year 8 maths

631
Short-answer questions
1 a 50 b 65 c 240
d 36 e 61 f 138
2 a 132 b 99 c 77
d 51 e 146 f 41
3 95°
4 a obtuse-angled scalene, a = 35
b acute-angled, isosceles, a = 30
c acute-angled, equilateral, a = 60
d right-angled, scalene, a = 19
e acute-angled, scalene, a = 27
f obtuse-angled, scalene, a = 132
5 a 67 b 141 c 105
6 a a = 98, b = 82 b a = 85, b = 106
c a = 231, b = 129
7 a 2 b 0 c 4 d 1
8 a 2 b 2 c 4 d 3
9 a 71 b 25 c 120
10 40
Extended-response questions
1 ∠BAE = ∠DCE = 70° (alternate angles in parallel lines)
a + 70 + 50 = 180 (angle sum of △ ABE)
a = 60
2 ∠BDE = 180° − 30° (angles on a straight line)
= 50°
∠BED = ∠BDE = 50° (equal angles are opposite equal sides)
∠ABE + ∠BED = 180° (cointerior angles in parallel lines)
∠ABE + 50° = 180°
∠ABE = 130°
3 ED = AB = 5 (opposite sides of a rectangle)
ED + DC = 13
5 + DC = 13
DC = 8
AE = BD = 8 (opposite sides of a rectangle)
∴ △ BDC = isosceles
∴ ∠DBC = a° (equal angles are opposite equal sides)
Also ∠BDE = 90° (angle in rectangle)
∴ ∠BDC = 90° (EC is a straight line)
a + a + 90 = 180 (angle sum of △ BDC)
2a = 90
a = 45
Chapter 7
Pre-test
1 a George b Amanda
2 a 1 b 1 c 0 d −3
3 a 6 b −1 c 0 d 2
4 a (1, 2) b (2, 1) c (3, 2)
5 a 7 b 4 c 2
6 a −7 b −3 c 3
7 a
b
x −2 −1 0 1 2
y −8 −5 −2 1 4
x −2 −1 0 1 2
y 6 5 4 3 2
8 a y = 3x b y = 2x + 1
c y = 3x − 2
Exercise 7A
d y = 5 − x
1 a (0, 0) b y
c 1st
d 3rd
e −2
f −5
2 a 3 b −1 c −2 d 0
e −2 f 0 g −3 h 0
3 A(1, 1), B(5, 0), C(3, 4), D(0, 4), E(−1, 2), F(−3, 3),
G(−5, 1), H(−3, 0), I(−4, −2), J(−2, −5), K(0, −3),
L(2, −3), M (5, −5)
4
y
4
O
E D 3 B
2
N 1 C
F
A
x
−4 −3 −2 −1
J
−1
1 2 3 4
G
−2
K
I
−3 P
M H −4
L
5 a house b fish
6 a B b C c E d D
7 a triangle b rectangle
c parallelogram
d kite
8 a (2, 4) b (−5, 2) c (−1, −2.5)
d (4.5, −4.5) e (0, 1) f (−2, 1)
9 a (1, −2), (1, −1), (1, 0), (1, 1)
b (−1, 0), (0, 0), (1, 0), (2, 0)
c (−2, 3), (−1, 2), (0, 1), (1, 0)
d (−2, −3), (−1, 0), (0, 3), (1, 6), (2, 9)
10 a quadrant 4 b quadrant 2
c quadrants 2 and 3 d quadrants 3 and 4
11 a line on the y-axis
12 a 10 b 4 c 7 d 11
e 6 f 4
13 a 5 b 13 c 25 d √13
e √90
f √61
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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