year 8 maths

624
10 a 2 km/h (uphill) and 5 km/h (downhill).
b Many possible stories, for example:
A weekend bushwalk started with a 20-km hike on the
first day. The first section of the hike was a 10 km,
3-hour hike to waterfalls where we had a half-hour rest.
The hike up the mountain was steep and we progressed
slowly, needing 2 1 hours to cover a distance of 5 km.
2
On the summit of the mountain, we had a 1 hour rest.
Finally we walked downhill for 5 km taking 1 hour to
reach our campsite. On this last downhill section, we
achieved our fastest average speed of 5 km/h compared
to the initial average speed of 3.3 km/h and the slowest
speed of 2 km/h when we were hiking up the mountain.
c
A bush hike
20
15
10
Distance from
start (km)
5
1
2 3 4 5 6 7 8
Time (hours)
11 a True, as these points correspond to the same position on
the distance scale.
b True, as this point is on a flat line segment.
c False, the line segment through A is flatter than the line
segment through D.
d False, Deanna was riding away from home at C and
turned towards home at E.
e True, as the line segment through F is steeper than the
line segment through A.
f False, as point F corresponds to a smaller distance than
point D from home.
g True, point F is at a later time on Deanna’s return trip
home.
12 Journey A: Isla as she walks from the front and stops
twice only.
Journey B: Adam as he has 3 stops and a very fast walk in
one section.
Journey C: Conner as he walks to the back of the
room twice.
Journey D: Ruby as her walk starts from the back.
13 Graph A: True, leaves from school (some distance from
home), rides further away to her friend, then rides
in the other direction and stops at library, which is
on the way home.
Graph B: False, vertical lines are incorrect as it is
impossible to change distance in zero time.
Graph C: False, distance must be on the vertical axis and
time on the horizontal axis.
Graph D: True, the school is a long way from home, her
friend is on the way home then Sienna must ride
away from home to go to the library, then she
changes direction and rides home.
14 Graph A: Incorrect as one rider didn’t stop.
Graph B: Incorrect as riders not stopped at the same time.
Graph C: Incorrect as riders not stopped at the same place.
Graph D: Correct, Jayden stopped first, Cooper stopped
same place same time, both left together.
15 a
160
Distance (in km) from Gurang
120
80
40
Key
Archie
Heidi
Ambulance
Tow-truck
Police
20
40 60 80 100 120 140
Time (minutes)
b Many possible endings; for example:
The tow-truck also comes from 15 km away and arrives in 15 minutes. The police come from 25 km away and arrive in 20
minutes. The ambulance paramedics treat Archie for 17 minutes and then drive to Northbrook Hospital, arriving in 45 minutes.
The tow-truck leaves the accident 10 minutes after the ambulance and arrives in Gurang after 1 hour. Heidi stays at the accident
scene for 30 minutes and then drives to Northbrook in 45 minutes. The police leave at the same time as the tow-truck and drive
to Northbrook in 45 minutes.
d Archie 120 km/h; Heidi 107 km/h; ambulance 120 km/h then 100 km/h; tow-truck 80 km/h; police 105 km/h, 107 km/h.
Yes, Archie could be charged for speeding; providing that the ambulance had flashing lights it would be legal for it to drive at
120 km/h.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.