Name: Class: No.

: Group: 3A / 3B / 3G

Sacred Heart Canossian College

2021-2022 Common Test 4
S3 Mathematics

Time allowed: 40 minutes

General Instructions:
(1) The full mark of this paper is 50.
(2) There are THREE sections, A, B and C, in this paper. Answer ALL questions in each section.
(3) The diagrams in this paper are not necessarily drawn to scale.
(4) Unless otherwise stated, numerical answers should either be exact or correct to 3 significant
figures.
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Section A (10 marks)

For each question, choose ONLY ONE answer and write the letter in the space provided. All questions
carry equal marks.

(1) _____ (2) _____ (3) _____ (4) _____ (5) _____

1. The figures below show the 2-D representations of a solid from various views.

top view front view side view

Which of the following could be the solid?

A. B. C. D.

front front front front

2. In the figure, the trophy is formed by a sphere and two cylinders. The
diameter of the sphere is 2a. The base radius and the height of the upper
cylinder are a and h respectively, while the base radius and the height of 2a
the lower cylinder are b and a respectively. By considering the
dimensions, determine which of the following could express the total
surface area of the trophy.
h

A. 3a  h . a
B. 2(a  a  b  h) .
1 a
C. a (4a 2  3ah  3b 2 ) . b
3
D. 2 (2a 2  ah  ab  b 2 ) .

3. The mean salary of 45 female staff and 75 male staff is $18 750. If the mean salary of the male
staff is $18 000, then the mean salary of the female staff is
A. $19 200.
B. $19 500.
C. $20 000.
D. $21 500.
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4. The following table shows the weights of 4 aspects in a speech competition and the scores that
Martin obtained in each aspect. Find the weighted mean score of Martin.

Content Creativity Presentation skill Organization

Score 75 50 90 67
Weight 5 5 3 3

A. 68.5
B. 69.5
C. 70.5
D. 71.5

5. The figure shows the graphs of 4x – 3y = 12 and 3x – 5y = 5. Which of the following statement is
true?

A. The exact solution is (1.5, 4.1).

B. The exact solution is (4.1, 1.5).
C. The approximate solution is (1.5, 4.1).
D. The approximate solution is (4.1, 1.5).

Section B (20 marks)

Show your working steps clearly in the space provided.

6. (a) Complete the table below. (1 mark)

2x  y  2  0
x –1 0 1
y

(b) Draw the graph of the equation 2 x  y  2  0 on the

rectangular coordinate plane provided. (1 mark)

2 x  y  2  0
(c) Solve the simultaneous equations  graphically by adding a suitable line on
2 x  1  0
the above rectangular coordinate plane. (Give the answer correct to the nearest 0.5.)
(2 marks)
From the graph, the solution is x = ,y= .
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7. The following solid is made up of 7 identical cubes. Draw the front view, side view and top
view of the solid. (3 marks)

Front View Side View Top View top

side

front

8. The figure shows a right pyramid VABCD with a rectangular base ABCD. M and N are the
mid-points of AB and BC respectively. It is given that AB = 6 cm, BC = 8 cm and VB = 13 cm.
V
(a) Name the projection of VD on the plane ABCD. (1 mark)

The projection of VD on the plane ABCD is ________ .

(b) Name the angle between the planes VBC and ABCD. (1 mark) C
D
O N
The angle between the planes VBC and ABCD is __________.
A M B
(c) Find the total surface area of VABCD. (3 marks)

(d) Find the volume of VABCD. (3 marks)

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9. The stem-and-leaf diagram below shows the distribution of the time spent on reading (in h) by
a group of S3 students in a month. The mode of the distribution is 24 h.
Time spent on reading by the group of S3 students
Stem (10 h) Leaf (1 h)
0 7 7
1 0 0 2 4
2 x 4 y 5

(a ) Find the values of x and y. (2 marks)

(b) Find the mean and the median of the distribution. (3 marks)

Section C (20 marks)

Show your working steps clearly in the space provided.
10. The frequency distribution table and the cumulative frequency distribution table below show
the distribution of the weights of the books on a bookshelf.

Weight (kg) Frequency Weight less than (kg) Cumulative frequency

0.1 – 0.4 2 0.45 2

0.5 – 0.8 0.85 13

0.9 – 1.2 15 1.25

1.3 – 1.6 6 1.65 34

1.7 – 2.0 2.05 35

2.1 – 2.4 1 2.45

(a) Complete the above frequency distribution table and the cumulative frequency
distribution table. (2 marks)
 Math_21-22_S3_CT4_P. 6

10. (b) Find the modal class of the distribution. (1 mark)

(c) Find the mean of the distribution. (2 marks)

(d) Draw a cumulative frequency polygon to represent the weights of the books on a
bookshelf. (2 marks)

Weights of the books on a bookshelf

Cumulative Frequency

40

30

20

10

0 0.05 0.45 0.85 1.25 1.65 2.05 2.45

Weight (kg)

(e) Hence, find the upper quartile of the weight of these books. (1 mark)
 Math_21-22_S3_CT4_P. 7

11. In Figure I, a wooden right circular cone is cut into two portions by a plane parallel to its base. The
lower portion is a frustum with height 24 cm, and the radii of the two parallel faces are 5 cm and
15 cm respectively.
(a) (i) Find the value of h. (2 marks)

h cm

Figure I
(ii) Find the volume of the frustum in terms of . (2 marks)

(iii) Find the curved surface area of the frustum in terms of . (2 marks)
 Math_21-22_S3_CT4_P. 8

11. (b) The pen-stand shown in Figure II is made by drilling a hole in the middle of the frustum in
Figure I. The bottom part of the hole is a hemisphere, while the upper part of the hole is right
cylinder. The radius of the hemisphere is equal to the base radius of the cylinder. It is given
that the height of the cylinder is 16 cm and the depth of the hole is 19 cm.
(i) Find the volume of the pen-stand in terms of . (3 marks)

Figure II

(ii) Find the total surface area of the pen-stand in terms of . (3 marks)

END OF PAPER