1. 1
CATHOLIC HIGH SCHOOL PRELIMINARY EXAMINATIONS (3) 2008
SECONDARY FOUR MATHEMATICS
Subject : Mathematics Paper 1
Level : Secondary 4 Date : 12 September 2008
Marks : 80 Time : 0815 – 1015
Name : ____________________________________ ( )
Class : Sec 4 - ____
INSTRUCTIONS TO CANDIDATES :
Write your NAME, CLASS and INDEX NUMBER in the spaces at the top of this page.
Answer all questions.
Write your answers in the spaces provided on the question paper.
If working is needed for any question, it must be shown with the answer.
Omission of essential working will result in loss of marks.
You are expected to use an electronic calculator to evaluate explicit numerical expressions.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give
your answer to 3 significant figures. Give answers in degrees to one decimal place.
For π, use your calculator value or 3.142, unless the questions requires the answer in term of π.
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 80.
For Examiner’s Use Only:
F o r E x a m in e r 's U s e
Types Qn No. Types Qn No.
Accuracy Graphs
80
Brackets Diagrams
Fractions Geometry
Units Others
This question paper consists of 20 printed pages, including this cover page.

2. 2
Mathematical Formulae
Compound interest
n
 r 
Total Amount = P 1 + 
 100 
Mensuration
Curved surface area of a cone = πrl
Surface area of a sphere = 4 πr 2
1
Volume of a cone = πr 2 h
3
4 3
Volume of a sphere = πr
3
1
Area of triangle ABC = ab sin C
2
Arc length = rθ , where θ is in radians
1 2
Sector area = r θ , where θ is in radians
2
Trigonometry
a b c
= = .
sin A sin B sin C
a 2 = b 2 + c 2 − 2bc cos A
Statistics
Mean =
∑ fx
∑f
∑ fx ∑ fx 
2
2 

Standard deviation = −
∑f 
 ∑ f 

3. 3
Answer all the questions in the spaces provided on the Question Paper.
1 Light travels 1 metre in 3.3 nanoseconds.
Find the total distance in metres, that light will travel in 6.6 microseconds.
Answer ___________________ m [1]
2 In Iceland, the highest air temperature recorded is 30.5 °C.
The lowest air temperature recorded is − 39.7 °C.
Find
(a) the difference between the two temperatures.
(b) the mean of the two temperatures.
Answe (a
___________________ °C [1]
r )
(b
___________________ °C [1]
)
4 x + 15
3 Find the integer values of x for which 1 − x < 3 x + 5 ≤ .
2
Answer ______________________ [3]

4. 4
1
4 2 3 × 12 , , π , − 2.5 , 0 , 3 2
3
(a) Complete the following table using the list of numbers provided above.
Rational Numbers:
Integers:
[2]
5 A polygon has n sides. Two of its exterior angles are 23º and 85º, while the other ( n − 2)
exterior angles are 14º each. Calculate the value of n.

5. 5
Answer ______________________ [2]
6 Solve ( 3x − 6) 2 = 100 .
Answer ______________________ [2]
7 Factorise 20ax − by − 5ay + 4bx .
Answer ______________________ [2]
3a 0 × ( a b 2 )
3
8 Simplify , leaving your answer in index form.
a

6. 6
Answer ______________________ [2]
9 The table shows the population statistics of Singapore from 2005 to 2007.
Total Population Singapore Residents
Year
(Millions) (Millions)
2005 4.27 3.47
2006 4.40 3.53
2007 4.59 3.58
Total population comprises Singapore residents and non-residents.
(a) Find the number of non-residents in Singapore in 2006, leaving your answer in
standard form.
(b) Calculate the percentage increase in the total population from 2005 to 2007.
Answe (a
______________________ [1]
r )
(b
______________________ [2]
)
10 (a) Express each of the numbers 66 and 168 as product of prime factors.
(b) Find the highest common factor of 66 and 168.
(c) Find the smallest integer value of n for which 66n is a multiple of 168.

7. 7
Answe (a
66 = _________________
r )
168 = _________________ [2]
(b
______________________ [1]
)
(c
______________________ [1]
)
11 (a) The first five terms of a sequence are 1, 3, 5, 7 , 9, 11.
Find in terms of n , the n th term of the sequence.
(b) Using the answers from part (a) or otherwise, write down an expression, in terms
of n, for the n th term of the sequence
(i) 1, 9, 25, 49, 81, 121, ……….
(ii) 25, 49, 81, 121, ……….
Answe
(a) ______________________ [1]
r
(b)(i
______________________ [1]
)
(ii) ______________________ [1]
12 A box contains 5 red balls, 3 black balls and 1 white balls.
Two balls are taken from the bag at random, without replacement.
Find the probability
(a) that both balls are white,
(b) at least one ball is black.
A third ball is now taken from the box at random.
(c) Find the probability that none of the three balls is red.

8. 8
Answe
(a) ______________________ [1]
r
(b) ______________________ [2]
(c) ______________________ [2]
13 (a) y is inversely proportional to x 3 .
y = 9 when x = 3 .
Find y when x = 10 .
(b) p is directly proportional to q 2 .
q is increased by 50%.
Find the percentage increase in p .
Answe (a
______________________ [2]
r )
(b
______________________ [2]
)
14 ε = { x : x is an integer and 0 ≤ x ≤ 10 }
A = { x : x is divisible by 3 }
B = { x : x is a prime number }
(a) Draw a Venn diagram to illustrate this information. Insert all elements of ε, A and
B in the Venn Diagram.
Answer (a)
[2]

9. 9
(b) Write down n ( A ∩ B ) .
(c) List the elements in the set A ∪ B ' .
Answer (b) ___________________________ [1]
(c) A ∪ B ' = ____________________ [1]
15 In the diagram, A is ( − 6 , 2 ) , B is ( 4 , 2 ) and C is ( 12 , k ) .
y
C (1 2 , k )
A (- 6 , 2 ) B (4 , 2 )
x
0
(a) Given that A, B and C form an isosceles triangle such that AB = BC, show that the
value of k is 8.
Find
(b) the midpoint of AC.
(c) the gradient of line BC.
(d) the equation of the line which passes through the midpoint of AC and is parallel to
BC.
(e) the area of triangle ABC.
Answer (a) ______________________________________________________________
______________________________________________________________
______________________________________________________________ [1]
(b
( _________ , _________ ) [1]
)

10. 10
(c
______________________ [1]
)
(d
______________________ [1]
)
(e
________________ units 2 [1]
)
16 (a) Sketch the graph of y = 1 − ( x + 2 ) 2 .
y
x
Answe (a
[2]
r )
(b)
The sketch represents the graph of
y
y = xn.
Write down a possible value of n.
x
O
Answer (b) n = ________________ [1]
(c)

11. 11
y
Write down a possible equation for the
graph
1
x _____________________
O
Answer (b) [1]
_
17
r cm
h
cm
2
h cm r cm
h
cm
2
C o n ta in e r A C o n ta in e r B
The containers shown in the diagrams has height h cm.
Their other dimensions are as shown.
The containers are being filled to the brim with water which flows into each one at the
same constant rate.
h
It takes 2.5 minutes for the water to reach a depth of cm in container A .
2
(a) Find the time taken for the water to reach the brim of
(i) container A,
(ii) container B.

12. 12
Answe (a)(i
______________ minutes [1]
r )
(ii) ______________ minutes [1]
(b) On the grid in the answer space, sketch the graph showing how the depth of the
water in each container varies with time.
h
D e p th
of h
Answer (b) w a te r 2
(c m )
0 10 20 30 40 [2]
T im e ( m in u te s )

13. 13
18 ABCD is a parallelogram and E is a point on AB.
BD and CE meet at X.
D C
X
A B
E
(a) Prove that triangles BEX and DCX are similar.
Answer (a) In triangles BEX and DCX, _________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________ [2]
(b) It is given that 4 AE = AB
Find the ratio

14. 14
(i) area of ∆ BEX : area of ∆ DCX ,
(ii) area of ∆ BCX : area of parallelogram ABCD .
Answe (b)(i
______________________ [1]
r )
(ii) ______________________ [1]
19 The diagram is the speed – time graph for the first 20 seconds of a journey.
25
20
Speed 15
(m e tre s p e r s e c o n d )
10
5
0 2 4 6 8 10 12 14 16 18 20
T im e ( t s e c o n d s )
(a) Find
(i) the deceleration when t = 9 ,
(ii) the speed when t = 17 ,
(iii) the average speed for the last 10 seconds.

15. 15
Answe (a)(i
_________________ m/s 2 [1]
r )
(ii) __________________ m/s [1]
(iii) __________________ m/s [2]
(b) Part of the distance – time for the same journey is shown in the answer space.
Complete this graph.
Answer (b)
180
160
140
120
D is ta n c e T ra v e lle d
(m e tre s ) 100
80
60
40
20
[2]
0 2 4 6 8 10 12 14 16 18 20
T im e ( t s e c o n d s )

16. 16
20 The points P and Q are ( 1 , − 6 ) and ( 7 , − 4 ) respectively.
 − 2
The point R is such that QR =   .
 4 
 
(a) Find the coordinates of R.
Answe (a
______________________ [2]
r )
 − 12 
(c) It is given that RS = 
 h . 
 
Find the two possible values of h which will make PQRS a trapezium.
You may use the grid below to help you with your investigation.

17. 17
Q
P
Answe (c
h = _______ or _______ [2]
r )
21 In the diagram, ABCD is a square and DEFG is a rectangle. EAB is straight line.
D C
G
E
A B
F
(a) Show that angle ADE = angle CDG.
(b) Prove that triangle ADE is congruent to triangle CDG.
(c) Hence, show that DEFG is a square.
Answer (a) _______________________________________________________________
__________________________________________________________________

18. 18
__________________________________________________________________
__________________________________________________________________ [2]
(b) In triangles ADE and CDG, _______________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________ [3]
(c) _______________________________________________________________
__________________________________________________________________
__________________________________________________________________ [1]
22 The plan of a triangular field has a scale of 1 cm to 50 m .
(a) Express this scale in the form 1 : n .
Answe (a
______________________ [1]
r )
N
The diagram below is part of a scale drawing of the field.
Another point, C , is 300m from B on a bearing of 063°.
(b) Complete the map to show position of C.
(c) On the same diagram, using ruler and compasses only, construct
(i) the bisector of angle ABC ,
(ii) the perpendicular bisector of the line AB.
A

19. 19
B
[3]
23 At School A, 160 pupils took an English Test.
The diagram below is the cumulative frequency curve for their results.

20. 20
160
140
120
100
80
60
40
20
0 20 40 60 80 100
M a rk s
Use the graph to find
(a) the interquartile range,
(b) the value of x , if 20% of the students scored x marks and above.
Answe (a
______________________ [1]
r )
(b
______________________ [1]
)
At another school, B, 120 pupils took the same English Test.
The diagram below is the box-and-whiskers plot for their results.

21. 21
10 15 41 54 98 M a rk s
(c) Compare the test results for the two schools in two different ways.
Answer (c) _______________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________ [2]
~ END OF PAPER ~
Catholic High School
2008 Mathematics Preliminary Examination 3
Paper 1 Answer Key
1. 2000 m 3. 0, 1 and 2
2. (a) 70.2°C (b) − 4.6 °C

22. 22
4. 2 3 × 12 ,
1
, − 2.5 , 0 ( 4 − 12) 2 + ( 2 − k ) 2 = 10
3
64 + ( 2 − k )
2
= 100
0 , 2 3 × 12 15. (a) (2 − k)2 = 36
5. 20 2−k =6
1 1 k = 8
6. x = 5 or x = −1
3 3
3
7. ( 4 x − y ) ( 5a − b) (b) ( 3 , 5) (c)
4
5
8. 3 a 2 b6 3 3
(d) y = x + 2 or 4 y = 3 x + 11
4 4
9. (a) 8.7 × 10 5 (b) 7.49%
(e) 30 units2
10. (a) 66 = 2 × 3 × 11
16.
168 = 2 × 3 × 7
3
y
(b) 6 ( - 2 ,1 )
(c) 28 -3 -1
x
11. (a) 2n − 1 (b) ( 2n − 1) 2 (c) ( 2n + 3) 2
-3
7 1
12. (a) 0 (b) (c)
12 21 (a)
13. (a) 0.243 (b) 125% (b) n = −2 (c) y = 2 − x
14. (a)
ε B
17. (a) (i) 20 min (ii) 40min
A
(b)
2
6 9 3 5 h
0 7
D e p th
of h
w a te r 2
1 4 8 10 (c m )
(b) 1 (c) { 0, 1, 3 , 4 , 6 , 8 , 9 ,10 }
0 10 20 30 40
T im e ( m in u te s )
18. (a) AAA Similarity
(b)(i) 9 : 16 (ii) 3 : 14
19. (a)(i) 5m/s2 (ii) 12.5 m/s (iii) 7.5m/s

23. 23
180
160
140
120
D is ta n c e T r a v e lle d
( m e tr e s ) 100
80
60
40
20
0 2 4 6 8 10 12 14 16 18 20
(b) T im e ( t s e c o n d s )
20. (a) ( 5 , 0) (b) h = − 4 or 10
21.
(a) ∠EDG = 90° （DEFG is a rectangle)
∠ADC = 90° （ABCD is a square)
∠EDG ＝ ∠ADC DC
∴
∠EDG = ∠ADE + ∠ADG ∠ADC = ∠ADG + ∠CDG
ADE + ∠ADG = ∠ADG + ∠CDG
∴ ∠
∠ADE = ∠CDG
(b) In triangles ADE and CDG ,
∠ADE = ∠CDG ( from part (a) )
AD = CD ( ABCD is a square)
∠DAE = 180° − 90° （DEFG is a rectangle)
90° (adjacent angle on a straight line)
=
triangle ADE is congruent to triangle CDG
(A.A.S. Congruency)
(c) Since triangle ADE is congruent to triangle CDG
DE = DG.
Since DEFG is a rectangle, DE = FG & DG = FE.
Since DE = DG, ∴ DE = FG = DG = FE.
∴ DEFG is a square.
23. (a) 16 (b) 66 or 67
(c) School B has a higher interquartile range at 39 as compared to that of School A at 16.
School A has a higher median at 55 as compared to that of School B at 41.