Instructions
1. Answer ALL questions.
2. Put the answers in the spaces provided. Answers written elsewhere will not be marked.
3. All questions carry equal mark
4. No mark will be deducted for wrong answers.
5. The diagrams in this paper are not drawn in scale.
Write your answers in the table below. (27 marks)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Q1/7
1.
Write down an inequality in x corresponding to the following diagram.
A.
B.
C.
D.
2.
x≤2
x≥2
x>2
x<2
0
2
If a > b > 0, which of the following is NOT true?
A. 2a > 2b
3 3
B.
<
a b
1
1
C. 1 − > 1 −
a
b
1
1
D. − 4a + > −4b +
2
2
3.
Betty is now more than twice as old as he was 9 years ago. What is her maximum age
now?
A.
B.
C.
D.
4.
A sum of $10 000 is deposited in a bank for 3 years. What is the amount at an interest
rate of 5% p.a. compounded yearly? (Give the answer correct to the nearest dollar.)
A.
B.
C.
D.
5.
$11 576
$11 567
$11 538
$11 500
If the length of a rectangle is increased by 20% while its width is decreased by 15%, find
the percentage change in its area.
A.
B.
C.
D.
6.
17
18
19
20
+3%
+2%
–2%
–3%
Suppose the tax rate for rates is 5% each year. Dick paid $1 250 for the quarterly rates of
his flat. Find the rateable value of the flat.
A.
B.
C.
D.
$25 000
$50 000
$75 000
$100 000
Q2/7
7.
Suppose the salaries tax rates are as follows.
Net chargeable income
On the first $30 000
On the next $30 000
On the next $30 000
On the remaining
Rate
2%
8%
14%
20%
Lawerence has a net chargeable income of $150 000. Find his salaries tax payable.
A.
B.
C.
D.
8.
Which of the following sets of line segments can form a triangle?
I. 2 cm, 3 cm, 4 cm
II. 4 cm, 6 cm, 8 cm
III. 3 cm, 12 cm, 16 cm
A.
B.
C.
D.
9.
$19 200
$17 200
$16 800
$15 000
I only
II only
I and II only
I, II and III
In the figure, O is the incentre of !ABC. Find "AOC.
A.
B.
C.
D.
107.5°
108°
109.5°
110°
10. In the figure, AD, BE and CF are three altitudes of !ABC.
If they intersect at M, then M is the
A.
B.
C.
D.
incentre of !ABC.
orthocentre of !ABC.
circumcentre of !ABC.
centroid of !ABC.
11. In the figure, ABCD is a parallelogram. AC and DE meet at F. AF = 8, CF = 6, DF = 4.
Find DE.
D
A
A.
B.
C.
D.
3
4
6
7
4
8
F
6
B
Q3/7
E
C
A
12. In the figure, ABCD is a rhombus. AD = AE = AF = EF. Find !ECF.
A.
B.
C.
D.
o
90
o
95
o
100
o
120
E
C
o
70
o
65
o
50
o
40
x
N
M
70
o
B
14. Find x in the figure.
A.
B.
C.
D.
F
A
13. Find x in the figure.
A.
B.
C.
D.
D
B
7
7.5
8
8.5
Q
C
4 cm
S
4 cm
U
x cm
7 cm
R
T
P
15. Refer to the figure. Find the order of rotational symmetry with respect to l.
A.
B.
C.
D.
0
1
2
3
l
16. The figure shows a net which can be folded into a rectangular box. In the box, find the
numbers on the faces that will meet at the point A.
1
A.
B.
C.
D.
1, 2, 5
2, 3, 5
2, 4, 6
2, 5, 6
2
A
Q4/7
3
4
6
5
17. Which of the following is the front view of the object on the right?
X
A.
B.
Front
C.
D.
18. Refer to the cube PQRSTUVW. A, B, C and D are the mid-points of PQ, QR, RS and PS
respectively. Name the line of intersection between the planes BDTW and TUVW.
A.
B.
C.
D.
D
P
BD
BW
VW
WT
A
S
C
Q
R
B
U
V
T
W
19. If a zero is added to a set of eight negative data, which of the following must be true?
I. The mean must increase.
II. The median remains unchanged.
III. The mode remains unchanged.
A.
B.
C.
D.
I only
I and II only
I and III only
II and III only
20. The table below shows the marks scored by Shirley in five tests and the corresponding
weights.
Test
1
2
3
4
5
Shirley’s
mark
75
80
x
70
60
Weight
2
3
4
1
2
The weighted mean mark of Shirley is 75. Find x.
A.
B.
C.
D.
65
70
75
80
Q5/7
21. Refer to the solid as shown, what is the dimension of
mπ (3m + 2n)?
A.
B.
C.
D.
0
1
2
3
n
2m
22. There are two similar cans. It is known that the capacity of the larger can is 900 cm3. If the
surface area of the smaller can is 19% less than that of the larger can, find the capacity of the
smaller can. (If necessary, give the answer correct to 4 significant figures.)
A.
B.
C.
D.
478.3 cm3
656.1 cm3
718.5 cm3
829.2 cm3
23. The vertices of a parallelogram ABCD are A(0, 3), B(–2, –1), C and D(3, 2). Find the
coordinates of point C.
A.
B.
C.
D.
(2, –1)
(1, –1)
(1, –2)
(1, –3)
24. In the figure, O is the origin. Find the slope of AB.
y
4
A. −
3
4
B.
3
3
C. −
4
3
D.
4
A
x
O
–8
–6
B
25. The top of a building MN is observed from two positions A and B on the ground 49 m
apart. The angles of elevation of M from A and B are 48° and 62° respectively. Find the
height of the building MN. (Give the answer correct to 3 significant figures.)
A.
B.
C.
D.
M
125 m
133 m
146 m
150 m
A
48° 62°
B
N
49 m
Q6/7
26. Two digits are chosen at random from the password 702507. Find the probability that the
two digits are different.
13
18
13
B.
15
4
C.
5
2
D.
3
A.
27. There are four $5 coins and six $10 coins in a pocket. If Jane picks a coin from the
pocket randomly, what is the expected value of the coin obtained?
A.
B.
C.
D.
$8
$8.5
$9
$9.5
~End of Paper~
Q7/7