year 8 maths

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14 a i (−2, 17)(−1, 14)(0, 11)(1, 8)(2, 5)(3, 2)(4, −1)(5, −4)
ii (−2, −3)(−1, −1)(0, 1)(1, 3)(2, 5)(3, 7)(4, 9)(5, 11)
b (2, 5) y = 11 − 3x y = 2x + 1
5 = 11 − 3 × 2 5 = 2 × 2 + 1
5 = 11 − 6 5 = 4 + 1
5 = 5 True 5 = 5 True
c It is the only shared point.
15 a i Any answer with y as a whole number is correct, e.g.
2x − 1 = −3, 2x − 1 = −1, 2x − 1 = 3
ii No. Many possible correct examples,
e.g. 2x − 1 = 2.5, 2x − 1 = −1.75, 2x − 1 = 2.8
b i Any answer with the y-value to one decimal place
is correct, e.g. 2x − 1 = −2.6, 2x − 1 = −1.8,
2x − 1 = 0.7
ii No. Many possible correct answers,
e.g. 2x − 1 = 0.42, 2x − 1 = −1.68, 2x − 1 = 2.88
c i 2x − 1 = 2.04, 2x − 1 = 2.06
ii Many possible correct answers, e.g. (1.521, 2.042)
(1.529, 2.058); 2x − 1 = 2.042, 2x − 1 = 2.058
iii Yes, for every two points on a line another point can
be found in between them, so there are an infinite
number of points on a line. Also an infinite number
of equations can be solved from the points on a
straight line if the graph has a suitable scale (digitally
possible).
16 a i x = 2, x = −2 ii x = 3, x = −3
iii x = 4, x = −4
iv x = 5, x = −5
b For each y-coordinate there are two different points, so
two different solutions.
c i x = 2.24, x = −2.24 ii x = 2.61, x = −2.61
iii x = 0.7, x = −0.7 iv x = 3.57, x = −3.57
v x = 4.34, x = −4.34
d The graph of y = x 2 does not include a point where y = −9.
e Many correct answers all with x 2 equal to a negative
number, e.g. x 2 = −5, x 2 = −10, x 2 = −20.
f Positive numbers or zero.
g x = −1, x = 2
Exercise 7H
1 a 15 b 45 c 5 d 125
2 a m = 3, b = 2 b m = −2, b = −1
c m = 4, b = 2
d m = −10, b = −3
e m = −20, b = 100 f m = 5, b = −2
3 a 60 cm b 150 cm c 330 cm
4 a 28 L b 24 L c 10 L
5 a
t 0 1 2 3
d 0 6 12 18
b
d
18
12
6
O
t
1 2 3
c d = 6t d 9 km e 2 hours
6 a
t 0 1 2 3 4 5 6 7 8
d 0 5 10 15 20 25 30 35 40
b d
40
30
20
10
O
t
2 4 6 8
c d = 5t d 22.5 km e 4 hours
7 a
t 0 1 2 3 4 5
v 20 16 12 8 4 0
b
V
20
16
12
8
4
O
t
1 2 3 4 5
c V = −4t + 20 d 11.2 L e 3 seconds
8 a
t 0 1 2 3 4
h 500 375 250 125 0
b
h
h i x = −2.77, x = 5.77
ii x = −8.27, x = 3.27
iii no solution
iv x = 3
500
375
250
125
O
t
1 2 3 4
c h = −125t + 500 d 275 m e 3 minutes
9 a M = −0.5t + 3.5 b 7 hours
c 4.5 hours
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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