The document is a preliminary examination paper for Secondary 4/5 students in Jurongville Secondary School. It consists of 22 questions on elementary mathematics covering topics like mensuration, algebra, trigonometry, statistics, and coordinate geometry. The paper is 80 marks and students are instructed to show working for questions where necessary. They are provided with relevant formulas and given 2 hours to complete the exam.

1. JURONGVILLE SECONDARY SCHOOL
PRELIMINARY EXAMINATION
2009
Elementary Mathematics (PAPER 1)
Secondary 4 Express/ 5 Normal (Academic)
2nd September 2009 (Wednesday) Duration : 2 hours
(0745 - 0945)
Marks :
Name : ________________________________ [ ]
80
Class : 4___ / 5N ___ Parent’s Signature:
_______________________
INSTRUCTIONS:
Write your name and index number on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer ALL questions.
Write your answers 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.
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  , use either your calculator value or 3.142, unless the question requires the answer in terms of  .
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 80.
*Observe our school values of Integrity and Excellence by not cheating
and doing your best in this paper
DO NOT OPEN THE BOOKLET UNTIL YOU ARE TOLD TO DO SO
Setter: Mdm Lucy Wu
This document consists of 18 printed pages and 2 blank pages.
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2. 2
Mathematical Formulae
n
 r 
Compound interest Total amount = P1  
 100 
Mensuration Curved Surface area of a cone = rl
Surface area of a sphere = 4r 2
1 2
Volume of a cone = r h
3
4 3
Volume of a sphere = r
3
1
Area of triangle ABC = ab sin C
2
Arc length = r , where  is in radians
1 2
Sector area = r  , where  is in radians
2
a b c
Trigonometry  
sin A sin B sin C
a 2  b 2  c 2  2bc cos A
Statistics Mean =
 fx
f
2
2
Standard deviation =
 fx   fx 
 
f f 
 

3. 3
1) (a) A new car is valued at $55 000. At the end of each year its value is reduced by
15% of its value at the start of the year. What will it be worth after
6 years?
(b) Throughout his life Mr Bean’s heart has beat at an average rate of 72 beats per
minute. Mr Bean is 60 years old. How many times has his heart beat during his
life? Give your answer in standard form correct to two significant figures.
Ans: (a) $__________________ [1]
(b) ___________________ [1]
2) 6 men take 4 hours to dig a hole. Find the time taken if 8 men are available. If it takes
1
hour to dig the hole, how many men are there?
2
Ans: _________________________ h [1]
______________________ men [1]
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4. 4
3) On a map of scale 1 : 20 000 the area of a forest is 50 cm2. On another map the area of
the forest is 8 cm2. Find the scale of the second map.
Ans: ___________________________ [2]
4) A group of NCC cadets are marching for their National Day Parade March Past. If they
marched in pairs, one cadet is without a partner. If they marched in 3’s, 5’s and 7’s,
there will be one cadet without a partner. Calculate the smallest number of pupils in the
March Past contingent.
Ans: ___________________________ [2]

5. 5
5) p
q
r
Find a formula for the shaded part in terms of p, q and r.
Ans: ___________________________ [2]
6) An intelligent fish lays black or white eggs and it likes to lay them in a certain pattern.
Each black egg is surrounded by six white eggs.
Here are 3 black eggs and 14 white eggs.
(a) How many eggs does it lay altogether if it lays 200 black eggs?
(b) How many eggs does it lay altogether if it lays n black eggs?
Ans: (a) ___________________ [1]
(b) ___________________ [1]
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6. 6
7) Each packet of Quaker Cereal carries a token and 5 tokens can be exchanged for a free
packet. How many free packets will I receive if I bought 125 packets?
Show clearly your working.
Ans: ___________________________ [2]
7
2
8) (a) Simplify 12 p 8  16 p
(b) Showing your working clearly, solve the equation
3
 1
(3x  2) 2 
64
Ans: (a) ___________________ [1]
(b) x = ________________ [2]

7. 7
9) (a) Channel U starts its transmission every evening at 17 30 and finishes at
03 45 the following morning. Calculate the duration of its transmission, giving
your answer in hours.
(b) If the minute hand of the clock moves through a duration of 36 minutes, what is
the corresponding angle that the hour hand move?
Ans: (a) _________________ h [1]
(b) _________________  [2]
10) If   { x: x is an integer such that 10  x  100}
A = { x: x when divided 15 leaves a remainder 7}
B = { x: x when divided by 17 leaves a remainder 14}
(a) Find the value of n (A).
(b) Find the value of n( A  B).
(c) State the largest member of B.
Ans: (a) ___________________ [1]
(b) ___________________ [1]
(c) ___________________ [1]
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8. 8
11) (a) Write the number 438 pico in standard form.
1 1
(b) If it takes of a second to write a zero and sec to write an integer other than a
5 10
zero, how long does it take to write the number?
Ans: (a) ___________________ [1]
(b) ________________ sec [2]
12) Given that 5  x  10 , y  k , where k is a constant and the smallest value of y is 2, find
x3
(a) the value of k,
(b) the largest value of y,
(c) the largest value of x  y .
xy
Ans: (a) k = ________________ [1]
(b) ___________________ [1]
(c) ___________________ [1]

9. 9
13) During the National Day Celebration, JVS ordered T-shirts of various sizes for the students.
The matrices show the order of various sizes of T-shirts and the cost ($) for the various sizes.
XL L M S
XL  15 
 
Boys  220

240 180 85 
 L 13.50 
Girls  50
 60 210 135 
 M  12 
 
S  9.20 
 
 220 240 180 85 
(a) Find 1 1  
 50 60 210 135 
 
(b) Explain what your answer (a) represent.
(c) Using matrix multiplication, find the total amount the school has to pay.
Ans: (a) ___________________ [1]
(b) __________________________________________________________________ [1]
(c) $ __________________ [1]
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10. 10
14) In the diagram, ABCDEF is a regular hexagon and APQRB is a regular pentagon. PXR
is a straight line. Calculate
(a)  BAP,
(b) ABX .
(c) Show that PR is parallel to AB. [2]
D C
R
Q
E B
X
P
F A
Ans: (a) __________________  [1]
(b) __________________  [1]
15) John sells cylindrical tins of pet food in his provision shop. The height of a tin is 8 cm
and the cost price is $3.20. He intends to sell another type which is geometrically
similar to the ones he is selling but whose height is 4 cm. Calculate the price to the
nearest one cent that he should sell this smaller tin so that he makes a profit of 35%.
Ans: $ _________________________ [4]

11. 11
16) In the diagram, O is center and angle PQT = 28o and angle RPT = 40 o, find the bearing
of
(a) P from T,
(b) R from T,
(c) P from R.
N
P
40
2 8
Q T
O
R
Ans: (a) __________________  [1]
(b) __________________  [2]
(c) __________________  [1]
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12. 12
17) In a video game, a spot on the screen bounces off the four sides of a rectangular frame. The
spot moves from A to B to C to D, as shown in the diagram below.
(a) What can you say about the angle at which the spot bounces off each side,
compared with the angle at which it approached the side?
(b) 3
The column vector describing the part AB of the movement is   . Write down
2
the column vector describing BC and CD.
(c) From D the spot moves to E on the fourth side of the frame. Given that the spot
continues in the same way, write down the vector DE.
(d) Given that the spot bounces off the fourth side at E and continues to move,
describe its subsequent path.
Ans: (a) ___________________ [1]
(b) ___________________ [2]
(c) ___________________ [1]
(d) __________________________________________________________________ [1]

13. 13
18) A racing car manufacturer makes two models, the Alfa and Beta which are alike in every aspect
except body design and styling. To determine if the body design of the Alfa has less wind
resistance, both cars were tested on the Bukit Speedway. The following table gives lap times in
minutes on a 5 km track;
Alfa 1.0 0.9 1.0 0.8 0.9 1.0 0.9 1.0
Beta 1.3 1.2 1.0 0.9 1.1 0.9 1.4 1.3
(a) Find the mean lap times for the Alfa and the Beta.
(b) Find the standard deviation for each car.
(c) Comment on the performance of each car.
Ans: (a)
Alfa _______________
Beta _______________ [2]
(b) Alfa _______________
Beta _______________ [2]
(c) _________________________________________________________________ [1]
19) Express y= x 2  10 x  31in the form ( x  a) 2  b where a and b are integers. Hence
sketch the graph of y. State its minimum value and the line of symmetry.
Sketch [1]
Ans: ___________________________ [2]
Min value __________________ [1]
Line of symmetry ____________ [1]
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14. 14
20) B
x y
A C
p D q
z
In the diagram, ABC  ADB  90 0 , AD = p and DC = q.
(a) Use similar triangles to show that x 2  pz .
(b) Find a similar expression for y 2 .
(c) Add the two expressions for x 2 and y 2 and hence prove the
Pythagoras Theorem.
Ans:
(a) __________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________ [2]
(b) __________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________ [2]
(c) __________________________________________________________________
__________________________________________________________________
__________________________________________________________________ [1]

15. 15
21) The diagram shows a grid of squares. A button is placed on one of the squares. The six
faces of a fair die are marked 1, 2, 3, 4, 5and 6. The fair die is tossed. If ‘1’ is shown,
the button is moved one square upwards followed by one square to the left. If ‘2’ or ‘3’
is shown, the button is moved one square downwards. If ‘4’ is shown, the button is
moved one square to the right. If ’5’ or ‘6’ is shown, the button is moved two squares to
the left. The table below illustrates the movement.
Number Direction of movement
shown P
1
U R G
2 or 3 I
D
4
5 or 6 E
(a) The button is placed on the square I. The die is tossed once. Find the probability
that the button finishes at the square U.
(b) On another occasion, the die is tossed once and the button is moved. When the die
is tossed a second time, the button is moved again.
(i) If the button is placed at G, find the probability that the button finishes at
square R.
(ii) If the button is placed on the square R, find the probability that the button
finishes at the square U.
Ans: (a) ___________________ [1]
(b)(i) ___________________ [2]
(b)(ii) ___________________ [2]
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16. 16
22) Speed in ms 1
80
24
Time in sec
0
4 10 15
The diagram is the speed-time graph of an object during a period of 15 seconds.
(a) (i) Calculate the retardation during the first 4 seconds.
(ii) Calculate the distance travelled in the first 4 seconds.
(iii) Given that the acceleration of the object between t = 10 and t = 15 is
20 ms 2 , calculate the speed of the object when t = 15.
Ans: (a)(i) _______________ ms-2 [1]
(a)(ii) ________________ m [1]
(a)(iii) _______________ ms-1 [1]

17. 17
(b) On the axes in the answer space, sketch the distance –time graph, indicating the [2]
distance travelled, for the journey.
Distance in m
0 Time in sec
4 10 15
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18. 18
23) (a) Using ruler and compasses, construct  XYZ in which XY = 10 cm, YZ = 9 cm
and XZ = 8 cm.
(b) Measure, and write down, the size of the smallest angle in the triangle. Give a
reason for your choice.
(c) A point P is 3.8 cm from X and also equidistant from Y and Z. On your diagram
and using suitable constructions find and mark the point P.
Constructions:
(a) XYZ [2]
(c) [2]
Ans: (b) __________________  [1]
Reason ___________________________________________________________ [1]

19. 19
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20. 20
No Answer No Answer
1 a) $20743.22 13 a) 270 300 390 220
b) 2.3 X 109 b) The total order for XL, L, M and
S sized T-shirts respectively.
c) $14 804
2 3 hours 14 a) 1080
48 men b) 60 0
QRF  36 0
 PRB  72 0
c)
PRB  RBA  180 0
Since they are interior angles,
PR is parallel to AB.
3 1 : 50 000 15 $0.54
4 211 16 a) 3320
b) 2200
c) 0120
5 q+r-p 17 a) Equally inclined to the
horizontal or negative
gradients to each other.
 6    9
b) BC    , CD   
  4   6
   
  6
c)   4 
 
d) E will move to A and
continue the path in the
same pattern.
6 A0 802 18 a) Mean
b) 4n + 2 Alfa: 0.9375
Beta:1.1375
b) Std deviation
Alfa: 0.0696
Beta: 0.180
c) Alfa is a better performing
car because it has consistently
smaller lap times.
7 31 19 y  ( x  5) 2  6
Min value = 6
Line of symmetry: x = 5.
8 
1 20 a) Proof
8
a) 3 p b) y 2  zq
2
b) x4
3

21. 21
x 2  y 2  qz  zp
c)
 z( p  q)  z 2
This is the Pythagoras Theorem.
9 1 21 1
a) 10 h a)
4 6
b) 18 0 1
b)i)
18
1
ii)
9
10 a) 6 22 a) i) 14 ms-2
b) 1 b) ii) 208 m
c) 99 c) 124 ms-1
11 a) 4.38 x 10 -10 23 b) 49 0  10
1 Reason: Angle opposite the shortest
b) 2 sec
10 side would be the smallest angle.
12 a) k = 2000
b) 16
c) 0.8
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