This week will be done online. It will be auto-corrected by the
computer.
If you get less than 70% on your first attempt, you need to go back and spend more time
reviewing the work. You are required to make second attempt at the quiz assessment. (If you get
more than 70% but less than 100%, it is optional for you to have another go.)
If you still get less than 70% on your second attempt, you must scan and submit your answers
showing the full working to your teacher (like what you did for the other weeks).
Your teacher will check your work and may suggest further work for you to do in order to show
satisfactory completion of the week!
1. The point Q on building B is visible from the point P on building A, as shown in the diagram above.
Building A is 16 metres taller than building B. The horizontal distance between point P and
point Q is 23 metres. The angle of depression of point Q from point P is closest to
A. 35°
B. 41°
C. 44°
D. 46°
E. 55°
SEND: Work for Submission for Week 4 Online Quiz Assessment
Further Mathematics Unit 4 Page 2 Week 4 SEND WORK
2. The diagram below shows the location of three boats, A, B and C.Boat B is on a bearing of
110° from boat A. Boat B is also on a bearing of 035° from boat C. Boat A is due north of
boat C. The angle ABC is
A. 35°
B. 65°
C. 70°
D. 75°
E. 110°
3. A cross-country race is run on a triangular course. The points A, B and C mark the corners of
the course, as shown below.
The distance from A to B is 2050 m. The distance from B to C is 2250 m. The distance from
A to C is 1900 m. The bearing of B from A is 140°. The bearing of C from A is closest to
A. 032°
B. 069°
C. 192°
D. 198°
E. 209°
Further Mathematics Unit 4 Page 3 Week 4 SEND WORK
4. The distances from a kiosk to points A and B opposite sides of a pond are found to be
12.6 m and 19.2 m respectively. The angle between the lines joining these points to the kiosk
is 63o .
The distance, in m, across the pond between points A
and B can be found by evaluating:
A. o1 12.6 19.2 sin (63 )
2 × × ×
B.
o
19.2 sin (63 )
12.6
×
C. 2 2
12.6 19.2+
D. 2 2 o
12.6 19.2 2 12.6 19.2 cos(63 )+ − × × ×
E. 1
( 12.6)( 19.2)( 63) , where (12.6 10.2 63)
2
s s s s s− − − = + +
5. Marcus is on the opposite side of a large lake from a horse and its stable. The stable is 150 m
directly east of the horse. Marcus is on a bearing of 170° from the horse and on a bearing of
205° from the stable.
The straight-line distance, in metres, between Marcus and the horse is closest to
A. 45 m
B. 61 m
C. 95 m
D. 192 m
E. 237 m
Further Mathematics Unit 4 Page 4 Week 4 SEND WORK
6. A man walks 4 km due east followed by 6 km due south. The bearing he must take to return
to the start is closest to:
A. 034 o
B. 056o
C. 304o
D. 326o
E. 346o
7. A boat sails at a bearing of 265o from A to B. What bearing would be taken from B to return
to A?
A. 005 o
B. 085o
C. 090o
D. 355o
E. 275o
8. From a point on a cliff 200 m above sea level, the angle of depression to a boat is 40 o
. The
distance from the foot of the cliff to the boat to the nearest metre is:
A. 238 m
B. 168 m
C. 153 m
D. 261 m
E. 311 m
9. A boat sails from a harbour on a bearing of 045o for 100 km. It then takes a bearing of 190 o
for 50 km. How far from the harbour is it, correct to the nearest km?
A. 51 km
B. 82 km
C. 66 km
D. 74 km
E. 3437 km
Draw appropriate labelled diagrams to solve Questions 6 –10
Further Mathematics Unit 4 Page 5 Week 4 SEND WORK
10. A hiker walks 3.2 km on a bearing of 1200 and then takes a bearing of 055 0 and walks
6 km. His bearing from the start is:
A. 013 o
B. 077 o
C. 235 o
D. 257 o
E. 330 o
11. A right pyramid with a square base is shown in the diagram. Each edge of the square base
has length 8 cm and the height of the pyramid is 16 cm. The length of a sloping edge of the
pyramid in centimetres is:
A. 288
B. 155
C. 125
D. 324
E. 425
12. In the figure ABCD the magnitude of angle BCA is
closest to
A. 19°
B. 39°
C. 51°
D. 55°
E. 59°
13. A tree is growing near the block of land. The base of the tree, T, is at the same level as the
corners, P and S, of the block of land. From point S, the angle of elevation to the top of the
tree is 22°.
Calculate the height of the tree in metres,
correct to one decimal place.
Further Mathematics Unit 4 Page 6 Week 4 SEND WORK
14. Chris leaves island A in a boat and sails 142 km on a bearing of 078° to island B. Chris then
sails on a bearing of 191° for 220 km to island C, as shown in the diagram.
(a) Show that the distance from island C to island A is approximately 210 km.
Write your response on the Quiz Completion report (you need to download it online) and
submit it as work submission for Week 4 [W04].
Submit it online, you can find the link
(b) Chris wants to sail from island C directly to island A. On what bearing should Chris sail? Give
your answer correct to the nearest degree.
15. The base of a lighthouse D, is at the top of a cliff 168 metres above sea level. The angle of
depression from D to a boat at C is 28o . The boat heads towards the base of the cliff, A, and
stops at B. The distance AB is 126 metres.
(a) What is the angle of depression from D to B, correct to the nearest degree?
(b) How far did the boat travel from C to B, correct to the nearest metre?
