This document provides instructions and information for candidates taking a preliminary mathematics examination. It consists of 9 printed pages containing 10 questions. Candidates are instructed to show all working and calculations, and to write their answers on the provided writing papers. Calculators should be used where appropriate. Formulas for topics like compound interest, mensuration, trigonometry, and statistics are also provided. The total marks for the paper are 100.

1. Name ( ) Class 4
Wednesday 26 August 2009 2 hours 30 minutes
INSTRUCTIONS TO CANDIDATES
Answer all questions.
Write your answers on the writing papers provided.
Omission of essential working will result in loss of marks.
Calculators should be used where appropriate.
If the degree of accuracy is not specified in the question, and if the answer is
not exact, give the answer to three significant figures. Give answers in degrees to
one decimal place.
For π, use either your calculator value or 3.142, unless the question requires
the answer in terms of π.
Attach this page on top of your answer scripts.
INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or
part question.
The total of the marks for this paper is 100.
Question 1 2 3 4 5 6 7 8 9 10
Marks
ANGLICAN HIGH SCHOOL
Preliminary Examination
Secondary Four
MATHEMATICS
4016/02
For Examiner’s Use
100

2. Anglican High School 2009 Preliminary Examinations Mathematics P2
This question paper consists of 9 printed pages.
Mathematical Formulae
Compound Interest
Total amount =
n
r
P 





+
100
1
Mensuration
Curved surface area of a cone = rlπ
Surface area of a sphere = 2
4 rπ
Volume of a cone = hr 2
3
1
π
Volume of a sphere =
3
3
4
rπ
Area of triangle ABC = Cabsin
2
1
Arc length = θr , where θ is in radians
Sector area = θ2
2
1
r , where θ is in radians
Trigonometry
C
c
B
b
A
a
sinsinsin
==
Abccba cos2222
−+=
Statistics
Mean = f
fx
Σ
Σ
Standard deviation =
22






Σ
Σ
−
Σ
Σ
f
fx
f
fx
2

3. Anglican High School 2009 Preliminary Examinations Mathematics P2
Answer all the questions.
1. (a) Simplify
22
1
2
2
23
−−
×
−
+
xx
x
xx
x
. [3]
(b) Express
2
1
23






+
−
yx
yx
n
nn
in the form ba
yx . [2]
(c) Sam was solving a quadratic equation using the ‘completing the square’ method but he
could not get the desired solution. His first four steps of working are shown below.
Identify the line that is wrong and continue solving for Sam. [3]
01642 2
=−+ xx
1642 2
=+ xx
( ) 16422 2
=−+x
416)22( 2
+=+x
2.
In the figure, A, B, C and D are four points on level ground. D is due south of C
and A is due east of D. CD = 20 m, AD = 35 m and AB = 25 m. X is a point on
AC such that angle BAX = 98° and angle ABX = 50°.
Calculate
(a) the bearing of C from A, [2]
(b) the length of BX, [3]
(c) the area of triangle ABX, [2]
(d) the shortest distance from A to BX. [2]
3
35 m
A
B
C
D
X
20 m
25 m
98°
50°
N

4. Anglican High School 2009 Preliminary Examinations Mathematics P2
3. (a) Susan saved 25% of her income in the bank and her monthly income was $1300.
(i) Calculate her savings in one year. [1]
(ii) The bank offered interest rate of 0.15% per year for savings less than
$30 000. Given that Susan had saved an additional $4 500 in her bank
account by the end of first year, calculate her interest in that year. [2]
(iii) Susan did not withdraw any amount of money from the bank and had
deposited her savings monthly. The interest was compounded over
the years. Calculate the compounded interest earned by the end
of 3 years. [3]
(b) Nelly, Nelson and Nat started a cake shop in 2007. They invested money in the
ratio 6 : 2 : 7 and agreed to share all profits in the same ratio as their investments.
(i) If Nat received $11 050 more than Nelson, calculate the total profit for
that year. [2]
(ii) The cake shop made a profit of 33
3
1
% on every cake sold. Calculate the
selling price of a 1.5 kg strawberry cake if the profit made was $5.40. [2]
4. The terms 1T , 2T , 3T of a sequence are given as follows.
1 2(1 3) 8T = + =
2 2(3 5) 16T = + =
3 2(5 7) 24T = + =
(a) (i) Write down the next two terms, 4T and 5T , in the sequence. [2]
(ii) Find an expression, in terms of n, for nT . [2]
(b) The terms 1S , 2S , 3S of a different sequence are given as follows.
1 1 3 3S = × =
2 3 5 15S = × =
3 5 7 35S = × =
(i) Find an expression, in terms of n, for nS . [2]
(ii) Find the value of 10S . [1]
(iii) Find the value of n when 1599nS = . [2]
4

5. Anglican High School 2009 Preliminary Examinations Mathematics P2
5. A water tank holds 2 m3
of water when it is full. A hot water tap supplies water at a rate of
x m3
per minute and a cold water tap supplies water at a rate of y m3
per minute. The water tank
can be filled in
3
1
3 minutes using both the taps.
Given that filling the tank using only the hot water tap will take 4 minutes longer than
filling the tank using only the cold water tap.
(a) Form an equation in x and show that it reduces to 031610 2
=+− xx . [7]
(b) Solve 031610 2
=+− xx , giving your answers correct to 2 decimal places.
[2]
(c) Find, to the nearest minute, the time taken to fill the tank using only the
hot water tap. [1]
6. In the diagram, the line AB is a tangent to the circle and O is the centre of the circle.
∠CAB = 45o
and ∠AOD = 120o
.
(a) Find the value of
(i) ∠CAO, [1]
(ii) ∠ABC. [3]
(b) Given that ∆ABC and ∆DBA are similar and the radius of the circle is 7 cm, find the
(i) length of AC, [1]
(ii) length of DA, [1]
(iii) exact value of
DBA
ABC
∆
∆
ofarea
ofarea
. [2]
5
45o
A
B
O
D
C
120o

6. CD
BA
10 O
24
13
P
°38
88
X
Y Z
R
P
Q
20
Anglican High School 2009 Preliminary Examinations Mathematics P2
7. (a)
A piece of wood has a uniform circular cross-section of radius 13 cm as shown in
the diagram. A smaller piece of wood of a uniform rectangular cross-section 24 cm
by 10 cm is to be cut from it. Find
(i) the reflex angle AOB in radians, [3]
(ii) the area of the major sector APB. [2]
(b) The diagram shows a zinc roof of a firewood shed.
The angle between the two identical zinc plates is °38 . XY = XZ = 8 m and QY = 20 m.
Calculate
(i) the length of the straight line YZ, [2]
(ii) angle YPZ. [3]
6

7. 12 cm
D
A
B
V
C
BA
D C
V
6 cm
Anglican High School 2009 Preliminary Examinations Mathematics P2
8. The diagram shows the cross-section of a hemispherical bowl of inner diameter 12 cm.
(a) Find
(i) the volume of the hemisphere with diameter 12 cm, [2]
(ii) the total surface area of the bowl, if the outer diameter is 15 cm. [3]
(b) A right solid pyramid, in Figure 1, with square base ABCD and height 6 cm is placed in
the bowl. The points V, A, B, C and D touch the inner surface of the hemispherical bowl
as shown in Figure 2.
(i) Find the surface area of the pyramid. [5]
(ii) Calculate the volume of the space not occupied by the pyramid in
Figure 2. [2]
7
Figure 1 Figure 2

8. Anglican High School 2009 Preliminary Examinations Mathematics P2
9. Answer the whole of this question on a sheet of graph paper.
The variables x and y are connected by the equation )5(
2
1 2
xxy −= .
Some corresponding values of x and y are given in the table below.
x 1− 0 1 2 3 4 5 6
y 3− 0 2 3 3 2 0 a
(a) Calculate the value of a. [1]
(b) Using a scale of 2 cm to represent 1 unit on each axis, draw a horizontal
x-axis for 61 ≤≤− x and a vertical y-axis for 44 ≤≤− y . On your axes,
plot the points given in the table and join them with a smooth curve. [2]
(c) Write down the equation of the line of symmetry of the curve
)5(
2
1 2
xxy −= . [1]
(d) Use your graph to find
(i) the greatest value of y, [1]
(ii) the solutions of 2)5( 2
=− xx .
[2]
(e) By drawing a tangent, find the gradient of the curve at the point where x = 1. [2]
(f) On the same axes, draw an additional graph to solve the quadratic equation
.034 2
=+− xx [3]
8

9. Anglican High School 2009 Preliminary Examinations Mathematics P2
10. (a) A fair coin is tossed and a fair six-sided die is thrown.
(i) Draw the possibility diagram to show all the possible outcomes. [1]
Find the probability of obtaining
(ii) a head and an odd number, [1]
(iii) a tail and a number greater than 4. [1]
(b) When a baby wakes up each night, the probability that she will cry for milk is
7
5
.
Over the weekend, find the probability
(i) the baby will wake up crying for milk on Saturday and Sunday, [1]
(ii) the baby will wake up crying for milk on either Saturday or Sunday, but
not on both nights. [1]
(c) The masses, in grams, of 68 hamsters are recorded in the table below.
Mass ( x g) 500 <≤ x 10050 <≤ x 150100 <≤ x 200150 <≤ x 250200 <≤ x
No. of hamsters 4 5 13 40 6
(i) Calculate an estimate of the mean mass of the 68 hamsters. [2]
(ii) In which class does the median lie? [1]
(d) A survey was done to find out how many television programmes a group of students
watched on the previous week. The table shows the results.
No. of programmes watched 0 1 2 3
No. of students 7 9 3 8
(i) Calculate the standard deviation. [2]
(ii) If the mean of another group of students was 2.1 and the standard deviation
was 0.7, comment on the results of the two surveys. [2]
9

10. Anglican High School 2009 Preliminary Examinations Mathematics P2
End of Paper.
10