Collins Int. LS WB 9 - Look Inside

12mm spine

Collins Cambridge Lower Secondary Maths STAGE 9: WORKBOOK

Cambridge Lower Secondary Maths STAGE 9: WORKBOOK

Series editor: Alastair Duncombe Authors: Belle Cottingham, 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 9 Student’s Book, for the 0862 Cambridge curriculum framework from 2020. The Workbook can be used for homework or in class.

Registered Cambridge International Schools benefit from high-quality programmes, assessments and a wide range of support so that teachers can effectively deliver Cambridge Lower Secondary.

Visit www.cambridgeinternational.org/lowersecondary to find out more.

This resource is endorsed by Cambridge Assessment International Education

✓ 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

78585 Secondary Maths WB9 cvr.indd 1 Maths Maths Maths9Lower 99Lower Lower Lower Second Second SecondWorkbook Workbook Workbook 2nd 2nd 2nd Edition.indd Edition.indd Edition.indd 111

Cambridge Lower Secondary

Maths STAGE 9: WORKBOOK

Find us at www.collins.co.uk/international facebook.com/collinsint @Collins_Int ISBN 978-0-00-837858-5

9 780008 378585

04/01/2024 11:26 13/11/20 13/11/20 13/11/20 3:04 3:04 3:04 pm pm pm

5.3 Laws of indices

Summary of key points a5 means a × a × a × a × a.

The number 5 is known as a power or index. It tells you how many times a is multiplied by itself.

When you multiply, add the powers.

When you divide, subtract the powers.

an × am = an + m

an ÷ am = an − m

Example: m2 × m4 = m6

Example: n12 ÷ n4 = n8

Exercise 3 1

Write these expressions in power form. a) t × t × t × t × t × t

………..

b) k × k × k × k × k × k × k ………..

2

3

32

Match the equivalent expressions. n4 n3

n5 n

n2 n3

n6 n2 n4

n5

n6

n7

n12

Write each expression as a single power of x. a) x5 × x6 = ……….........

b) x7 × x × x3 = ……….........

c) x12 ÷ x6 = ………........

3 4 d) x ×5 x = ………......... x

Chapter 5: Expressions

78585_P026_038.indd 32

24/11/20 5:42 PM

4

Use ticks (✓) and crosses (✘) to mark Priti’s homework.

5

Complete these statements.

6

a) t × t 4 = t 8

b) t 3 × t = t 11

14 c) t = t 5 t

d)

t 10 = t2 t ×t

Explain why p4 × q3 cannot be simplified. ………………………………………………………………………………………………… …………………………………………………………………………………………………

7

Toni thinks that (d4)3 simplifies to d 7.

Treya thinks that it simplifies to d12.

Who is correct?

……………………..

Explain how you know. …………………………………………………………………………………………………. ………………………………………………………………………………………………….

8

Draw a ring around the pair(s) of numbers that give the same value for xy and yx. x=1

x=2

x=4

x=0

x=3

y=4

y=3

y=2

y=5

y = –3

Think about 9

Make up 10 questions involving multiplication and division of indices that simplify to y10.

Chapter 5: Expressions

78585_P026_038.indd 33

33

24/11/20 5:42 PM

5.4 Algebraic fractions

Summary of key points To manipulate algebraic fractions, you apply the same rules as you use for arithmetic fractions.

Examples: 3y Work out: x + 4 10 First find a suitable common denominator, in this case 20.

Simplify 12 x + 4 4 12 x + 4 4 (3 x + 1) factorising the numerator = 4 4

3y 6y x 5x = and = 10 20 4 20 ×5

=

4 (3 (3 x + 1 1) cancelling the common factors 4

( 44 = 1)

×2

6y So, x + 3 y = 5 x + 6 y = 5 x + 6 4 10 20 20 20

= 3x + 1

Exercise 4 1

Work out: a) x + 4 x .............

7 7

2

b)

9 y 3y ............. − 5 5

c) 4 + 3 ............. r r

Is each statement true or false?

True

False

n n + 1 2n + 1 + = 7 7 7 a b a−b − = 8 2 6 7n n n − = 10 5 2 n m 3n + 4m + = 3 4 12 3

Calculate: a)

t t − 2 8

………..

34

b)

n m + 15 3

………..

c)

n 3 + 2 10

………..

Chapter 5: Expressions

78585_P026_038.indd 34

24/11/20 5:42 PM

4

Complete these statements. a)

5

+ 1 = 2n + 3 9 3 9

b)

− 2h = 3h n n n

c)

t + u = 3t + 4 12

Complete these calculations. a) 12a − 9 = 3 (....... − 3) = ………………………..

3 3 b) 10b + 25c = 5

....... ( 2b 2b + .......) = ………………………..

5

2 ....... (....... + 2) c) 3 x + 2 x = = ……………………….. x x

6

7

8

Simplify these fractions.

21 a) 7 x + 2 7

b) 24 x − 16 8

………..

………..

d) 60a − 24 12

2 e) 4m + 5m m

………..

………..

c)

12 x + 15 y 3

……….. f)

4x 2 + 6x 2x

………..

Simplify these fractions. a) 4 x × 2 5 3

2 b) x × x 2 3

………..

………..

c)

3m 2m × 4 9

………..

Draw a ring around the calculations that simplify to 2x + 3.

2 2 × x 3

150 x + 225 75

2x 2 + 3x x

2x 3 + 5 5

6x + 9 3

4x2 + 1 12 3

Chapter 5: Expressions

78585_P026_038.indd 35

35

24/11/20 5:42 PM