year 8 maths

16
Chapter 1
Algebraic techniques 2 and indices
Example 6b,c
7 Simplify the following by combining like terms.
a 7f + 2f + 8 + 4
b 10x + 3x + 5y + 3y
c 2a + 5a + 13b − 2b
d 10a + 5b + 3a + 4b
e 10 + 5x + 2 + 7x
f 10a + 3 + 4b − 2a − b
g 10x + 31y − y + 4x
h 11a + 4 − 2a + 12a
i 7x 2 y + 5x + 10yx 2
j 12xy − 3yx + 5xy − yx
k −4x 2 + 3x 2
l −2a + 4b − 7ab + 4a
m 10 + 7q − 3r + 2q − r
n 11b − 3b 2 + 5b 2 − 2b
8 For each expression choose an equivalent expression from the options A–E listed.
a 7x + 2x
b 12y + 3x − 2y
c 3x + 3y
d 8y − 2x + 6y − x
e 4xy + 5yx
A 10y + 3x
B 9xy
C 9x
D 3y + 3x
E 14y − 3x
PROBLEM-SOLVING AND REASONING
9, 10, 15 10–12, 15, 16
12–14, 16, 17
9 Write expressions for the perimeters of the following shapes in simplest form.
a
7x
b
c
3
2y
4x
3a + 3b
x
5a − b
4a + 2b
10 Towels cost $c each at a shop.
a John buys three towels, Mary buys six towels and Naomi buys four
towels. Write a fully simplified expression for the total amount
spent on towels.
b On another occasion, Chris buys n towels, David buys twice as
many as Chris and Edward buys three times as many as David.
Write a simplified expression for the total amount they spent
on towels.
11 State the missing numbers to make the following equivalences true.
a 10x + 6y − □ x + □ y = 3x + 8y
b 5a − 7b + □ a + □ b = 11a
c □ c + □ d + □ = 4c + 2d + 1 + 3c + 7d + 4
d □ a2 b + □ b2 a + 2a 2 b + b 2 a = 7b 2 a + 10a 2 b
y
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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