c practice 5 - all - the bemrose · pdf fileshape and space can you cope with ... this...

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NAME:__________

C Practice A collection of targeted

GCSE questions

C Practice 5 (set A) Student self assessment – Assess how good you think you are before you start each section (sheet)

Topic Sheet Objectives

A1 Write and understand numbers in terms of its factors including HCF and LCM

A2 The four rules of fractions A3 Change and order fractions, decimals and

percentages

A4 Find percentages of amounts and increase/decrease by percentages

A5 Mixed percentage questions A6 Substitution positive and negative

numbers into formula and expressions

A7 Simplifying algebraic expressions A8 Factorising algebraic expressions A9 Solving linear equations A10 Algebra mixture of substituting,

simplifying, expanding and factorising

A11 Angles – Parallel Lines A12 Interior and exterior angles of Polygons A13 Construction of triangles, quadrilaterals

and bearings

A14 Transformations – Reflections and Rotations

A15 Completing two way tables A16 Probability – particularly probability tables A17 Mixed bag - sequences (generalisation),

long multiplication, Simple Interest

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Can you cope with these questions? Decide how good you think you are before you look at the questions – are you confident, close or clueless

Make a note here of the areas of work that you still feel you need to improve on.

C Practice 5 The C Practice 5 sets of questions are based closely on the requirements of the EdExcel Modular GCSE course, targeting intermediate level entry. Set A – The seventeen question sheets provide a resource targeting the content of the Stage 1 Intermediate exam and include valuable questions on most of the areas tested. Set B – The twelve question sheets are targeted at the needs of the Stage 2 Intermediate paper Set C – Stage 3 is the final assessment and the 23 question sheets provide a comprehensive coverage of the likely content. These materials of course will also provide very suitable practice for all Intermediate GCSE examination course for mathematics.

C Practice 5 (set B) Student self assessment – Assess how good you think you are before you start each section


B1 Rounding to significant figures and decimal places

B2 Expressing numbers in standard form

B3 Sharing amounts in a given ratio

B4 Expanding brackets and factorisation of quadratic equations

B5 Solving algebra equations through trial and improvement. Formula questions

B6 Drawing straight line graphs

B7 Area and Volume (cuboids)

B8 Area and circumference of circles. Angles involved with tangents to a circle

B9 Pythagoras’ Theorem and Trigonometry

B10 Transformations – Scale factor Enlargement

B11 Stem and Leaf diagrams, Cumulative Frequency and Box Plots

B12 Pie Charts and Scatter Graphs

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C Practice 5

The three sets of C Practice 5 questions can be used in a number of ways –

They may be used as a starter activity at the beginning of the lesson to refresh minds of the topic to be learnt during that lesson.

They may prove useful as a round up of the work completed during a unit. They may prove useful as quick revision practice before the module tests.

C Practice 5 (set C) Student self assessment – Assess how good you think you are before you start each section


C1 Estimating solutions and rounding C2 Using Place Value and Lowest Common

Multiples

C3 Working with Indices and using standard form

C4 Finding percentages and percentage

increase and decreases

C5 Finding ratios of amounts and four rules of fractions

C6 Questions involving proportion C7 Number questions in context (money etc)

and Currency exchange

C8 Simplifying expressions involving expanding brackets

C9 Solving simple algebra inequalities and by

graph

C10 Algebra equations – linear, simultaneous and quadratic

C11 Straight line graphs C12 Travel graphs and curved graphs C13 Surface area and volume of prisms C14 Units of measure including length, area

and volume

C15 Finding angles in polygons Z C16 Circle Geometry – involving angles C17 Construction of triangles, perpendicular

lines and drawing nets

C18 Pythagoras’ Theorem and Trigonometry C19 Transformations – enlargement, and

elevations

C20 Estimates for means and moving averages

C21 Stem and Leaf, cumulative frequency,

box plots and quartiles

C22 Probability problems and Tables C23 Probability through probability Trees

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‘C’ Practice 5 (set A1)

Number: Factors and Multiples

1. List all of the factors of 48 2. If the product of the primes is:

2 x 2 x 3 x 5 What is the number?

3. What is the Highest Common Factor (HCF) of 16 and 40?

4. What is the Lowest Common Multiple of 12 and 18?

5. (a) Express 120 as a product of its Prime Factors (b) Express 75 as a product of its Prime Factors (c) Using the results above work out: (i) The HCF of 75 and 120

(ii) The LCM of 75 and 120


Number: Fractions

1. Work out: x Give your answer in its simplest form

2. Work out: +

3. Work out: ÷

4. Work out: x

5. (a) Write as an improper fraction (b) Write as an improper fraction (c) Work out: - Give you answer as a mixed number

1 2

4 5

1 8

3 4

2 3 4

2 3

4 5 1 1

3 2 3

1 5 6

3 2 3 1 5

6


Number: Fractions, Decimals and Percentages

1. Work out 0.8 as a fraction 2. Write 30% as a decimal

3. Put these in order of size, starting with the smallest: 0.3, 28%,

4. Express as a percentage

5. Complete this table

Fraction Decimal Percentage

0.375

70%

8%

1 4

2 5

16 64

3 2


Number: Percentages


1.

2. Increase £350 by 10% 3. SALE 20% OFF How much would a jacket priced at £90, cost in the sale?

5. A house cost £50 000 three years ago. I sold it for £90 000. What percentage profit have I made?

£120

17.5%

70%

20% 99%

5% 1%

50%

2.5%

10%

25% 35%

2%

4. The cost of a CD player is £200 + VAT. The rate of VAT is 17.5%. What is the cost of the CD player?


Percentages: General

1. Increase £250 by 10% 2. Fiona had £12.50 she gave 8% to charity, how much had she left?

3. The cost of a digital camera is 4. Put these in order of size. £240 plus VAT. Smallest first. The rate of VAT is 17.5%. What is the cost of the camera? 0.345, 1/3, 35%, 2/5 5. Here are 6 numbers:

0.8, 3/5, 75%, 80%, 2/3, 5/8 a. Circle the two numbers that are equal to 4/5 b. Explain why 5/8 is not 58%. c. What is 3/5 as a percentage?


Algebra: Substitution

1. If a = 3, b = 5 find the value of:

a) 2a + b

b) 2ab

2. When n = 8, evaluate the expression 3(2n - 2)

3. T = 3x + 4y

Find the value of T when x = -5 and y = 3.

4. Evaluate A = 3(2b – 4) when:

(i) b = -2 (ii) b = -5

5. Given that P = Q 2 - 2Q, find the value of P when Q = -3.


Algebra: Expressions

B#

‘

Find the perimeter of this shape:

5. 1. Simplify the expression:

4p + 9q + 5p – 3q

2. Simplify the expression:

5p 2 + 3q - p 2 + 2q

3. Multiply out:

6(4x – 3)

4. Find the perimeter of this shape:

4(x - 2)

3x

(t + 3)

(t - 1)

(t - 2)

5. Find the perimeter of this shape:

C’ Practice 5 (set A8)

Algebra: Factorising

1. Factorise 12x + 4. 2. Factorise 6x + 18y.

3. Factorise 8xy + 12x. 4. Factorise 6x 2 - 3xy.

5. (a) Multiply out each of these: 8(2x – 3) 3(4x + 1) (b) Now simplify this expression and factorise 8(2x – 3) + 3(4x + 1)


Algebra: Solving Equations

1. Solve the equation:

8x – 3 = 21


4(3n + 7) = 16


4(x + 2) = 6x + 4

4. Perimeter = 38cm

Find the value of t.

5. Solve the following equations:

(12 + x) = 5 3

3

x - 5 = 3

(t + 3)

(t - 1)

(t + 4)


Algebra: General

1. If T = x² - 6x 2. P = 4x – 3y Work out the value of T if x = -7 Work out the value of P

if x = -3 and y = 5 3. (a) Simplify 5q + 7q + 3p – 2q 4. (a) Expand 3(4x –2) (b) Factorise 6x + 18y (b) Factorise 4xy – 6x 5. Work out the value of x (x + 40)º 3xº


Angles (Parallel Lines)

1. Write down the size of angles x & y. 2. Write down the size of angles x Give reasons for your answers & y. Give reasons.

125º

62º 40º

3. 4. Find angles x & y. Give 28º reasons for your answers.

Find the angle marked g. Give a reason for your answer 5. Find all of the missing angles in this question, giving a reason for each. 21º 92º

x

y

x x

y

95º

g 68º 120º y

x

y

z


Shape and Space: Polygons

1. (a) What do the external angles total (b) What is the value of x?

2. The exterior angle of a regular polygon is 45°. How many sides has the polygon?

3. Find the value of x

4. Find the size of the interior angle of this regular octagon.

5. (a) Work out the size of the interior angle of the regular hexagon. (b) Use this information to work out the value of x.

x

x

x

x

x

34°

48°

107°

x 47°

63°

x


Shape and Space: Scale Drawing

1. Here is a sketch of a triangle. Draw it accurately

2. Here is a sketch of a quadrilateral Draw it accurately

3. Construct this triangle accurately AB = 5.3cm, BC = 6cm, Angle ABC = 112º

4. Measure the Bearing of (a) A from B (b) B from A

5. An airplane is at a bearing of 050º from Birmingham and 290º from Norwich. Shows its position on the map below

5cm

7cm

75º

4cm

5cm

6cm

140º

85º

x

x

B

A N

N

Birmingham

Norwich

x

x N

N


Shape and Space: Reflections and Rotations

‘

1. Draw a reflection of Triangle A in the given line

2. (a) Reflect triangle B in the x axis (b) Reflect triangle B in the line YZ

3. (a) Draw a reflection of C in the y axis and label C’ (b) Rotate C 90º clockwise about O and label C”

4. Rotate triangle D 45º anticlockwise about the point A. Label the new triangle D’.

5. (a) Reflect triangle A in the x axis and label B (b) Rotate triangle A anticlockwise 90º about O. Label C

A

y

x

Y

Z

B

C

y

x O

A ·

D

O

A

C’ Practice 5 (set A15)

Handling Data: 2 Way Tables

1. Each student in Y11 studies exactly one modern foreign language.

Complete this two-way table

2.

40 Students answered a question 24 of the students were girls 7 boys got the question correct 11 girls got the question incorrect Use this information to complete this 2 way table

3. Students were asked if they preferred baked, chipped, or mashed potatoes. Complete the two-way table

4. 100 adults were asked which sport they disliked most The two-way table shows some of the information about their answers

Complete the table.

5. Draw a two-way table to record whether boys and girls have completed their maths homework. Use this information to complete the table: 10 boys and 8 girls complete their homework. There were 15 boys and 14 girls in the class.

Total German

Spanish

French

Total 58 26

Female 32

Male 24 41 5

Total Girls Boys

Total

Incorrect

Correct

Boys 38 5 58

Girls 2 21

Total 65

Chips Total

mash

baked

Female 23 11 41 Male 24 59 Total 35 38 100

football rugby hockey

Total


Handling Data: Probability

1. The probability of it raining is 0.3. What is the probability of it not raining?

2. A train can be early, on time, or late. The probability of it being late is 0.63, the probability early: 0.1. What is the probability of it being on time?

3. Complete this probability table: Colour grey blue brown pink Prob. 0.1 0.3 0.2

Work out the probability of choosing blue.

4. Complete this table: Animal rabbit dog mouse cat Prob. 0.22 0.4 0.26

Work out the probability of a mouse

5. Complete this probability table (change all to decimals)

Colour green yellow red blue

Probability

5%

0.27

(a) Work out the probability of choosing yellow (b) What fraction chose green? (c) What percentage chose Blue?

3 10


Mixed Bag

1. Write the next two numbers in each sequence (a) 1, 5, 11, 19, 29 …..?

(b) -8, -2, 5, 13, 22, ….?

2. In each of these find the rule for the nth term. (a) 3, 7, 11, 15, ….. (b) -1, 4, 9, 14, 19, ……

3. Two girls get different answers: 3 + 4 x (5 – 2) = 15 3 + 4 x (5 – 2) = 21 (a) Who is correct? (b) Explain why

4. If 74 x 163 = 12062 Work Out: (a) 0.74 x 163 = (b) 12062 ÷ 740 = (c) 75 x 163 =

5. (a) What is the interest on £580 at 5% for 1 year? (b) What is the Simple Interest on £580 at 5% for 3 years? (c) What is the Simple Interest on £3800 at 4% for 2 years?

‘C’ Practice 5 (set B1)

Number: Accuracy and rounding

1. Write each of these numbers correct to 1 significant figure (a) 26 366 (b) 0.0004349 (c) 45 071 (d) 0.050869

2. Write each of these numbers correct to 2 decimal places (a) 54.26741 (b) 0.026638 (c) 526.8449 (d) 1.795

3. Work out the value of: (i) √59 – 3.4² (write all of the figures on the calculator display) (ii) Write down your answer to (i) correct to 2 significant figures.

4. Work out the value of: (a) Write all of the figures on the

calculator display (b) Write down your answer

correct to 2 decimal places

5. Alison said that the length of her kitchen was 3.5467m. The length given by Alison is not sensible. (a) Explain why her answer was not sensible What is the length of her kitchen to

(a) 1 significant figure (b) 2 decimal places

6.2 – 7.1² 0.7


Number: Standard Form

1. (a) Write 2.7 x 10³ as an ordinary number (b) Write 3.12 x 10 as an ordinary number

2. (a) Write 38 500 000 in standard form (b) Write 0.000005 in standard form

3. (a) Write half a million in standard form (b) Write 0.00000036 in standard form

4. Work out the value of 0.03 x 0.02 (a) Write the answer as an ordinary number (b) write the answer in standard form

5. List these numbers in order of size smallest to largest 3.7 x 10 ; 0.04 x 0.008; 2.6 x 10 ; 0.05 x 0.08

-3

-5 -6


Number: Ratio

1. Share £250 in the ratio 3:7 2. Ann and John share £140 in the ratio 2:5. How much does Ann receive?

3. Andy, Belinda and Carl share £126 in the ratio 5:3:1. How much does Belinda get?

4. When Bill reached his 100th birthday he had 12 grand daughters and 20 grandsons. Write down the number of grand daughters to the number of grandsons as a ratio in its simplest form.

5. The ratio of blue to black pens in a packet is 3:4 (a) What fraction of the pens are black? There are 35 pens in the packet. (b) How many more black pens than blue pens are there?


Factorisation and Quadratics

1. Factorise (a) x² + 2x =

(b) y² - 6y = (c) 8x² - 20xy =

2. Expand these brackets (a) 7(x + 3) = (b) x(x + 3) = (c) 2y(3y – 5) =

3. Expand these brackets (a) (x + 1)(x + 3) = (b) (x – 6)(x + 2) = (c) (x – 4)(x + 7) =

4. Factorise (a) x² + 3x + 2 = (b) x² + 7x + 12 = (c) x² + 2x – 15 = (d) x² - 2x – 35 =

5. Match an expression in cloud A with an expression in cloud B.

A

(a) x² + 5x + 6

(b) 3x² + 6x

(c) x² + 2x - 8

(d) x² - 4x - 5

(e) 8x² - 20x

B

(1) (x + 1)(x – 5)

(2) (x + 3)(x + 2)

(3) 4x(2x – 5)

(4) 3x(x + 2)

(5) (x – 2)(x + 4)


Algebra: Trial and Improvement + Formulae

1. Use trial and improvement to solve: x³ + 2x = 50 to 1 dec. place Where x lies between 3 and 4.

x x³ + 2x big/small 3 27 + 6 = 33 4

2. Use trial and improvement to solve: ½ x³ - x = 90 (1 dec. pl) Where x lies between 5 and 6

x ½ x³ - x big/small

3. Find the value of: (a) t² - 4t when t = 3 (b) p² - 3p when p = -4

4. If P = q² - 5q (a) Find P when q = -2 (b) Find P when q = ½

5. If I buy n first class stamps at 30p and m second class stamps at 22p. (a) Write a formula for the total cost (T) of buying these stamps. (b) I buy 5 first class stamps and the total cost is £3.26. How many second class stamps did I buy?


Graphs

1. Complete this grid for the function: y = 3x + 1

2. Complete this grid for the function: y = 2x - 5

3. Use the grid box from Q1 to plot & draw the graph of y = 3x + 1

4. Use the grid box from Q2 to plot & draw the graph of y = 2x - 5

5. Complete the grid box for the function y = ½ x + 7 Now plot the function y = ½ x + 7 on the grid provided

x -3 -2 -1 0 1 2 3

y -2 7

x -3 -2 -1 0 1 2 3

y -9 -3

-3 -2 -1 1 2 3

9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8

2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

-3 -2 -1 1 2 3

x

y y

x

x -3 -2 -1 0 1 2 3

y 6 8

-3 -2 -1 1 2 3

8 7 6 5 4 3 2 1

-1 -2

x

y


Shape and Space: Area and Volume

1. Work out the area of this trapezium. 13cm 7cm

10cm

2. Work out the volume of this cuboid.

10cm

15cm

3. A cuboid has: Height = 3m Length = 9m Width = 5m What is its volume?

4. A cuboid has: Volume = 160cm³ Length = 8 cm Height = 4 cm Work out the width of the cuboid

5. A box in the shape of a cube has sides of length 2 cm. These cube boxes are placed into a larger cuboid box with dimensions

Height = 8cm Length = 10cm Width = 6cm

How many cubed boxes fit into the cuboid box exactly?

6cm


Shape and Space: Circles

1. The radius of a circle is 6.4 cm. Work out the area of the circle. (Answer correct to 3 sig. figs)

2. The radius of a circle is 5.2 m. Work out the circumference of the circle. (correct to 2 d.p)

3 AT and BT are tangents to a circle centre O.

If angle AOB is 140º: (a) Name any right angles (b) Find the size of angle ATB

4. AS and AT are tangents to a circle centre O. Calculate the size of angle SAO if angle SOA is equal to 48º.

5. A cycle has a wheel diameter 0.8 m. The wheel goes round 25 times. How far has the cycle moved, give your answer correct to 3 significant figures

6.4cm 5.2m

A

B

O T A

S

T

O


Shape and Space: Trigonometry and Pythagoras

‘

1. A 9m B 5m C Use Pythagoras to work out the length of AC.

2. A 8.3m 2.5m B C Work out the length of BC

3. A B Calculate the length AB C

4. A 2.4m B 3.8m C

Find angle BAC.

5. The diagram shows the distance between three towns. Calculate the Bearing of Aitown from Beetown 9.5 km

15.2 km

24º

7.4cm

Beetown

Aitown Ceetown

C’ Practice 5 (set B10)

Shape and Space: Transformations

1. The big triangle is a scale factor enlargement of the smaller triangle. Find x and y

2. The big trapezium is a scale factor 4 enlargement of the smaller trapezium. Find x, y and z.

3. Enlarge this L by scale factor 2 about point A.

4. Enlarge this shape by scale factor ½ about point X.

5. Describe fully the single translation that takes shape A to shape B

x

15cm y

3cm

12cm

4cm x

5cm y

4cm

16cm

8cm

z 60º

A

X

A

B

‘C’ Practice 5 [less 1] (set B11)

Handling Data: Stem and leaf and cumulative frequency

1. Complete this stem and leaf diagram for the weights of 10 newly born boys.

4.1kg, 3.6kg, 4.5kg, 2.9kg, 3.8kg, 3.2kg, 3.6kg, 2.8kg, 3.7kg, 2.5kg

Weight of boys 2 3 6 4 1 5

2. The stem and leaf table shows the number of students late each day to school last month 1 2 3 3 6 6 8 9 2 0 1 1 5 6 9 3 0 0 2 2 2 4 6 7 (a) Find the median (b) Work out the range

3. 60 students took a test, the graph shows information about their marks

(a) What was the median mark? (b) What was the lowest mark? (c) Estimate how many students scored 12 or less marks. (c) Estimate the interquartile range?

4. This box plot shows information about 40 students’ test marks Decide which of these statements are true and which are false (a) The top mark was 57 (e) 10 students scored less than 31 (b) The lowest mark was 22 (f) The interquartile range was 44 (c) The Range was 35 (g) ½ the students scored less than 38 (d) The Median was 44

Key 1 2 means 12 students absent

60 55 50 45 40 35 30 25 20 15 10 5

2 4 6 8 10 12 14 16 18 20

Cumulative Frequency

Mark

20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 Mark


Handling data: pie charts and scatter graphs

1. Sixty Y11 students were asked – What do you want to do next year? Their replies are shown in the Pie chart

How many students hoped to go to college?

2.

3. Here is a scatter graph. One axis is labelled ‘Height’

(b) Circle the most appropriate label for the other axis –

GCSE maths mark No. of cousins

Size of feet Colour of eyes

4. For each scatter graph draw in probable correlations

5. Lose-a-lot Comprehensive School played 30 hockey matches. The table shows information about their results. Complete the Pie Chart.

60º 120º

College Sixth Form

Don’t Know

Work

2. Forty students took the Intermediate maths exam last year.

Grade ‘B’ - 3 Grade ‘C’ - 15 Grade ‘D’ - 14 Grade ‘E’ - 8

If these results were shown in a Pie Chart, what is the size of angle for each grade?

x x x x x x x x x x x x x x x x x x x x x x x x x x x

Height

(a) For this graph state the type of correlation

Height Height

Age Colour of eyes

Won Drawn Lost

7 3 20

‘C’ Practice 5 (set C1)

Rounding and Estimation

1. Estimate the value of: 79.7 _ 2.13 x 7.85

2. Estimate this 14.74 x 19.3 6.076 + 3.85

3. The length of a newly born baby is 56cm. (to the nearest cm) (a) What is the longest length (b) What is the shortest length That the baby can be?

4. The weight of a car is 843 kg (to the nearest kg). (a) What is the heaviest (b) What is the lightest weight that the car can be?

5. Using a calculator work out the value of – 14.23 x 3.98 2.31 + 5.84 (a) Write down the calculator display. (b) Write down the answer to the appropriate degree of accuracy.

No No


Place Value, LCM and Ordering

1. Using the information that 14 x 23 = 322 Write down the value of (i) 1.4 x 2.3 = (ii) 322 ÷ 2.3 =

2. Using the information that 58 x 117 = 6786 Write down the value of (i) 0.58 x 117 000 = (ii) 67.86 ÷ 5.8 =

3. Use the information that

11 x 19 = 209

To find the Lowest Common Multiple (LCM) of 33 and 19.

4. Use the information that

39 x 17 = 663 to find the Lowest Common Multiple (LCM) of 13 and 17.

5. Write these numbers in order of size. Start with the smallest number (i) 0.73; 0.084; 0.8; 0.82; 0.802 ……………………………………………… (ii) 4; -5; -9; 1; -3 ……………………………………………… (iii) 1 2 2 3 2 3 5 4 .................................................................


Indices and Standard Form

1. Work out the value of (3²)³ 2. Work out the value of – (i) 6 x 6 (ii) 6 ÷ 6

3. The approximate distance to the Sun is 93 000 000 miles. Write this number in standard form.

4. Work out

(6.1 x 10 ) x (5.8 x 10 ) Give your answer in standard form correct to 2 significant figures.

5. The number 28 can be written as 2 x n where m and n are prime numbers. Find the value of m and n.

5 4

m

3 5

7 4


Percentages

1. I spend 35% of £600. How much money have I left?

2. There were 250 pupils in Y10. 120 of these were girls. What is this as a percentage?

3. In the MIF kitchen sales, there was 20% off every kitchen. I paid £1200 for my kitchen units. What was their price before the sale

4. Wow TV/DVD player 30% off. New Price = £126

What is the normal price (pre sale price).

5. A new motor-bike costs £2400 but depreciates 10% in value each year. (a) What is its value after 1 year? (b) What is its value after 3 years?


Ratio and Fractions

1. Share £720 in the ratio 5:1 2. Share £320 in the ratio 1:3:4

3. Work out 3 - 2 4 3

4. Express 5 x 2 8 9 in its simplest form.

5. Amjad and Bhati share £270 in the ratio 2:7. (a) How much do Amjad and Bhati each receive? Amjad gives ¼ of his share to Chaz Bhati gives 4/7th of his share to Chaz. (b) How much does Chaz receive? (c) What fraction is this?


Proportion

1. If 8 pens cost 72p. How much do 5 pens cost?

2. If 3 coffees cost £4.17 What would 7 coffees cost?

3. These two triangles are similar Find x and y (lengths in cm)

4. A photo is enlarged as shown Show that these two rectangles are not similar (lengths in cm)

5. This recipe will make 12 cookies (a) How much sugar would you need for 18 cookies? (b) Rewrite the recipe to make 36 cookies.

20 30

y

x 12

5

65

50

90

70

150g butter 200g granulated sugar 300g of self-raising flour 100g of chocolate chips 1 egg A few drops of vanilla essence A pinch of salt


Money Questions and Currency Exchange

1. A class go on a visit by train. Each ticket costs £2.45. How much will 27 tickets cost?

2. The weight of a box is 17.6 kg. What is the weight of 38 boxes?

3. £1 = 1.47 euros An iPod costs 118 euros in Spain The same iPod costs £79.50 in Birmingham. Which is best value?

4. £1 = 2.15 Australian dollars What is the value of Aus $800 in pounds?

5. Prize money in a similar TV Challenge game in different countries is – USA - $100 000 where £1 = $1.85 Germany – 80 000 euros where £1 = 1.47 euros Which is the greatest prize and by how much.


Algebra: Expressions

1. Simplify: (i) x + y + x + y + x (ii) 4d + 5e – 3d – 2e

2. Expand and simplify: 2(4a + 2) – 3(2a – 4)

3. Simplify: (i) r² + r² + r² (ii) 3q² - q²

4. Simplify (i) 3a²b x 7ab³ (ii) (x + 2)² (x + 2)

5. This table shows some expressions Two of the expressions always have the same value as 6y. Tick the boxes underneath the two expressions

3(y + y) 3y + y 2y x 3y 3y + 3y 3 + 3y


Algebra: Inequalities

1. If -2 < m ≤ 4 And m is an integer Write down all of the possible values of m.

2. Given -3 ≤ p < 2 And p is an integer. Write down all of the possible values of p.

3. Solve the inequality 2x + 7 > 1

4. Solve the inequality 3y - 6 < 15

5.

1

2

3

4

-1

-1 1 2 3 4 O

The line with equation 2y + x = 4 is drawn on the grid. (i) On the grid, shade the region of points whose coordinates satisfy the four inequalities - y > 0; x > 0; 2x < 3; 2y + x < 4

y

x


Algebra: Equations (and simultaneous!)

1. Solve 4x – 9 = 13 2. Solve 15r – 4 = 7r + 12

3. Solve 6 – 5x = 2(2x – 6) 4. Solve x + 3y = 13 3x + 2y = 4

5. (i) Factorise x² - 5x - 12 (ii) Solve the equation x² - 5x - 12 = 0


Graphs: Straight Line

1. A straight line has equation y = 3x - 8 (i) Find the gradient of the line (ii) Find the intercept of the line

2. A straight line has equation y = 3(3 – 2x) Find the gradient of the straight line

3. A straight line has equation y = 3x + ½ Write down the equation of a line parallel to this line.

4. A `straight line has equation y = ½ x +3 The point P lies on the straight line. P has a y-coordinate of 5. Find the x-coordinate of P

5.

7

1 A

y

C

B

x 0

D

ABCD is a rectangle A is the point (0,1) C is the point (0,7) The equation of the straight line through A and B is y = 2x + 1. Find the equation of the straight line through D and C.

‘C’ Practice 5 [less 2] (set C12)

Graphs: Travel and curved

1. 2.

2. 4.

3. (a) Complete this table of values For y = x³ + x - 2 (b) On the grid draw the graph Of y = x³ + x - 2

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Time in minutes

34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2

Distance in km from Mo’s house

This is part of a travel graph of Mo’s journey from his house to the Sports Hall and back. (i) Work out Mo’s speed for the first 30 mins of his journey. Give your answer in km/h. Mo spent 10 mins at the Sports Hall collecting his sister. Then travels back to the house at 60 km/h. (ii) Complete the travel graph

12 noon 1pm 2pm 3pm 4pm 5pm time

20 18 16 14 12 10 8 6 4 2

Distance from home in km

A girl left home at 12 noon to go for a cycle ride. The travel graph represents part of the journey. At 12.30 pm the girl stopped for a rest (i) For how many minutes did she rest? The girl stopped for another rest at 2 pm. She rested for one hour. Then she cycled home at a steady speed. It took her 1hr 30 mins. (ii) Complete the travel graph

x -2 -1 0 1 2 -12 0 y

-2 -1 1 2

10 8 6 4 2

-2 -4

-6 -8 -10

x

y

O


Shape and Space: Surface Area and Volume

1. 2.

3. 4.

5.

20 cm²

12 cm

The area of the cross section of the triangular prism is 20 cm². The length is 12 cm Work out the volume of the prism.

4

7

9 10

All measurements are in cm.

Work out the surface area of this triangular prism

10cm

5 cm The cylinder has a height of 10cm and a radius of 5cm. Calculate the volume of the cylinder.

10 cm

3cm Radius = 3cm Height = 10 cm Calculate surface area correct to 3 significant figs.

4.2 cm

1.9cm

This solid cylinder of ice has radius 4.2cm and a thickness of 1.9cm. The ice has a density of 0.9 grams per cm³ Work out the mass of the ice, correct to three significant figures.


Shape and Space: Units change; Measures Length, Area, Volume

1. Change 4m² to cm² (Be careful!) 2. Change 45 cm² to mm².

3. In these expressions a, b and c represent lengths. The numbers have no dimension. Two of the expressions could represent areas, tick the box underneath these expressions

4. In these expressions a, b and c represent lengths. π and 2 have no dimension. Three of the expressions could represent areas, tick the box underneath these expressions

5. In these expressions a, b, c and d represent lengths. π and 2 have no dimension.

The expressions could represent either: length(L), area(A) or volume(V) or none(N) of these. Write in the box underneath each expression whether it is length, area, volume or none. 2a² πa²b 2a³ a(b + c) ab + cd 2a² - πb 2d(ab + c²) πa 2

(a+b)c ac + b 3abc 3a² + 2b² ab + bc 2a

πa³ 2ab πa² + b² π(2a + b) a(b + c)


Shape and Space: Polygons and Angles

1. Work out the exterior angle of an octagon.

2. (i) Work out angle x (give reasons) (ii) Work out angle y (give reasons)

3. ABCD is a quadrilateral, work out the size of the largest angle.

4. Work out the size of the missing angles in this pentagon.

5.

108º xº

yº

B

yº 73º D C

A

3yº 119º

(x + 47)º

(2x + 20)º

xº

106º 87º

ABCD is a rhombus. All the sides of the shape are equal in length. Work out the size of each of the angles. B D

C

A E

?


Shape and Space: Circle Geometry

1. 2.

3. A, B, C and D are points on a circle. Angle ADB = 54º Work out angle ACB Give a reason for your answer.

4.

5.

A B

C

If AB is the diameter of the circle, give a reason why angle ACB is a right angle

A

B

C

D

115º Given angle BCD equals 115º. (i) Work out the size of angle BAD. (ii) Give a reason for your answer

54º

A B

D C

x B

O

C

D

96º

A In the circle centre O the angle BOD = 96º (i) Find angle BAD (ii) Work out Angle BCD.

A

B

C D E

35º

60º

A, B, C and D are 4 points on the circumference of a circle. Angle BAC = 35º. Angle EBC = 60º (i) Find the size of angle ADC. (ii) Find the size of angle ADB.


Shape and Space: Construction

1. Use ruler and compasses to construct an equilateral triangle of side length 3cm.

2. Construct a triangle of sides length 3cm, 4cm and 5cm.

3. Use ruler and compasses to construct a perpendicular to the line AB at point P.

4. Use ruler and compasses to construct a right angle.

5. The diagram shows a triangular prism The cross-section of the triangular prism is an equilateral triangle Draw a sketch for the net of the triangular prism

B

A

P X


Shape and Space: Trigonometry and Pythagoras

1. Find the length of AC in this right angled triangle.

2. Find the length of AC in this right angled triangle.

3. Find the size of the angle marked x. Give your answer to 1 dec. pl.

4. Find the length of AB. Give your answer correct to 3 significant figs.

5. A lighthouse L is due East of a harbour, H. A yacht Y is 3.2 km due North of the lighthouse. (a) Find the distance of the yacht from the harbour HY (b) Calculate the size of the angle marked x. Give your answers correct to 3 significant figures.

C

A B 5 cm

12cm

A B

C

10.5cm

17.5cm

x

10cm 12cm

A

B C

70º

5.2cm

L

Y

H

3.2

3.7

xº


Shape and Space: Elevations and Transformations

1. On the grid enlarge the shape with a scale factor of 2

2. On the grid enlarge the shape with a scale factor of ½.

3. Given the elevations of a 3D shape sketch it below.

4. The diagram shows a solid object Draw a plan, front and side elevation for this object

5. Here is a plan and front elevation of a prism (ii) Make a 3D sketch of the prism

plan front elevation

side elevation

(i) On the grid draw a side elevation

Front elevation

plan


Handling Data: Means and Moving Averages

1. The table shows how much TV 20 students watched in a week.

No. of hours Frequency 0<h≤20 8

20<h ≤40 7 40<h≤60 5

Work out an estimate for the mean number of hours that students watched the TV.

2. This table shows how much money 25 students had at school.

Amount (£) Frequency 0<t≤4 11

4<h ≤8 3 8<h≤12 11

Work out an estimate for the mean amount of money that each student has.

3. The table shows the number of flower bouquets delivered each day of a week day Mon Tue Wed Th Fri Sat No. 12 8 13 15 14 19

Work out the 3 day moving average for this data.

4. The table shows the daily takings for an ice-cream salesman.

Day Mo Tu We Th Fr Sa Su (£) 50 36 24 90 130 156 264

Work out the 4 day moving average for this data

5. The table shows information about how much 50 students earn from their part-time jobs per week

Amount (£) Frequency 0<a≤10 6

10<a ≤20 4 20<a≤30 12 30<a≤40 6 40<a ≤50 16 50<a≤60 6

Work out an estimate for the mean amount each receives.

‘C’ Practice 5 [less 1] (set C21)

Handling Data: Mixture

1. Shahid listed the number of goals scored by each team in his local hockey league in order - 7, 12, 13, 18, 19, 24, 31, 34, 39, 42, 56

Find (i) The lower quartile (ii) The upper quartile

2. Here are the times, in minutes taken to complete maths homework 12, 25, 19, 24, 27, 31, 37, 11, 28, 29, 35, 38, 10, 11, 27, 32, 29, 16 Draw a stem and leaf diagram to show this.

3. 4.

4. This box plot shows information about the time taken for 24 girls at the swimming club to swim 800m in training.

3. 100 students took a test, the graph shows information about their marks

0 10 20 30 40 50 60 70 80 90 100

100 90 80 70 60 50 40 30 20 10 0

marks

No. students (i) Estimate the lowest and highest marks? (ii) Estimate the median score? (iii) Find the inter-quartile range?

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Describe the times of the swimmers with reference to median, slowest, fastest and inter-quartile range.

mins


Handling Data: Probability and Tables

1. Mrs Green, the head of the Sports College, plays one sport every day. She chooses hockey, swimming or netball. The probability she chooses hockey is 0.3. The probability she chooses netball is 0.25. What is the probability she chooses swimming?

2. 120 people who buy coffee were surveyed as follows – powder granules filter Total 50g 2 4 0 100g 15 21 50 200g 12 Total 55 120 Complete the two-way table

3. A box contains cubes that are red, yellow, blue and purple. The probability of taking a cube of a certain colour is shown in the table. Colour red yellow blue purple Prob 0.15 0.3 0.4 Work out the probability that you will take a purple cube.

4. A packet contains sweets with flavours mint, fruit, cola, fizz and choc The probability of taking a flavour of sweet is shown in the table. Flavour mint fruit cola fizz choc Prob 10% 0.35 0.15 25%

Work out the probability that you will take a choc flavoured sweet.

5. A dice is biased The probability that the dice will land on each of the numbers 1, 3 and 4 is given in the table. The probability that the dice will land on either a 2, 5 or 6 are equal. Number 1 2 3 4 5 6 Probability 0.2 x 0.15 0.2 x x (i) Work out the value of x (ii) The dice is thrown 200 times Write an estimate for the number of times it will land with a 3.

6 5

4


Handling Data: Probability and Probability Trees

1. Shay throws a dice 60 times. He scores 6 twenty times. Is the dice fair? Explain.

2. The probability of a green light at traffic lights is 50%. What is the probability of hitting green lights at two consecutive traffic lights?

3. Complete this Probability tree for throwing a fair red dice and a fair blue dice.

4. Look at question 3. What is the probability of not throwing a six with either a red or a blue dice?

5. We have 10 CDs in the car. Four belong to my mother and are by Cliff Richard. I take one of these CDs at random and play it and then put it back. I then take another CD at random to play.

(i) Complete this probability tree diagram (ii) What is the probability of picking a Cliff Richard CD twice?

six

Not six

Red Dice

Blue Dice

1 6

Cliff Richard

Not Cliff Richard

Cliff Richard

Not Cliff Richard

Not Cliff Richard

Cliff Richard

0.4

…….

…….

…….

…….

…….

six

six

Not six

b

c practice 5 - all - the bemrose · pdf fileshape and space can you cope with ... this...

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