lowest possible total.

Write the three numbers and their total.

You must not use the same number more than once.

.... + .... + .... = 2 marks

Total 6 marks

9. Rods

Helen has these eight rods.

2cm3cm

4cm

5cm5cm

6cm7cm

8cm

110

She can use 5 of her rods to make a rectangle.

2cm6cm

5cm5cm

8cm

(a) Show how to make a different rectangle with a different shape with 5 of Helen's rods.

1 mark

111

(b) Show how to make a rectangle with 6 of Helen's rods.

1 mark

112

(c) Show how to make a square with all 8 of Helen's rods.

1 mark

Total 3 marks

113

10. Florida

This graph shows the range in the temperature in Miami each month.

For example, in January the temperature ranges from 17°C to 24°C

JanFebMarAprMayJuneJulyAugSepOctNovDec

0 10 15 20 25 30 35

Miami

Temperature (ºC) in Miami

(a) In which month does Miami have the smallest range in temperature?

1 mark

(b) In July, the range in the temperature in Miami is 5 °

There are five other months in which the range in the temperature is 5°

Which five months are they?

2 marks

114

(c) This graph shows the range in the temperature in Orlando each month.

JanFebMarAprMayJuneJulyAugSepOctNovDec

0 10 15 20 25 30 35

Orlando

Temperature (ºC) in Orlando

In which three months is the maximum temperature in Miami greater than the maximum temperature in Orlando?

1 mark

Total 4 marks

11. Symmetry

An equilateral triangle has It has rotational symmetry 3 lines of symmetry. of order 3

115

Write the letter of each shape in the correct space in the table below.

You may use a mirror or tracing paper to help you.

The letters for the first two shapes have been written for you.

AC

B DF

E

Number of lines of Symmetry

0 1 2 3

1

2

3

B

A

Order ofRotationalSymmetry

Total 4 marks

116

12. Areas

The diagram shows a rectangle 18cm long and 14cm wide.

It has been split into four smaller rectangles.

Write the area of each small rectangle on the diagram.

One has been done for you.

............... cm2

40cm 2

............... cm2

............... cm2

10cm 8cm

10cm

4cm

1 mark

What is the area of the whole rectangle?

......…………....... cm2

1 mark

What is 18 × 14?

18 × 14 = .…………….

1 mark

Total 3 marks

117

1. Calculations (a) Indicates 486 1

(b) Indicates 543 1

(c) Indicates 37 1

(d) Indicates 3569 1

(e) Indicates 384 1 [5]

2. Angles

(a) Indicates angle E 1 Accept an angle size in the range 21 to 27 inclusive.

(b) Indicates angle D 1 Do not accept an angle size eg: ♦ ‘90°’

(c) Indicates angle B 1 Accept an angle size in the range 136 to 142 inclusive.

[3]

3. Measures

(a) Indicates 2 litres, eg: 1

(b) Indicates 2m high, eg: 1

(c) Indicates 100 grams eg: 1

[3]

118

4. Beads

(a) For 3m indicates: 3 for unlikely, bag B for equally likely, bag E for likely, bag C for certain, bag A

For only 2m indicates three of the four bags correctly.

For only 1m indicates two of the four bags correctly.

(b) Indicates that there must be more black than white beads in the bag, eg: 1 • 6 • More than 5 • More black than white beads. • 9 or 10

Accept any indication eg: Beads drawn in or next to the bag.

(c) For 2m indicates 10 black and 10 white beads. 2

For only 1m indicates an equal number of black and white beads which do not give a total of 20 beads, eg: • 5 black beads and 5 white beads.

[6]

5. Arrangements (a) Indicates 7531 1

(b) Indicates that all the cards are odd, eg: 1 • You need to end in an even number. • There isnt an even card. • None of them are in the 2 times table. • You cannot make an even number out of odd cards. • There must be an even number card.

Accept ‘uneven’ as a term for ‘odd eg: ♦ ‘They are all uneven numbers.’ Do not accept explanations which imply that all of the cards must be even eg: ♦ ‘You cannot make an even number if you have an odd

card.’ ♦ ‘They are not even numbers.’ ♦ ‘Most of them are odd.’ ♦ ‘They must be even number cards.’

(c) Indicates 51 1

Indicates 57 1

119

(d) Indicates 3751 1

Indicates 1537 1

Indicates 1573 1 [7]

6. Holiday

(a) Indicates the point for £130 on 28 August. 1

Indicates the point for £90 on 4 September. 1

Indicates the points for £75 on 11 and 18 September. 1

£160

£140

£120

£100

£80

£60

£40

£20

£0 5 12 19 26 3 10 17 24 31 7 14 21 28 4 11 18

June July August September

Cost Cost of holidays

Starting Date (Saturdays) (b) Indicates £130 1

(c) Indicates a reason which could explain the difference in the cost, eg: 1 • More people want to go when the weather is best. • Because of the weather. • The weather is different, so the cost is different. • The summer is hotter. • It costs more in the high season. • The seasons are different. • It costs less during the school term. • Its more expensive when more people go. • Amount of people visiting the camp. • You can go swimming when its hot. • It depends what activities there are. • Sometimes there are special offers. • Later on people will be saving up for Christmas.

Accept explanations which indicate that there is a relationship between cost and the number of people going eg: ♦ ‘When a big group goes together each person has to

pay less so the holiday is cheaper.’ Irrelevant information which accompanies an acceptable response should be ignored, but should not be accepted on its own eg: ♦ ‘The longer you go the more it costs.’ ♦ ‘They get a better cash flow when more people go on

holiday.’ Explanations implying that prices vary by month which accompany an acceptable response should be ignored,

120

but should not be accepted on their own eg: ♦ ‘It all depends which month you go.’ Do not accept explanations which indicate that in winter the holidays are more expensive than in summer. The table indicates that they are not eg: ♦ ‘Heating costs make it more expensive in winter.’ Do not accept explanations which indicate that the prices rose and did not fall again eg: ♦ ‘They put in more facilities, so it got more expensive.’

(d) For 2m indicates £63.75 2 If £148.75 is given for the final answer, award all three marks for this part.

For only 1m shows 21.25 or 21¼ in working or in the answer space, eg: • 85 → 42½ → 21¼

or Shows 20 and 1.25 or 20 and 1¼ in working.

or Shows 63¾ in working or in the answer space.

or Shows 0.75 × 85 or equivalent in working.

Indicates £148.75 1 Allow follow through from an incorrect cost for a child found above, ie the total of £85 plus the incorrect cost for a child.

[8]

7. Clock

(a) Indicates the correct angle, eg: 1 • 90 • A right angle. • Right.

Accept the reflex angle eg: ♦ ‘270°’ ♦ Three right angles.’ Accept angles in the range 87 to 93 inclusive.

(b) Indicates 6 1 Accept any indication of the correct time, eg: ♦ ‘18’ ♦ ‘Eighteen hundred’

(c) Indicates the correct angle, eg: 1 • 30

Accept the reflex angle eg: ♦ ‘330°’ Angles in the range 27° to 33° inclusive.

121

(d) Indicates an angle in the range 147° to 153° inclusive, eg: 1

• 150 Accept the reflex angle eg: ♦ ‘210°’ Allow follow through from the previous part, provided this was not 0 and the answer to this part is a number between 0 and 360 inclusive. ie accept five times the previous response (minus a multiple of 360, where this is greater than 360). or Accept 360 minus five times the previous response (where this is less than 360).

(e) Indicates 1hour or 60 minutes, eg: 1 • Hour. • 60min

Correct units must be given. [5]

8. Transformations (a) Indicates the correct centre of rotation on the diagram, eg: 1

Drawings need not be accurate provided the pupil’s intention is clear.

(b) Indicates 90° as the angle of rotation. 1 Accept responses in the form 360n + 90, where n is a whole number. Accept any indication eg: ♦ ‘Right angle.’ ♦ ‘Quarter turn.’ ♦ ‘Left 90’ Do not accept ambiguous responses, eg: ♦ ‘Right.’ ♦ ‘Turn left.’

(c) Draws the reflection, eg: 1

Drawings need not be accurate provided the pupil’s intention to draw a triangle with base 5 and height 3 in the correct position is clear.

[3]

9. Height

122

(a) Indicates a height in the range 90cm to 92cm inclusive. 1 Do not accept failure to specify the units in this part of the question.

(b) Indicates a height in the range 95cm to 97cm inclusive. 1 Do not accept failure to specify the units in this part of the question, unless a mark has been lost for an otherwise correct response given without units in part (a).

(c) Indicates 18 months 1 Accept a correct response in years, with or without the units eg: ♦ ‘1 ½’ ‘1.5 years’ Otherwise, do not accept failure to specify the units in this part of the question, unless a mark has been lost for an otherwise correct response given without units in part (a) or part (b). If a correct response in months is given, ignore an incorrect attempt to convert this to years.

(d) Units are not required anywhere in this part of the question. Completes the start and end heights correctly within the following limits: 1

86 93 to 95 inc 93 to 95 inc 100 to 102 inc

and

gives the same end and start heights for 36 months.

Completes the final column correctly, following through from their values 1 in the first and second columns eg: for 2m • 94 8

94 101 7 For the award of the second mark, two values must be given in the final column, and these must match the pupil’s own values in the previous columns.

(e) Units are not required anywhere in this part of the question. For 2m indicates 198 2

For 2m accept answers given as a range provided 198 is the maximum eg: ♦ ‘178 – 198’ ♦ ‘Up to 198’

For only 1m shows a complete, correct method, with all the required steps, and only one computational error, eg: • 194 + 168 = 362

362 ÷ 2 = 180 Answer: 197

123

or Shows a correct method with no computational errors, with all but the final

step carried out correctly, eg: • shows 188 in working or in the answer space.

For only 1m do not accept the omission of any but the final step eg: ♦ ‘168 + 194 = 362 ♦ 362 ÷ 2 = 181 ♦ Answer: 191’

[7]

10. Arms (a) Indicates the grey tiles, eg: 1

• The number of grey. • The tiles around it. • The other tiles. • The ones you add on. • Grey. • The grey tiles. • One set of grey tiles. • The pattern of tiles around the black one. • The sets of three around the edge. • The three tiles which are added on each time. • 3 grey tiles × pattern number.

Accept any indication, eg: ♦ ‘The shaded tiles.’ ♦ ‘Not black.’ ♦ ‘The plain tiles.’ ♦ ‘The white tiles.’ Do not accept a response indicating that there are a specific number of grey tiles ♦ ‘Three grey tiles.’ ♦ ‘The grey tile.’

‘3 more tiles.’ ♦ ♦ ‘The three you add on.’

o ot accept responses whD n ich refer to only one arm of the pattern eg: ♦ ‘How many grey tiles there are on one side ♦ of the black tile.’ Do not accept responses which refer only to the N eg:

o not refer to the tiles

‘3 times the number of the pattern.’

(b) Indicates 1 black 1

o not accept a remainder, eg:

(d) Indicates 1 + 1 ee correct patterns with tiles totalling 5, 9 and 13, eg:

♦ ‘N represents the grey tiles.’ Do not accept responses which deg: ♦

and 36 grey.

(c) Indicates 20 1 D♦ ‘61 ÷ 3 = 20 rem 1’

6N (e) For 2m draws thr 2

124

•

For only 1m draws 2 out of the 3 p atterns correctly.

r but with the second pattern

o Draws three patterns with incorrect numbers of tiles, formed by adding four tiles to the first, and the third pattern formed by adding fourtiles to the second, eg:

•

Throughout the question drawings need not be

dding four

h

Ign s drawn, whether or not they are correct.

[6]

accurate, provided the pupil’s intention is clear. For 2m the second pattern must be formed by atiles to the first, and the third pattern must be formed by adding four tiles to the second. However, the way in whicthe sequence would continue to the fourth pattern need not be defined. ore extra pattern

Ignore shading, or lack of it, in the diagrams. Ignore labelling of the diagrams.

125

11. Ratios

(a) Indicates 1: 3 1 Throughout the question ignore units eg for part (a) ‘1 litre : 3 litres’ Throughout the question accept equivalent ratios eg for part (a) ♦ ‘¼:¾’ ♦ ‘25: 75’

(b) Indicates the correct ratio, eg: 1 • 2 : 3 • 1 : 1½

Throughout the question Incorrectly expressed fractions eg for part (b)

♦ ‘2121

21 2

1:

21

’

If the correct ratio of orange to apple is given instead of the ratio of apple to orange in both part (a) and part (b), then award the mark for part (b) only eg: ♦ ‘15 : 5’ in part (a); ‘1.5 : 1’ in part (b)

(c) Indicates one carton of orange juice, eg: 1 • A carton of orange. • 1 orange. • Another orange.

Accept a combination of apple and orange juice cartons which, when added to the juice which is already there, gives the required ratio eg: ♦ ‘1 apple and 3 orange.’ Ignore references to water or other ingredients added in addition to the orange and apple juice. Do not accept orange juice given with no indication of the number of cartons required eg: ♦ ‘Orange.’ Do not accept references to juice being taken out of the jug eg: ♦ ‘Take out half a carton of apple juice.’

[3]

126

12. Enlargements

(a) For 2m draws the cuboid on the isometric grid provided, correctly enlarged by 2 scale factor 2, eg:

• For only 1m draws the outline correctly but adds or omits lines, eg:

• or Draws a correct cuboid with an integral enlargement scale factor greater than 2

For 2m the correct enlargement may be drawn with or without the thirty-two constituent cubes, or with the correct enlargement of each of the four cubes in the original cuboid, or composed of eight cuboids, each congruent with the cuboid given in the question. Accept drawings in any orientation eg:

For 2m or only 1m accept hidden edges shown only if they are distinct from visible edges eg for 2m

For 2m or only 1m ignore drawings given in addition to a correct response.

For 2m or only 1m ignore shading.

(b) Indicates 24 1 Accept an indication of the number of cubes needed in addition to those already used eg: ♦ ‘Mohinder needs 21 more.’

[3]

127

1. Milk Shakes

(a) 9 1

(b) 22 1

(c) 11 1

(d) 4 1 Do not accept incomplete processing, eg for part (b) ♦ 10 + 12

[4]

2. Three coins

All 6 entries correct (see below) 3

or For 2 Any 4 or 5 correct entries

or For only 1 Any 3 correct entries

12p13p14p15p16p17p18p

10 1 1 or 5 5 2

10 2 2 5 5 510 5 110 5 2 (ie not possible)

Accept coins in any order Accept trials for 18p that are unambiguously rejected eg ♦ 10p crossed out.

! Entries made for 10p, 11p and 13p Ignore.

! Incorrect response alongside correct response Ignore any incorrect response. Do not accept no decision taken for 18p, eg ♦ entry for 18p left blank.

[3]

3. Time

(a) 7:55 1

(b) 33 1

(c) 14:20 1 [3]

4. Sums

14 1 645 1 144 1 27 1

[4]

128

5. Calendar

(a) Tuesday 1 Accept unambiguous abbreviation , eg ♦ Tues, Tu Do not accept ambiguous abbreviation that could refer to Thursday , eg ♦ T

(b) 30 (th) 1 Accept unambiguous indication, eg ♦ Marking of diagram.

(c) 122 1 [3]

6. Sixty-fives

(a) 325 1 6 1 780 1 1300 1

(b) 1040 2

or Shows a reasonably efficient correct method, even if there are processing errors , eg • 8 × 65, then doubled. • 10 × 65 add 6 × 65 • 390 + 650 • Added 4 of them, to 2 of them, to 10 of them. • Their 12 × 65 + 260 • 130 × 8 • 520 + 520

! Method uses long multiplication Accept, provided there is not more than one processing error.

! Method uses repeated addition from 650 Accept provided there is not more than one computational error. The correct intermediate values are: 715, 780, 845, 910, 975 Do not accept method uses repeated addition without building on from 650, or better, eg ♦ Adding 65 sixteen times. ♦ Adding 130 eight times. ♦ Adding 260 four times.

129

! Follow through from part (a)

For 2 or 1, where a pupil has used, unambiguously, an incorrect answer from 12 × 65 or 20 × 65 to calculate 16 × 65, allow follow through. For example, suppose their 12 × 65 = 723, accept for 2

723 + 260 = 983 However, it must be clear from the working that this incorrect value has been used, hence in this example 983 without working.

[6]

7. Spinners

(a) Spinner A with a correct reason 1

The most common correct reasons refer to:

Fewer numbers / sections / sides on A eg • A, less digits. • B has more numbers. • A has one piece missing. • A has only 5 sides, not 6 • A because B has 6 triangles.

Accept minimally acceptable reason , eg ♦ There’s 5 not 6 ♦ Gaps on A are bigger than on B

! Use of ‘bigger’ or ‘smaller’ without qualification Ignore eg, accept ♦ A, less numbers and A is smaller than B eg, do not accept ♦ A is smaller (or bigger) than B

or Greater probability on A eg

• The probability is 51 not

61

• A has a bigger probability. Accept a correct probability but expressed in words At this level, accept, eg ♦ Spinner A is 1 out of 5

! Accept a ‘correct’ probability expressed as a ratio ! In parts (a) and (b), penalise the first occurrence only

eg ♦ In (a), 1 to 5 (or 1 to 4), with reason ♦ In (b), 1 to 6 (or 1 to 5), with reason

Mark as 0, 1

130

! Use of ‘chance’ with a descriptor

As this restates the question asked, do not accept unless accompanied by a correct response. Do not accept incorrect probability Even if accompanied by a correct response.

or Bigger angles on A eg

• Each triangle on B has a smaller angle in the middle. Accept minimally acceptable reason, eg ♦ A’s triangles are wider.

! Reference to force of spin Ignore

eg, accept ♦ Depends how hard you spin it, but A has a 1 in 5 chance.

(b) Doesn’t matter with a correct reason 1

The most common correct reasons refer to:

Same numbers / sections / sides eg • Both numbered 1 to 6 • Same amount of numbers. • Same shape.

Accept minimally acceptable reason, eg ♦ Same numbers. ♦ Both have only one 3 ♦ Same gaps.

! Use of ‘different size’ without qualification Ignore

eg, do not accept ♦ It doesn’t matter even though they are different sizes. ♦ Doesn’t matter if one is bigger than the other.

or Same probability eg

• Both 61

• C is same probability as B • Same chance.

Accept a correct probability incorrectly expressed Mark as part (a) of this question

eg. Accept ♦ Both spinners are 1 in 6

or Same angles eg • Both 60°

Accept minimally acceptable reason eg

♦ The triangles are the same width.

131

(c) Two 3s and three 4s in any order. 2

or For only 1 Partially correct, ie exactly two 3s seen.

or Exactly three 4s seen. [4]

8. Shapes

(a) Both correct, ie 1

(b) (5,7) 1 Accept co-ordinates of A given alongside B

eg ♦ (3,3 , 5,7) Accept label included within the co-ordinates

eg ♦ (B5, 7)

(c) Correct place, eg

x

(d) Correct place, eg

x

Accept place identified by correct co-ordinates ! Label rather than point identified

Accept any indication, eg cross or B, provided it is nearer to the correct co-ordinate than to any other co-ordinate with integer values.

[4]

132

9. Birthdays

(a) 21 1

(b) 1989 or 89 1 ! Follow through as 2010 – (a)

Accept provided their (a) > 12 and is not a multiple of 10

(c) 1995 or 95 1 Accept follow through as part (b) + 6 Accept correct birth date or month given

eg ♦ 15.3.95 ♦ March 95

[3]

10. Rainfall

(a) Tuesday 1 Friday 1

Accept any unambiguous indication eg

♦ 0.8 for Tuesday ♦ 0.05 for Friday

(b) 0.25 1

(c) 1.5 1 Their number of cm converted to mm 1

[5]

11. Angles

(a) Q 1 Do not accept unambiguous indication

eg ♦ Second.

(b) Angle within ± 2°, unambiguous 2

eg, using an end point of the given line, or starting again

eg, cutting the given line

133

or For only 1 Angle within ± 4° unambiguous

or Using end point or starting again: correct angle drawn ± 2°, but reflex angle indicated

eg

or Cutting the given line: correct angle drawn ± 2°, but no, or incorrect, indication of which

angle to choose eg

or Draws the supplement to ± 2° eg

(c) 38 with explanation that focuses on most frequent eg 1

• More of them. • Mode. • Most. • Twice as many said 38 as the others put together. • 10 people aren’t likely to be wrong.

Accept minimally acceptable explanation eg

♦ 10 people measured it. Accept correct response accompanied by an incorrect, irrelevant or ambiguous statement

eg ♦ More people chose it and it’s the middle number. ♦ It’s the average, there’s more of them. Do not accept use of ‘average’ without a correct response

eg ♦ It’s the average.

135 with correct explanation 1

The most common correct explanations are:

135 being the mode / median / mean when 45° removed eg • 10 said about 135, only half of that said 45 so it’s 135 • 45 is too different, 135 most likely. • Discard 45, then 135 is the average. • 45 is too different, then 135 is in the middle.

or That 45 is due to incorrect reading of the scale eg • The 45s are errors, 135 most likely. • 135 is the mode. The 45s are probably reading the scale incorrectly. • 135 lies by 45 which is the wrong side.

Accept minimally acceptable explanation referring to 45 eg

♦ 45 is too different to the others, so 135 ♦ 135, fewer people but 45 is nothing like the rest.

134

! Minimally acceptable explanation that does not refer to 45

The explanation must justify why 135 chosen rather than 134 or 136

eg, accept ♦ Most of them are around 135 ♦ 135 is between 134 and 136 Do not misinterpreting the table or other incorrect or ambiguous response

eg ♦ Only 1 said 45, 3 said 134-136, and 135 is in the middle of

them so it’s 135 ♦ Out of 3, 4 and 5, 4 is the middle so 135 ♦ The average is 3 but there are 2 answers with 3 so I chose

135 as it’s in-between. ♦ Most of them are 135 (no reference to 45 or around 135) ♦ 135 is the middle of the table (no reference to 45)

[5]

12. Prism

(a) Correct edge, ie 1

A Accept unambiguous indication or use of different labels

eg, for edge A

A

135

(b) Correct edge, ie 1

B Do not accept ambiguous indication that could refer to more than one edge

eg, for edge A

A

! Both edges identified correctly but no indication of which is

which Mark as 0, 1

(c) Both correct, ie 1

! Different symbols

Accept if unambiguous, but do not accept use of letters A and/or B

[3]

13. Race

3 and 1200 and Maria and 6 2 Accept times within ± 0.1 minutes

or For only 1 Any two or three of these correct Accept distance within ± 25 metres

1.5, or equivalent 1 ! Ignore name (already assessed)

[3]

14. Percentages A

4.50 1 45(.00) 1 35 1 5(.00) 1

[4]

15. Museum

(a) 288 2

136

or For only 1 Digits 288 seen

or Complete correct method, with not more than one computational error eg 240

×12014000

480018800 Answer 188.00 • 240 × £1 = £240, and 240 × 20p = £240 ÷ 5 = 46

so the answer is 286 Do not accept conceptual error

eg 240×12240480720

240×20240480720

(b) 500 2

or For only 1 Gives an answer of 5 followed only by one or more zeros, eg • 5000 • 50

[4]

16. Simplify

7 + 5t 1 3b + 17 1

Do not accept expression not simplified [2]

137

1. Menu

(a) 1.06 1

3.94 1

(b) 16 1 ! Follow through from an incorrect total

Allow provided the total is more than £1, and is not an integral number of pounds.

[3]

2. Making shapes

(a) 1

Do not accept for part (a), the example repeated

(b) A line through a vertex and a side, eg 1

•

(c) A line through opposite sides, eg 1

•

(d) 1

! Line not ruled but intention clear In parts (a) to (d), penalise only the first occurrence. ! Line not drawn accurately

Accept lines to a vertex to ± 2m. However, lines to a side must be unambiguously to a side rather than to a vertex, hence lines that are within ± 2m of a vertex.

(e) Four congruent squares, each midpoint and line within ± 2m, and ruled, ie 1

[5]

138

3. Calculations

(a) 662 1

(b) 6000 1

(c) 483 1

(d) 56 1 Do not accept answer – 56

[4]

4. Sun cream

(a) 8 1

(b) UK 1

(c) Medium 1 Accept unambiguous indication

eg ♦ Blackpool. ♦ A warm place. Accept abbreviation

eg ♦ M

[3]

5. Rulers

(a) 120 1 ! Incorrect units – Ignore.

(b) 11.60 1 ! Both money answers omit final zero

Mark as 0, 1

(c) 2.90 1

(d) 5 1 ! Incorrect units

Ignore. [4]

139

6. Measuring

(a) 190 ± 1 1

(b) Correct place identified, eg 1

Accept within ± 2m Accept any unambiguous identification Do not accept scale redrawn using an easier numbering system

[2]

7. Shapes

(a) Area 5 1

Perimeter 12 1

(b) Any shape of area 6cm2 1 Accept shape connected at vertices If unambiguous, eg

(c) Correct perimeter 1

Note: If the pupil uses whole squares, aligned with complete edges touching, the perimeter is 10, 12 or 14 cm.

! Follow through from incorrect shape using whole squares Allow provided the area > 4 cm² and the shape is not a copy of

the diagram in (a). ! Follow through from shape using diagonals

Allow measuring, ± 2m, but do not allow answers rounded to the nearest centimetre unless a more accurate value is seen. Do not accept follow through from shape with an enclosed space

eg

(d) 7 1

140

(e) Explains that the diagonals of the grid are greater than 1 1

Accept minimally acceptable explanation eg Because the lines go through the middle of a square.

Accept diagonal measured as 1.3 to 1.5 cm inclusive Accept Perimeter measured as 9 to 10 cm inclusive Do not accept partial response

eg ♦ I measured the perimeter.

[6]

8. Tokens

(a) Correct explanation focusing on more gold, eg 1 • 4 gold and only 1 silver. • Not as many silver. • Gold to silver is 4 to 1

or Explains there would need to be an equal amount of each colour, eg • There’s not the same number of gold and silver. • Only one silver. There should be 4

Accept minimally acceptable explanation eg

♦ Better/More chance of getting gold. ♦ Only, one silver. Accept correct probability expressed in words At this level, accept

eg ♦ It’s a 1 in 5 chance of getting silver Do not accept incorrect information, even if accompanying a correct response

eg ♦ More gold, it’s a 1 in 4 chance of getting silver. ♦ More gold, so she must take out a gold. Do not accept information restated with no indication of more gold

eg ♦ 4 gold and 1 silver. Do not accept use of ‘even’ for ‘equal’

(b) 3 1 Accept gold and silver inserted in the correct proportions

eg ♦ 2 gold, 5 silver.

(c) At least one of 5, 6, 7 or 8 1 Accept any unambiguous indication

eg ♦ Tokens drawn.

141

accept a correct range

eg ♦ More than 4

6 – 8 Accept a correct value expressed as a ratio or fraction of 8

eg ♦ 7/8 Do not accept not quantified

eg ♦ More gold than silver.

[3]

9. Temperatures

(a) 77 1

80 1

(b) 32 and 30 in the correct order. 1

(c) Shows both rules give a value of 50, eg 2 • 10 × 1.8 + 32 = 50, 10 × 2 + 30 = 50

or For only 1 m 50 seen Accept minimally acceptable response

eg ♦ 50, 50

! Incorrect units Ignore.

[5]

10. Coaches

(a) 58 2

or For only 1 57 or 57.(..) seen

or 3000 ÷ 52 seen ! 58 shown as a minimum

eg 58 or more

(b) 24360 1 ! Follow through as their (a) × 420

If their answer to (a) is not all integer, accept their (a) rounded or truncated, and accept the answer then rounded or truncated to the nearest penny.

(c) 8.12 1 Accept follow through from their part (b) ie (b) ÷ 3000 Accept answer from their (b) rounded or truncated to the nearest penny

[4]

11. Cereal

(a) ¼, or equivalent probability 1

142

½, or equivalent probability 1

(b) 0, or equivalent probability 1

2/3, or equivalent probability 1 Accept correct response accompanied by description of the probability

! Ignore the description eg

♦ 25%, that’s fairly likely. Accept probability of zero expressed in words or as a fraction, even

if the denominator is ‘incorrect’, or as a ratio eg

♦ None. ♦ Impossible. 0/3 0/4 0:4

[4]

12. Drawing

(a) 1

(b) 1

(c) 1

(c)

or

1

143

Accept freehand if the pupil’s intention is clear. Accept hidden lines made visible Accept internal lines omitted

eg, ♦ for part (c)

Do not accept external edges omitted

eg, ♦ for part (d)

! Shading Ignore.

[4]

13. Huts

(a) 33 2

or For only 1 Correct method, eg • 4 × 8 + 1

Accept for 1m, method is repeated addition with not more than one computational error

eg ♦ 13 + 4 + 4 + 4 + 4 + 4

17, 21, 25, 29, 32

(b) 20 2

or For only 1 Correct method, eg • 80 ÷ 4 seen

(c) Correct expression of m = 5h + 1,

eg. 1

• [5]

144

14. Canteen

Gives a correct explanation. 1 The most common correct explanations are: Explaining events are not equally likely, eg

• Not many people work in the canteen. • They might not be equal chances. • The probability is different for each group. • There are different amounts of pupils and teachers. • The number of pupils is more than one third. • The probability needs to be out of all the pupils, teachers and canteen staff.

or Explaining the statement implies equal numbers of pupils, teachers and canteen staff, eg • It would be true if there were 20 pupils, 20 teachers and 20 dinner people.

or Giving a counter-example, eg • Suppose there were 190 pupils, 8 teachers and 2 canteen staff. The probability

would not be a third. ! Explanation infers exact quantities required

If accompanied by a correct response eg, accept

♦ Each probability is different. ♦ You need to know the numbers in each group.

eg, do not accept ♦ You need to know the exact numbers in each group. Do not accept incorrect statement, even if accompanied by a correct response

eg ♦ It’s not equal chances, the probability is 1 divided by the

whole school. ♦ It depends on how many children there are. ♦ If there were 10 children the probability would be 0.1 Do not accept incomplete or ambiguous statement

eg ♦ More pupils. ♦ There is more than 1 pupil, 1 teacher and 1 canteen staff. ♦ More than 3 people. ♦ There are 3 choices b ut there’s more than 3 papers in the

box. It dep♦ ends on how many pupils, teachers and canteen staff there are.

[1]

145

15. Percentages

2.12 1

12.25 1 ! Redundant % sign

eg ♦ 2.12%

Penalise first occurrence only. Accept 25p expressed as a fraction of a pound

[2]

16. Sign

8 1 Accept Answer between 8 and 8.1 inclusive

[1]

17. Teachers

(a) 20 to 23 inclusive 1

(b) 35 to 39 inclusive 1

(c) 40 000 to 50 000 inclusive 1

(d) Indicates second statement with a correct justification. 1

The most common correct justifications are:

Comparing, at least one category for- both males and females, eg • There are more 10-29 year old females than males. • More males are over 50 • Females start with bigger slices but then it changes. • The striped part is longer on the females than the males. • More black and striped part for females than males.

or Comparing categories by using percentages within the inclusive ranges shown below, or reference to the approximate value shown in brackets (do not accept approximation without indication that it is only an estimate), eg • 13 % of men are age 20-29, but it’s more like 20%, for women. • 50% of men will be over 50, but only about 40% of women.

146

males females

50+ 48-52 35-39 (40) 40-49 22-26 (20) 20-24 30-39 11-15 (10) 16-20 20-29 11-15 (10) 21-25 (20) 39 or less 24-28 (30) 39-43 49 or less 48-52 61-65 (60) 40 or more 72-76 (70) 57-6 1 30 or more 85-89 (90) 75-79 (80)

! Response does not refer to the chart Accept only if accompanied by a correct response

eg ♦ There are more 20-29 year old females than males and

there are more young female teachers in my school. ! Different categories compared for males and females

Only if one implies the other eg,

♦ accept ♦ 50% of males are 50+, but over 50% of females are

younger than 50 eg,

♦ do not accept ♦ 50% of males are 50+, about 40% of females are younger

than 30 ! Use of ‘young’ or ‘old’ without categories specified

Only if justification implies which categories are being compared

eg ♦ 13% men, 23% women are young. ♦ young to refer to the first, or the first two, or the first three

categories eg,

♦ 62% females young, only 50% males. Do not accept no comparison, eg ♦ 50% of males will be 50+ Do not accept incorrect statement, eg ♦ Less females in each group ♦ Female teachers most likely to be 20-29 Do ot accept ambiguous response with categ n ories or gender not identified.

eg ♦

Female is higher on the chart. There are more 50+ but less 20-29

[4]

147

1. Multiplication Table

(a) 312 1 22 1 12 1

(b) 24 × 11 or 22 × 12 1

The other pair as shown above. 1 Accept numbers in a pair in either order

1 Other pairs of factors of 264 eg

♦ 44 × 6 ♦ 88 × 3

Penalise the first occurrence only. [5]

2. Number Cards

(a) 60 , 10 (either order) 1

and

40 , 30 (either order) Do not accept numbers or operations other than those specified

eg, ♦ for part (b) 100 – 60 + 30

eg, ♦ for part (d) 3 × 30 + – 20

(b) 60 , 6 , 4 (any order) 1 Do not accept repeated values

eg, ♦ for part (b) 30, 30, 10

(c) 100 , 30 (either order) 1

(d) 10 , 40 in the correct order only 1

3. Computation

(a) 65 1 13 1 36 1 7 1 1725 1 569 1

(b) 43 1

(c) 14 1 [8]

148

4. What’s the Point?

(a) (5, 2) 1

(b) (2, 1) 1 [2]

5. Temperature

(a) Indicates 7ºC 1 ! Values incorrectly or not labelled

Accept If unambiguous.

(b) Indicates –5ºC 1

(c) 5 1

(d) 11 1 Do not accept temperatures shown as negative

eg ♦ –5 ♦ –11

[4]

6. Twenty-seven

(a) 1½ 1 Accept equivalent fractions or decimals

123 1 54 1 108 1

Accept follow through as 2 × their incorrect 54

(b) Two numbers that multiply to make 27 1

eg • 3 × 9 • 54 × 0.5

Do not accept values given that are not exact eg

♦ 81 × 0.33

Two numbers that divide to make 27, in the correct order 1

eg • 27 ÷ 1 54 ÷ 2

Accept follow through from their incorrect part (a) eg,

♦ from a quarter of 107 (error) = 27, allow 107 ÷ 4 = 27 eg,

♦ from 50% of 52 (error) = 27, allow 52 ÷ 2 = 27 [6]

149

7. Clocks

(a) A different time to 09:15 with both hours and minutes as multiples of 3 1

eg • 09:18 • 12:12 • 12:15 • 6:15 • 03:12

Accept zero as a multiple of 3 eg

♦ 00:12 15:00 00:00

Do not accept minutes written without the leading zero eg

♦ 12:9 Do not accept impossible time

eg ♦ 12:60

(b) 2 or 8 1 ! Answer of the form 2 + (a multiple of 6)

Provided it is less than 60 eg

♦ 14 20 26

Do not accept specific time, rather than time interval eg

♦ 12:00 [2]

8. Folding and Cutting

(a) Correct diagram, ie 1

– – – –

(b) Correct diagram, ie 1

– – – –

(c) Correct diagram, ie 1

– – –

– [3]

150

9. Motorway

(a) 22 1

(b) 5 1 ! more than one junction indicated

Accept If unambiguous eg, accept

♦ 1 to 5 eg, do not accept

♦ 4 to 5

(c) 70 1 [3]

10. Using Brackets

(a) 18 and 10 (correct order) 1

(b) 60 1

(c) (4 + 5 + 1) × 5 1 ! Multiple brackets

Accept if the brackets are paired and unambiguous, even if redundant

eg, ♦ for part (c), accept ((4 + 5) + 1) × 5

However, if multiple brackets are not paired, but there is no further ambiguity, penalise the first occurrence only

eg ♦ for part (c) (4 + 5) + 1) × 5

eg, ♦ for part (d) 4 + (5 + 1) × 5) ♦ Mark as 0, 1

(d) 4 + (5 + 1) × 5 1 ! Change in order of numbers

eg, ♦ for part (d)

(1 + 5) × 5 + 4 Ignore if alongside a correct response, otherwise do not accept

Do not accept calculations separated into a series of operations eg,

♦ for part (c) (4 + 5) = (9 + 1) = (10 × 5) = 50

[4]

151

11. Box

Two sections drawn on each of N, S, E and W, even if incorrect. 1

Both E and W completely correct. 1

Both N and S completely correct. 1

6 × 1.5

6 × 1.5

6 × 1

6 × 1

W E

both 1 × 3 both 1 × 3

N

S Accept outer rectangle(s) on = and W shown as partial flaps at least 1.5cm in length, eg

! Lines not ruled and/or not accurate

Accept if the pupil’s intention is clear and if the 1.5 width is closer to 1.5 than 1 or 2

! Flaps drawn Ignore if unambiguous. ! Fold lines not shown within sections

For the second and third marks, accept if the overall dimensions of the sections representing E/W (or N/S) are correct, eg, ♦ mark the following as 0, 1, 0

6 × 2(incorrect)

6 × 2(incorrect)

each2 × 3

152

! Extra lines shown within sections that have overall correct

dimensions Penalise one mark only eg,

♦ mark the following as 0, 1, 1

6 × 2.5

6 × 2.5

2 × 32 × 3

[3]

12. Fractions

(a) Both placed correctly, and labelled, ie 1

13

56

! Arrows, or other indication, inaccurate Only if ambiguous

! No labelling Only if both are correct and no surplus arrows are indicated.

(b) All three correct, ie 1, 24, and 4 2

or

Any two correct. 1 [3]

13. Crisps

(a) Plain 1

101 or equivalent probability. 1

Do not accept table not interpreted eg

♦ 5

(b) 81 or equivalent probability. 1

Accept Rounded values ie

♦ 0.12 or 0.13 or 12% or 13%

153

(c) All correct, ie 2

plain 7 vinegar 3 chicken 2 cheese 0

or

At least two correct, and the total sums to 12 1

eg

plain 7 vinegar 3 chicken 1 cheese 1

Accept the value for cheese left blank [5]

14. Sunshine

(a) 28, ie 1

(b) Indicates ‘not possible to tell’, ie 1

Do not accept number of days in the month specified

eg ♦ 25 written in the ‘not possible to tell’ box.

(c) Indicates month B and gives a correct explanation 1

eg • B has more ‘more than 8 hours’ days. • A has a greater number of less than 4 hours. • B is probably summer as it had lots of days with more than eight.

A only had a few so it’s probably winter. ! Explanation does not explicitly compare the months

Provided box B is indicated eg

♦ Box B ticked and the explanation as B has lots of days with more than 8 hours of sunshine.

Do not accept no interpretation eg

♦ There’s a big piece on the pie chart. [3]

154

15. Shapes

(a) Correct simplified fraction, ie31 1

! Shaded area consistently expressed as a simplified fraction or percentage of the unshaded area

eg,

♦ for part (a) 21

eg

♦ for part (b) 66 32 (or 67)

Mark as 0, 1

(b) 40 1

(c) Chooses shape A and gives a correct explanation. 1

The most common correct explanations:

State that A has one quarter shaded (or equivalent percentage or decimal) but that B has less

eg

• A has 41 shaded, B is less than

41 as it has only one leg shaded.

• A is a quarter, but B needs an extra quarter square to make it up to a quarter. • Diagram showing how the shaded part of B needs to be changed to make it 25%

! Percentage value for B Between 23 and 24 inclusive, or accept between 20 and 25 exclusive if the approximate nature of the percentage is specified. Accept minimally acceptable explanation

eg

♦ A has 41

shaded, B has less.

♦ Part of one square on shape B should be shaded. Do not accept incomplete explanation

eg ♦ A has a quarter shaded, B hasn’t. ♦ B has a bit less shaded than A.

Use the fraction 133 to compare to A

eg

• B has 133 shaded. If they were the same then it would have

133

A is123 , B is

133

155

Focus on four equal parts in both shapes

eg • A has 4 equal parts, B has 4 equal and another square in the middle. • If you shade 3 more like the part on B you wouldn’t fill the shape.

If you do it on A you do fill it. Accept minimally acceptable explanation

eg

♦ A has 41 , B has

133

Do not accept incomplete explanation eg

♦ B has 133

Do not accept Incorrect statement eg

♦ A has 31 shaded, B has

133

[3]

16. Trip

(a) 12168 2

or 1

Shows a complete correct method with not more than one computational error

eg

12268468

1170052

234

(error)

•

12

0

13

0

24

00

47

5

66

0

88

1 5

1 2

Answer 11768 •

156

Do not accept conceptual error

eg

♦ 1638468

117052

234

(b) 13 1

[3]

157

1. Cards

(a) £ 3.20 1

(b) £ 102(.00) 1

(c) 14 1 [3]

2. No. 1 Singles

(a) 7 1

(b) Madonna 1

(c) 6 1

(d) Abba and Spice Girls, either order 1 ! Reference to fourth place Ignore

[4]

3. Using Number Lines

(a) 50 and 75; correctly placed 1

(b) 20, 40, 60, 80; correctly placed 1

(c) 40, 80, 120, 160; correctly placed 2

or

Any three correct, with follow through of steps of 40 from not more 1 than one incorrect value

eg • 40, 80, 120, 170 (error) • 40, 90 (error), 130, 170 • 50 (error), 90, 130, 170

! Follow through as double their values from part (b) Provided their values form an increasing sequence

eg, from part (b) as 20, 40, 50, 70 accept for 1 ♦ 40, 80, 100, 140 Do not accept follow through values greater than 200

(d) 4 1 [5]

4. Map

(a) 5 1

(b) West 1 Accept abbreviations

eg ♦ W ♦ NE

158

North-east 1

Accept Bearings eg, for W

♦ 270 eg, for NE

♦ 045 ♦ 45 Accept unconventional but unambiguous notation

eg, for North-east ♦ East North

(c) 4 1 [4]

5. Ruler

(a) 1.5 1 Accept equivalent fractions or decimals, or use of words

5 1 Do not accept distance in mm without units specified

(b) Indicates 4.5 and 11.5 2

or

One correct 1

or

Scale misread but arrows placed symmetrically about point E Accept Accuracy within ± 2m

[4]

6. Getting There

(a) 64 and 864 1 675 1

(b) 2520 1 15 1

[4]

159

7. Squares

(a) 9 1 ! Units given Ignore

(b) 4 1

(c) 4 1 14 1

! Answers for part (c) reversed Mark as 0, 1

[4]

8. Disco Costs

(a) £ 4.(00) 1

(b) Correct explanation. 1

The most common correct explanations:

Interpret the spreadsheet to explain why there is one charge

eg • The hire of the hall is a fixed charge. • You only hire the hall once. • You only hire one hall.

Explain the hire is independent of the number of people attending eg

♦ You pay for the hall however many people come. ♦ It is not affected by the other columns. Accept minimally acceptable explanation

eg ♦ It always costs the same to hire the hall. Accept implication that only one hall is available

eg ♦ You use the same hall no matter how many people there

are. ♦ The hall is always the same size. ♦ It’s the same hall. Accept incomplete explanation that does not interpret the spreadsheet

eg ♦ It’s the hire of the hall. ♦ It’s always the same.

(c) 19 1

(d) 27 1

(e) £ 28.50 1 ! Money quantified Ignore

[5]

9. Cooking

(a) 51 1

160

(b) 245 1

(c) 56 2

or

Shows either 39 or 95 1 rrect answer in hours and minutes

! hours and minutes gnore any further

0. Pieces

cates Yes, and gives a correct explanation. 1

n the complete area

e both 8 les and 2 halves.

t minimally acceptable explanation

t was the same. missing

ete explanation e

♦ e area of both is 9 you don’t count the halves.

! no

(b) Correct piece, ie 1

Accept Coeg, for part (b)

♦ es 4 hours 5 minutIncorrect conversion toIf the correct number of minutes is shown, iworking.

1

(a) Indi

The most common correct explanation focuses o

eg • They’r• Both have 7 who• 8 is half of 16

Accepeg

♦ me number of squares. Sa♦ I counted the squares and i♦ The one square jutting out fills the two half squares

on the right hand piece. Do not accept restatement of the question

g e♦ Both have same space inside. Do ot accept Incorrect or incompl

g n

♦ Each one has 7 squares. Th

♦ When you work out areaUnits incorrect

Ig re

– – – – [2]

1. Areas

correct, ie 1

1

(a) All –

161

(b) 40 2

or

Shows the value 10 1

or

Follows through from an incorrect side length to find the perimeter, provided the side length is not 25

eg • Side is 8, so perimeter is 32

12. Ferry

(a) The line representing the ferry crossing, within the tolerances shown 2 by the diagram.

or

One angle drawn within the tolerance shown by the diagram, and at least 1 of length as shown by the diagram, even if their angle does not start at the end of the given line.

Accept line(s) not ruled but within tolerance ! Pupil draws their own base line

For 2 provided the base line is the correct length within the tolerance shown. If the base line length is incorrect but the angles are correct, mark as 1, 0

(b) Their length ± 2m 1

(Note that the calculated value is 5.59) ! Rounded to the nearest integer

If their measurement is within 2m of an integer length, otherwise do not accept.

(c) Correct response using their (b) or their length 2

eg • Their (b) × 20 and metres given. • Their (b) × 2000 and cm given.

or

Their part (b), or their length, multiplied by either 20 or 2000, even if the 1 units are incorrect or omitted.

or

Shows a correct method with consistent units

eg • × 20 seen, and metres given. • × 2000 seen, and centimetres given.

Correct units with no length [5]

162

13. Swimming

(a) 48 and 72 1 Accept No values within the table but correct points plotted on the graph

(b) 3 or 4 points plotted correctly ± 1m, and joined with the correct 2 ruled straight line.

or

3 or 4 points plotted correctly ± 1m, but not joined. 1

or

3 or 4 points plotted correctly ± 1m, but joined incorrectly or line not ruled. ! Line ruled but does not pass exactly through the correct points

provided the pupil’s intention is clear. ! Bar chart drawn Ignore bars.

Accept for 1, follow through from part (a)

(c) 50 and 64 1 Accept no values within the table but correct points plotted on the graph

(d) 3 or 4 points plotted correctly ± 1m, and joined with the correct ruled 2 straight line.

or

3 or 4 points plotted correctly ± 1m, but not joined. 1

or

3 or 4 points plotted correctly ± 1m, but joined incorrectly or line not ruled. ! line not ruled

If this error has already been penalised in part (b). ! Line does not pass exactly through the correct points

Provided the pupil’s intention is clear. ! Bar chart drawn Ignore bars. Accept for 1m, follow through from part (c)

(e) 22 1 Accept follow through their graph, including non-integer values, even if rounded to the nearest integer

! Their graph shows more than one intersection All such values must be listed.

! Cost shown Ignore.

[7]

163

14. Mints

(a) 5y + 6 and 6 + 5y, in either order 2

or

Only one of the correct expressions given; the other incorrect or omitted. 1

(b) Indicates Yes, and gives a correct explanation 1

eg • If you take away the 6, then it is divisible by 5 • Could be 10 in a packet. • 5 × 10 + 6

Accept definitive statement eg

♦ There must be 10 mints in a packet. [3]

15. Algebra Pairs

Both pairs correct, and no incorrect, ie 2

or

At least one correct pair identified, with not more than one incorrect pair. 1 [2]

164

1. Half

Both correct, ie 1

more than half

half

[1]

2. Robot

(a) Correct diagram, ie 1

Accept unambiguous indication

eg

! Arrows incorrect or omitted Ignore

(b) A correct route, showing 2 Norths and 1 East 1

eg • North

North East

• N E N

• East N N

165

Accept Identical steps combined

eg, in part (b) ♦ Move 2 north, then 1 east

! Other compass points used eg, in part (b)

♦ North-east East West-north

Penalise only the first occurrence

(c) A different correct route, also showing 2 Norths and 1 East 1 ! More than the specified number of steps used

in part (d). Otherwise penalise only the first occurrence, unless this error occurs alongside the error given above (other compass points used) in which case ignore

! Follow through from part (b) to part (c) If the compass directions in part (b) are incorrect, accept the same directions used in part (c) but in a different order eg, from part (b) as W, N, N N W N

(d) A correct route, showing one step in any direction and its inverse 1

eg • North

South • W

E Do not accept compass directions not specified the route shown only by lines on the diagram, or other ways of specifying directions

eg ♦ Forward ♦ Right ♦ Forward

[4]

3. Computation

(a) 573 1

(b) 446 1

(c) 168 1

(d) 26 1 [4]

166

4. Olympic Games

103 3 or

Shows or implies correct totals of 131 and 28 and the intention to subtract, 2 even if the notation is incorrect

eg

• 41 + 43 + 47 = 131, 11 + 10 + 7 = 28 131 – 28 = 117 (error)

• 28 – 131 = 117 (error) • 117 given as the answer

! Intention to subtract not explicit Implicit intention to subtract

eg ♦ 131 and 28 seen, with 102 given as the answer

or

Shows or implies correct differences of 30, 33 and 40 and the intention to add

eg

• 41 – 11 = 30, 43 – 10 = 33, 47 – 7 = 40 30 + 33 + 40

! Intention to add not explicit Accept implicit intention to add

eg ♦ 30, 33 and 40 seen, with 113 given as the answer

or

Shows a complete correct method with not more than one error, that is followed through correctly to an answer

eg • 41 + 43 + 47 = 132 (error), 132 – 28 = 104 • 30 + 23 (error) + 40 = 93

! Method not explicit Accept implicit methods

eg 121 (error) and 28 seen, with 93 given as the answer but no

other working shown

or

Shows the totals 131 and 28 1

or

Shows the differences 30 and 33 and 40

or

Shows a complete correct method with not more than two errors [3]

167

5. Pictogram key

Correct for both male and female, ie 2 2 circles for male, 1½ circles for female

! Drawings not accurate or the same size, or the half circle is not closed Provided the pupil’s intention is clear

or

Correct for either male or female 1 ! Symbol other than circle used to represent 4 people

Do not accept multiple symbols, eg

♦ circles and squares used. However, if the only error is to use a different symbol

consistently for both male and female, mark as 1, 0 [2]

6. Two steps

(a) 40 1

46 1

(b) 12 1 ! Units given Ignore

eg, accept ♦ 12 cm

! Step size shown on diagram If unambiguous, but do not accept incorrect further working

eg, do not accept ♦ 12 shown correctly on the diagram, but 24 given as the

answer ! Both step sizes shown

If unambiguous eg, accept

♦ 12, 12 ♦ 12 and 12 Do not accept if ambiguous

eg ♦ 12 + 12

[3]

168

7. Calculations

All four decisions correct, ie 2

or

Any three correct decisions 1

or

Both crosses are left blank, ie

[2]

8. Areas

(a) 12 1

(b) 3 1 Accept follow through as part (a) ÷ 4 If their (a) ÷ 4 is not an integer, accept values rounded or truncated to one or more decimal places

(c) 12 1 Accept follow through as part (b) × 4, or as part (a) Note that follow through from part (b) must be exact

eg, ♦ from 3.2 in part (b), accept 12.8 only

[3]

9. Signs

5 + 2 = 10 – 3 1 Accept other correct signs

eg, ♦ for the first mark

5 + +2 = 10 + –3 eg, for the first mark ♦ 6 ÷ –6 = 7 ÷ –7

169

12 – 3 = 3 × 3 1

2 + 1 = 9 ÷ 3 1

6 – 6 = 7 – 7 1

or

6 ÷ 6 = 7 ÷ 7 [4]

10. Angles

(a) Indicates ‘acute’, ie 1

(b) Indicates ‘No’ and gives a correct explanation 1

The most common correct explanations:

State the angles are the same

eg • They are both 45° • They both have the same amount of turn • The first diagram is an enlargement of the second diagram • Angle B fits onto angle A exactly • They are the same, you just see more of A

! Angles measured Accept as 45 ± 2° provided both angles are the same, but incorrect measurements

eg, do not accept ♦ Both are 45° or 135° Accept minimally acceptable explanation

eg ♦ They are the same Accept A and B used to refer to the diagram rather than the angle

eg ♦ If you enlarge B it is the same as A

! Response refers to the squares If there is unambiguous reference to the angles

eg ♦ They both go through the diagonal Do not accept if ambiguous

eg ♦ They both have the same number of squares within them

(could be referring to area)

170

Address the misconception

eg

• It’s how much turn, not how long the lines are

• Just because the arms are longer it doesn’t make it bigger Accept minimally acceptable explanation

eg ♦ It’s just that the lines are longer ♦ Because one is smaller in size doesn’t mean the angle is

smaller Accept implicit reference to the length of the lines

eg ♦ B is a bit smaller but it’s the same angle ♦ A has been drawn bigger than B

[2]

11. Factors

(a) All five correct factor pairs, in any order, with none duplicated or incorrect 2

eg • 1, 16

2, 8 4, 4 8, 2 16, 1

or

At least three factor pairs correct 1

(b) All correct, ie 2

1 2 3 4 5 6

7 8 9 10 11 12 or

At least four correct and none incorrect 1

or

At least five correct and not more than one incorrect

or

Identifies all numbers that are not factors of 12, ie

1 2 3 4 5 6

7 8 9 10 11 12 [4]

171

12. Thinking of rules

(a) 12 1 Accept multiple steps

eg, for the first rule ♦ 2, then add another 10 ♦ 3, then × 2

3 1

Correct response 1

eg • Add 6 • + 6

× 2

3

Add the number you first thought of ! The starting value of 6 is repeated

Ignore if inserted before the given operation eg, accept

♦ first rule: 6 add 12 If 6 is inserted immediately after the given operation, penalise only the first occurrence

eg ♦ first rule: add 6 + 12 6 repeated after their rule

eg ♦ first rule: add 12 + 6 Do not accept for the third rule, the operation is not specified

eg ♦ 6

(b) Gives a correct rule 1

eg • Divide by 2 • ÷ 2 • Halve the first number • Take half of the first number away

! Embedded rule Provided both calculations are shown and use the same rule

eg ♦ 10 ÷ 2 and 8 ÷ 2 Accept use of ‘half’ for halve

eg ♦ Half Do not accept incorrect rule

eg

♦ 21–

172

Do not accept inverse rule

eg ♦ Double Do not accept result used to define the rule

eg ♦ Take the smaller number away from the bigger 10 – 5 = 5, 8 – 4 = 4

[4]

13. Car parking

75 p 2

or

Shows a correct multiplicative method even if there are computational errors 1

eg • 15 ÷ 8 × 40 • 40 ÷ 8 × 15 • 15 × 5 • 15 × 10 ÷ 2

or

Shows a correct additive method with not more than one computational error

eg • 15 + 15 +15 + 15 + 15 • 8 15

16 30 24 45 32 50 (error) 40 65

[2]

14. Heights

(a) 1.2(0) 1 Accept correct height in centimetres, with units given

(b) 1.15 1

(c) 170 1 Do not accept height in metres

[3]

173

15. Spinning

(a) Gives a correct probability 1

eg

41

•

82

25%

(b) Gives a correct probability 1

eg • 1 • 100%

Accept equivalent fractions eg

88

♦

11

•

1 Probability not quantified Ignore descriptors alongside correct probabilities, but on their own

eg, do not accept ♦ Certain ♦ Definite

(b) Shows exactly two fours, exactly two even numbers other than four, and any two 2 odd numbers

eg

22

3

4

43

1918

17

4

84

Use of zero Note zero is defined as an even number

174

or

Shows exactly two fours 1

or

Shows exactly four even numbers, even if the other two entries are left blank Accept four fours

[4]

16. Interpreting algebra

Gives a correct interpretation, by referring to at least 3 of the 4 aspects listed below 1

1. The meaning of a and b (eg by using Ann and Ben, or A and B)

2. The meaning of the + and = signs (eg by using key words such as ‘sum of’ or ‘total’ or ‘altogether’ or ‘add’)

3. The value 69

4. The given context (eg by referring to age or years)

eg, accept • The sum of the ages of Ben and Ann is 69

(all aspects shown) • Altogether A and B are 69 years old

(all aspects shown) • Altogether, a and b are 69 years old

(1st aspect missing) • Ann’s + Ben’s age = 69

(2nd aspect missing) • The sum of the ages of A and Ben

(3rd aspect missing) • Together, Ann and Ben are 69

(4th aspect missing) ! Ben’s age taken to be 30

Ann’s age unambiguously shown as 39, with reference to both the meaning of a and the given context

eg, accept ♦ Ann is 39 years old

A’s age = 39 A is 9 years older than B

In English, ages are commonly referred to without years, so also accept the following

A is 39 However, other responses that do not refer to both the meaning of a and the given context

eg ♦ Ann = 39 Also, incorrect computation

eg ♦ Ann is 29 years old

175

Gives a correct interpretation, by referring to the given context 1 (eg by referring to age or years) and at least 1 of the 2 aspects listed below

1. The meaning of b and c (eg by using Ben and Cindy, or B and C)

2. The meaning of the ‘2’ or ‘2 ×’ (eg by using key words such as ‘twice’ or ‘half’ or ‘two times’)

eg, accept • Ben is twice as old as C • C is half B’s age • B is twice C’s age • b is twice c’s age

(1st aspect missing) • B = 2 × C’s age

(2nd aspect missing) ! Ben’s age taken to be 30

Cindy’s age unambiguously shown as 15, with reference to both the meaning of c and the given context, and applying the additional guidance as given in part (a)

Gives a correct interpretation by referring to the mean 1 and either the given context, or 28, or both

eg • The mean age of Ann, Ben and Cindy is 28 • 28 is the mean age • 28 is the mean

(no reference to the given context) • The mean age

(no reference to 28) Accept use of ‘average’ for mean

or

Gives a correct interpretation by referring to the total of 84 and the given context

eg • The total age of Ann, Ben and Cindy is 84 • 84 is the sum of their ages

eg ♦ The total of their ages is 3 × 28 3 × 28 = 82 (error) which is the sum of their ages

or

Gives a correct interpretation, by referring to the given context and the denominator of 3 (eg by showing ÷ 3) and at least 2 of the 3 aspects listed below

1. The meaning of a, b and c (eg by using Ann, Ben and Cindy, or A, B and C, or by using inclusive key words such as ‘their’ or, minimally, ‘the’)

2. The meaning of the + signs (eg by using key words such as ‘sum of’ or ‘total’ or ‘altogether’ or ‘add’)

3. The value 28

176

eg, accept • The sum of their ages divided by 3 is 28 • Add A’s age to B’s age to C’s age then divide by 3 gives the answer 28 • Their total age ÷ 3 is 28 • The ages of A + B + C, then divide by three equals 28

(2nd aspect missing) • Add up the ages then divide by 3

(3rd aspect missing) ! Ambiguity as to whose age is divided by 3

Pupils who reproduce the statement in the order shown can introduce ambiguity Such responses

eg, accept ♦ (Ann + Ben + Cindy’s age) ÷ 3 = 28 ♦ Ann + Ben + Cindy’s ages ÷ 3 = 28

eg do not accept ♦ Ann + Ben + Cindy’s age ÷ 3 = 28 Ann’s + Ben’s + Cindy’s age ÷ 3 = 28

! Ben’s age taken to be 30 Ignore if accompanying a correct response, otherwise do not accept

eg, do not accept ♦ (39 + 30 + 15) ÷ 3 = 28

! Within the question, two equations solved correctly but with no credit given

eg ♦ a = 39, c = 15 ♦ Mark as 0, 0, 1

[3]

17. Growing shapes

(a) Completes the bigger triangle, ie 1

or

! Lines not ruled or accurate Accept provided the pupil’s intention is clear

177

(b) Completes the trapezium, ie 1

or

! Parts (b) and (c) transposed Mark part (b) as 0, then part (c) as 1

! Internal lines missing eg,for part (b)

♦ Penalise only the first occurrence

(c) Completes the parallelogram, ie 1

or

Do not accept incorrect internal lines ♦ eg, for part (c)

Do not accept four more congruent triangles or trapezia joined ♦ eg, for part (b)

eg, for part (c)

Penalise only the first occurrence [3]

18. Halfway

9.2 or equivalent value 1

24 1 [2]

178

19. Survey

(a) English 1 Accept unambiguous indication

eg, for English ♦ 2

eg, for Maths ♦ 7

(b) Maths 1

(c) Gives a correct explanation 1

The most common correct explanations:

Calculate the percentages to show they are different

eg • 30% for boys, but only 15% for girls

Do not accept percentages calculated incorrectly Do not accept incomplete explanation

eg ♦ The percentages are different for boys and girls

Show that the totals are different

eg • It’s 3 out of 10 for boys but 3 out of 20 for girls • There are more girls so it’s a smaller percentage • The total for girls is 20, but for boys it is 10 • There are twice as many girls as boys • Take the boys to be 100%, then the girls will be 200%

Accept minimally acceptable explanation eg

♦ There are more girls ♦ It’s out of different numbers ♦ It depends on how many boys and girls there are ♦ You need to look at the percentage, not just the number ♦ The percentage for boys is higher ♦ There are 10 boys and 20 girls (implicit comparison) Do not accept incorrect explanation accompanying a correct statement

eg Be♦ cause he asked 20 girls and 10 boys and that is not a fair thing to do in a survey e are more girls than boTher ys so girls (error)have a bigger percentage than the boys

There are 10 boys and 20 girls so it couldn’t be equally popular Do not accept incomplete explanation

eg ♦ e total for girls is 20 Th

(d) English 1 [4]

179

20. Solving

(a) All three correct, ie 2 23 20 33

Do not accept incorrect notation eg

♦ 23x for 23

or

Any two correct 1

(b) 3 2 Ambiguous notation

eg ♦ × 3

Mark as 1, 0

or

Subtracts 11 from both sides to give a correct algebraic equation 1

eg • 2y = 17 – 11 2y + 11 – 11 = 17 – 11 2y = 6

[4]

180

1. Game

(a) 430 1

(b) 609 1

(c) 391 1 ! Follow through as 1000 – their (b)

Provided their (b) < 1000 [3]

2. Travelling to school

(a) 5 1

(b) 6 1

(c) 4 1

(d) Indicates the triangle west of the school 1 ! More than one symbol ringed

Do not accept if more than one triangle is ringed. If the only triangle ringed is the correct one, as some pupils may mark the diagram to help with other parts of the question

181

(e)

N

S

W E

1 km

2 km

3 km

Draws a square, within the angle tolerance as shown on the diagram, 2

touching the 3km line ! Square not accurate

Including in any orientation, provided there is no ambiguity within the context of the question

! Square touches the lines indicating the angle tolerance Provided the square does not extend beyond the dashed lines shown on the diagram

182

or

Fulfils any two of the three conditions below. The symbol drawn is a square; has direction within the angle tolerance as shown on the diagram; touches the 3km line

! Rings round existing symbols Ignore in part (e)

[6]

3. Holiday

(a) £10 1 Do not accept incorrect response

eg ♦ – 10

(b) £22 3

or

Shows the digits 22 2

eg • 220 • 2.20

or

Shows the values 586 and 608

or

Shows one of the values 586 and 608 and correctly subtracts using their incorrect total

eg • Woman 586, man 648 (error),

648 – 586 = 62 194 + 196 + 196 = 486 (error)

289 + 319 = 608 so it’s 122 more

or

Shows a complete correct method with the only error in the final answer

eg • 289 + 319 – (194 + 196 + 196) = 32 (error)

or

Shows one of the values 586 or 608 1 [4]

183

4. Describing shapes

(a) Draws a square 1 ! Lines not ruled, or internal lines drawn

Provided the pupil’s intention is clear

(b) Draws a rectangle, or draws a square that is a different size from the one in part (a)1

(c) Draws a parallelogram with no right angles 1

eg

•

•

• (d) All four entries correct, ie 2

4 4 2 4

Accept unambiguous indication that the sides are the same length

eg, for the final value of 4 ♦ All ♦ The ♦ Yes

or

At least two entries correct 1 [5]

184

5. School trip

(a) 60 1

(b) All three correct, ie 2 5 6 10

or

Any two correct 1 [3]

6. Place names

(a) 49 1

(b) 30 1 [2]

7. Dinner time

(a) All three rows correct, ie 2

or

Any two rows correct 2 ! Frequencies shown

For 2 or lm, if the correct box for a row has been identified ignore any frequencies shown, even if incorrect. If the correct box for a row has not been identified, and all 9 frequencies are correct, mark as 1, 0

eg

38

36

36

18

26

28

42

44

30

185

(b) 12 2

or

Shows at least one of the following totals: 106 (or 70), 94 (or 58)

or

Shows both of the differences 2 and 14, with no evidence of an incorrect method ! Signs incorrect

Ignore [4]

8. Which calculation?

(a) Joins the first to 4 – 3 1

Joins the second to (3 × 27) + (4 × 25) 1

Joins the third to (4 × 25) – (3 × 27) 1 The following shows the correct responses:

(b) The question refers to the total number of pupils in year 9 1

eg • Altogether, how many people are in year 9? • How many pupils are there in year 9?

Accept response is a statement rather than a question eg, for the first category

♦ It’s the total number of people in year 9 ♦ All the pupils in all the classes in the oldest year Do not accept incomplete response

eg ♦ How many pupils altogether?

or

The question refers to both 4 and 25, and interprets the significance of the multiplication sign

eg • How many pupils are there altogether in 4 classes of 25?

186

Do not accept response processes the 4 × 25 correctly

eg ♦ Altogether there are 100 pupils in year 9

100 pupils are in year 9 Do not accept incomplete response

eg ♦ How many pupils altogether in 4 classes? ♦ It’s the number of classes in year 9 with the number of

students ♦ Four classes with 25 pupils in year 9

or

Interprets the calculation in a valid way whilst still referring to year 9

eg • If there were always 4 classes in year 9, how many classes would there have

been in 25 years? Do not accept response does not refer to the given context

eg ♦ 25 pupils each have 4 rulers. How many rulers do they have

altogether? Do not accept response matches a different calculation

eg ♦ If there are 100 students in year 9 and only 4 teachers, how

many pupils are in each class? [4]

9. Throwing coins

(a) Indicates ‘True’ and gives a correct explanation that implies there are two outcomes, 1 both of which are equally likely

eg • There are two equally likely possibilities, heads or tails • A head is just as likely as a tail • Both sides are equally likely

Accept minimally acceptable explanation eg, implicit reference to equally likely

♦ There are 2 sides ♦ It can land on H or T

eg, implicit reference to two outcomes ♦ It’s 50 – 50

It’s an even c♦ hance ♦ As it’s a fair coin Do not accept incomplete explanation

eg ♦ u don’t know what will come up next ♦ Coins sometimes land on heads

Yo

♦ It is equal ♦ It’s a fair chance

187

(b) Indicates ‘False’ and gives a correct explanation 1

The most common correct explanations:

State the outcome cannot be predicted with certainty

eg • Each throw is random • You don’t know what you will get. It’s just chance • You don’t know until you’ve thrown • You never know which side the coin will land on

Show there are alternative outcomes

eg • You might get 4 heads • There are more possibilities like HHHH, HHHT, HHTH and so on • You could get just one tail

Accept minimally acceptable explanation eg, for the first category

♦ It’s random ♦ It’s chance

eg, for the second category ♦ You might get something different ♦ You don’t know that’s what you’ll get ♦ Each one could land on any side

! Explanation refers to one throw of one coin Condone provided reference is made to both uncertainty and two outcomes

eg ♦ It can land on either side ♦ It could land on H or T Do not accept incomplete explanation

eg ♦ It could be anything ♦ You don’t know

It’s not certain ♦

Do not accept incorrect or ambiguous explanation eg Th♦ ere are five different outcomes

♦ You are as likely to get 3 heads and 1 tail It’s 0 – 50 5

[2]

188

10. Folding

(a) Both correct, ie 2 12 by 4 (either order) and 6 by 8 (either order)

or

One correct, the other incorrect or omitted 1

(b) 3 1 [3]

11. Yards

(a) 91.44 1 Accept 91 or 91.4

(b) 109 or 109.(...) with no evidence of an incorrect method 2 ! Answer of 110

Provided a more accurate value or a correct method is seen Do not accept correct answer from an incorrect method

eg 100 – 91.44 = 8.56, 100 + 8.56 is about 109

or

Shows the digits 109(...) but the decimal point is positioned incorrectly or omitted 1

or

Shows the correct inverse operations, in any order

eg • × 100, ÷ 2.54, ÷ 36

or

Shows ÷ 91.44 ! Answers to parts (a) and (b) reversed

Treat as a misread and deduct the first mark only [3]

12. Scales

(a) 14 to 14.2 inclusive 1

(b) 220 to 230 inclusive 1 Accept fractional value

(c) 35 to 36 inclusive 2 ! Follow through from part (a)

Provided it is explicit in the working that the method incorporates this incorrect value

189

or

Shows how to use the scale to find 1000g, even if the scale is read incorrectly 1

eg • Work out what it is for 100g, then × 10 • 400g + 400g + 200g 200g is 7, 5 × 7 100g is 4 (error) ounces, 4 × 10 500g is 17 (error), then double 17 250 is 9, 9 × 4 = 32 (error)

Do not accept poor mathematical communication Do not infer incorrect reading of the scale

eg ♦ 3 × 10 (No indication of method through written

working or through markings on the scale, and answer to the calculation is outside the acceptable range)

or

Shows a correct multiplication, or a correct addition, that would give an answer within the correct range, even if this is followed by incorrect processing

eg • 3.6 × 10 • 5 × 7 • 14 + 14 + 7

[4]

13. Security lock

(a) 24, with no incorrect working 2 Do not accept 24 obtained from listing that indicates duplication

or

Shows a correct method 1

eg • 4 × 6 • There are 6 ways for the letter A and it is the same for each of the other letters

or

Lists in a systematic way for any one of the letters or any one of the numbers

eg • C1, C2, C3, C4, C5, C6 • A / 6, 5, 4, 3, 2, 1 • A1, B1, C1, D1

190

(b) 61 or equivalent probability 1

! Decimal or percentage rounded or truncated 0.17 or 0.167 or 0.166(...), or the equivalent % values. 0.16

[3]

14. Screenwash

(a) 600 1

(b) 50 1

Indicates ‘No’ and gives a correct explanation 1

The most common correct explanations:

State that 25% implies a total of 4 parts but there are 5

eg • There are 5 parts not 4 • There are 4 parts of water not 3

Accept minimally acceptable explanation eg, for the first category

♦ 1 : 4 means 5 parts altogether ♦ It’s 1 out of 5 ♦ There are 5 parts

State what 25% would imply

eg • 25% would be 1 part screenwash to 3 parts water • It would give a total of 125%

Use of information from part (a) eg

♦ 150ml × 5 = 750 not 600

Refer to the correct percentage of 20%

eg • It’s 20% • 1 out of 5 = 20 out of 100

Do not accept incomplete explanation eg

♦ It’s less than a quarter screenwash ♦ It’s more than 75% water ♦ There are more than 4 parts ♦ 1 part with 4 parts

[3]

15. Net

(a) Indicates the correct shape, ie 1

(b) Lines correct 1

ie uses a ruler to draw both straight lines from a common point,

191

within the tolerance for length as implied by the diagram

Accept Lines correct length but outside of the arcs shown on the diagram

Angle correct 1 ie draws or indicates the angle within the tolerance as shown on the diagram

Arc correct 1 ie draws the arc within the tolerance as shown on the diagram. (Ignore continuation of the arc beyond the lines denoting the angle)

Accept follow through from an incorrect angle ! Follow through from incorrect straight lines

Provided both lines are the same length and compasses have been used. Note the dashed lines on the diagram are a visual aid to help identify those who have not used compasses Do not accept Arc shown as a series of points

! Extra information added to the net in an attempt to show a 3-D drawing Penalise one mark only, by withholding the final mark that would otherwise have been awarded

[4]

192

16. Piles of cards

(a) Correct expression, eg 1 • 4n + 5 6n + 8 – (2n + 3)

Do not accept Incorrect expression eg, for part (a)

♦ 6n + 8 – 2n + 3 eg, for part (b)

♦ 6n + 8 ÷ 2

(b) Correct expression, eg 1 • 3n + 4

286 +n

(6n + 8) ÷ 2 Accept Correct expression repeated

eg ♦ 3n + 4 and 3n + 4

(c) 105 2

or

Shows the value 20 1

or

Using an incorrect value of n, evaluates 5n + 5 correctly

eg, from n = 26 • 5 × 26 + 5 = 135 eg, from n = 23 • 120

! Value for n if not stated If embedded

eg ♦ 5 × 21 + 5 = 110 If not specified and not embedded

eg ♦ 120 (neither n = 23, nor 5 × 23 + 5 shown)

or

Using an incorrect value of n, evaluates 6n + 8 correctly and then subtracts 23

eg, from n = 24 • 6 × 24 + 8 = 152, 152 – 23 = 129 eg, from n = 23 • 6 × 23 + 8 = 146, 146 – 23 = 123

[4]

193

17. Cycling

Gives a correct explanation 2

The most common correct explanations:

Show the mean is 39.9 which is less than 40

eg • 32.3 + 38.7 + 43.5 + 45.1 = 159.6, 159.6 ÷ 4 = 39.9 which is 0.1 too small • 39.9 < 40

! Response does not refer to 40 eg

♦ The mean is 39.9 Provided this is not accompanied by an incorrect statement

eg, for 2 do not accept ♦ 159.6 ÷ 4 = 39.9 so she rode more than 40km a day

Show the total distance is 159.6 which is less than 160

eg

• 40 × 4 = 160, 160 > 159.6 ! That 159.6 is less than 160 is not stated explicitly

The values of 159.6 and 160 must be shown, but accept implicit comparison

eg ♦ It’s159.6 not 160 ♦ As in the previous category, for 2 do not accept a correct

response accompanied by an incorrect statement

Compare and interpret the daily differences in distance from 40

eg • – 7.7 + – 1.3 + 3.5 + 5.1 = – 0.4 so it’s under 40 • 7.7 + 1.3 > 3.5 + 5.1

Do not accept no interpretation eg

♦ On Mon she did 7.7km less, Tues was 1.3km less, Wed was 3.5km more, Thurs was 5.1km more

! Values rounded eg

♦ 32 + 39 + 44 + 45 = 160 so the mean is 40 Mark as 1, 0

or

Shows the value 159.6 or 160 1

or

Shows a correct method to find the mean, or the difference between the mean and 40, with not more than one computational error

eg • 32.3 + 38.7 + 43.5 + 45.1 = 158.6 (error)

158.6 ÷ 4 = 39.65 • – 8.7 (error) – 1.3 + 3.5 + 5.1 = –1.4

194

! Median calculated correctly

For lm, provided the word median is used and the statement is contradicted

eg, accept for 1 ♦ The median is 41.1 so she is correct

eg, do not accept ♦ The average is 41.1 so she is correct

or

Describes a complete correct method but does not completely evaluate

eg • When you add them all up it doesn’t come to more than 4 × 40

Do not accept incomplete method with no evaluation or interpretation

eg ♦ (32.3 + 38.7 + 43.5 + 45.1) ÷ 4

195

1. Pictogram

(a) Draws two circles 1 Accept circles not shaded

! Circles inaccurate in size and/or shape Accept provided the pupil’s intention is clear

(b) 2 1 [2]

2. Missing numbers

Gives any three numbers that add to 15, eg 1 • 5 + 6 + 4 • 5 + 5 + 5

Accept throughout the question, use of fractions, decimals, negatives or zeros

Gives any two numbers that multiply to 15, eg 1 • 3 × 5 • 1 × 15

Gives any two numbers that divide to give 15, eg 1 • 30 ÷ 2 • 15 ÷ 1

Do not accept incorrect order, eg ♦ 2 ÷ 30

Gives any three numbers that combine as shown to give 15, eg 1 • 2 × 6 + 3

Accept brackets inserted to change order of operations, eg ♦ 3 × (1 + 4) Do not accept incorrect order of operations, eg ♦ 3 × 1 + 4

[4]

3. Scales

(a) 60 1 Accept value between 59 and 61 inclusive

! Units given Ignore

(b) Indicates the correct position, eg

0 100

1

•

196

Accept unambiguous indication, eg

0 60 100

! Follow through Accept follow through from part (a), provided their (a) is not 0, 50 or 100

! Position not indicated accurately Accept within ±2mm

4. Prices

(a) Indicates a correct amount in pounds or pence and gives the correct units, eg 1 • 75p • £0.75

Indicates a correct amount in pounds or pence and gives the correct units, eg 1 • £1.05 • 105p

Indicates one eraser 1

(b) Indicates a correct way, other than two rulers, eg U1 • 4 pencils • 3 erasers • 1 eraser and 1 green pen • 1 ruler and 2 pencils

Indicates a correct way, other than one previously credited U1

Indicates a correct way, other than one previously credited U1 ! Units incorrect or omitted

Penalise only the first occurrence, eg ♦ 75 (units omitted)

1.05p (units incorrect) Mark as 0, 1

Accept quantity of one implicit but not specified, eg, for the third mark in part (a)

♦ Eraser eg, for part (b)

♦ Ruler and two pencils Accept unambiguous indication

eg, for the third mark in part (a) ♦ E ♦ Rubber

eg, for part (b) ♦ R and 2P

[3]

197

5. Clock

(a) Indicates only the two correct clocks, eg 1

! Indication other than ticks, eg •

♦ x used Accept provided unambiguous

(b) 5:15 or 05:15 1 Accept superfluous indication of morning, eg

♦ 5:15 am Do not accept time incorrect, eg

♦ 5:15 pm ♦ 17:15

(c) 17:15 1 ! Follow through

Accept follow through as 12 hours later than their (b), even if their (b) was 17:15, provided this is written as a possible time eg, from part (b) as 03:26, accept

♦ 15:26 Accept superfluous indication of evening, eg ♦ 17:15 pm Do not accept time incorrect or not using 24 hour clock, eg ♦ 17:15 am ♦ 5:15 pm

[3]

6. Calculations

(a) 72 1

(b) 22 1

(c) 97 1

26 1

1256 1

4348 1 [6]

7. Chains

(a) Gives both correct values correctly positioned, ie 20 and 320 1

(b) Gives both correct values correctly positioned, ie 5 and 2½ or equivalent 1 5Accept for 2½, /2

198

8. Puzzling out

Indicates the numbers 1, 3, 5, 7, 9 in any order 2

or Indicates any five numbers that are less than 10, eg 1 • 0, 2, 4, 6, 8 • 7, 7, 1, 2, 6 • –4, –4, –4, –4, –1.5

or Indicates any five odd numbers, eg • 7, 7, 15, 13, 9

[U1] [2]

9. Wind chill

–19 1

16 1

–22 ! Incorrect notation for negative numbers, eg

♦ 19– Penalise only the first occurrence

Do not accept –16 given for 16 [3]

10. Throwing dice

(a) Indicates only the five points with positive integer coordinates 2 whose sum is 6, eg

××

××

×

• or Indicates at least four correct points with no incorrect points 1

or Indicates all five correct points with not more than one incorrect point ! Point(s) not indicated accurately

Accept in parts (a) and (b) provided the pupil’s intention is clear ! Additional points indicated that assume zero to be on the dice,

eg (0, 6) and/or (6, 0) indicated

If this is the only error, mark as 1, 0

199

! Additional points with non-integer coordinates whose sum is 6

indicated, eg

If this is the only error, mark as 1, 0

(b) Indicates only the six points with positive integer coordinates such that y = x 2 eg

• ×

××

××

×

or Indicates at least five correct points with no incorrect points 1

or Indicates all six correct points with not more than one incorrect point ! Additional point indicated that assumes zero to be on the dice,

eg (0, 0) indicated

If this error has been penalised in part (a), condone If this is the only error and it has not been penalised in part (a), mark as 1, 0

Additional points with non-integer coordinates such that y = x indicated, eg

If this error has been penalised in part (a), condone If this is the only error and it has not been penalised in part (a), mark as 1, 0

(c) Completes the sentence to give a correct rule, eg 1 • One less than the number on the red dice • Red – 1 Needing 1 added to get the number on the red dice

Accept minimally acceptable rule, eg ♦ 1 below the other dice ♦ The number below the red dice

! Rule expressed algebraically, eg ♦ b = r – 1 r – 1

200

! Rule that does not use the given starting phrase

Accept only if unambiguous eg, accept

♦ Red = blue + 1 eg, do not accept

♦ 1 more on the red Do not accept ambiguous rule, eg – 1 1 below A number below the red dice The number lower than the red dice Followed by the number on the red dice

Do not accept incomplete rule, eg Less than the number on the red dice Do not accept rule not generalised

Do not accept rules only shown through particular numerical examples, eg ♦ 2 – 1 = 1, 3 – 2 = 1, 4 – 3 = 1 etc

[5]

11. Perimeter and area

(a) Indicates No and gives correct explanation 1 ! Units given

Ignore

The most common correct explanations:

Quantify the areas, eg • The area of the hexagon is 6 but the triangle is only 4 • The hexagon has two more triangles

Accept minimally acceptable explanation, eg ♦ 6 and 4 ♦ 2 more Do not accept incomplete or incorrect explanation, eg ♦ The hexagon is 6 ♦ The hexagon has 5 triangles, the triangle has 4 ♦ The hexagon has one more shape in it than the triangle

Interpret ‘area’, eg • Different amount of space inside • Different numbers of triangles

Accept minimally acceptable explanation, eg ♦ Count the triangles ♦ They have different numbers of shapes ♦ One has less triangles

! c hapes in an otherwise correct explanation

Condone,

Ina curate description of s

eg, accept They have a different number of squares inside ♦

201

Do not accept incomplete explanation that does not interpret area, eg ♦ Different sizes ♦ Different numbers of dots ♦ Different

Identify which shape has the bigger area, eg • The area of the hexagon is greater • The triangle has a smaller area

Accept minimally acceptable explanation, eg ♦ The hexagon is bigger ♦ The triangle is smaller ♦ The triangle has only 4

[U1]

(b) Indicates Yes and gives a correct explanation 1 ! Units given

Ignore

The most common correct explanations:

Quantify the perimeters, eg • The perimeter of both is 6 • They both have 6 along the sides

! Perimeters measured Accept values between 8.4cm and 9.6cm inclusive, even if units are not given

Accept minimally acceptable explanation, eg ♦ 6 and 6 ♦ Both 6 sides Do not accept incorrect explanation, eg They have 5 lines round the sides

Interpret ‘perimeter’, eg • Both have the same distance around the edges • The number along the sides is the same • Each side of the triangle = two sides of the hexagon

Accept minimally acceptable explanation, eg ♦ Same length edges ♦ Same amount of triangle sides ♦ Same number of dots ♦ Same number of points ♦ Dots to dots is the same ♦ Same number of sides between the dots

n ambiguous explanation, eg

umber of squares

♦ I counted around them Do ot accept incomplete or♦ They are the same size ♦ They are both the same ♦ They take up the same n♦ Same number of sides ♦ I counted the sides ♦ I measured them

202

! Responses to parts (a) and (b) transposed but otherwise

completely correct, even if there is incorrect use of words ‘area’ and ‘perimeter’

Do not award the mark for part (a), but award the mark for part (b) [U1]

[2]

12. Weighing

1.2 2 Accept equivalent fractions and decimals

or Shows 2.4 1

or Shows the digits 12

or Shows or implies a complete correct method, with not more than one error, eg • (5 – 2.6) ÷ 2 • 5 – 2.6 then ÷ 2 5 – 2.6 = 3.4 (error), 3.4 ÷ 2 = 1.7

! For 1m, necessary brackets omitted As this is a level 4 mark, condone eg, accept for 1m

♦ 5 – 2.6 ÷ 2 Do not accept for 1m, incorrect order of subtraction, eg 2.6 – 5 then ÷ 2

[U1] [2]

13. Patterns

(a) Shows two rectangles in a pattern with two lines of symmetry, eg 1

203

(b) Shows two rectangles in a pattern with only one line of symmetry, eg 1

(c) Shows two rectangles in a pattern with rotation symmetry of order 2, eg 1

! Lines of symmetry drawn

Ignore ! Rectangles not shaded

Accept only if unambiguous ! Edges of rectangles not explicit

Pupils may use the edge of the grid or not show an edge when the rectangles are adjacent. Accept only if unambiguous

! Rectangles placed within the grid but covering only parts of squares

Accept provided the pupil’s intention is clear eg, for the first mark, accept

♦

204

! Rectangles placed with parts or all outside the grid

Accept provided the pupil’s intention is clear eg, for the third mark, accept

♦

! Rectangles overlapping Accept only if unambiguous eg, for the third mark, accept

♦ ! Incorrect size of rectangles

Do not treat as a misread, ie do not accept Do not accept grid not taken to be part of the pattern

[3]

14. Simplifying

8k + 7 1

2k + 5 1 Do not accept use of multiplication sign in simplified expressions

eg, for the first mark ♦ 8 × k + 7 Do not accept partially simplified expressions

[2]

205

15. Car parking

Indicates the remaining five combinations in any order, with no duplicates and 2 none incorrect

10p 20p 50p

7 0 0

5 1 0

3 2 0

2 0 1

1 3 0

0 1 1

or Indicates at least four correct combinations, with not more than one duplicated, 1 incorrect or omitted

Accept zeros omitted ! Amounts given rather than numbers of coins

Accept provided the number of each type of coin is unambiguously implied eg, for the combination 2 0 1, accept

♦ 10p 20p 50p

10p 10p

50p

eg, for the combination 2 0 1, do not accept

10p 20p 50p

20p 50p [2]

16. Thinking fractions

40 1

150 1

30 1 [3]

17. Moving C

(a) Gives correct coordinates, eg 1 • (6, any value except 6 or 1) • (4, 5) • (8, 5) • (4, –3) • (8, –3)

206

! Use of overlay

As there is an infinite number of correct coordinates, a marking overlay is available for use if pupils give non-integer coordinates. Accept coordinates of any point that lies exactly on the straight line or on one of the circles, provided their point is neither (6, 6) nor on the same straight line as A and B

(b) Gives correct coordinates, 1 ie (4, 5) or (8, 5) or (6, 3) or (4, –3) or (8, –3) or (6, –1)

Accept same correct position used for part (b) as for part (a) [2]

18. Shoe sizes

(a) 6 1

(b) 2 1 [U1]

[2]

19. Construction

Constructs a completed triangle with the vertices in the regions indicated, and arcs 2 within the tolerance, shown on the overlay

or Draws a completed triangle with the vertices in the regions indicated on the overlay, 1 with either no arcs or incorrect arcs

or Draws arcs that are within the tolerance shown on the overlay, even if there is an incorrect or no completed triangle

! Longer arcs drawn than are shown on the overlay Ignore inaccuracies in sections of arcs extending beyond those shown on the overlay

[2]

20. Travel to work

(a) £729(.00) 2

or Shows the digits 729, eg 1 • 72900 • 72.90

or Shows a complete correct method with not more than one computational error, but with the decimal point correctly positioned, eg • 20 × 45 = 900

16 × 45 = 8 × 90 = 720 720 + 9

207

• •

1620 4564800 8100

73900 (error) so £739

0

0

2

3

0

1

0

04

5

4

0

8

0

0

0

0 4

7 51

6 2

0 0

1

9

0

(error) So £ 719

• (b) £ 14 1

Do not accept conceptual error, eg 1620

456480

8100 14580 so £145.80

[3]

21. Solving

2 1

2½ or equivalent 1 ! Throughout the question, incorrect notation

eg, as an answer for the first mark ♦ k = × 2

Withhold one mark only for the first occurrence [2]

208

1. Hexagons

(a) Gives a correct explanation, eg 1 • Each shape has six sides • They all have six corners • 6 sides

Accept minimally acceptable explanation, eg ♦ 6 edges ♦ 6 lines ♦ 6 points

! Incorrect statement alongside a correct explanation Condone, eg, accept

♦ 6 equal sides

(b) Draws a regular hexagon of any size with vertices on the dots of the grid 1 ! Lines not ruled or accurate

Accept provided the pupil’s intention is clear ! Internal lines shown

Ignore provided the outer shape is a regular hexagon, eg, accept

♦ [2]

2. Cities

(a) 172 1

(b) Indicates York and London, in either order 1

(c) Indicates London and gives the value 13 1

(d) 332 2

or Shows the three correct values 120, 91 and 121 1

or Shows three values, two of which are correct, then adds them correctly, eg • 120 + 91 + 134 (error) = 345

[5]

3. Number cards

(a) Four hundred and nine 1

or Nine hundred and four

Four hundred and ninety 1

or Nine hundred and forty Accept correct words even if cards not completed, or completed incorrectly

209

! Digits used

Accept provided the place value is interpreted, eg, for the first mark, accept ♦ 4 hundred and 9 ♦ 400 and 9 ♦ 400 and 9 units

! Omission of the word ‘and’ Accept if unambiguous, eg, for the first mark, accept

♦ Four hundred nine ♦ 4 hundred – nine ♦ 4 hundreds 9 units ♦ 4 hundred + nine ♦ 400 + 9, eg, for the first mark, do not accept ♦ 400 9

! Within their number in words, digits other than 4 and 9 used Provided both their digits are non-zero, and the number shown by the cards and the number in words are the same, penalise only the first occurrence Otherwise, do not accept

Do not accept place value not interpreted, eg, for the first mark ♦ Four, zero and nine

(b) 853 1

538 1 U1

[4]

4. Late

(a) 10 1

(b) 19 1

(c) Indicates Wednesday and gives a correct explanation 1 U1

The most common correct explanations:

Refer to the number of pupils or to the number of lates, eg • 24 were late that day, more than on any other day • More pupils were late than on any other day • Biggest number of lates

210

Refer to the heights of the bars for the three year groups, eg

• That day is always the tallest • It’s the one that was highest most often

Accept unambiguous abbreviation, eg ♦ Wed ♦ W

Markers may find the following totals useful: ♦ Monday 10 ♦ Tuesday 12 ♦ Wednesday 24 ♦ Thursday 8 ♦ Friday 8 Accept minimally acceptable explanation

eg, for the first category ♦ 24 ♦ 8 in Y7, 7 in Y8, 9 in Y9

It has many lates, eg, for the second category ♦ The charts show more w ere late then ♦ Taller bars

! ld be referring to all three year groups/charts or to just one year group/chart

Do not accept explanations that refer e

Explanation cou

xplicitly to one year group/chart, eg The tallest bar is 9 and that is a Wednesday ♦

♦ More pupils were late in yr 9 on that day ♦ The chart shows more were late then ♦ Tallest bar

Otherwise accept, eg ♦ hest

! b ent, eg was late

nse, but do not accept on its own [3]

. Slicing cubes

1

! Number of faces of both pieces given (a) accept

♦

Wednesday is the hig♦ Most pupils Am iguous statem

That was the day everyone Year 7, 8 and 9 all came late

Ignore if accompanied by a correct respo

5

(a) 6

(b) 6 1

(c) 5 1

Accept if unambiguous, eg, for part6 and 6

♦ 6 + 6

211

! Total number of faces given

Penalise only the first occurrence, provided answers of 12 are given for both parts (a) and (b). Otherwise do not accept, eg

♦ 12, 12, 10 Mark as 0; 1; 1

♦ 12, 12, 9 Mark as 0; 1; 0

♦ 12, 14, 10 Mark as 0; 0; 0

! For part (c), follow through Accept follow through as their (b) – 1, provided their (a) is equal to their (b), eg

♦ 5 (part (a)) 5 (part (b)) 4 (part (c))

[3]

6. Buying a bicycle

£ 26.89 2 U1

or Shows the digits 20688 1

or Shows or implies a correct method, eg • 8.62 × 24 – 179.99 • 27 with no evidence of an incorrect method • –26.89 • Digits 2689 seen

! Answer rounded to 27 Accept for 2m only if a correct method or a more accurate value is seen

Do not accept For 2m, negative value, eg –26.89

! Incorrect order for subtraction Condone, eg, accept

♦ 179.99 – 8.62 × 24 [2]

7. School uniform

(a) 54 1

(b) 16 1

(c) Gives all three correct values correctly positioned, ie 10, 20, 10 2

or Gives any two correct values correctly positioned 1

or Gives three values that sum to 40, one of which is correct and correctly positioned

or Gives the correct value for No, ie 20, and gives values for Yes and Don’t know that are the same, eg • 5, 20, 5

212

(d) Gives two labels in the two boxes of either the first row or the first column 1

specifying sex and gives two labels in the two boxes of either the first row U1 or the first column specifying yes or no, or other mutually exclusive labels that address the question, eg, for sex • Boys, girls • Female, male • G, B

eg, for yes or no • Yes, no

N, Y Have a pet, Do not have a pet

[5]

8. Kings and queens

(a) 50 1

(b) Elizabeth (I) 1

(c) Indicates (81, 63) on the chart 1 Do not accept point identified but not interpreted, eg f

! Point not accurately indicated Accept provided the point is nearer to (81, 63) than to any other point with integer coordinates

[3]

9. Admission

£5.65 3 U1

or Shows the digits 565, eg 2 • 56.50

or Shows the values 11.15 and 16.8(0) ! Values or differences shown in working in pence,

without units given Accept for 2m, provided both values or all differences are in pence

or Shows one of the values 11.15 or 16.8(0), then follows through using their incorrect value to give their correct saving, eg

• 11.15 before, 4.90 + 3.50 + 3.50 + 4.90 = 14.80 (error) after, 14.80 – 11.15 = 3.65

or Shows the correct difference for each category, eg • 1.7, 1, 1.95 • 1.7 + 2 × 1 + 1.95

or Shows the correct difference for two of the categories, then follows through using their incorrect difference to give their correct saving, eg

213

• 1.7 + 1 + 1 + 1.85 (error) = 5.55

or Shows the value £ 4.65 (from calculating using one child, rather than two)

or Shows any of the following: 1

Digits 1115

or Digits 168(0)

or Any two of the correct differences 1.7(0), 1, 1.95

or Digits 465 (from calculating using one child, rather than two)

or The values 8.65 and 13.3(0) (from calculating using one child, rather than two) ! Values or differences shown in working in pence,

without units given Accept for 1m

[3]

10. Temperature

(a) 1.5 or equivalent 1

(b) 37.9 or equivalent 1

(c) 46.5 or equivalent 2

or Shows or implies a complete correct method with not more than one error, eg 1 • (115.7 – 32) × 5 ÷ 9

59

327.115×

−

115.7 – 32 = 82.7 (error), 82.7 × 5 ÷ 9 = 45.9(…)

46 47 Digits 465 seen

! For 1m, necessary brackets omitted As this is a level 4 mark, condone, eg, accept

♦ 115.7 – 32 × 5 ÷ 9 [4]

11. Drawing

(a) Draws a rectangle of area 12, eg 1 • 1 by 12 • 2 by 6 • 3 by 4 • 1.5 by 8

(b) Draws a rectangle of area 12, with different dimensions from 1 one credited in part (a)

214

(c) Draws a triangle of area 6, eg 1

• Base 6, perpendicular height 2 • Base 4, perpendicular height 3 • Base 5, perpendicular height 2.4

! Lines not ruled or accurate Accept provided the pupil’s intention is clear

Accept edge of grid used as edge of shape [3]

12. Cubes in bags

(a) 27 1

(b) Both correct, ie 24 and 28, either order 2

or At least one correct and not more than one incorrect, eg 1 • 20, 24, 28 • 24, 27

or Gives the values 6 and 7 [3]

13. Grid percentages

(a) 60 1

60 1 ! Percentage of diagram not shaded given

Provided correct percentage unshaded is given consistently, ie 40 given for both, mark as 0, 1

(b) Gives a correct explanation in which both 1/8 and the link to 100% 1 are shown or implied, eg • It’s 1/8 and 1/8 of 100 is 12 • 1 out of 8 is equivalent to 12.5 out of 100 • 8 × 12½ = 100 • 100 ÷ 8 = 12.5 It’s 1/8, and 1 ÷ 8 = 0.125

(c) Indicates a total of three squares on the diagram 1 Accept minimally acceptable explanation, eg ♦ 8 squares is 100 so 1 is 12 ♦ 100 ÷ 8 ♦ 100 divided by the number of squares ♦ = 0.125

! The link is to a different percentage Accept provided the relevant fraction is shown or implied, eg, accept

♦ 2 squares is 25%, 1 square is half of that ♦ 4 squares is 50%, 50 ÷ 4

215

Do not accept incomplete explanation, eg ♦ 8 squares is 100% ♦ 1 square out of 8 shaded ♦ 12 % = Do not accept incorrect order of division, eg ♦ 8 ÷ 100 = 12 1

[4]

14. Ages

(a) Gives complete correct interpretations for both Barry and Carol, 2 by referring to both the following aspects:

The given context of age

The meaning of the given numbers and operations, eg, for Barry • One year younger (than Tina) • Aged one less (than T)

eg, for Carol • Twice as old (as T) • Double her age • 2 × Tina years old

or Gives a complete correct interpretation for either Barry or Carol 1 by referring to both aspects

or Gives interpretations for both Barry and Carol that give the meaning of the given numbers and operations but contain no reference to the given context of age, eg • For Barry, Tina minus 1

For Carol, Twice Tina ! Incomplete interpretation

Do not accept as complete an interpretation that lacks reference to one of the two aspects, eg, for Barry ♦ Tina minus 1 [no reference to the given context] ♦ Younger [no reference to the m1] ♦ One year different [ambiguous reference to subtraction], eg, for Carol ♦ Twice Tina [no reference to the given context] ♦ Much older than Tina [no reference to the × 2] ♦ 2 Tina’s age [no reference to the multiplication]

! Interpretation using comparison with age of person other than Tina

Accept provided the interpretation is unambiguous, eg, accept as complete and correct for Barry Four years younger than Ann ♦

216

(b) Gives all three correct expressions in their simplest forms, eg 2

• n + 4, n, 2n + 1

or Gives any two correct expressions in their simplest forms 1

or Gives all three correct expressions, even if not simplified Accept 1n or n1 for n in a fully simplified expression Do not accept n ± 0 as a fully simplified expression for n

! Use of multiplication sign If a multiplication sign is used, an expression cannot be accepted as fully simplified, eg, for Carol, do not accept as fully simplified

♦ 2 × n + 1

(c) 61 1

62 1 Do not accept incomplete processing, eg, for the first mark ♦ 2 × 30 + 1, eg, for the second mark ♦ 2 × 31 Do not accept incorrect notation, eg, for the first mark ♦ 61n

[6]

15. Data collection

(a) Indicates 1 or 2 and gives a correct explanation 1 eg, for 1 U1 • It will take a lot of time to write the name every time • You won’t have time to put the whole name • It will not tell you straightaway how many of each type there are • It will just give a long list of words • It would take ages to count up all the trees at the end • You could easily miscount the totals • It’s hard to draw a graph from it • It will take up a lot of paper

eg, for 2 • It will not tell you straightaway how many of each type there are • It will just give a long list of letters • It would take ages to count up all the trees at the end • You could easily miscount the totals • It’s hard to draw a graph from it • It will take up a lot of paper • Some names of trees might start with the same letter • You might not have a code for the type of tree you see

Accept minimally acceptable explanation for 1 or 2, eg ♦ Too long ♦ Not efficient ♦ It does not tell you how many there are

! Explanation for 1 or 2 that refers to an improvement to the design

217

Accept provided the improvement relates to one of the correct explanations,

♦ rite only the first letter,

t tells you how many there are,

ter r 2 that refers to pupils not

mes use of codes, eg

(b) Indicates 3 a 1 U

ach type mmon

ls quickly

tally chart

ptable explanation, eg

ogether

any there are n n, eg

ive

rstood nfusing

eg, for 1, accept It’s quicker to w

eg, for 1 or 2, accept ♦ Using a tally chareg, for 1 or 2, do not accept ♦ Using a tally chart is betDo not accept explanation for 1 oknowing what type the trees are, eg ♦ They might not know the trees’ naDo not accept explanation for 2 that refers to♦ They might find the codes confusing ♦ They could forget the key

mes ♦ It does not list the actual na

nd gives a correct explanation eg 1 • It is quick to do a tally chart • Tally marks are easy to write • It’s easy to see the number of e• It shows clearly which types are most co• It’s easy to see the mode • You can count up the tota• It is less likely you will miscount • It’s more likely to be accurate • It’s easy to draw a graph from a• It does not take up much space

Accept minimally acce♦ It’s quick

nt ♦ It’s efficie♦ You just put a line ♦ It collects the data t♦ It’s easy to understand ♦ It’s simple to use ♦ It’s organised ♦ It tells you how mDo ot accept incomplete explanatio♦ It’s easy ♦ It’s simple ♦ It’s effect♦ It’s clear ♦ It can be unde♦ It’s not co

218

! Reference to disadvantages of the design, eg There might be lots of ‘Other’ and they will not know what

type they were They have to decide in advance which sorts to include

Ignore alongside a correct explanation [2]

16. Coins

(a) Gives a correct explanation, eg 1 • 2/4 = ½ • Two of the four coins are 10p so half of them are 10p • 20p is ¼, so is 1p, and ¼ + ¼ + ½ = 1 • Each coin has ¼ chance and ¼ + ¼ = ½

Accept minimally acceptable explanation, eg ♦ 2/4 ♦ Two out of four ♦ Two is half of four ♦ Two are tens, two not Do not accept incomplete explanation, eg ♦ It’s 50/50 ♦ There are two tens, a twenty and a 1p ♦ There are two 10ps ♦ Half the coins are 10ps ♦ 20p is, so is 1p 1

(b) Identifies the values of the four coins as 20, 10, 2 and 1 and 1 gives the probability ¼, or equivalent probability U1

! Values of coins identified but doubt expressed as to whether this is the only possible combination

Condone Do not accept probability stated without values of coins identified

[2]

17. Explaining why

Indicates AD and CD are both 12, and justifies that triangle ACD is equilateral, eg 1 • The sides are the same length U1 • All sides are 12 • AC = AD = CD

Accept minimally acceptable justification, eg ♦ Sides are the same

They are equal ♦

219

Do not accept incorrect justification, eg ♦ The sides are even

! Reference to angles Ignore, ie do not accept a justification based on angles alone and do not penalise incorrect information about angles given alongside a correct response

Indicates angle y is 60 and gives a correct justification either as a calculation 1 or as a known fact, eg U1

• 180 ÷ 3 • 60 × 3 = 180 • That’s how many degrees there are in one angle in an equilateral triangle

Accept minimally acceptable justification, eg 60 × 3 60 + 60 + 60 All the angles are the same Do not accept incomplete justification, eg Angles in a triangle add up to 180

! Incorrect notation Ignore for both this mark and the next, eg, for angle y as 60, accept

♦ 60°C

Indicates angle x is 30 and gives a correct justification, eg 1 • Triangle ADB is a reflection of triangle ABC so x is half y U1 All angles in an equilateral triangle are 60°

The reflection shows half so it must be 30° Angles in ABC add up to 180, and 180 – 90 – 60 = 30

Accept minimally acceptable justification, eg x is half y 2x = y 60 ÷ 2 It is half 180 – 90 – 60

! Follow through Accept for angle x as their y ÷ 2 provided it is accompanied by a correct justification that either does not use a value for y or uses their value for y, and provided their y is not 0, 90 or greater than or equal to 180

[3]

220

18. Water

(a) 8 2

or Shows a complete correct method, eg 1

22510008.1 ×

• • 1.8 ÷ 0.225 • 225 × 2 = 450

450 × 2 = 900 900 × 2 = 1800 2 × 2 × 2

or Shows the value 1800 or 0.225 Accept value qualified, eg ♦ About 8

(b) 48 1 [3]

221

1. Answer of 100

32 1

5 1

3 1

30 1 [4]

2. Pupils

(a) 3 1 Accept pupils identified eg ♦ A, M, S ♦ Mike and two others

(b) Drama 1

(c) Paul 1 Do not accept pupil not identified eg ♦ 6

(d) Sule 1 [4]

3. Number pyramids

(a) Completes the pyramid correctly, ie 1

10

7 3

6 1 2

222

(b) Completes the first pyramid correctly 1

eg

20

15 5

11 4 1

Add to20Add totheir 5

Add totheir 15

Accept numbers used are decimals, fractions, negatives or zero Do not accept zeros omitted

Completes the second pyramid correctly, in a different way from one 1 credited for the first pyramid U1

! Numbers credited for the first pyramid but shown in a different order Accept if the centre numbers of the bottom rows are different eg, accept

20 20

10 1010 10

4 66 44 6

♦ eg, do not accept

20 20

9 1111 9

4 65 56 4

♦ [3]

4. Stacking

(a) Gives all three correct and in the correct order 1 ie 9, 18 and 27

(b) 30 1

(c) 6 1 ! In both parts (a) and (b), bottom layer not included

ie ♦ 0, 9 and 18 [for part (a)]

24 [for part (b)] Mark as 0; 1

[3]

223

5. Calculations

(a) 523 1

(b) 182 1

(c) 147 1

(d) 40 1 [4]

6. Coins

Shows all five correct ways, with none incorrect or duplicated 3 eg • 0 2 4

0 3 2 0 4 0 1 0 3 1 1 1

Accept zeros omitted ! Values of coins given

eg 0 4 4 0 6 2 0 8 0 5 0 3 5 2 1 Provided this is the only error,mark as 1, 0, 0

or Shows at least four correct ways, with not more than one incorrect or duplicated 2

or Shows at least three correct ways, with not more than two incorrect or duplicated 1

[3]

7. Matchboxes

(a) 10.6 1

7.2 1

3(.0) 1 Accept equivalent fractions or decimals

(b) 8 1 ! Answer of 4

Accept only if it is clearly stated that another 4 boxes are needed eg, accept ♦ 4 more eg, do not accept ♦ 4

[4]

8. Folding shapes

(a) Indicates the correct diagram, ie 1

224

(b) Completes the diagram correctly, ie 1

Completes the diagram correctly, ie 1

Completes the diagram correctly, ie 1

! Lines not ruled or accurate

Accept provided the pupil’s intention is clear [4]

9. Television

£ 130 2

225

or

Shows or implies both – 900 and ÷ 3, and carries out at least one 1 of these calculations correctly eg

• 1290 – 900 = 330 (error) 330 ÷ 3 = 110

• 390 ÷ 3 • Digits 13(0) seen

[2]

10. Measuring

Gives a correct explanation that shows the relationship between the 1 volume of the jug and one litre eg

• It’s 2 jugs • Fill the jug once, pour it in the bucket and fill it again • He uses 500 + 500 • A jug is half a litre • Empty into the bucket twice U1

Accept minimally acceptable explanation eg ♦ Fill it twice 500ml × 2 Accept jug assumed to be calibrated eg ♦ Put 200ml in the jug, then repeat to give a total of 5 times

[1]

11. Grid shapes

(a) B and E in either order 1 Accept shape A given alongside a correct response

(b) D and E in either order 1 ! Responses for parts (a) and (b) transposed but otherwise correct

Mark as 0; 1

(c) 30 1 Accept the given shape C excluded eg ♦ 29 more ♦ 29

[3]

226

12. Club

(a) Indicates False and gives a correct explanation 1

The most common correct explanations:

Identify the statement is incorrect for week 2 eg • True for the first and last weeks only

Identify the statement is incorrect for one of the Wednesdays eg • The most popular day was a Wednesday • The highest ever bar was Wednesday • One Wednesday there were 27 U1

Accept minimally acceptable explanation eg ♦ Not true for one of the weeks ♦ Wed was higher

! Explanation unclear as to whether it refers to one week or all three weeks Condone eg, accept ♦ Wed was the most popular day Do not accept incorrect explanations eg ♦ Each week Wed was most popular

! Number of pupils identified Where the value is a multiple of 5, do not accept incorrect values. Otherwise, within a correct response, accept integer values between the relevant multiples of 5, eg for Monday of week 3 accept 26, 27, 28 or 29 Do not accept incomplete explanation eg ♦ Not always true

(b) Indicates True and gives a correct explanation 1

The most common correct explanations:

Identify that for each week 20 pupils attended eg • 20 pupils went each Friday

Identify the relevant feature of the charts eg • The bars are all the same height U1

227

Accept minimally acceptable explanation eg ♦ 20 ♦ The bars are the same Do not accept incorrect explanation, or incomplete explanation that simply restates the information given eg ♦ They are all 25 (error) ♦ Same amount went ♦ It’s the same number each week

(c) Indicates Not enough information and gives a correct explanation 1

The most common correct explanations:

State that names are not shown eg • It doesn’t give their names so we don’t know who went each week

State that the people could be different eg • Same amount went each week but it could be different people • Different pupils might have gone on different Fridays

State that only the total is shown eg • It doesn’t say the same pupils went. It just says 20 pupils went on Friday • It doesn’t tell you about each pupil, it tells you about the total U1

Accept minimally acceptable explanation eg ♦ No names Accept minimally acceptable explanation eg ♦ It doesn’t tell you which pupils ♦ Could be different each week Accept minimally acceptable explanation eg ♦ It only gives the total ♦ It just says 20 ♦ All it says is ho w many Do ot accept incomplete exp n lanation eg ♦ You don’t know ♦ The charts don’t show it

detail [3]

♦ It doesn’t give that much

228

13. Points of intersection

(a) Draws three straight lines intersecting at one point 1 eg

(b) Draws three straight lines intersecting at three different points 1

eg

! Ruler not used

Condone, provided the pupil’s intention is clear Accept lines meet rather than intersect eg, for part (a)

♦

eg, for part (b) in tiers 3–5 and 4–6

229

! Diagrams for parts (a) and (b) in tiers 3–5 and 4–6 transposed

but otherwise correct Mark as 0; 1

! Other diagrams shown Ignore, as these may be working for the last part of the question Do not accept diagram is ambiguous The drawing must clearly show the correct number of points of intersection eg, for part (b) in tiers 3–5 and 4–6 do not accept

♦

(c) Parallel 1 ! Words used to describe parallel

Accept if applicable to all sets of parallel lines eg ♦ Never meeting ♦ At the same angle ♦ In the same direction ♦ Not touching each other Do not accept if applicable to only some eg ♦ Vertical ♦ Horizontal Do not accept incomplete response describing parallel eg ♦ Like railway tracks ♦ Apart U1

[3]

14. Daylight hours

Gives a complete correct response with both 3 months identified correctly and correct values given within the ranges as shown below, ie

June 18.5 to 19.5 inclusive December 5 to 6 inclusive

230

or

Makes not more than one error, but if the error is in identifying a month 2 the pupil must follow through from that incorrect month eg • Jun

20 (error) Dec 6

• June 19 February (error) 10

or

Makes not more than two errors or omissions, but if the error is in 1 identifying month(s) the pupil must follow through from that incorrect month(s) • eg

June 12 (error) Dec 7 (error)

July (error) 18 Oct (error) 9

June 12 (error) Jan (error) 7

! Months not written in full Accept unambiguous indications eg, for December ♦ D Do not accept ambiguous indication that could refer to other months eg, for June ♦ J

! Dates given Ignore eg, for June accept ♦ June 15th

231

! Follow through

Note that follow through must be applied from incorrect months. Ranges for correct values are shown below

Jan 6.5 to 7.5 inclusive Feb 9.5 to 10 inclusive Mar 12 to 12.5 inclusive Apr 15 to 16 inclusive May 17.75 to 18.25 inclusive (Jun 18.5 to 19.5 inclusive) Jul 17.5 to 18 inclusive Aug 15 to 15.5 inclusive Sep 12 to 12.5 inclusive Oct 9 to 9.5 inclusive Nov 6.5 to 7.5 inclusive (Dec 5 to 6 inclusive)

! Months omitted or months identified ambiguously Treat each omission or ambiguous response as one error eg, for 2m accept ♦ J (ambiguous)

19 Dec 5.8

eg, for 1m accept ♦ (omits)

19 (omits) 5.8

[3]

15. Plasters

(a) 351 1

(b) 3516 1

(c) 3519 1

! Answer given as a decimal or a percentage without a correct fraction shown Accept decimals within the following ranges, or their percentage equivalents: part (a) 0.028 to 0.03 inclusive part (b) 0.45 to 0.46 inclusive part (c) 0.54 to 0.55 inclusive

! Words given alongside a correct probability Ignore eg, for part (a) accept

♦ Unlikely, 351

[3]

16. Calculators

£ 27.50 2

232

or Shows the digits 275 1 eg

• 27.5 • 2750 • 2.75

or Shows a complete correct method for how to multiply 1.25 by 22, with not more than one computational error, but with the decimal point correctly positioned eg

• 12.50 + 12.50 + 1.25 + 1.25 11 × 2.50 = 10 × 2.50 + 2.50

12522

25002740

240 (error)

so 27.40

Do not accept conceptual error eg

125 22250250500

×

so 5.00

♦ ! Method is repeated addition

For 1m, at least some multiplication must be shown or implied eg, for 1m do not accept ♦ 1.25 + 1.25 + …..

[3]

17. Delivery charges

(a) Completes the table correctly, ie 1 8 7.(00) 9 7.60

Accept for 9 books, a value between 7.55 and 7.65 inclusive ! 7.60 shown as 7.6

Condone

(b) 60 p 1 ! Follow through from part (a)

Accept provided their 7.60 > their 7.00

233

(c) Draws the correct straight line y = x, 1

at least of length 6cm, including the point of intersection with the given line, with no errors

! Line not dashed Condone

! Line not ruled or accurate Accept provided the pupil’s intention is clear Do not accept series of points that are not joined

(d) 6 1 ! Follow through from an incorrect line in part (c)

Provided there is only one point of intersection, follow through as the closest integer value above their x-value eg, from their intersection as (7.2, 6.5), accept ♦ 8 eg, from their intersection as (4, 4.6), accept ♦ 5

! Maximum of 10 books assumed Condone eg, accept ♦ 6 to 10 books U1

[4]

18. Magic square

(a) Gives all six correct values, ie 2

13 12 5

2 10 18

15 8 7

or

Gives at least three correct values 1

(b) Gives all three correct values, ie 2 a = 16, b = 4, c = 9

or

Gives the correct value for b or the correct value for c 1 Do not accept incomplete processing

[4]

234

19. Fractions

31 or equivalent fraction 1

127 or equivalent fraction 1

61 or equivalent fraction 1 1

! Decimals used

For 31 , accept 0.33 or better

For 127 , accept 0.58, 0.583(...)

For 61 , accept 0.17, 0.16, 0.166(...)

[3]

235

1. Sports

(a) Shows a correct amount, with units 1 eg • £181.99

(b) Shows a correct amount, with units 1 eg • £8.02

! Value rounded In part (a), accept £182 but do not accept £181 unless a correct value is also seen In part (b), do not accept £8 unless a correct value is also seen

! Units omitted Penalise only the first such occurrence

(c) 3 1 ! Reference to money left over

Accept the correct change shown eg ♦ 3 r (£)5.03 Do not accept reference to part of a racket eg ♦ 3.3(...)

[3]

2. Travelling by train

(a) 24 1

(b) Completes the bar for girls correctly and in the correct position, ie 1

20

16

12

8

4

0

Number ofpupils

Boys Girls ! Bar not shaded or lines not ruled or accurate

Accept provided the pupil’s intention is clear and the top of the bar is not more than 1mm from the line indicating 14

236

(c) Gives all four correct entries, ie 2

0 18

4 4

Accept for 2m, zero omitted

or

Gives at least two correct entries 1 U2

[4]

3. Maze

(a) Identifies the correct square, ie 1

A

Accept unambiguous indication eg ♦ Correct square marked A

(b) Indicates the correct set of instructions, ie 1

6, south 3, east

(c) Indicates the correct set of instructions, ie 2

3, west 2, north

or

The only error is to order the instructions incorrectly, ie 1 2, north 3, west

or

One instruction is completely correct and correctly ordered, even if the other instruction is incorrect or omitted

or

Both compass directions are correct and correctly ordered eg • 2 (error), W

3 (error), N

237

! For part (b), 6 south and 2 east given

Condone Accept unambiguous indication eg, for part (b) ♦ 6.S

3.E ♦ s, 6

e, 3 Do not accept directions other than compass points used eg, for part (b) ♦ 6 down ♦ 3 right

[4]

4. ABC

34 1

8 1

4 1 [3]

5. Windmills

(a) Completes the windmill pattern correctly, ie 1

(b) Completes the windmill pattern correctly, ie 1

! Squares not shaded

Accept provided the pupil’s intention is clear [2]

238

6. Odd v even

(a) Gives a correct counter example 1

The most common correct counter examples:

Show an even number multiplied by three eg • 2 × 3 = 6 which is even • 3 × 10 = 30

Give an even number that is shown to be a multiple of 3 eg • 18 ÷ 3 = 6 • 30 is in the 3 times table • 3 goes into 12 U1

(b) Gives a correct counter example 1

The most common correct counter examples:

Show a multiple of four divided by two eg • 8 ÷ 2 = 4 which is even

21 of 12 is 6

• • 16 → 8

Give an even number that is multiplied by two to give another even number eg • 2 × 10 = 20 U1

! Other trials shown Ignore if at least one correct counter example is shown

! Calculation not processed Accept if a correct comment is given eg, for part (a) ♦ 6 × 3 isn’t odd 3 × 10 is even Even × 3 is even Otherwise, do not accept eg, for part (a) ♦ 6 × 3 Even × 3

239

! Examples use addition or subtraction rather than multiplication

or division For part (a), accept answers of the form n + n + n where n is even, or repeated addition of 3 where the number of 3s is even eg, accept ♦ 2 + 2 + 2 = 6 ♦ 3 + 3 = 6 For part (b), accept answers of the form 2n − n = n where n is even, or n + n = 2n where n is even eg, accept ♦ 4 − 2 = 2 ♦ 12 + 12 = 24

! Correct counter example accompanied by an incorrect statement Ignore incorrect statements eg, for part (a) accept ♦ 2 × 3 = 6, 6 isn’t odd but most of the time the answer will

be odd Do not accept incorrect notation eg, for part (a) ♦ 3 ÷ 18 = 6 ♦ 10 = 30

[2]

7. Triangular tiles

(a) Shows how eight tiles join to make a square 1 eg

•

240

(b) Shows how four tiles join to make a square, ie 1

! Lines not ruled or accurate

Accept provided the pupil’s intention is clear ! Internal lines not shown

Diagonal lines must be shown but pupils may use the given grid lines to represent horizontal or vertical lines Do not accept internal lines incorrect

! In both parts (a) and (b), tiles make an internal square even if there is no shading eg

♦

Mark as 0, 1

! In both parts (a) and (b), two tiles taken to be one larger tile eg

♦

Mark as 0, 1

[2]

241

8. Recycling rubbish

(a) Gives a value between 6 and 16 inclusive 1 Accept value qualified eg ♦ About 10

(b) Indicates only Germany and Norway 1 Accept unambiguous indication eg ♦ N, G

[2]

9. Shaded shape

(a) 18 1

(b) Draws a rectangle of area 18 cm2 1 eg • 3 by 6 rectangle • 2 by 9 rectangle • 4 by 4.5 rectangle

Accept follow through from part (a) ! Lines not ruled or accurate

Accept provided the pupil’s intention is clear [2]

10. Making 27

(a) 6 1 11 1

(b) Gives a correct explanation 1

The most common correct explanations:

Refer to the fact that an even number of 5p coins gives an even total, and that addition of 2p coins will keep the total even eg • An even number of 5p coins gives an amount that is even, leaving an odd

amount to make up 27p. You can’t make an odd number with 2p coins • An even number of 5s is even, adding 2s keeps it even, but 27 is odd • An even number of 5s always ends in zero, leaving you to make an odd number

with 2s which is not possible

Produce a set of possible solutions eg • 0 × 5p = 0p leaving 27p, impossible

2 × 5p = 10p leaving 17p, impossible 4 × 5p = 20p leaving 7p, impossible 6 × 5p = 30p, which is too big

• You can’t make 27, 17 or 7 using 2s U1

242

Accept minimally acceptable explanation eg ♦ An even number of 5s leaves an odd number and you can’t

make an odd number from 2s ♦ 27 is odd, so you have to have an odd number of 5ps or the

2s would make it even Do not accept explanation refers only to 5s, or only to 2s eg ♦ An even number of 5s is even but 27 is odd ♦ An even number of 5s always ends in zero ♦ You can’t make an odd number with 2s Do not accept justification not given eg ♦ You can only make even totals ♦ You can only do it using an odd number of 5s ♦ Can’t both be even ♦ 27 is an odd number ! Only one case considered As this is a level 4 mark, Condone eg, accept ♦ 2 × 5p = 10p leaving 17p, not possible 4 × 5p = 20p leaving 7p, can’t You can’t make 7 using 2s Two 5s make 10 and eight 2s that is as close as I can get Add 2ps to 10, you get 12, 14, 16, 18, 20, 22, 24, 26, 28 ..... Do not accept justification not given eg ♦ 26 is as close as I can get ♦ You can make 26 or 28

[3]

11. Patterns on a grid

(a) Gives the correct coordinates, ie (2, 1) 1

(b) Gives both pairs of coordinates in either order 1 eg • (3, 3) (4, 4)

(c) Gives both pairs of coordinates in either order 1 eg • (16, 16) (17, 17)

(d) Makes a correct decision and gives a correct explanation that 2 shows or implies 14 and justifies that 16 more are needed eg • Yes, 1 + 2 + 3 + 4 = 30 2 2 2 2

• There are enough because 1 + 4 + 9 = 14, 4 × 4 = 16 and 14 + 16 = 30 The next square is 16 tiles (4 by 4 square drawn) and you’ve used up 14• of them, so

there’s just enough You have 16 tiles lef• t and 4 × 4 = 16; all the tiles are used

243

or

States or implies that the next square uses 16 tiles 1 eg • You need 16 to make the next square • Draws a 4 by 4 square with 16 cells • 4 × 4 seen

! 16 not justified Accept only if the response makes it clear that exactly 30 tiles are used eg, for 2m accept ♦ Used 14, got another 16 so you will use up all the 30 tiles 30 − 14 = 16, so yes you have exactly the correct amount eg, for 2m or 1m, do not accept ♦ 14 used, 16 left so yes you can 30 − 14 = 16, so yes you have enough

-

or

States or implies that exactly 30 tiles will be used, but does not justify that 16 more are needed eg • You need all 30 • There would be no tiles left over • It all adds up to 30

or

Identifies the pattern of differences eg • +3, +5, +7 U1

! 4 by 4 square drawn correctly, but the number of squares incorrectly processed For 1m, Condone Do not accept their explanation could imply that 7 more squares are needed, ie a total of 21 eg

so yes, there are enough

♦ [5]

244

12. Caribbean cordial

(a) 21 or equivalent 1

43 or equivalent 1

450 1 ! Change of units

Accept provided the new units are clearly shown eg, for the second mark accept ♦ 750ml ♦ 75cl

! Incorrect units inserted in an otherwise correct response eg, for the first mark ♦ 0.5g

Penalise only the first such occurrence

(b) 200 1 [4]

13. Shape rotation

(a) Indicates the correct four faces 1 eg

Accept unambiguous indication eg

•

♦ Grey faces labelled G

(b) Draws a correct view of the cuboid in either of the orientations below, 2 using the isometric grid

Accept incorrect or no shading For 2m, internal lines omitted eg

♦ ! Lines not ruled or accurate

Accept provided the pupil’s intention is clear or

The only error is to draw the cuboid in the wrong orientation 1 eg

245

• or

The only error is to omit some external lines or to show some hidden lines eg

•

! Cuboid enlarged For 2m or 1m, accept provided a consistent scale factor has been used for all lengths Do not accept shape is not a cuboid

[3]

14. Multiples

(a) 105 1 108 1

(b) Indicates Yes and gives a correct explanation interpreting the word factor 1 eg • 140 will divide by 7 with no remainder • 140 is a multiple of 7 • 140 is in the 7 times table • 7 goes into 140 exactly • 7 × 20 = 140

246

Accept minimally acceptable explanation eg ♦ 140 will divide by 7 ♦ 7 goes into 140 70 × 2 = 140

! Explanation refers to 14 rather than 140 Accept provided the relationship between 7 and 14 is shown or implied eg, accept ♦ 7 goes into 14 7 × 2 = 14 7 times table goes 7, 14 and so on Otherwise do not accept eg ♦ 14 goes into 140

! Use of repeated addition Condone eg, accept ♦ Keep going up in 7s and you get to 140

! Use of ‘it’ or other ambiguous language Condone provided either 7 or 140 is used, implying ‘it’ is the other number eg, accept ♦ 7 goes into it ♦ 140 divides by it Otherwise do not accept eg ♦ It goes into it ♦ You can divide them

! Response contains an incorrect statement Condone only if accompanying a correct response eg, accept

Yes, 7 ♦ divides into 140 as it is a multiple of 140 eg, do not accept

7 ÷ 140 = 20 ♦ ♦ 7 is a multiple of 140 ♦ 140 will go into 7 ♦ 7 goes into 140 thirty times

[3]

Nepal

1

–3 to 12, aligned with 5000

s intention is clear

15.

(a) 8

(b) Draws a bar from 2 on the y-axis, and of the correct thickness

! Lines not ruled or accurate Accept provided the pupil’

247

or

Indicates that the maximum temperature is 12 1 eg • –3 + 15 = 12 seen • Draws a bar with a right-hand end at 12

or

Indicates on the graph the correct positioning for –3

or

Draws a bar that is 15 units, ie 721 squares, in length

! For 1m, bar incorrectly aligned with the 5000, or bar of incorrect thickness Condone

[3]

16. Angles

(a) Indicates No and gives a correct explanation 1 that shows the angle sum is incorrect eg • 30 + 60 + 100 = 190 but it should sum to 180 • They should add to 180 but these add to 190 • 30 + 60 + 100 is 10 degrees too big U1

(b) 130 2

or

Shows or implies a correct method with not more than one 1 computational error eg • 360 −(70 + 70 + 90) • 360 − 230 • 2 × 70 + 90 = 200 (error), 360 − 200 = 160 • 70 + 70 = 140, 140 + 90 = 330 (error), answer 30 • 180 − 50 U1

Accept minimally acceptable explanation Accept responses that state the angles should not add to 190, or that the angles should add to 180 eg ♦ They add to 190 which is wrong ♦ Angles in a triangle add up to 180 ♦ The angles don’t make 180 ♦ They should add to 180

248

Do not accept incomplete or incorrect explanation eg ♦ The angles add to 190 ♦ When you add up the angles you get the wrong angle sum Angles add to 200 (error) not 180

! Incorrect units Ignore eg, accept within a correct explanation ♦ 180ºC

[3]

17. Right angles

(a) Draws any quadrilateral with exactly two right angles 1 eg

• (b) Draws any quadrilateral with exactly one right angle 1

eg

! Lines not ruled or accurate Accept provided the pupil’s intention is clear

•

[2]

18. Prime grid

(a) Gives a correct explanation 1

The most common correct explanations:

State that 35 is a multiple of 5 and/or 7 eg • 35 is a multiple of 5 • 7 is a factor of 35

249

State that prime numbers have only two factors but that 35 has

more than two factors eg • A prime has 2 factors, 35 has 4

State that the last digit of any prime number greater than 5 is 1, 3, 7 or 9 eg • All prime numbers must end in 1, 3, 7 or 9 with the exception of 2 and 5 U1

Accept minimally acceptable explanation eg ♦ 5 goes into it ♦ It’s in the 7 times table 7 × 5 1, 5, 7, 35 It has more than two factors 35 divides by more than one and itself Do not accept incomplete explanation eg ♦ 35 is in some of the times tables ♦ 35 has factors ♦ Because it ends in 5

! Correct explanation accompanied by a statement that uses mathematical language incorrectly Throughout the question, Condone eg, for part (a) accept ♦ 35 has more than 2 factors, eg 35 goes into 5 ♦ 5 goes into 35, so it has 2 factors

(b) Gives a correct explanation 1

The most common correct explanations:

State or imply the numbers in column Y will all be multiples of 6 (or 2, or 3) eg • They are all in the 6 times table, so they must be multiples of 6 • They are all multiples of 3

State or imply the numbers in column Y will all have a factor of 6 (or 2, or 3) eg • They all have a factor of 3 • 2 is the only prime that is even and all these numbers are even and U1

greater than 2 Accept minimally acceptable explanation eg ♦ It’s the 6 times table ♦ You can divide them by 3 ♦ They are all even ♦ The only even prime is 2 ♦ None of the numbers ends in 1, 3, 7 or 9

re all even and even numbers are never prime

Accept that column Y starts at 6 is not explicitly stated Condone eg, accept ♦ They a

250

Do not accept incomplete explanation eg ♦ They are all in times tables ♦ They all divide by something other than one and itself 6 ÷ 3 = 2 It goes up 6 each time

! Misunderstanding of prime A common misconception is to confuse prime with odd. Hence do not accept statements that refer only to odd eg, do not accept ♦ The numbers are not odd

(c) Gives a correct explanation 1

The most common correct explanations:

State or imply the numbers in column X will all be multiples of 3 eg • They are all in the 3 times table, so they must be multiples of 3

State or imply the numbers in column X will all have a factor of 3 eg • They are all in the 3 times table, so they are all divisible by 3 U1

Accept minimally acceptable explanation eg ♦ They are all in the 3 times table ♦ 3 goes into them Do not accept incomplete explanation eg ♦ They are all in times tables ♦ They will all divide by something other than one and itself ♦ All the other numbers have factors ♦ It goes up 3 each time

! Misunderstanding of prime A common misconception is to confuse prime with odd. Hence do not accept statements that refer only to odd eg, do not accept ♦ The numbers are not odd U1

[3]

19. Crisps

40 1 ! Incorrect units given

Ignore [1]

251

20. Shoe sizes

Indicates Yes and gives a correct explanation 3 that shows or implies both of the values 40.75 and 41.375 eg • 7 × 1.25 + 32 = 40.75, 7.5 × 1.25 + 32 = 41.375, so they both round to 41 • 8.75 + 32 rounds to 41 and so does 9.375 + 32 • 8.75 gives 9 and 9.375 gives 9 before adding 32, so they will end up the same

or

Shows or implies both of the values 40.75 and 41.375 even if there is an 2 incorrect or no decision, or incorrect further working eg • Tom wears 40.8 and Karl wears 41.4 so they don’t wear the same size • 40.75 and 41.375 so they both wear 40

or

Shows the value 41.375 1

or

Shows the value 40.75 or 41 with correct working eg • 7.5 × 1.25 + 32 = 41

or

The only error is to add 1.25 rather than multiplying eg • Indicates No and shows the values 40.75 and 40.25 • Indicates No and shows the values 41 and 40

Accept minimally acceptable explanation eg, with Yes indicated ♦ They are both 41 ♦ They are 40.75 and 41.375

! 40.75 rounded or truncated Accept 41, 40.8 or 40.7 Do not accept 40

! 41.375 rounded or truncated Accept 41, 41.4, 41.3, 41.38 or 41.37 Do not accept 42

! 40.75 from incorrect working Note that pupils who add 1.25 rather than multiplying generate the shoe sizes 40.25 and 40.75 For 3m or 2m, do not accept explanations based on such misconceptions eg ♦ They are both 41 as 7.5 + 1.25 + 32 = 41

7 + 1.25 + 32 = 41 [3]

252

21. Same area

8 1 [1]

22. Holiday

£ 556.75 2

or

Shows or implies a complete correct method, even if there are 1 rounding errors eg

• 10017 × 3275

• 3275 ÷ 100 × 17 • 556 • 10% = 327.5(0)

5% = 163.75 1% = 32.75 327.5(0) + 163.75 + 2 × 32.75

• 1% = 32.75, 33 (premature rounding) × 17 = 561

or

Shows the digits 55675 ! Value rounded

Accept 557 or 560 For 2m, do not accept 556 unless a correct method or a more accurate value is seen

[2]

253

1. (a) 133 1

(b) 7 1 [2]

2. Gives three different correct pairs of numbers 2

eg

• 2 × 12 3 × 8 4 × 6

• 24 × 1 12 × 2 6 × 4

or

Gives two different correct pairs of numbers 1 Accept fractions, decimals or negative numbers

! For 2m or 1m, correct pair of numbers repeated, but in reverse order Do not accept as a different correct pair

[2]

3. (a) Gives a value that is greater than 1000, but less than 1100 1 eg

• 1001

• 1099 Accept fractions or decimals Do not accept for part (a), number given in words

(b) Gives a decimal that is greater than 0, but less than 1 1 eg

• 0.5

• 0.12

• Point two Do not accept for part (b), number given as a fraction

254

4. (a) Indicates C 1

(b) Indicates A and = in either order 1 ! Unambiguous indication

Accept eg, for part (b) accept • Cube and cuboid eg, for part (b) do not accept • Square and rectangle

(c) 7 1 [3]

5. (a) Gives all four correct numbers, ie 1

537 573 735 753 in any order

(b) Identifies the smallest and the biggest numbers from their list 1 (including the two given numbers), provided their list has at least four numbers

Correctly adds any numbers they identify, even if they are not from their list, 1 provided their numbers each have at least three digits and the addition requires at least one ‘carry’

eg

• 357 + 753 = 1110

• 537 + 753 = 1290

• 333 + 777 = 1110

• 357 + 375 + 537 + 573 + 735 + 753 = 3330

or

Gives the value 1110, without identifying their smallest and biggest numbers For both marks, follow through Markers may find the following sums using the values from a correct list useful:

+ 357 357

- 375

375 732 -

537 537 894 912

- 573

573 930 948 1110 -

735 735 1092 1110 1272 1308

-

753 1110 1128 1290 1326 1488 [3]

255

6. Gives all four different correct shapes in any orientations with none 3

incorrect or duplicated

Eg

or

Gives at least three different correct shapes, even if there are other 2 incorrect or duplicated shapes

or

Gives two different correct shapes, even if there are other incorrect or 1 duplicated shapes U1

! Lines not ruled or accurate, shapes not shaded or internal lines omitted Accept provided the pupil’s intention is clear

! For 3m, correct shapes duplicated even if orientation is different Condone duplication of the given shape, ie a 1 by 4 rectangle For 3m, do not accept other duplicates Do not accept squares not joined correctly side-to-side Do not accept as a correct shape eg

[3]

256

7. (a) £ 1.55 1

(b) Indicates the correct item of food and the correct drink, ie 2 Pizza and juice, in either order

or

Shows the digits 24(0) 1 U1

Accept unambiguous indication eg • P, J

[3]

8. 53 1

17 1

–5 1

Gives both the values –9 and (+)3 in the correct positions 2

or

Gives one correct value in the correct position 1 or

Gives both the values (+)3 and –9 but with the positions reversed [5]

9. Gives all three correct areas, ie 2

16 4 8

or

Gives any two correct areas 1 ! For 1m, follow through

Provided their 2nd < their 3rd < their 1st, accept the following: For their 2nd, accept follow through as their 1st ÷ 4 For their 3rd, accept follow through as their 1st ÷ 2 or their 2nd × 2 eg, for 1m accept • 20 (error), 5, 10

• 1 (error)41 ,

21

• 16, 2 (error), 4 eg, for 1m do not accept • 16, 8 (error), 16

[2]

10. (a) 10.2 or equivalent 1

(b) 9.5 or equivalent 1

(c) 1270 1

257

(d) 57 1 [4]

11. (a) 900 1 200 1 U1

! Follow through Accept follow through as 1100 – their value for the first mark, provided this gives a positive value

(b) Indicates 1000, ie 1

1 10 100 1000 10 000 [3]

12. (a) Gives two ages with a difference of 7 years 1

eg

• 1 and 8

• 7 and 14

• 7 and 0

• 20 and 13 ! Ages given using part-years

Accept provided the difference is 7 years eg, accept

• 6 months and 217

(b) 0 1 ! Response given in words

Accept provided there is no ambiguity eg, accept • Zero • Nothing eg, do not accept • No range

! Units amended Accept responses giving a short time interval eg, accept • A few minutes • A couple of hours

[2]

258

13. Gives all four fractions in the correct positions, 2

ie

or

Gives at least two fractions in the correct positions 1

or

Converts at least three of the four correct values into a form enabling comparison, even if the positions are incorrect and there are other errors eg

• At least three of: 12090 ,

12015 ,

12040 ,

12072

• At least three of: 0.75, 0.125, 0.33, 0.6

• 4030 ,

405 ,

4024

• 2418 ,

243 ,

248

• 6045 ,

6020 ,

6036

Accept unambiguous indication of fractions

For 31 as a decimal, accept 0.33 or better

For 81 as a decimal, accept 0.13 or better

eg, for 2m accept

[2]

14. (a) Draws a correct bar for Don’t know that indicates 9 people 1 ! Bar not ruled, accurate or shaded

Accept provided the pupil’s intention is clear, and the height of the bar is closer to 9 than to either 8 or 10

! Bar incorrectly positioned or of an incorrect width Condone

259

(b) Indicates 3 circles for Don’t know 1

U1 ! Circles not shaded or inaccurate in size

Accept provided the pupil’s intention is clear ! Follow through from part (a)

Accept the number of circles drawn as the height of their bar for Don’t know ÷ 3 If this results in a part circle, condone any inaccuracy in their part circle

[2]

15. (a) 7 1 ! For the first mark, ‘out of 10’ repeated

eg

• 107

Condone

50 1

(b) Completes the sentence correctly with two values that are in the ratio 1 : 20 1

eg

• 1 out of 20

• 5 out of 100

• 0.5 out of 10

• 10 out of 200

• 2.5 out of 50

Completes the sentence correctly, in a different way from one 1 previously credited U1

! Follow through Accept as two values in the same ratio as their two values for the first mark, provided their first value < their second value eg, from their first mark as 1 out of 5 accept • 2 out of 10

[4]

260

16. Gives correct triangles for both grids with vertices within the 2

tolerances as shown on the diagram below, ie

! Lines not ruled or accurate

Accept provided the pupil’s intention is clear

or

Gives a correct triangle for either grid with vertices within the 1 tolerances as shown on the diagram below, even if the other is incorrect or omitted eg

•

(error)

or

Completes two rotations of 90° clockwise that do not use the given centre of rotation eg

•

or

Fails to complete the first rotation correctly but draws a shape that is a triangle, then follows through to rotate their triangle correctly through 90° clockwise about the given centre of rotation eg

[2]

261

17. 21 2

or

Shows or implies that 2 × my number is 42 1 eg

• 2 × my number = 357 – 315

= 42

• 2x = 42

• 42 ÷ 2

or

Shows a complete correct method with not more than one computational error, even if their choice between alternative answers is incorrect or omitted eg

• 15 × 10 = 150, 150 + 150 + 15 = 315, so it’s 10 + 10 + 1

• 357 – 170 – 170 – 17 – 17 (error) = 0, so it’s 10 + 10 + 1 + 1 = 22

• 1)(1 31515

error

• 21

31515

• 1)(5 35717

error

U1 [2]

18. 32 1 ! For the first and second marks, incomplete

processing Penalise only the first occurrence eg, for the first and second marks • 4 × 8 48 ÷ 4 Mark as 0, 1

12 1

Gives a correct expression in x with a value of 48 when x is 8 1

eg

• 6x

• x + 40

• 3x + 24 ! For the third mark, unconventional notation

Condone eg, for the third mark accept

262

• 6 × x • x6

[3]

19. (a) Shows that the mean is 10 1

eg

• 9 + 11 + 10 = 30, 30 ÷ 3

• (9 + 11 + 10) ÷ 3

• 10 is already 10, then 9 is 1 below and 11 is 1 above Accept minimally acceptable explanation eg • 30 ÷ 3 • 30 ÷ 10 = 3 • 9 + 11 = 20, 20 ÷ 2 • Add one to 9 and take one off 11 • 10 is halfway between 9 and 11 Accept method described eg • You add them up then divide by how many there are Do not accept incorrect statement eg • 9 + 10 + 11 ÷ 3 = 10 • 3 ÷ 30 = 10

Gives a correct explanation of why the median is 10 1 eg

• 10 is the middle number when the numbers are in order

• The median is the middle number when the numbers go from smallest to largest Accept minimally acceptable explanation eg • It is the middle number • It’s the middle largest • It’s the second smallest

• 9 11

• It is in between

263

Do not accept incomplete or incorrect explanation eg • 9 10 11 • 10 is halfway between 9 and 11

(b) Gives four values that total 40 and whose middle two numbers, when ordered, 1 add to 20, with none of the values being 10

eg

• 8 9 11 12

• 0 0 20 20

• 9 11 9 11

• 7 13 9 11 Accept fractions, decimals and negatives

[3]

20. Shows angle a as 50 1

Shows angle b as 130 1 ! For the second mark, follow through

Accept follow through as 180 – their a, provided their a < 90 and is not 54 to 56 inclusive

Shows angle c as 20 1 ! For the third mark, follow through

Accept follow through as 150 – their b or their a – 30, provided this gives a positive value

[3]

21. 5 1

3 1 ! Incorrect notation

eg, for the first mark • ×5 Penalise only the first occurrence

! Incomplete processing eg, for the first mark

• 3

15

Penalise only the first occurrence [2]

264

22. 8602 2

or

Shows a complete correct method with not more than one computational error 1 eg

• 3740 + 3740 + 374 × 3 = 7480 + 1122

•

•

Do not accept conceptual error eg •

[2]

23. (60, 60) 1 [1]

265

1. (a) Correctly divides the square into quarters in a different way from the 1 given example eg

(b) Correctly divides the square into eighths 1

eg

! Throughout the question, lines not ruled or accurate, or lines

not using the intersections of the grid Accept provided the pupil’s intention is clear

266

! Throughout the question, quarters or eighths are not

congruent Accept provided the intention is clear for all pieces to have the same area eg, for part (a) accept •

eg, for part (b) accept •

[2]

267

2. (a) Indicates the correct times in the correct order 1

eg

• 6 and 9:30 Accept indication of morning eg • 6 am and 9:30 am

! Times not accurate Accept ± 5 minutes of the correct times eg, for 9:30 accept • 9:25 to 9:35 inclusive

! Use of ‘half’ Accept colloquial use of ‘half’ or

21

eg, for 9:30 accept

• Half (or 21 ) 9

Do not accept an incorrect time eg, for 9:30 do not accept

• 9 half (or 21 )

Do not accept time(s) incorrect eg • 6 pm and 9:30 • 6 and 21:30 • 6 and 9.5

213 or equivalent 1

! Follow through from the first mark Accept as the time interval between their two times, provided their answer is not a whole number of hours

! ‘Half’ in words Condone eg, accept • 3 and a half

(b) Indicates only 17(:00) and 23(:00) correctly on the diagram, with no 2 incorrect times shown

or

Indicates either 17(:00) or 23(:00) correctly on the diagram, 1 with not more than one error

or

Indicates any two times on the diagram with a difference of 6 hours

268

! Positions not accurate

Accept provided the pupil’s intention is clear ! Arrows do not indicate ‘on’ or ‘off’

For 2m, condone unless the times are incorrectly labelled as ‘on’ or ‘off’ In this case, mark as 1, 0 For 1m, ignore any labels

[4]

3. (a) 5 1

(b) 6 1 Do not accept for the first mark, £5

! Values not rounded Penalise only the first occurrence, even if the non-integer part is incorrect eg, for parts (a) and (b) • 5.2(...) or 5.3 6.8(...) or 6.9 Mark as 0, 1

(c) £ 22 1 U1

[3]

4. (a) Indicates grams 1 Accept unambiguous indication

Indicates litres 1 ! For both responses, correct but less suitable units indicated

Mark responses of kilograms then millilitres as 0, 1

(b) Indicates one of the given units not credited in their (a), and gives 1 an example of something it could measure U1 eg

• Use metres to measure the distance of a running track

• Use millimetres to measure the length of a ruler

• Use kilograms to measure the mass of a person [only if kilograms not given for the first mark in (a)]

• Use millilitres to measure the volume of drink in a can [only if millilitres not given for the second mark in (a)]

• Use grams to measure the mass of a piece of cheese [only if grams not given for the first mark in (a)]

• Use litres to measure the capacity of water in a swimming pool [only if litres not given for the second mark in (a)]

269

! Imprecise description of the property to be

measured Condone provided the pupil’s intention is clear eg, accept • Use metres to measure the size of a garden • Use millilitres to measure the amount/quantity of drink in a can • Use kilograms to measure the weight of a person

! Units for the correct property given, but not the most suitable for their example Condone eg, accept • Use millilitres to measure the volume of water in a swimming pool

! Property given with object unspecified or omitted Condone eg, accept • Use millimetres to measure the length of something • Use kilograms to measure the mass Do not accept object given without explicit indication of the property to be measured eg • Use millimetres to measure a ruler • Use kilograms to measure a person Do not accept units used that are not from the given list eg • Use centimetres to measure the length of a ruler

[3]

5. (a) 19 1 Do not accept for part (a), –19

(b) 2100 1 Do not accept for part (b), –2100

! Responses to parts (a) and (b) transposed but otherwise correct Mark as 0, 1

270

(c) Completes the three entries of the table correctly, ie 2

123 Australia 3824

or

Shows the value 123 or 3824, even if in an incorrect position 1 ! Abbreviation or incorrect spelling of

Australia Condone eg, accept • Aus • A

! For or 1m, 3824 rounded Accept 3800 or 3820 Do not accept 4000

[4]

6. (a) £ 2.84 1

(b) £ 13.98 1 [2]

7. (a) 187 860 1

(b) 1350 1 Do not accept –1350

[2]

8. (a) October 1 Accept unambiguous indication of month eg • O

! Correct frequency of 32 given Ignore alongside indication of the correct month, but do not accept on its own

(b) 11 1 [2]

9. (a) Indicates Yes and gives a correct explanation 1 eg U1

• 3 × 10 = 30

• 30 ÷ 3 = 10

• 30 is a multiple of 3

• 3 goes into 30 exactly

• 30 is in the 3 times table Accept minimally acceptable explanation eg • 3 × 10

271

• 30 ÷ 3 has no remainder • 30 divides by 3 • 3 goes into 30 • 30 ÷ 10 • 3 + 0 = 3 which is in the 3 times table

! Use of repeated addition Condone eg, accept • Keep going up in 3s and you get to 30

! Use of ‘it’ or other ambiguous language Condone provided either 3 or 30 is used, implying ‘it’ is the other number eg, accept • 30 divides by it • The lower number goes into it • It’s in the 3 times table eg, do not accept • It goes into it 10 times

! Response contains an incorrect statement Ignore alongside a correct response eg, accept • 30 divides by 3 as 3 is a multiple of 30 eg, do not accept • 3 ÷ 30 = 10 • 30 goes into 3 exactly Do not accept incomplete or incorrect explanation eg • 3 is a factor of 30 • 30 ÷ 3 • It adds up to 30 • They’re both in the 3 times table • Because there is a 3 in it

(b) Gives a factor of 30 greater than 3, ie 1 5, 6, 10, 15 or 30

[2]

10. (a) 20 1

(b) 60 1 ! Follow through

Accept follow through as their (a) × 3, provided their (a) was not 5

(c) 4 1 U1

! Operation repeated eg • × 4 Condone

272

Do not accept more than one number given eg • 2 × 2

[3]

11. £ 276 2

or

Shows the digits 276 1 eg

• 2.76

or

Shows the value 23, with no evidence of an incorrect method

or

Shows or implies a complete correct method with not more than one computational or rounding error eg

• 11253 × 12

• 253 ÷ 11 = 13 (error) 253 + 13 = 266

• 12 ÷ 11 = 1.09(…), 1.09 (premature rounding) × 253 = 275.77

Do not accept for 1m, incorrect method eg • 11 + 12 = 23

[2]

12. (a) 10.2 to 10.4 inclusive and 6.6 to 6.8 inclusive, in either order 1

(b) Gives the correct area using their values for the lengths of the diagonals in part (a) 1 eg

• From 10.3 and 6.7 in part (a), area of 34.505 (or 3450.5)

or

Gives the correct area using two values seen in part (b), even if they are different from their values for the lengths of the diagonals in part (a) eg

• From 10 and 7 seen in part (b), area of 35 Throughout the question,accept equivalent fractions or decimals Accept follow through as the product of their two values for part (a) ÷ 2 As this is an algebra mark, accept follow through from whole numbers as well as decimals

! For part (b), their value rounded Accept correct rounding to the nearest integer or better, or truncation to one decimal place or better

273

Do not accept incorrect rounding or truncation to an integer unless a correct method or a more accurate value is seen Markers may find the following values for the diagonals and corresponding areas useful: (error)

6.5 6.6 6.7 6.8 10.2 33.15 33.66 34.17 34.68 10.3 33.475 33.99 34.505 35.02 10.4 33.8 34.32 34.84 35.36 10.5 34.125 34.65 35.175 35.7

(error)

Shows the correct unit for their area 1 eg

• 34.505 cm2

• 3450.5 mm2

• Product of their two values for part (a) ÷ 2 and cm2 seen

• Product of their two values for part (a) ÷ 2 × 100 and mm2 seen ! Area not followed through from their (a) or

omitted, but units given If the first mark in part (b) for their correct area has not been awarded, condone either cm2 or mm2 seen for the second mark in part (b)

[3]

274

13. Gives a value between 1 and 2 inclusive 1

Gives a value between 49.5 and 50.5 inclusive 1 ! ‘Million’ repeated

eg, for the first mark

• 121 million

• 1 500 000 Condone

Gives a value between 10 and 12 inclusive 1 [3]

275

14. Gives both correct ways that are different from the example given, ie 2

2 , 3..... ..... 1 , 4 , 5..... ..... .....

1 , 4..... ..... 2 , 3 , 5..... ..... .....

and

or

Gives one of the two correct ways that are different from the example 1 given

! Operations given Ignore eg, for 2, 3 accept • 2 + 3

! First and second groups transposed within an otherwise completely correct response [answer lines ignored] eg

1, 4, 5 2, 3

2, 3, 5 1, 4

and

Mark as 0, 1 Do not accept if response satisfies the conditions, but does not use all the numbers and/or uses repeats eg

1 , 1..... ..... 1 , 1 , 2..... ..... .....

3 , 3..... ..... 4 , 4 , 4..... ..... .....

and

[2]

15. (a) Draws a triangle with no right angle 1 eg

276

(b) Draws a quadrilateral with no right angles 1

eg

! Lines not ruled or accurate

Accept provided the pupil’s intention is clear ! Vertices not on grid intersections

Accept provided it is clear that the conditions have been satisfied

(c) Indicates 1 1 Accept unambiguous indication including angle marked on diagram

[3]

16. (a) £ 4 1

(b) Completes the pie chart correctly 2 eg

277

or

Draws all four sectors correctly but fails to label or labels incorrectly 1

or

Draws and labels any two of the sectors correctly

or

Makes an error in drawing either the rent or the food sector provided rent sector > food sector, and follows through correctly to divide the remaining space into two equal sectors for entertainment and other

! Labels abbreviated Accept unambiguous indications of category names eg, for 2m accept

Do not accept amounts of money as the only labels, but ignore alongside correct labels

! Lines not ruled or accurate Accept provided the pupil’s intention is clear Do not accept if sector not continuous Do not accept as a correct sector eg, for the rent sector do not accept

[3]

278

17. Completes the grid correctly, giving simplified expressions, ie 1

Completes the grid correctly, giving simplified expressions 2

eg

or

Gives two correct simplified expressions 1 ! For 1m, follow through

Accept follow through from their incorrect expression for 6a + 5b, provided their incorrect expression contains only a term in a and a term in b

[3]

18. Indicates the village shop and gives a correct justification, based on 2 correctly calculating a pair of comparable values U1 eg

• At the supermarket 6.25 × 6 = 37.5(0) At the village shop 7.20 × 5 = 36

• 6.25 × 6 – 7.2 × 5 = 1.5

• 6.25 ÷ 5 = 1.25, 7.20 ÷ 6 = 1.2(0)

• £75 for 60 or £72 for 60

• For £1 you get 54 of a pen or

65 of a pen

• You pay 95p extra for 1 more pen, but they’re at least £1.20 each so it must be a better deal

279

or

Shows a correct pair of comparable values but makes either an incorrect 1 or no decision or Shows a complete correct method for finding a pair of comparable values with not more than one computational or rounding error, and follows through to make their correct decision eg

• 6 × 6.25, 5 × 7.20 [village shop indicated]

• 6.25 ÷ 5 = 1.05 (error), 7.20 ÷ 6 = 1.20 [supermarket indicated]

or

Makes a correct decision but the justification uses only the difference between a pair of comparable values eg

• The packs of 6 would be £1.50 cheaper

• A pen is 5p cheaper For 2m, do not accept no decision Accept for 2m, correct decision and any pair of comparable values shown Note that common pairs (in pounds) are: 37.5 and 36 (per 30 pens) 1.25 and 1.2 (per 1 pen) 6.25 and 6 (per 5 pens) 7.5 and 7.2 (per 6 pens) 75 and 72 (per 60 pens) 18.75 and 18 (per 15 pens) 0.95 and 1.2 [or 1.25] (1 extra pen) 0.8 and 0.83(…) (pens per pound)

! For 2m or 1m, comparison is per 5 pens or per 6 pens but the given price is not restated Condone eg, for 2m accept • At the supermarket, 6 pens would be £7.50 Additional incorrect working Ignore

[2]

19. (a) 160 ± 2 1

(b) 350 ± 5 1

280

(c) Indicates the correct position of Madrid within the tolerance 2

as shown on the diagram below

or

Indicates an angle of 195° ± 2° clockwise from north, within the 1 tolerance as shown on the diagram

or

Shows a length of 6.5 cm ± 0.2 cm, within the tolerance as shown on the diagram, even if it is incorrectly positioned

! For 2m, Madrid not labelled Condone provided the intended position is clear

! For 1m, angle indicated with a short line Accept provided the angle is within the tolerance as shown on the diagram, were the line to be extended

! For 1m, angle or length indicated by a point without a line joined to London Accept provided the angle or length is within the tolerance as shown on the diagram

[4]

20. (a) 31 or equivalent probability 1

(b) 3 1 ! Value rounded

Accept 0.33 or better, or the percentage equivalents [2]

281

21. (a) Gives the correct number of boys and girls, ie 1

Number of boys Number of girls

18....... 9....... (b) Gives the correct number of boys and girls, ie 1

Number of boys Number of girls

15....... 13....... (c) Gives the correct number of boys and girls, ie 1

Number of boys Number of girls

9....... 18....... ! Numbers correct but numbers of boys and girls transposed

Penalise only the first occurrence eg, for all three parts • 9, 18 13, 15 18, 9 Mark as 0, 1, 1

! Values given as tallies Condone provided they are grouped in fives

[3]

282

22. Draws only two more lines on the grid to make a pentagon with area 14 cm2 1

eg U1

! Lines not ruled or accurate

Accept provided the pupil’s intention is clear Do not accept more than two lines drawn eg • Given line(s) extended

[1]

23. 4410 1

2.5 or equivalent 1 ! For the second mark, answer given as an

improper fraction Accept only if fully simplified eg, accept

• 25

eg, do not accept

• 42

105

[2]

283