Collins Int. LS WB 7 - Look Inside

11mm spine

Collins Cambridge Lower Secondary Maths STAGE 7: WORKBOOK

Cambridge Lower Secondary Maths STAGE 7: WORKBOOK

Series editor: Alastair Duncombe Authors: Alastair Duncombe, Rob Ellis, Amanda George, Claire Powis, Brian Speed This Workbook provides plenty of practice exercises for each chapter of the Collins Cambridge Lower Secondary Maths Stage 7 Student’s Book, for the 0862 Cambridge curriculum framework from 2020. The Workbook can be used for homework or in class.

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Cambridge Lower Secondary

Maths STAGE 7: WORKBOOK

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✓ Provides learner support as part of a set of

resources for the Cambridge Lower Secondary Mathematics curriculum framework (0862) from 2020

✓ Has passed Cambridge International’s rigorous quality-assurance process

✓ Developed by subject experts ✓ For Cambridge schools worldwide

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Find us at www.collins.co.uk/international facebook.com/collinsint @Collins_Int ISBN 978-0-00-837856-1

9 780008 378561

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Expressions

5

You will practice how to: • Understand that letters can be used to represent unknown numbers, variables or constants.

• Understand that a situation can be represented either in words or as an algebraic expression, and move between the two representations (linear with integer coefficients).

• Understand that the laws of arithmetic and order of operations apply to algebraic terms and expressions (four operations).

5.1 Letters for numbers

Summary of key points In algebra, a letter is used to represent an unknown number or measurement (a variable).

An expression is a mathematical statement about a variable. For example, if you have a number, t, then add 5, you could write t + 5.

In t + 5, t and 5 are both terms in the expression. t is a variable and 5 is a constant term in the expression.

The expression 5f represents 5 × f. The 5 is called the coefficient of f.

An equation is a mathematical statement where an expression is made equal to something. For example, t + 5 = 12. Equations can be solved to find the value of the unknown variable.

Exercise 1 1

28

Rewrite the number puzzles as equations by using a letter to represent the missing number.

Number puzzle

Equation

Example

26 + …….. = 100

26 + t = 100

a)

11 + …….. = 20

……....……..……..……..……..

b)

…….. − 2 = 15

……....……..……..……..……..

c)

…….. × 10 = 240

……....……..……..……..……..

d)

45 = …….. × 9

……....……..……..……..……..

Chapter 5: Expressions

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2

Draw lines to match each statement to the correct algebraic expression.

7m

m−7

‘I think of a number and add 7.’

m 7

m+7

‘I think of a number and multiply it by 7.’

‘I think of a number and subtract 7.’

‘I think of a number and divide it by 7.’

3

Use letters to represent the side lengths of these shapes.

4

Here are some statements. c + 3 = 11 This is known as an equation.

f+g+2 This involves two terms, f and g.

A parcel has mass (m + 2) kg.

This is an expression.

4c = 12 The coefficient of c is 12

Tick the statements that are true.

For the statements that are false, write the true statement.

Think about 5

Give examples to explain each of these algebraic words: variable, equation, expression and term.

5.2 Forming expressions

Summary of key points Example A shop sells these clothes.

The price of the scarf is c dollars.

Chapter 5: Expressions

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The jumper costs twice as much as the scarf.

The price of the jumper can be written as 2c dollars.

The trainers cost 10 dollars more than the jumper.

An expression for the cost of the trainers is 2c + 10 dollars.

Exercise 2 1

A shop sells boxes of crayons. Each box contains b crayons.

b crayons

Write down the number of crayons in each picture. b crayons

a)

b)

…………… crayons 2

c)

…………… crayons

An apple costs a cents. A banana costs b cents. Write expressions for the cost of the fruit in each picture. b)

a)

…………… cents

…………… cents c)

d)

…………… cents

30

…………… crayons

…………… cents

Chapter 5: Expressions

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3

Nathan thinks of a number. Call his number n. Write an expression in terms of n for the result when you: a) add 2 to Nathan’s number ……………….. b) subtract 4 from Nathan’s number ……………….. c) multiply Nathan’s number by 9 ……………….. d) multiply Nathan’s number by 4 and then add 1 ………………..

4

A pen costs p dollars. Write an expression in terms of p for the cost of 6 pens. …………… dollars

5

A hat costs h dollars. It is reduced by 4 dollars. Write an expression in terms of h for the new cost of the hat. …………… dollars

6

There are c cakes in a packet. A boy eats 3 cakes. Write an expression in terms of c for how many cakes are left. …………… cakes

7

Sheena has n badges. She shares them equally between her two children.

Write an expression in terms of n for how many badges each child has. …………… badges

8

The cost of train tickets is: Child ticket $c Adult ticket $a What is the total cost of 5 child tickets and 2 adult tickets? $……………

9

Four people are talking about how old they are. Clara’s age is c years. Write an expression in terms of c for the age of all the other people.

Clara c years Dimitri

‘I am two years older than Clara.’

…………… years

Eva

‘I am three times as old as Clara.’

…………… years

Faiyaz

‘I am six years younger than Eva.’

…………… years

10 Here is a triangle with side lengths as marked on the diagram.

Write an expression for the perimeter of the triangle.

t cm

u cm

The perimeter is the total distance around the edge of a shape.

4 cm

…………… cm

Chapter 5: Expressions

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