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Name:_________________________________( ) Class : Sec 4_____

TAMPINES SECONDARY SCHOOL

PRELIMINARY EXAMINATION 2009

SECONDARY FOUR EXPRESS MATHEMATICS 4016 / 1 PAPER 1 14 September 2009

2 hours

Candidates answer on the Question Paper.

READ THESE INSTRUCTIONS FIRST Write your name, class and register 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. 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 a scientific 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 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 . At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

Calculator Model: _________________

80

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Examiner’s Use

For Examiner’s

Use Mathematical Formulae

Compound Interest

Total amount . )100

rP(1 n

Mensuration Curved surface area of a cone = rl

Surface area of a sphere = 24 r

Volume of a cone = hr 2

31

Volume of a sphere = 3

34 r

Area of a triangle ABC = Cab sin21

Arc length = r , where is in radians

Sector area = 221 r , where is in radians

Trigonometry

Statistics

Mean

ffx

Standard deviation = 22

ffx

ffx

Abccba

Cc

Bb

Aa

cos 2

sin

sin

sin

222

3

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Use

For Examiner’s

Use Answer all the questions.

1. (a) Evaluate 875.045.37

461.2

. Give your answer correct to 2 significant figures.

(b) Given that 21092.5 m and that 31012.4 n , calculate nm

1 . Give your

answer correct to 3 significant figures.

Answer (a) ………………………….. [1]

(b) ………………………….. [1]

2. (a) 72 of a plank is sawn off and

94 of the remaining piece is then thrown away. What

fraction of the original plank remains? (b) Find the number of 22-cent stamps that can be bought with $x.

Answer (a) …………………….……. [1]

(b) ….……………................ [1] 3. (a) The Punggol Promenade which will transform Punggol into a beautiful waterfront

town costs $16.7 million to build. Express 16.7 million in standard form. (b) Punggol town has a population of 53600 and this is projected to grow by 30% by

2011. What will the population be by 2011? Express your answer in standard form.

Answer (a) ………………………….. [1]

(b) ………………………….. [1]

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Use 4. The pie chart shows the cost breakdown of a holiday.

(a) Find the percentage of the total cost spent on food and hotel.

(b) Given that 15% of the total cost was spent on travel, find x.

Answer (a) ……………………..… % [1]

(b) x = ..…………………….. [1]

5. (a) Simplify 3

5

aaa and give your answer in the form na .

(b) Given that 32732 k , find the value of k.

Answer (a) ………………………….. [1]

(b) k = ..…………………….. [1] 6. The resistance of a wire of constant length varies inversely as the square of its

diameter. The resistance is 23 ohms when the diameter is d mm. Find the resistance of the wire when the diameter is halved.

Answer …..……………………ohms [2]

Food

Hotel Travel

Others

180o

xo 72o

5

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Use

For Examiner’s

Use 7. A marathon race was 42.195 km long. A runner took 4 hours 40 minutes to finish the race.

(a) Express 4 hours and 40 minutes in hours. (b) Calculate the speed of the runner. Give your answer in metres per second.

Answer (a) …………………… hours [1]

(b) ..……………………. m/s [1]

8. The diagram shows two quadrants with centre O. The radii of quadrants ABO and EFO are 2 cm and 3 cm respectively. Find the perimeter of the shaded region.

Give your answer in the form ba .

Answer …..………………………cm [2] 9. The equation of a straight line, p, is .3634 xy (a) A straight line l is parallel to p and passes through the origin. Write down the equation of l. (b) The point (2, k) lies on the line p. Find the value of k.

Answer (a) ………………………….. [1]

(b) k = ..…………………….. [1]

O

E

A 3

F B 2

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Use 10. (a) Express in set notation, the set represented by the shaded area in terms of P and Q.

(b) xx :{ is an integer, 30 ≤ x ≤ 100} A = {x: x is divisible by 4} B = {x: x is a perfect square} C = {x: x is an odd number} (i) List the elements contained in the set A B. (ii) Write down n(A C).

Answer (a) ………………………….. [1]

(b)(i) …….………………….. [1]

(ii) …………..…………… [1] 11. In the diagram, ABD is a straight line, AB = 2 cm, BD = 5 cm, BC = 3 cm,

CD = 4 cm and BCD = 90o. (a) Giving your answers as fractions, find (i) tan BDC, (ii) sinABC. (b) Find the value of AC2.

Answer (a)(i) ………………………….. [1]

(ii) ………………………….. [1]

(b) …………………………….. [2]

A B D

C 4

5

3

2

P

Q

7

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Use

For Examiner’s

Use 12. A drink stall sells ice-lemon tea and barley drink, each available in Small, Regular and Large glasses. The number of glasses of drinks sold over a 10-minute period is given in the table below.

Size of cup Small Regular Large Ice-lemon tea 4 8 2 Barley 1 5 0 Price per glass $1.30 1.50 $1.80

It is given that M =

051284

and N =

8.15.13.1

.

(a) (i) Find MN. (ii)Explain what your answer to (a)(i) represents.

(b) (i) Given that P = 11 , find PM. (ii) Explain what your answer to (b)(i) represents.

Answer (a)(i) [1]

Answer (a)(ii) …………..……………………………………………………………..

…………………………………………………………………………… [1]

Answer (b)(i) [1]

Answer (b)(ii) …………..……………………………………………………………..

…………………………………………………………………………… [1]

13. (a) A regular polygon has n sides. The size of each interior angle is seven times the size of one exterior angle. Calculate the value of n.

(b) Three regular polygons, two of which are congruent octagons, meet at a point so

that they fit together without any gaps. Describe the third polygon.

Answer (a) n =…………………….. [2]

Answer (b) ..…………..………………………………………………………… [2]

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Use 14. The scale drawing in the answer space below shows the positions of two corners,

A and B, of a horizontal triangular field. A and B are 320 m apart. (a) Find the bearing of A from B.

Answer (a) ……….…..……….. [1]

(b) The third corner, C, of the field is due south of A and is 240 m from A.

Find and label the position of C. (c) A hut, H, in the field is equidistant from B and C.

(i) Construct a perpendicular bisector of the line BC. (ii) Given also that H is on a bearing of 264o from B, find and label the position of

H. Answer (b) and (c) [3]

North

A

B

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Use

For Examiner’s

Use 15. (a) A study was done to see how long people waited for taxis outside a hospital. The result is shown in the stem-and-leaf diagram below.

Time (in minutes)

0 3 4 5 5 6 8 9 1 1 1 2 2 3 4 4 5 7 8 2 1 1 1 2 3 3 0 0

(i) Write down the modal length of time.

(ii) Find the median length of time.

Answer (a)(i) .……………………mins [1]

(ii) ….…………………mins [1] (b) Classes A and B have 40 students each. The box-and-whisker diagram below

shows the distribution of their marks in a Science test.

(i) Complete the following table. [2]

Class A Class B Median Interquartile range

(ii) What conclusion can you make about the test performance of the two classes? Explain your answer clearly. Answer (b)(ii)…………………………………………………………………………………. ………………………………………………………………………………………………[1]

key 2 1 means 21

55 60 65 70 75 80 85 90 95 100

Class A

Class B

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Use 16. Two similar pots have base radii 6 cm and 15 cm. (a) Calculate the height of the smaller pot if the height of the larger pot is 18 cm.

(b) If the cost of the material used to manufacture the base of the smaller pot is $3, what is the cost of using the same material to make the base of the larger pot?

(c) The mass of the larger pot is 200g. Find the mass of the smaller pot.

Answer (a) ………………………cm [1]

(b) $…….………………….. [2]

(c) ……….………..………g [2]

17. (a) Solve the inequality )2(32

34

xx .

Answer (a) x ……………………….. [2]

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Use

For Examiner’s

Use 17. (b) Solve the simultaneous equations. 4y = 9 – 3x 2x – y = 6

Answer (b) x = ……………………..

y = …..………………….. [3] 18. (a) (i) Express 240 as the product of its prime factors.

(ii) Find the highest common factor of 84 and 240. (iii) Find the lowest common multiple of 84 and 240.

(b) A map is drawn to a scale of 1 : 250 000. (i) The length of a road is 30 km. Calculate the length of the road on the map in

centimetres. (ii) A forest is represented by an area of 50 cm2. Calculate the actual area of the

forest in square kilometres.

Answer (a)(i) .……………………….. [1]

(ii) ….…………………….. [1]

(iii) …………..…………… [1]

(b)(i) …….………………cm [1]

(ii) …………..………km2 [1]

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Use 19. The diagram shows the speed-time graph of a van’s journey from point P.

(a) Calculate the total distance travelled by the van.

(b) Find the acceleration of the van when t = 25. (c) At t = 20, a car started from rest at point P and accelerated at a constant rate. It

passed by the van at t = 70. Calculate the speed of the car when the two vehicles met.

Answer (a) ………………..……… m [2]

(b) ………………..…… m/s2 [1]

(c) …………..……..…… m/s [2]

Speed in m/s

t

Time in seconds 20 30 70

16

22

0

13

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Use

For Examiner’s

Use 20. In the diagram, PQ = 2a and PR = b. QS is parallel to PR and PRQS

23

.

T is the point on QR such that QRTR41

. M is the midpoint of PQ.

(a) Express, as simply as possible, in terms of a and b, (i) QR ,

(ii) PT

(iii) MS (b) Find the ratio PT : MS.

Answer (a)(i) QR = ..……………….. [1]

(ii) PT = ..……………….. [2]

(iii) MS = .…..…………… [1]

(b) ……..….... : ……….….. [1]

M Q P

T

R

S

b

2a

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Use 21. (a) The diagram shows the graph of a quadratic function ))(( qxpxy . (i) Find the value of m. (ii) Write down the equation of the line of symmetry of the graph.

Answer (a)(i) m = ……….. …….. [2]

(ii) …………….……… [1] (b) (i) Sketch the graph of .3)2( 2 xy

(ii) Write down the coordinates of the turning point of the curve.

Answer (b)(i)

[2]

(ii) (…….. , ….…) [1]

0 x

y

y

x

y = (x – p)(x – q)

-4 1 0

m

15

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Use

For Examiner’s

Use 22. (a) Factorise completely yxwywx 22 .

Answer (a) ………………………….. [2] (b) Simplify ).1)(23(4 mmm

(b) ………………………….. [2]

(c) Given that 723

2

qp

p , express p in terms of q, giving your answer in its

simplest form.

(c) …….………………….. [3]