Tampines Prelim 2009 Em 1

Name:_________________________________(

)

Class : Sec 4_____

TAMPINES SECONDARY SCHOOL PRELIMINARY EXAMINATION 2009 SECONDARY FOUR EXPRESS MATHEMATICS PAPER 1 14 September 2009 Candidates answer on the Question Paper.

4016 / 1 2 hours

Calculator Model: _________________

READ THESE INSTRUCTIONS FIRST

80

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.

This document consists of 15 printed pages Setter : Mdm Loh MW

[Turn Over

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Mathematical Formulae

Compound Interest Total amount  P(1 

r n ) . 100

Mensuration Curved surface area of a cone =

rl

Surface area of a sphere = 4r

2

1 2 r h 3

Volume of a cone =

Volume of a sphere = Area of a triangle ABC =

4 3 r 3 1 ab sin C 2

Arc length = r , where  is in radians Sector area =

1 2 r  , where  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

Standard deviation =

 fx f

2

  fx    f   

2

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Answer all the questions. 1.

(a) Evaluate

2.461 37.45  0.875

. Give your answer correct to 2 significant figures.

(b) Given that m  5.92  10 2 and that n  4.12  10 3 , calculate

1  n . Give your m

answer correct to 3 significant figures.

Answer (a) ………………………….. [1] (b) ………………………….. [1] 2.

(a)

2 4 of a plank is sawn off and of the remaining piece is then thrown away. What 7 9 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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4.

The pie chart shows the cost breakdown of a holiday.

Food 180o Others o

x

72o Hotel

Travel (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  a5 and give your answer in the form a n . 3 a (b) Given that 3 2 k  27  3 , find the value of k. (a) Simplify

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]

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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 a  b . E A 3

F

O

B 2

Answer …..………………………cm [2] 9.

The equation of a straight line, p, is 4 y  3 x  36. (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]

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10.

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

Q

(b)   {x : x 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 C (i) tan BDC, 4 (ii) sinABC. 3 (b) Find the value of AC2. A

2

B

5

D

Answer (a)(i) ………………………….. [1] (ii) ………………………….. [1] (b) …………………………….. [2]

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12.

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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 Ice-lemon tea Barley Price per glass

Small 4 1 $1.30

 4 8 2 It is given that M =   1 5 0

Regular Large 8 2 5 0 1.50 $1.80 1 . 3    and N = 1.5  . 1.8   

(a) (i) Find MN. (ii)Explain what your answer to (a)(i) represents. (b) (i) Given that P = 1 1 , 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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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)

North

A

B

[3]

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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.

0 1 2 3

3 1 1 0

4 1 1 0

Time (in minutes) 5 5 6 8 9 2 2 3 4 4 1 2 3

5

7

8

key 2 1 means 21

(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. Class A

Class B 55

60

65

70

75

80

85

90

(i) Complete the following table. Class A

95

100

[2] 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]

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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

4x  3  3( x  2) . 2

Answer (a) x ……………………….. [2]

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17.

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(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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19.

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

22 Speed in m/s

16

0

t 20

70

30 Time in seconds

(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]

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20.

In the diagram, PQ = 2a and

PR = b. QS is parallel to PR and QS  3 PR . 2

1 T is the point on QR such that TR  QR . M is the midpoint of PQ. 4 S

R T b

Q

2a

P

M

(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]

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21.

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(a) The diagram shows the graph of a quadratic function y  ( x  p )( x  q ) . (i) Find the value of m. (ii) Write down the equation of the line of symmetry of the graph. y y = (x – p)(x – q)

-4

0 1

x

m

Answer (a)(i) m = ……….. …….. [2] (ii) …………….……… [1] (b) (i) Sketch the graph of y  ( x  2) 2  3. (ii) Write down the coordinates of the turning point of the curve. y Answer (b)(i)

0

x

[2]

(ii) (…….. , ….…) [1]

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22.

(a) Factorise completely

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wx  2 wy  x  2 y .

Answer (a) ………………………….. [2]

(b) Simplify 4m  (3m  2)(m  1).

(b) ………………………….. [2]

p2  2q  7 , express p in terms of q, giving your answer in its 3p simplest form.

(c) Given that

(c) …….………………….. [3]