Question 3
The value of x in the following figure is
3.
A. 20
B. 25
C. 33
D. 45
E. 55
[Hint: Separate out the similar triangles and match up the corresponding sides and angles]
Question 4
Ben is making a 1:100 model of a car with an engine capacity of 2.3 litres (2300cm3 ). If Ben
wants to include a scale model of the engine, then the capacity of the model engine should be
A. 0.0023 cm3
B. 0.023 cm3
C. 0.23 cm3
D. 2.3 cm3
E. 23 cm3
Question 5
Triangle ABC is similar to triangle AXY.
AX = 3
2 AB
If the area of ∆ABC = 108 cm2 , the area of ∆AXY is
A. 32 cm2
B. 48 cm2
C. 54 cm2
D. 72 cm2
E. 81 cm2
B
X
A C
Y
2522
10
x

Further Mathematics Unit 4 Page 3 Week 2 SEND Work
Question 6
A cylindrical block of wood has a diameter of 12 cm and a height of 8 cm.
A hemisphere is removed from the top of the cylinder, 1 cm from the edge, as shown below.
The volume of the block of wood, in cubic centimetres, after the hemisphere has been removed is
closest to
A. 452
B. 606
C. 643
D. 1167
E. 1357
Question 7
A triangular prism with a cross-section of an equilateral
triangle is shown on the right.
The side lengths of the triangle are 4cm and the length of
the prism is 10cm.
The total surface area in square cm is
A. 46.93
B. 80
C. 93.86
D. 126.93
E. 133.86
4 cm
10 cm

Further Mathematics Unit 4 Page 4 Week 2 SEND Work
Question 8
A proposed swimming pool is to be constructed in the western suburbs of Melbourne. The design of
the swimming pool is shown in the diagram below. The pool has two sections: one section has a flat
base, while the other section has a sloping base.
From the shallow end of the pool, the first 25 metres of the pool has a constant depth of 0.9 metres.
Halfway along the length of the pool, the depth begins to increase at a constant rate, reaching a
maximum depth of 2.2 metres.
(a) Name the shape of the quadrilateral ABCF.
___________________________________________
(b) Calculate the distance EI. Write your answer in metres, correct to two decimal places.
[Hint: draw out the triangle that is involved in calculating EI].
(c) Calculate the area of the side of the pool bound by ABCDEFA. Write your answer in square metres,
correct to one decimal place.

Further Mathematics Unit 4 Page 5 Week 2 SEND Work
(d) Using your answer to part c., find the volume of water required to fill the pool. Write your answer correct
to the nearest cubic metre.
(e) The sloping section of the base of the pool bound by the rectangle BCGH is painted first and that
section of the pool is filled before the flat section of the base is painted.
Calculate the volume of water required to fill the section of the pool with the sloping base, up to the
level of the flat base. Write your answer correct to the nearest cubic metre.
[Hint:Visualise the section that will be filled up with water and draw the 3-D diagram that represents it]
Question 9
The top two-metre section of a five-metre high cone is removed.
Calculate the percentage of the total volume of the remaining (bottom) part.

Further Mathematics Unit 4 Page 6 Week 2 SEND Work
SEND: Work for Submission – Week 2 Online Quiz
Every week there are five multiple-choice questions to attempt online as part of the work
submission. Log in to VSV online, select Further Maths and click the link for Week 2 Quiz.
Restrict your time to 10 minutes only.
Below are the quiz questions. You can do them first and then go online to enter your responses and
get immediate response. If you get less than 4/5, this indicates that you need to spend more time
reviewing the work for the week.
Please submit this section together with the other questions in the main section.
Circle the letter beside the correct answer.
1. The volumes of two similar solids are in the ratio 8:27. The ratio of their surface areas is:
A. 2 : 3
B.
C.
D. 4 : 9
E.
2. In the given triangles the length of XZ is 50% greater than AC. The ratio of the areas is:
A. 4 : 25
B. 9 : 4
C. 16 : 9
D. 81 : 16
E. 7 : 5
3:2
27:8
163 : 813

Further Mathematics Unit 4 Page 7 Week 2 SEND Work
3. An inverted right circular cone of capacity 1000 cm3 is filled with water to half of its depth. The
volume of water (in cm3 ) is:
A. 125
B. 500
C. 250
D. 300
E. 400
4. The perimeter of the figure shown in centimetres is:
A. 34
B. 24 + 5 π
C. 24 + 2.5π
D. 29 + 5π
E. 29 + 2.5π
5. The formula for the total surface area for the object shown is:
A. ½ abh
B. 2 × ½ bh + ab + 2 × ah
C. 3(½ bh + ab)
D. ½ bh + 3ab
E. bh + 3ab

Further Mathematics Unit 4 Page 1 Week 3 SEND Work
SEND: Work for Submission for Week 3
Show the essential working in the spaces provided for ALL questions
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.