Anglo-Chinese School (Barker Road)
Mathematical Formulae
Compound Interest
Total amount
MensurationCurved Surface area of cone
Surface area of a sphere
Volume of a cone
Volume of a sphere
Area of a triangle
Arc length , where is in radians
Sector area , where is in radians
Trigonometry
Statistics
Mean
Standard deviation
Preliminary Examination 2009 2 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Anglo-Chinese School (Barker Road)
For Examiner’s
Use
Paper 1 [80 marks]Answer all questions in the space provided.
For Examiner’s
Use
1. Evaluate
(a) ,
(b) , giving your answer as a decimal.
Answer (a) [1]
(b) [1]
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2. (a) Given that x is a positive integer, 3 < x ≤ 6 and x ≠ 5, write down the possible
values of x.
(b) Make x the subject of the formula y =
Answer (a) x = [1]
(b) x = [1]
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Preliminary Examination 2009 3 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Anglo-Chinese School (Barker Road)
For Examiner’s
Use3. (a) Express 7759 correct to 2 significant figures.
(b) In 2008 the number of adults in Singapore was .
The number of children was .
What was the total population of Singapore in 2008?
Give your answer in standard form.
Answer (a) [1]
(b) [1]
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For Examiner’s
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4. (a) Ben left home at 0745 and arrived at school at 0839.
How many minutes did the journey take?
(b) On the return journey he traveled 7 km in 40 minutes.
Calculate his average speed in kilometers per hour.
Answer (a) mins [1]
(b) km/h [1]
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Preliminary Examination 2009 4 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Anglo-Chinese School (Barker Road)
For Examiner’s
Use5. A bag contains 3 red balls, 2 white balls and 1 blue ball.
Two balls are taken from the bag at random, without replacement.
Find the probability that
(a) both balls are red,
(b) the two balls are the same colour.
Answer (a) [1]
(b) [1]
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For Examiner’s
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6. PQRST are part of a regular 15-sided polygon. QRWX is a square. Find
(a) QRS
(b) RSW
Answer (a) QRS = o [1]
(b) RSW = o [1]
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Preliminary Examination 2009 5 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Diagram is not drawn to scale
X W T
S
R Q
P
Anglo-Chinese School (Barker Road)
For Examiner’s
Use7. Simplify
(a) .
(b) .
Answer (a) [1]
(b) [1]
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8. Joey paid $29.25 for high tea. This amount included 10% service charge and 7% Goods
and Services Tax (GST). How much did the high tea cost excluding service charge and
GST?
Answer $ [2]
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Preliminary Examination 2009 6 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Anglo-Chinese School (Barker Road)
For Examiner’s
Use 9. The lengths of the sides of a triangle ABC are such that AB : BC : CA = 3 : 4 : 5.
The perimeter of the triangle is 30 cm.
Calculate the length of CA.
Answer cm [2]
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10. A farmer has a plot of land in the shape as shown. PQ = 44 m, QR = 66 m, and
angle PQR = 55o.
For each square metre of the field, he needs to use 50 ml of insecticide.
Find the amount of insecticide, in litres, he needs for the entire field.
Answer l [2]
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Preliminary Examination 2009 7 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
A
B C
P
Q
R
55o66
44
Anglo-Chinese School (Barker Road)
For Examiner’s
Use11. Find
(a) the missing number in the sequence 1, 3, 6, …., 15, 21, 28,
(b) the 7th term in the sequence whose nth term is 3n-1,
(c) an expression, in terms of n, for the nth term of the sequence 5, 9, 13, 17, 21, ….
Answer (a) [1]
(b) [1]
(c) [1]
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For Examiner’s
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12. A soccer player scored the following number of goals in twelve matches:
3, 0, 0, 2, 2, 0, 1, 2, 3, 1, 2, 1
(a) Write down the modal score,
(b) Find the median,
(c) State the least number of goals the soccer player can score in the next match such that
the median is 1 goal.
Answer (a) [1]
(b) [1]
(c) [1]
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Examiner’s Use
13. (a) Express 84 as the product of its prime factors. For Examiner’s
Use
Preliminary Examination 2009 8 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Anglo-Chinese School (Barker Road)
(b) Written as the product of its prime factors, 360 = . Find the lowest
common multiple of 84 and 360.
Give your answers as the product of its prime factors.
(c) Find the smallest positive integer k such that 84k is a square number.
Answer (a) [1]
(b) [1]
(c) k = [1]
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14. A pencil costs x cents and a notepad costs y cents.
(a) Roy bought 4 pencils and 2 notepads.
The total cost was $2.80.
Write down an equation in x and y and show that it reduces to .
(b) Given that the cost of 1 pencil is $0.30, find y.
Answer (a) Refer to working [1]
(b) y = [2]
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Preliminary Examination 2009 9 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Anglo-Chinese School (Barker Road)
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Examiner’s Use
15. The scale of the map is 4 cm to 100 km.
(a) Express this ratio in the form 1: n
(b) What is the distance in km between two towns which are drawn 8.7cm apart on the map? Give your answer in km.
Answer (a) [1]
(b) km [2]
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16. In the diagram, ABD and ACE are straight lines. Given that ACB = 62o,
find the values of
(a) reflex angle AED,
(b) x.
For Examiner’s
Use
Preliminary Examination 2009 10 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
62B C
A
Anglo-Chinese School (Barker Road)
Answer (a)reflex angle AED= º [1]
(b) x = º [2]
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Examiner’s Use
17. (a) Factorise
(b) Expand and simplify .
Answer (a) [1]
(b) [2]
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For Examiner’s
Use
Preliminary Examination 2009 11 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
ED
x
Anglo-Chinese School (Barker Road)
18. (a) W is directly proportional to . If W = 16 and x = 2,
find the value of x when W = 324.
(b) If each worker works 8 hours a day, 15 workers will take 3 days to paint a house.
How many workers are needed to paint the house in 5 days if each worker works
8 hours a day?
Answer (a) x = [2]
(b) workers [2]
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Preliminary Examination 2009 12 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Anglo-Chinese School (Barker Road)
For Examiner’s
Use1. 19. In the diagram, PQ = 41 cm, QR = 9 cm, QRST is a straight line and SRP = 90.
Given that tan SPR = ,
Calculate
(a) PR,
(b) PS,
(c) sin TSP.
Answer (a) cm [1]
(b) cm [1]
(c) [2]
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For Examiner’s
Use
For Examiner’s
Use20. By completing the square, can be expressed in the form .
(a) Find
(i) a,
For Examiner’s
Use
Preliminary Examination 2009 13 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
S
T
R9
41
Q
P
Anglo-Chinese School (Barker Road)
(ii) b.
(b) Hence, or otherwise, solve = 0.
Answer (a)(i) a =
(a)(ii) b = [3]
(b) x = or [2]
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21. Solve the simultaneous equations.
Answer x = , y = [4]
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Preliminary Examination 2009 14 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Anglo-Chinese School (Barker Road)
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Examiner’s Use
22. In triangle ABC, AB = 7.9 cm, BC = 5 cm and AC = 11 cm.
The side AB is drawn in the answer space below.
(a) Complete the two possible triangles.
(b) (b) For one of these triangles, construct
(i) the bisector of angle BAC,
(ii) the perpendicular bisector of the line AC.
(c) These two lines intersect at the point P.
Complete the sentence in the answer space.
Answer (a) and (b)
For Examiner’s
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Preliminary Examination 2009 15 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
A
B
Anglo-Chinese School (Barker Road)
[2]
[2]
Answer (c) The point P is equidistant from the points and and
equidistant from the lines and . [1]
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___________________________________________________________________ Preliminary Examination 2009 16 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Anglo-Chinese School (Barker Road)
For Examiner’s
Use
23. The diagram shows a container made up of a cylindrical top and a cone base.
The radius of the cylinder is 3 cm and its height is 4 cm.
[Volume of cone = x base area x height]
(a) Given that the height of the cone is 8 cm, find the volume of the container in
terms of .
(b) Two taps filled the container at the same time, at the rate of 3 cm³/s and x cm³/s
respectively.
Given that the container was filled to the brim with water in 8 seconds,
find the value of x.
(c) The container is filled to the brim with water. A small hole is cut at the vertex of the
cone and the water drips at a constant rate of 12 cm³/s. Calculate the amount of water
in terms of , left in the container after 4 seconds.
Answer (a) cm³ [2]
(b) [2]
(c) cm³ [1]
For
Examiner’s Use
Preliminary Examination 2009 17 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
4 cm
8 cmA
3 cm
Vertex
Anglo-Chinese School (Barker Road)
For Examiner’s
Use
24. The points A (3, 1) and B are shown on the grid below.
(a) Write down the coordinates of B.
(b) Find the gradient of the line AB.
(c) Find the equation of the line AB.
(d) Find the length of AB.
1 2
3
4 0 -1 -2
-1
1
2
3
4
x
y B
A
Answer (a) ( , ) [1]
(b) [1]
(c) [2]
(d) unit . [2]
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For Examiner’s
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Preliminary Examination 2009 18 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
Anglo-Chinese School (Barker Road)
For Examiner’s
Use
25. PQRS is a parallelogram. M is the mid-point of PQ and N is a point on RS.
MR meets NQ at X.
(a) Prove that and are similar.
Answer:
____________________________________________________________ [2] ____________________________________________________________ ____________________________________________________________
(b) Given that RN = 3NS, find
(i)
(ii)
Answer (bi) [2]
(bii) [2]
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END OF PAPER 1
Preliminary Examination 2009 19 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1
M
N RS
QP
X
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