Edexcel GCSE Maths Grade 1-3 Workbook

Contents

How to use this book

1

Multiples, factors and primes 1

1.1 Multiples 1.2 Factors 1.3 Prime numbers 1.4 Lowest common multiple and highest common factor 1 Problem solving

iv

1 2 4 5 7

2 Fractions, decimals and percentages 9 2.1 Equivalent fractions 9 2.2 Arithmetic with fractions 10 2.3 Fractions and decimals 12 2.4 Percentages 13 2.5 Working with fractions and percentages 14 2 Problem solving 16

3

Working with numbers

3.1 Order of operations 3.2 Powers and roots 3.3 Rounding numbers 3.4 Standard form 3.5 Units 3 Problem solving

4 Sequences of numbers 4.1 Describing a sequence 4.2 Recognising sequences 4.3 The nth term of a sequence 4 Problem solving

5

Coordinates and graphs

5.1 Coordinates 5.2 The equation of a straight line 5.3 Intercept and gradient 5.4 Quadratic graphs 5 Problem solving

18 18 19 20 22 23 24

26 26 27 28 30

32 32 33 35 37 40

6

Expressions and equations 42

6.1 6.2 6.3 6

Substituting into formulae Simplifying expressions Solving equations Problem solving

42 43 44 45

7

Ratio and proportion

7.1 7.2 7.3 7.4 7

Ratio notation 47 Dividing using a ratio 49 Proportion 50 Ratios and fractions 52 Problem solving 54

8 Percentages 8.1

47

56

8.2 8.3 8

One number as a percentage of another Comparisons using percentages Percentage change Problem solving

56 57 59 60

9

Angles and polygons

62

9.1 Points and lines 9.2 Triangles 9.3 Quadrilaterals and other polygons 9.4 Shapes on coordinate axes 9 Problem solving

10

62 63 64 66 68

Perimeter, area and volume 71

10.1 Perimeter and area 10.2 Circles 10.3 Solids 10 Problem solving

71 73 75 77

11 Transformations

80

11.1 Reflections 11.2 Translations and rotations 11.3 Enlargements 11 Problem solving

80 81 83 85

12 Probability 12.1 12.2 12.3 12

Relative frequency Calculating probabilities Possibility spaces Problem Solving

13 Statistics 13.1 13.2 13

Tables, charts and diagrams Calculating statistics Problem solving

Answers

87 87 88 90 92

94 94 96 98

101 iii

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How to use this book This workbook aims to help you build your confidence and surpass your expectations in your Mathematics GCSE. It gives you plenty of practice, guidance and support in the key topics and main sections that will have the most impact when working towards grades 1–3.

These sections are colour coded: Number, Algebra, Ratio, Proportion and Rates of Change, Geometry and Measures, Probability and Statistics.

Question grades You can tell the grade of each question or question part by the colour of its number: Grade 1 questions are shown as 1 Grade 2 questions are shown as 1 Grade 3 questions are shown as 1

Use of calculators Questions when you could use a calculator are marked with a

icon.

Hint: A common factor of 18 and 27 is a factor of both numbers.

1 Multiples, factors and primes

Hint boxes

The ‘Hint’ boxes provide you with guidance as to how to approach challenging questions.

Key words The ‘Key Words’ 1.1 boxesMultiples highlight important terms and mathematical language

Key words multiple

that you will need to understand for your exam. Definitions are provided in the Here are some multiples of 5. Write down the next three. glossary at the end of the1 workbook.

Problem solving

20, 25, 30, 35, 40,

,

common multiple

,

2 of Here are thesolving first fivequestions. multiples of Write next three. solving and This section gives examples problem It 7. helps todown buildthe your problem communication skills.

7, 14, 21, 28, 35,

Checklists

3

,

,

What is another name for the multiples of 2?

At the end of each chapter, a checklist is provided that lists the key skills and knowledge that have been covered.

Use it to identify what you have mastered and what you may still need to work on. By checking off each skill, you will be putting yourself 4 in the best position to tackle your exam.

List the first six multiples of 11.

Answers You will find answers to all the questions in the tear out section at the back of the book. If you are working on your 5 List all the multiples of 20 that are less than 150. own you can check your answers yourself. If you are working in class your teacher may want to go through the answers with you.

6

List the multiples of 3 between 20 and 40.

7

Find a number that is a multiple of 4 and a multiple of 5.

8

Look at these numbers 90

91

92

a Put a circle

iv

How to use this book b Put a square

93

94

95

96

97

98

99

100

around each multiple of 3. around each multiple of 4.

c Which number in the list is a common multiple of 3 and 4?

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5 Coordinates and graphs 5.1 Coordinates

Key words coordinates

1

y 5

midpoint

4

axis vertices

3 B

A

2

vertex

1 −5 −4 −3 −2 −1 O −1

1

2

3

4

5 x

−2

a Write down the coordinates of the other three vertices, A, C and D.

−3 C

The coordinates of B are (−3, 2).

−4

A=

D

−5

C=

D=

b The midpoint of AB is (0, 2). Mark it with a cross.

Hint: Half way between A and B c Put a cross on the midpoint of each of the other sides. Write down their coordinates.

2

y 5

a Put these points on the grid. Join them in order with straight lines.

4

(5, 1) (5, 3) (1, 5) (−3, 3) (−3, 1) (1, −1) (5, 1)

3

b You have drawn a hexagon. Draw the diagonals by joining opposite corners.

2 1 −5 −4 −3 −2 −1 O −1

1

2

3

4

5 x

c Write down the coordinates of the point where the diagonals meet.

−2 −3 −4 −5

32

5 Coordinates and graphs

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3

y 5 4 3 2 1 −5 −4 −3 −2 −1 O −1

1

2

3

4

5 x

−2 −3 −4 −5

a Mark each point with a cross. (3, 0) (−1, 2) (5, −1) (−3, 3) b Join the points with a straight line. c Write down the coordinates of the point where the line crosses the y axis.

4

y 5

a Mark five points with an x-coordinate of 2.

4

b Join them with a straight line.

3

c Mark five points with an y-coordinate of −4.

2

d Join them with a straight line.

1 −5 −4 −3 −2 −1 O −1

1

2

3

4

5 x

e Write the coordinates of the point where they cross.

−2 −3 −4 −5

5.2 The equation of a straight line 1

C

equation

y 5

A

B

a The equation of line A is x = 3.

4 3

F

2 1 −5 −4 −3 −2 −1 O −1

Key word

Write down the equation of Line B

line C

b The equation of line D is y = −2.

1

2

3

4

5 x

−2

D

−3

E

Write down the equation of

line E

−4 −5

line F.

5.2 The equation of a straight line

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33

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2

a Work out the following. i

ii

−1 + 3 =

iii

−2 + 3 =

−5 + 3 =

b Complete the following table. x

2

y=x+3

5

c

0

−4

The table gives the coordinates of four points. Plot them on the grid.

y 5 4

d Join the points to show the straight line y = x + 3.

3 2 1 −5 −4 −3 −2 −1 O −1

−2

1

2

5 x

3

4

ii

2 × −3 =

e Write down the coordinates of two more points on the line y = x + 3.

−2 −3 −4 −5

3

a Work out the following. i

2 × −2 =

iii

2 × −5 =

b Complete the following table. x

−2

−1

y = 2x c

0

1

2

−2 y 5

The table gives the coordinates of five points. Plot them on the grid.

4

d Join the points to show the straight line y = 2x.

3 2 1 −5 −4 −3 −2 −1 O −1

1

2

3

4

5 x

e Write down the coordinates of one more point on the line y = 2x.

−2 −3 −4 −5

34

5 Coordinates and graphs

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5 Problem solving 1

y 6 4 2

−6

−4

O

−2

2

4

6 x

−2 −4 −6

a Plot A(6, 3), B(−4, 3) and C(6, −3). b Write down the coordinates of the midpoint of AB.

Hint: Draw AB.

c Write down the coordinates of the midpoint of AC. d Work out the equation of the straight line through A and B. e Draw the line y = x f Write down the coordinates of the point where AB and y = x cross. g A, B and C are three vertices of a rectangle.

Write down the coordinates of the fourth vertex.

2

y 9 8 7 6 5 4 3 2 1 −3 −2 −1 0

40

1

2

3 x

5 Coordinates and graphs

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a Complete the following table. x

0

1

3x

2

3

6

b Draw the line y = 3x c Write down the gradient of the line y = 3x. d Complete the following table. x

−3

x+6

3

−2

−1

0

1

2

3

8

e Draw the line y = x + 6. f Write down the gradient of the line y = x + 6. g Write down the intercept on the y-axis of y = x + 6. h Complete the following table. x

−3

x2

−2

−1

0

1

2

4

3

4

i Draw the curve y = x2 j Write down the coordinates of the point where the three lines meet.

Checklist I can plot points with positive or negative coordinates draw a straight line from its equation find the gradient of a straight line find the intercepts of a straight line, i.e. where it crosses the axes draw a simple quadratic curve.

5 Problem solving

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