year 8 maths

7D
Gradient
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PROBLEM-SOLVING AND REASONING
7, 8, 11 8, 9, 11, 12
8–10, 12, 13
7 Abdullah climbs a rocky slope that rises 12 m for each 6 metres across. His friend Jonathan climbs
a nearby grassy slope that rises 25 m for each 12 m across. Which slope is steeper?
8 A submarine falls 200 m for each 40 m across and a torpedo falls 420 m for each 80 m across in
pursuit of the submarine. Which has the steeper gradient, the submarine or torpedo?
9 Find the gradient of these lines. You will need to first calculate the rise and run.
a
y
b
y
(4, 5)
(3, 5)
O
(−4, −1)
x
(−1, −5)
O
x
c
y
d
y
(−3, 4)
(−4, 4)
O
x
O
x
(3, −5)
(6, −3)
10 Find the gradient of the line joining these pairs of points.
a (0, 2) and (2, 7) b (0, −1) and (3, 4)
c (−3, 7) and (0, −1) d (−5, 6) and (1, 2)
e (−2, −5) and (1, 3) f (−5, 2) and (5, −1)
11 A line with gradient 3 joins (0, 0) with another point, A .
a Write the coordinates of three different positions for A , using positive integers for both the
x - and y -coordinates.
b Write the coordinates of three different positions for A using negative integers for both the
x - and y -coordinates.
12 A line joins the point (0, 0) with the point (a, b) with a gradient of 2 .
a If a = 1 , find b . b If a = 5 , find b .
c Write an expression for b in terms of a .
d Write an expression for a in terms of b .
13 A line joins the point (0, 0) with the point (a, b) with a gradient of − 1 2 .
a If a = 1 , find b . b If a = 3 , find b .
c Write an expression for b in terms of a .
d Write an expression for a in terms of b .
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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