Show the relevant working even for the multiple-choice questions.
1. Given XZ = 8, XY = 10, sin
α = 3
2 , then Sin β equals
A. 4
15 B. 15
8 C. 12
5 D. 4
5 E. 6
5
2. A rectangle is 8 cm long and 6 cm wide. The acute angle θ , correct to the nearest degree is
A. 37º
B. 41º
C. 49º
D. 74º
E. 83º
3. In the figure shown (not drawn to scale), ABCD is a rectangle. The angle ACD is
equal to
A. tan–1 0.1
B. tan–1 0.25
C. tan–1 0.5
D. tan–1 0.75
E. tan–1
3
4
θ 6 cm
8 cm
8
Y
Z
10
α
β
X
A B
CD
40 cm
30 cm
Further Mathematics Unit 4 Page 2 Week 3 SEND Work
4. In ABC, the length AC in centimetres is determined by evaluating
A. 0
100 96 cos 120+
B. 0
100 96 cos 120−
C. 0
100 96 cos 60−
D. 64 36 96+ −
E. 0
100 (1 2 cos 120 )+
5. A yacht follows a triangle course MNP as shown.
The largest angle between any two legs of the course is closest to
A. 50º
B. 70º
C. 120º
D. 130º
E. 140º
6. For the triangle ABC, ∠ABC = θ, cos θ equals
A. 1
4
−
B. 1
2
−
C. 1
4
D. 1
2
E. 3
4
7. The correct expression for the area of the shape shown is:
A. o1 6.13 4 sin (80 )
2 × × ×
B. o1 6.13 4 cos (100 )
2 × × ×
C. o1 6.13 4 sin (100 )
2 × × ×
D. 1 6.13 4
2 × ×
E. None of the above
θ
A
B
C
3
4
2
M
N
P
5 km
6 km
10
Further Mathematics Unit 4 Page 3 Week 3 SEND Work
Problem Solving Questions 8 to 11 (Copy out the diagram)
8.
In the above figure, AD = 35 cm, BC = 16 cm and
a. What is the size of ? Give your answer to 1 decimal place.
b. What is the length of AC ? Give your answer to 1 decimal place.
c. Find the area of triangle ABC.
Further Mathematics Unit 4 Page 4 Week 3 SEND Work
9. A flagpole AB is secured by guy wires AC and AD. The wires are secured 5m apart at points C
and D. Work out the length of the flagpole to one decimal place.
A
1100 350
C
250
DB 5 m
Further Mathematics Unit 4 Page 5 Week 3 SEND Work
Copy the diagram and show detailed workings in your response.
10. Children using the swing, shown below find that if they swing high enough,
they will see over the fence. The swing is 0.9 metres above the ground originally.
The swing makes an angle of 62º when it moves from position A to position C.
Find the vertical distance x above the ground after the swing moves through 62º?
B
A
C
0.9 m
2.4 m
x
620 2.4 m
ground level
Further Mathematics Unit 4 Page 6 Week 3 SEND Work
11. A farmer has his house built near a river. The house, H, is 780 metres from the pier, P, and
325 metres from the swimming platform, S, shown in the diagram below. Beside the river
are two paddocks, PHS and FHS as shown.
(a) Find the area of each paddock.
(b) Find the length, FH, in metres, correct to one decimal place
