year 8 maths

58 Chapter 1 Algebraic techniques 2 and indices
3 Substitute the following values of a to evaluate the expression 8 − a + 2a 2 .
a −1 b 2 c −3 d 0
4 Substitute x = 2 and y = −3 into each of the following.
a 2y + 3 b 3x + y c xy + y
d 4x − 2y
5 For what value of x is 3 − x equal to x − 3 ?
e
5xy
6 + 2 f −3x + 2y
x + y
6 Simplify each of these expressions by collecting like terms.
a 7m + 9m b 3a + 5b − a c x 2 − x + x 2 + 1
d 5x + 3y + 2x + 4y e 7x − 4x 2 + 5x 2 + 2x f −8m + 7m + 6n − 18n
7 Simplify:
a 9a × 4b
b 30 × x × y ÷ 2
c −8x × 4y ÷ (−2)
8 Copy and complete the following equivalences.
a 3x + 4y = 8x − □ + 4y b 3ab × □ = −12abc
3x
c
4 = □ d
20
9 Express each of the following in their simplest form.
5x
a
12 − x
2a
b
6
5 + b
c
15
10 Expand and simplify when necessary.
9a 2 b ÷ □ = 3a
6x
5 × 15
2x 2
d
4a
7 ÷ 8a
21b
a 3(x − 4) b −2(5 + x) c k(3l − 4m) d 2(x − 3y) + 5x
e 7 − 3(x − 2) f 10(1 − 2x) g 4(3x − 2) + 2(3x + 5)
11 Factorise fully.
a 2x + 6 b 24 − 16g c 12x + 3xy d 7a 2 + 14ab
12 By factorising first, simplify the following fractions.
5a + 10
a
5
13 Find the missing values.
b
12x − 24
x − 2
c
16p
64p + 48pq
a 7 5 × 7 2 = 7 □ b 5 4 ÷ 5 = 5 □ c (3 2 ) 3 = 3 □ d 3 0 = □
14 Use the index laws to simplify each of the following expressions.
3 4 2 3
a 5 2 × 5 5 b 6 7 × 6
7
c
7 3
d
5 6
5 5 e (2 ) f (6 )
15 Simplify:
a 6 × 5 0 b (6 × 5) 0 c 6 0 × 5
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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