AQA 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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1 Multiples, factors and primes Key words

1.1 Multiples 1

multiple

20, 25, 30, 35, 40,

2

common multiple

Here are some multiples of 5. Write down the next three. ,

,

Here are the first five multiples of 7. Write down the next three.

7, 14, 21, 28, 35,

,

,

3

What is another name for the multiples of 2?

4

List the first six multiples of 11.

5

List all the multiples of 20 that are less than 150.

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 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?

1.1 Multiples

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9

a Write down the first six multiples of 4.

b Write down the first six multiples of 6.

c Write down two common multiples of 4 and 6.

10

a Write down the first six multiples of 15.

b Write down the first nine multiples of 10.

c Write down three common multiples of 15 and 10.

d Find the smallest common multiple of 15 and 10.

11

Find five common multiples of 2 and 3.

1.2 Factors

Key word factors

1

15 = 1 Ă— 15

15 = 3 Ă— 5

Use these facts to write down the four factors of 15.

2

List all six factors of the number 20.

3

Two factors of 100 are 2 and 5.

Use this fact to work out two more factors of 100.

2

1 Multiples, factors and primes

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4

Here is a list of numbers.

1

2

3

4

5

6

From the list write down the factors of

5

a 8

b 12

c 15

d 17

a Write down the six factors of 18.

b Write down the four factors of 27.

c Write down the common factors of 18 and 27.

Hint: 6

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

a Write down the five factors of 16.

b Write down the six factors of 28.

c Write down the common factors of 16 and 28.

7

Find three common factors of 20 and 50.

8

121 has three factors. Two of them are 1 and 121. Find the other factor.

1.2 Factors

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1 Problem solving 1

60 chairs are put into rows in a hall. There are the same numbers of chairs in each row. All the chairs are used. a Show that there could be 10 chairs in each row.

b Show that there cannot be 8 chairs in each row.

c There is not enough space for more than 14 chairs in each row. i Find the largest possible number of rows.

ii Find the smallest possible number of rows.

2

10 can be written as the sum of two prime numbers in two different ways: 10 = 3 + 7

or

10 = 5 + 5

a Find two ways to write 14 as the sum of two prime numbers.

Hint: What are the primes that are less than 14?

b Find all the ways to write 24 as the sum of two primes.

c Show that 11 is a prime factor of 385.

Hint: Divide 385 by 11.

1 Problem solving

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d 385 has two other prime factors. What are they?

Hint: Use your answer to part c.

e 385 has eight factors altogether. You have found three of them. Find the other five.

Checklist I can list the multiples of a whole number list the factors of a number work out the lowest common multiples of two numbers work out the highest common factor of two numbers identify prime numbers.

8

1 Multiples, factors and primes

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