1. Evaluate . Give your answer correct to 2 significant figures in standard form.

Answer ………………….………….[1]

2. During a sale a shopkeeper reduced the prices of all his goods by 15%. Calculate the discount amount of a wallet which was sold for $25.50 in the sale.

Answer $………………..………….[2]

3. Factorise (1–2a)5b + (2a – 1) completely.

Answer [2]

CHS 2011 Prelim III Maths 4016/1 Page 1

4. When it is 01 15 in New York the time in Singapore is 13 15.

(a) What is the time in New York when it is 23 55 in Singapore?

(b) A plane leaves Singapore at 23 55 to fly to New York. The flight takes 18 hours.

Find the time in New York when it arrives.

Answer (a)………………………….[1]

(b)……………………….[1]

5. On a particular day the temperature varied by 26 C. The highest temperature recorded

was 12 C. Find

(a) the lowest temperature recorded on that day,

(b) the average of the lowest and the highest temperatures.

Answer (a)……………….…… C [1]

CHS 2011 Prelim III Maths 4016/1 Page 2

(b)………………….… C [1]

6. (a) Express 2520 as the product of its prime factors.

(b) Given that 2520k is a perfect square, write down the smallest possible integer value of k.

(c) Find the smallest positive integer value of n for which 2520n is a multiple of 65.

Answer (a) 2520 = [1]

(b) k = [1]

(c) n = [1]

7. The world population was recently estimated to be 6.94 billion. The total land surface

area of the world is approximately km2.

(a) Express km2 in m2.

(b) Find the average number of people per square kilometer of the land surface area. Give your answer in nearest whole number.

Answer (a) m2[1]

CHS 2011 Prelim III Maths 4016/1 Page 3

(b) [2]

8. Given that y is inversely proportional to the square of x, and that y = 90 when x = 3, find

(a) an expression for y in terms of x,

(b) the value of y when x is increased by 200%.

Answer (a) y = [2]

(b) y = [1]

9. Solve the following simultaneous equation.

3y = 2x – 15 5x – 6y = 33

CHS 2011 Prelim III Maths 4016/1 Page 4

Answer x = , y = [3]

10. (a) Solve the inequality 5 – p < 3(2 + 4p).

(b) Solve the equation

y+13

+ 2y=2

.

Answer (a) [2]

(b) y = or y [3]

11. (a) Express the following as a single matrix.

(i)

(ii)

(b) Given that , find the value of k..

Answer (ai) [1]

CHS 2011 Prelim III Maths 4016/1 Page 5

(aii) [1]

(b) k = [1]

12. Two unbiased dice are thrown and the scores are noted. Find the probability that

(a) the product of the scores is 30.

(b) both the scores are the same.

(c) both the scores are different.

Answer (a) [1]

(b) [1]

(c) [1]

13. Find the equation of the curve given in the diagram below.

5

- 2

- 2

y

x

Answer y = [2]

CHS 2011 Prelim III Maths 4016/1 Page 6

14. The stem-and-leaf diagram below shows the weights in kilograms of 18 men.

Find (a) the modal weight,

(b) the median weight,

(c) the inter-quartile range.

Answer (a) kg [1]

(b) kg [1]

(c) kg [2]

15. The ratio of the volumes of two geometrically similar solid statuses is 8 : 125.

(a) Write down the ratio of the heights of the two statuses.

(b) Both statuses are completely painted white. The cost of paining the smaller status

is $12.50. Find the cost of painting the larger status.

CHS 2011 Prelim III Maths 4016/1 Page 7

5 4 8 96 2 2 3 3 3 4 8 97 3 3 4 5 6 7 8

C

B

A

y

x642-4 -2

-6

-4

-2

2

4

6

8

Answer (a) [1]

(b) $ [ 1]

16. A, B and C are the points , and respectively.

(a) Write down the equation of the line AB.

Answer (a) [1]

(b) Find the length of the line BC.

Answer (b) units. [1]

(c) Find the area of the triangle ABC.

Answer (c) units2. [1]

CHS 2011 Prelim III Maths 4016/1 Page 8

(d) D is the point such that the area of the triangle ABD is half of that of triangle ABC. Find the two possible values of k.

Answer (d) k = or [1]

17. Just before a Mathematics test, a class of 30 students was asked if they had foolscap paper and/or graph paper. F denotes the set of students with foolscap paper and G denotes the set of students with graph paper.

(a) On the Venn Diagram below, shade the set .

(b) Describe in words the set of students represented by .

(c) It was found that and . Find the largest possible value of

.

F

G

CHS 2011 Prelim III Maths 4016/1 Page 9

Answer (a) On Diagram [1]

(b) [1]

(c) [1]

CHS 2011 Prelim III Maths 4016/1 Page 10

A

B

C

D18.

The diagram shows part of a regular polygon with n sides. Each interior angle of this polygon is 150o. Find

(a) the value of n,

(b) ∠ ACD .

(c)

Answer (a) n = [1]

(b) ° [1]

(c) ° [1]

19. (a) Find the value of

xy , given that

2 x−3 y5 x+2 y

=1

.

(b) Given thatx=√ub+ 1

2a2 b

. Make a be the subject of the formula..

CHS 2011 Prelim III Maths 4016/1 Page 11

=

Answer (a) [2]

(b) a = [2]

20. In the diagram below, the container has a uniform cross-section which comprises of a

semi-circle of radius 7cm and a rectangle with a breadth 5cm. Water is being filled into

the container at a constant rate. It takes 14 minutes to fill up the semi-circle cross-section

of the container.

1 8 cm

7 cm

5 cm

(a) Find the time taken to fill up the entire container.

(b) On the axes in the answer space, sketch the graph showing how the depth of the water, d

centimeters, in the container varies with time.

[Take π=22

7 ]

Answer (a) min [1]

CHS 2011 Prelim III Maths 4016/1 Page 12

L

M N

P Q

R

1 4

D ep th o f

w a te r (d cm )

T im e (m in u te s)

Anwers (b) On Graph

[1]

21.

LMN is an isosceles triangle with LM = LN. P and Q lie on LM and LN respectively such

that PN and QM bisect angle LNM and angle LMN respectively. PN and QM intersect at

R.

(a) Show that triangles LMQ and LNP are congruent.

(b) Name another two triangles that are also congruent.

CHS 2011 Prelim III Maths 4016/1 Page 13

Answer (a) In s LMQ and LNP ……………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………….. [2]

Answer (b) ………… and …………….[1]

CHS 2011 Prelim III Maths 4016/1 Page 14

22. In the diagram, .

(a) On the grid in the given answer space, mark and label clearly

(i) the point B such that ,

(ii) the point C such that .

(b) Find .

(c) Express as a column vector.

(d) Given that and , find the values of m and n.

O

A

Answer (ai) On digram [1]

(aii) On digram [1]

(b) [1]

(c) [1]

CHS 2011 Prelim III Maths 4016/1 Page 15

(d) m = and n = [2]

23.

The diagram shows a circle with centre O and radius 5 cm. A, B, C and D are points on the circles and OYA, OXB, OWC and OZD are identical semicircles formed with OA, OB, OC and OD as diameters respectively.

(a) Find the perimeter of the shaded region. Give your answer in terms of .

(b) Express the area of the shaded region as a percentage of the area of the circle ABCD.

Answer (a) cm [2]

(b) % [2]

CHS 2011 Prelim III Maths 4016/1 Page 16

24. A developer bought a triangular piece of land, ABC, where C is due east of A, AB = 85 m

and ∠BAC=85 ° .

(a) Using a scale of 1 cm to represent 10 m, construct an accurate scale drawing of the plan of the land in the space below. [2]

(b)    The developer intends to build a house H on the land.  The house H is on a bearing of 060° from A and on a bearing of 290° from C.  Find and label the position of house H. [2]

(c) The developer intends to build a children’s playground on the land at location P which is equidistant from A, B and C. By using ruler and compass only, construct perpendicular bisectors and hence locate the position of P. [2]

CHS 2011 Prelim III Maths 4016/1 Page 17

A C

CHS 2011 Prelim III Maths 4016/1 Page 18

25. The first four terms in a sequence of numbers, are given below.

(a) Write down an expression for and show that .

(b) The nth term, , of the sequence can be written as . Find the values of a, b and c.

Answer (a) T5 = [1]

(b) a = , b = , c = [4]

~~~~~~~~~~~~~~~~~~End of Paper~~~~~~~~~~~~~~~~

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