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Class Register No Name

This document consists of19 printed pages.

READ THESE INSTRUCTIONS FIRST

Write your Class, register number and name 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 theanswer 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 is brackets [ ] at the end of the each question or part question.The total number of marks for this paper is 80.

For Examiners Use

Bukit Merah Secondary School

Preliminary Examination 2009Secondary Four Express

Secondary Five Normal Academic

MATHEMATICS (Revised)

Paper 1

Candidates answer on the Question Paper.

4016/01

15 September 2009

2 hours

E/N

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BMSS Prelims 2009/4016 Paper 1 [Turn Over

Mathematical Formulae

Compound Interest

Total amount =

n

rP 1001

MensurationCurved surface area of cone = rl

Surface area of a sphere = 24 r

Volume of cone = hr2

3

1

Volume of sphere = 3

3

4r

Area of triangleABC= Cabsin2

1

Arc length = r , where is in radians

Sector area = 22

1r , where is in radians

Trigonometry

C

c

B

b

A

a

sinsinsin

Abccba cos2222

Statistics

Mean =

f

fx

Standard deviation =

22

f

fx

f

fx

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ForExaminers

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Answer all the questions. ForExaminers

Use

1. Evaluate

(a)22.128.2

15.411

,

(b) 31029.1553.1289.6 ,leaving both your answers to 3 significant figures.

Answer (a) ... [1]

(b) ... [1]

2. i) Given that ....3818181.0x , find the value of xx 101000 .ii) Hence express 0.3818181 in the form

b

a, where a and b are integers.

Answer i) ..... [1]

ii) .................... [1]

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3. A computer operating system has a storage capacity of0.12 terabytes.

(a) Express 0.12 terabytes in bytes, giving your answer in standard form.(b) A 4-minutes long music file is 35 megabytes. Find the number of songs that

can be stored, leaving your answer in standard form.

ForExaminers

Use

Answer (a) [1]

(b) ....

[1]

4.i) Solve the inequality 1

2

127 xx .

ii) Hence, write down the smallest rational numberx which satisfies1

2

127 xx .

Answer i) .. [1]

ii)....... [1]

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5. The number 228, written as a product of its prime factors, is 1932228 2 .

(a) Express 416as a product of its prime factors.(b) Using your results, find

i) the largest integer which is both a factor of228 and 416,ii) the smallest integer kfor which 416kis a multiple of228.

ForExaminers

Use

Answer (a) .... [1]

(b) i) ... [1]

ii) [1]

6.PQRS are vertices of a regular n-sidedpolygon which has interior angles of162.(a) Find the value ofn.(b) Find PSR.(c) State the special name given to the quadrilateral PQRS.

Answer (a) [1]

(b) ..... [1]

(c) . [1]

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7. (a) In the Venn diagram given below, shade the region representing 'QPP

[1]

(b) There are 35 girls in a class. 18 of these girls are in Dance and 21 girls are inBand.

Given that

Classin theGirls

DanceinarewhoGirlsD

BandinarewhoGirlsB

i) Find the smallest value of BDn .ii) Express the following in set notation:

{Girls who is neither in Dance nor Band}

ForExaminers

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Answer (b) i).. [1]

ii) ... [1]

P Q

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8. The diagram shows a triangle with pointsA,B and Cas its vertices.

(a) Find the gradient of the lineAB.(b) Find the area of triangleABC.(c) Write down the value of .

ForExaminers

Use

Answer (a) ..... [1]

(b) ......... units2 [1]

(c) .. [1]

C

A

B

2

x

6

4

-2

y

-1 0 1 2

-4

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9. (a) A girl boughtydozens of roses at $2 per dozen and sold them at 60 cents each.Calculate her profit earned in terms ofy.

(b) It takes Alan 45 minutes to pitch a tent alone. The time will reduce by 20minutes if Alice helps him with it. Find the time taken by Alice to pitch the tent

alone.

ForExaminers

Use

Answer (a) $......[1]

(b) mins. [2]

10. A man bought an iPhone for $359, inclusive of7% goods and services tax (GST).

(a) Calculate the amount of GST paid.The exchange rate between US dollars (US$) and Singapore dollars (S$) was US$1 =

S$1.38.

(b) He sold the phone to a friend for US$235. Calculate his profit/loss made.

Answer (a) $ . [1]

(b) profit / loss

$ ... [2]

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11. The costs of two geometrically similar cylindrical cup of mixed fruit juice are $1.08and $2.56respectively.(a) Write down the ratio of the heights of the cylindrical cup.(b) The cost of making the smaller cylindrical cup is 18-cents. Calculate the cost of

making the larger cup.

(c) The content of the mixed fruit juice was divided between oranges, apples andpineapple in the ratio 4 : 2 : 3 respectively. Calculate the percentage of

pineapple in the mixed fruit juice.

ForExaminers

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Answer (a) . [1]

(b) $ ......... [1]

(c) ..% [1]

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12.

(a) Simplify 23

2

9

4

x, leaving your answer in positive indices.

(b) Given that 22 381

1243

k

, find the value ofk.

ForExaminers

Use

Answer (a) . [1]

(b) k = .............. [2]

13. A railway track1.5km long is represented by a 5cm line on a map.

(a) Find the scale of the map, giving your answer in the form 1 : n.(b) Find, in square metres, the actual area of a city that is 0.2cm2 on the map.

Answer (a) .. [1]

(b) ... m2 [2]

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14. The amount of light,L units, received is inversely proportional to the square of thedistance,D metres. For a particular value ofD, the amount of light received is 25units.(a) Find the value ofL whenD is quartered.(b) Find the percentage change in the amount of light received whenD is increased

by 400%.

ForExaminers

Use

Answer (a) .. [1]

(b) .....% [2]

15. i) Express 372 xx in the form bax 2 .ii) Hence, solve 8372 xx .

Answer i) ... [1]

ii) ...... [2]

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16. (a) The number of goals scored by Liverpool Football Club during their pre-seasontour were as follows:

4 5 1 x 2 6 2 1

Given that the median goal scored is 2.5, find the value ofx.

(b) The mean ofset A consisting of12 numbers is 11 and the mean ofset Bconsisting ofy numbers is 4. Given the difference between their total is 8, find

2 possible values ofy.

ForExaminers

Use

Answer (a) x = .... [1]

(b)y = ...... or ..... [2]

17. A purse containing a certain number of coins and has a total value of$5.20. There areonly 5 cents and 20 cents coins in the purse and thrice as many 20 cents coins than 5cents coins. By forming two equations, find the number of5 cents coins in the purse.

Answer ...[3]

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18. In the diagram below,ABCD is a quadrilateral and ABD = BCD = 90. ForExaminers

Use

Given thatAB = 7cm, CD = 8.5cm and ADB = 33.

Find(a) BD(b) ABC

Answer (a) .cm [1]

(b) ....... [2]

19. (a) Expand and simplify 222 yxxy .(b) Factorise completely wywxwwx 22 2 .

Answer (a) . [2]

(b) ..... [2]

33

A

CB

D

7cm

8.5cm

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20. In the diagram below,ABCD is a square andAECFis a rectangle. ForExaminers

Use

Stating your reasons clearly,i) Show that FAQ = ECP.ii) Hence, show that FAD ECB.

Answer:

i)

.. [1]

ii)

..[2]

A

B C

D

P

Q

EF

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21. An equilateral triangle of side 10cm is inscribed in a circle, centre O as shown. Theradius of the circle is r cm.

ForExaminers

Use

(a) Find the value ofr2.(b) Hence, find the area of theshadedregion,

giving your answer in the form ba .

Answer (a) r2 = . [2]

(b) .......cm2 [2]

22. (a) The point (1, 2) is marked on the diagram in the answer space. On thediagrams, sketch the graphs of

i) 3 xy ii) 22 xy

Answer i) Answer ii)

[2]

O

r

A

B C10cm

x

y

x

y

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(b) A container consisting of3sections,A,B and Cis shown in the diagram below. ForExaminers

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Water is poured into the container at a constant rate. It takes 6 minutes to fill upsection A.

i) Write down the time taken to fill up section C.ii) On the axes given below, complete the graph showing the relationship

between the depth of water, h cm as its varies over time, t minutes.

Answer (b) i) ..mins [1]

Answer (b) ii)

[2]

A

B

C

r

r

r

h cm

2h cm

h cm

Time(minutes

Depth (cm)

0 2 4 6 8

4h

3h

2h

h

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23. The diagram is the distance-time graph for the first 50 seconds of a cars journey. Thecar started from rest.

ForExaminers

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(a) Find the speed of the car when t= 30.(b) The car moved with a constant acceleration for the first 20 seconds. Find this

acceleration.

(c) On the grid in the answer space, draw the speed-time graph for the samejourney, given that the car decelerates to come to rest in the last 10 seconds.

Answer (a) .. .m/s [1]

(b) ...... m/s2 [1]

Answer (c)

[2]

0 10 20 30 40 50

400

300

200

100

Distance (metres)

Time(t seconds)

0 10 20 30 40 50 Time (second)

Speed (metres per second)

15

10

5

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24. The table below shows the number of radiators needed for small, medium-sized andlarge houses.

ForExaminers

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Size of HouseType of Radiator

A B C D

Small 5 2 1 0Medium 2 0 3 3Large 0 1 6 4

There are 25 small houses, 36medium-sized houses and 12 large houses in an estate.

(a) Represent the above data by 43 matrix P.(b) If 123625Q and QPN ,

i) EvaluateN.ii) Explain what information can be derived from matrixN.

(c) The cost of the radiators are $20 for type A, $40 for type B, $45 for type Cand$70 for type D.

Using matrix multiplication, find the total cost of all the radiators for the estate.

Answer (a) .. [1]

(b) i) ... [1]

ii) ... [1]

(c) ... [2]

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25. The diagram, drawn to a scale of1cm to 500m, shows two position ofTown A andB . ForExaminers

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(a) A Town Cis northeastofTown A and on a bearing of335from Town B. Findand label the position ofTown C.

(b)

A petrol kioskP is to be set up such that it is equidistant fromI : Town A and Town B and

II : ACandBC.

By construction, find and label the possible position the petro kiosk.

(c) Measure the distanceBP.Answer (a) and (b)

[4]

Answer (c) ..m [1]

END OF PAPER

A

B

North

bmss em09 p1

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