web view1/11/2017 · the l-shape below has an area of 12 cm2all corners are right...

GCSE Exam Revision: Scalby School

Q1. This shape is made from five cubes.

Draw what the shape looks like when seen from A, B and C.

Which view is i) The front elevation ………. ii) The plan view ……..

iii) Side elevation ……..


Q2.The diagram shows a badge made from two similar pentagons.

Not drawnaccurately

Work out the width of the badge.

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Answer ................................................................ cm(Total 5 marks)


Q3. You need a ruler and compasses to answer this question.

A map of an island is shown on the centimetre grid below.

Treasure is buried on the island.

The treasure is nearer to point A than B.

The treasure is within 5cm of point B

Shade the region as to the places where the treasure could be.(Total 3 marks)


Q4. ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

S = square numbers

E = even numbers

(a) Complete the Venn diagram.

(3)

(b) One of the numbers is chosen at random.

Write down P (S ∩ E)

Answer ............................................(1)

(Total 4 marks)


Q5. The perimeter of the rectangle is 37 cm.

Not drawnaccurately

x

x + 3

Work out the value of x.

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x = ...................................................................... cm(Total 3 marks)

Q6. Write an expression that represents the area of the shape below.

Not drawn accurately

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Q7. The L-shape below has an area of 12 cm2

All corners are right angles.All lengths are in centimetres.

Not drawnaccurately


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Answer ................................................................ cm(Total 4 marks)


Q8. The diagram shows a rectangle.

(a) Write down an expression for the perimeter of the rectangle.

Simplify your answer.

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Answer ......................................................................(2)

(b) Write down an expression for the area of the rectangle.

Simplify your answer.

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Answer ......................................................................(2)

(c) You are given that a and b are prime numbers.The area of the rectangle is 315 cm2

Work out the values of a and b.

Answer ..................................... cm and ..................................... cm(2)


Q9. A parallelogram and a trapezium are shown.All lengths are in centimetres.

The area of the parallelogram is equal to the area of the trapezium.


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x = ....................................................... cm(Total 4 marks)


Q10. The diagram shows two rectangles.

Not drawn accurately

Show the shaded area, in cm2, is given by 12x2 − 9x + 6

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Q11. Solve the simultaneous equations

2x − 3y = 24

6x + 2y = −5

You must show your working.

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Answer ......................................................................

Q12. Solve the simultaneous equations

3x − 4y = 20

4x − 2y = 25

You must show your working.

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Answer ......................................................................

GCSE Exam Revision: Scalby SchoolQ13. At a fish and chip shop

2 fish and 1 portion of chips cost £10.05 3 fish and 4 portions of chips cost £19.20

Work out the cost of 4 fish and 3 portions of chips.

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Answer £ ....................................................................

Q14. 3 fence panels and 4 posts cost £82.975 fence panels and 6 posts cost £131.95

Rav builds fences.

He says,

“£200 should be enough for 8 panels and 9 posts”

Is he correct?You must show your working.

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.................................................................................................................................(Total 6 marks)

GCSE Exam Revision: Scalby SchoolQ15.


M1.A

Only outline needed. Can be anywhere on gridInternal lines not necessary (may be dashed)Shape may be shaded (even in chequer-board fashion)

B1

Only outline needed. Can be anywhere on gridInternal lines not necessary (may be dashed)Shape may be shaded (even in chequer-board fashion)

B1

C

Any orientation (as shown)Only outline needed. Can be anywhere on gridInternal lines not necessary (may be dashed)Shape may be shaded (even in chequer-board fashion)

B1[3]

M2. oe

Scale factor 3 or seen or impliedM1


3x (x + 4) = 36x oe36 ÷ 3 (= 12)

M1

3(x + 4) = 36 oetheir 12 − 4

or 3x2 + 12x = 36xM1

3x + 12 = 36(x =) 8

or x + 4 = 12

or x = 8or their 8 × 3

or 3x2 − 24x = 0

or 3x2 = 24xM1

(3x =) 2424

A1[5]

M3. Two pairs of intersecting arcs with equal radii from centres A and B


M1

Straight line between the intersecting arcs (may go outside the island and / or not be all the way across the island)

A1

Line goes all the way across the island but no furtherMust have gained M1ft their lineStrand (ii) Accurate interpretation of contextSC1 Line in tolerance but no arcs

Q1ft[3]


M4. (a)

B2 Any 2 or 3 of the 4 sections correctB1 Any 1 of the 4 sections correct

B3

(b) oeft their Venn diagram

B1ft[4]

M5.x + x + 3 + x + x + 3 (=37) oe(2x + 3) × 2 condone missing brackets37 − 6

M1

4x + 6 = 37

or 4x = 37 − 6oe


M1dep

(x =) 7.75 oeA1

[3]

M6.3x or 2x seen for missing sidesMay be on diagram or in working

B1

4x + 4x + 2x + 3x + 2x + x (= 56) oe16x implies B1M1

M1

their 16x = 56M1

3.5 or or

SC2 for or 5.09… or 5.1

SC2 for or 4.3…SC2 for 4SC applies if method marks not awarded.

A1ft[4]

GCSE Exam Revision: Scalby SchoolM7.1 × x or 3 × (x + 2)

or 1 × (3 + x ) or 3 × (x + 1)Shows the area of any appropriate rectangleAllow invisible brackets

M1

x + 3(x + 2)or (3 + x ) + 3(x + 1)

Allow invisible bracketsM1dep

x + 3x + 6 = 12or 3 + x + 3x + 3 = 12

oe eg 4x + 6 = 12Invisible brackets expanded correctly

M1dep

1.5oe

A1

Alternative method 1

(x + 2)(x + 3) or x(x + 1)Allow invisible brackets

M1

(x + 2)(x + 3) − x(x + 1)Allow invisible brackets

M1dep

x2 + 2x + 3x + 6 − x2 − x = 12oe Invisible brackets must be expanded correctly

M1dep


1.5

oe eg A1


Guess a value for x and correctly works out area below 12 cm2

eg x = 1 gives (1 + 9) = 10or (4 + 6) = 10x = 0.5 gives 8

M1

Guess a value for x and correctly works out area above 12 cm2

eg x = 2 gives (2 + 12) = 14or (5 + 9) = 14x = 2.5 gives 16, x = 3 gives 18,x = 3.5 gives 20

M1

Tries a value between 1 and 2 and correctly works out areaM1dep

1.5oeSC2 3 × 3.5 and 1 × 1.5 seenor 3 × 2.5 and 1 × 4.5 seen

A1[4]

M8.(a) 3a + 5b + 3a + 5boe

M1

GCSE Exam Revision: Scalby School6a + 10b or 2(3a + 5b)

oe do not ignore fw for final markA1

Additional Guidance

3a + 5b × 2 = 6a + 10b (recovered)M1A1

3a + 5b × 2M1A0

(3a + 5b)2M1A0

6a10bM1A0

3a × 2 + 5b × 2M1A0

3a × 2 5b × 2M0A0

(b) 15abB1 for 3a × 5bB1 for partially simplified answerB1 for 15 × ab

B2

Additional Guidance

Penalise further working, e.g. 3a × 5b = 15ab = 3(5ab) gets B1

15baB2

A = 15abB2

A(15ab)B2

15ab cm2

B2

A(3a × 5b)

GCSE Exam Revision: Scalby SchoolB1

(3a)(5b)B1

3a5bB1

15(ab)B1

3(5ab)B1

ab15B1

(15ab)2

B015ab2

B0(3a × 5b)2

B03a × 5b2

B0

(c) 315 ÷ 15 or 21 seenM1

7 and 3 in any orderSC1 for 15 and 21or 9 and 35

A1

Additional Guidance

1 and 21 on the answer lineM1A0

[6]

M9.

5(x + 3) (=) × 6 × (x + 12)

oe e.g. 5x + 15 (=) × 6 × (12 − x) + 6x


B1 5(x + 3) or × 6 × (x + 12)oe

B2

5x − 3x = 36 − 15Collects like termsft their areas but must have at least B1 and have both areas in terms of x

M1

10 oe ft from B1 M1Do not ft if negative solution

A1ft[4]

M10.(a) 3x(4x + 1) − 2(6x − 3)if expanded straight away allow one sign or arithmetic error eg 12x2 + 3x − 12x − 6 (Must have an x2 term, 2 ‘x’ terms and a constant term)Condone missing brackets eg3x × 4x + 1 − 2 × 6x − 3

M1

12x2 + 3x − 12x + 6A1

(b) 12x2 − 9x + 6 = 6

or 12x2 − 9x = 0

or 12x2 = 9xoeIf their equation in (a) is 12x2 − 9x − 6 leading to 12x2 − 9x − 12 = 0 award M1

M1


x(12x − 9) or 3x(4x − 3) or x(4x − 3)

or 12x = 9

use of formula or completing the square oe

or oe

from equation aboveM1dep

x = oeIf x = 0 given do not award A1

A1[5]

M11. Alternative method 14x − 6y = 48and18x + 6y = −15

6x − 9y = 72

(and6x + 2y = −5)

oeEquating coefficients

M1

22x = 33

or x = 1.5

−11y = 77

or y = −7oeElimination of one variable

GCSE Exam Revision: Scalby SchoolM1 dep

x = 1.5 and y = −7oeSC1 for x = 1.5 and y = −7 withoutworking or using trial and improvement

A1


oeRearranging

M1

22x = 33

or x = 1.5

−11y = 77

or y = −7oeElimination of one variable

M1 dep

x = 1.5 and y = −7oeSC1 for x = 1.5 and y = −7 withoutworking or using trial and improvement

A1[3]

M12.8x – 4y = 50

or

12x – 16y = 80

and 12x – 6y = 75

GCSE Exam Revision: Scalby Schooloeallow one error

M1

5x = 30

or x = 6

–10 y = 5

or y = oecorrect elimination of one unknown for their equations

M1 dep

x = 6 and y = oeSC1 correct answer without working or with use of trial and improvement

A1

Alternative method

x = or y =

or x = or y = oeallow one error

M1

10x = 60

or x = 6

10y = −5


or y = oecorrect elimination of one unknown for their equations and simplification to two terms

M1dep

x = 6 and y = oeSC1 correct answer without working or with use of trial and improvement

A1[3]

M13.8f + 4c = 40.2(0)

and

3f + 4c = 19.2(0)

6f + 3c = 30.15

and

6f + 8c = 38.4(0)oeallow one error

M1

5f = 21(.00)

5c = 8.25oe correct elimination of one unknown for their equations

M1dep

(f =) 4.2(0)

GCSE Exam Revision: Scalby School(c =) 1.65

A1

21.75oe

A1


3f + 4(10.05 − 2f ) = 19.2(0)

or + c =10.05oeallow one error

M1

5f = 21(.00)

5c = 8.25oe correct elimination of one unknown for their equations

M1dep

(f =) 4.2(0)

(c =) 1.65A1

21.75oe

A1


GCSE Exam Revision: Scalby School5f + 5c = 29.25

M1

f + c = 29.25 ÷ 5 or f + c = 5.85M1dep

(f =) 4.2(0) or (c =) 1.65A1

21.75A1


5f + 5c = 29.25M1

f + c = 29.25 ÷ 5 or f + c = 5.85M1dep

2f + 2c = 10.7(0)A1

21.75A1

[4]

GCSE Exam Revision: Scalby SchoolM14.

3f +4p = 82.97Or5f + 6p = 131.95

Must be algebraic not word formM1

9f + 12p = 248.91And10f + 12p = 263.90

or 15f + 20p = 414.85and15f + 18p = 395.85Condone one error in totals

M1

f = 14.99A1

p = 9.5(0)A1

£205.42B1ft

Logical argument with steps shown and correct conclusion madeMust gain method marks and make conclusion QWC strand iii

Q1ft

Alternative method3f +4p = 82.97Or5f +6p = 131.95

M1

15f + 20p = 414.85and15f +18p = 395.85

M1

p = 9.5(0)A1

GCSE Exam Revision: Scalby School82.97 + 131.95 − their 9.5(0)or 214.92 − their 9.5(0)

Subtracting cost of one post from total of 8 panels and 10 posts

M1

£205.42ft their 9.50

A1 ft

Logical argument with steps shown and correct conclusion madeMust gain method marks and make conclusion QWC strand iii

Q1 ft[6]

web view1/11/2017 · the l-shape below has an area of 12 cm2all corners are right...

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