2009 RV EM P1

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2009 RVHS Preliminary Examination Page 1 of 16 O Level Mathematics (4016) P1

RIVER VALLEY HIGH SCHOOL

2009 PRELIMINARY EXAMINATION

SECONDARY FOUR

CANDIDATE

NAME

CLASS 4 INDEX NUMBER

___________________________________________________________________________

MATHEMATICS 4016/01

Paper 1 15 September 2009

2 hours

Candidates answer on the Question Paper.

___________________________________________________________________________READ THESE INSTRUCTIONS FIRST

Write your class, index number and name on all the work you hand in.

Write in dark blue or black pen on both sides of the paper.

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.

Calculators should be used where appropriate.

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.

The total of the marks for this paper is 80.

For Examiners Use

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Mathematical Formulae

Compound interest

Total amount = P( 1 +100

r)n

Measuration

Curved surface area of a cone = rl

Surface area of a sphere = 4r2

Volume of a cone =3

1r2h

Volume of a sphere =3

4r3

Area of triangle ABC =21 ab sin C

Arc length = r, where is in radians

Sector area =2

1r

2, where is in radians

Trigonometry

C

c

B

b

A

a

sin=

sin=

sin

a2

= b2

+ c2 2bc cos A

Statistics

Mean =fx

f

Standard deviation =

22fx fx

f f

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Answer all the questions.

1 Evaluate

(a)693.08.23

23.5

,

(b) )1013.2()1096.8( 36 .

[Leave both your answers in standard form.]

Answer(a) .[1]

(b) .[1]

_________________________________________________________________________

2 The pie chart shows how 120 students come to school.

Find

(a) the value ofx,

(b) the number of children who take

bus to school,

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

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

30

o

cycle

walk

car

bus

MRT

xo

xo

2xo

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3 (a) Simplify

3

2

3

x

(b) Given that k213 3813 , find the value of k

Answer(a)[1]

(b) k = [1]

___________________________________________________________________________

4 The time in Auckland is 4 hours ahead of Singapore.

(a)Mr Yeo in Auckland calls his wife on her mobile phone at 13 38 Auckland time.

Find the time in Singapore when Mrs Yeo receives the call.

(b) They spoke briefly for 8 minutes before Mrs Yeo's mobile phone runs out of battery.

She rushes home by bus, taking 1 hour 23 minutes, and calls her husband

immediately. Find the time in Auckland when Mr Yeo gets the call.

Answer(a)[1]

(b)[1]

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5 (a) A dealer sold a camera for $184. She made a profit of 15%. Calculate the cost price

of the camera.

(b) The selling price of a camera decreases from $560 to $480 during a sale. Calculate

the percentage reduction in the selling price of the camera.

Answer(a) $ ... [1]

(b) ......................................... % [1]

___________________________________________________________________________

6

O

A

B

14cm

In the diagram, OAB is a quadrant of a circle, with a radius of 14cm. OB is the diameter

of a semicircle. Take to be7

22, calculate the total length of curves ODB andACB.

Answer.... cm [2]

14 cm

A

B

C

D

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7 The population of a city is 1.2 107. There are 8.0 106 senior citizens. The rest areyoung citizens.

(a) What fraction of the population are senior citizens?

(b) Find the number of young citizens, leaving your answer in standard form.

Answer(a)... [1]

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

___________________________________________________________________________

8

The sketch represents the graph of y = mx + c.

(a) Write down the value ofc.

(b) Find the value ofm.

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

(b) m =..........................................[1]

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9

ABCis a triangle in which BAC= 90,AC= 40 cm andBC= 41 cm.The lineACis produced to Q.

(a) Showing your working clearly, explain whyAB = 9 cm. [1]

(b) Express as a fraction (i) tan BCA, (ii) cos BCQ.

Answer(b)(i) tan BCA = ... [1]

(b)(ii) cos BCQ =.......................[1]___________________________________________________________________________

10 For Valentines Day, a gift shop offers two types of packages consisting of roses,

chocolates and candies. The matrices show the two types of packages and the cost of

each rose, chocolate and candy.

Roses Chocolates Candies $

1.23 3 5

0.56 9 8

0.3

RosePackage A

ChocolatePackage B

Candy

(a)Find

3.0

5.0

2.1

896

533

(b)Explain what your answer to (a) represent.

Answer(a)... [2]

(b) ............................................................................................................................................

.....................................................................................................................................[1]

B

P

41

A 40 C Q

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(a) On the Venn diagram above and shade the region that represents

(A B) C. [1](b) Given that

={x :x is a positive integer },A = { 1, 2, 3, 4, 5, 6 },

B = {x :x is a multiple of 3, 3

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13 It is given that y varies inversely asx andy = 20 whenx = 40.

(a) Find an expression for the relationship betweeny andx.

(b) Ifx increases by 50%, find the percentage change iny.

Answer(a)[1]

(b)[2]___________________________________________________________________________

14

The dot diagram shows the number of pets kept by a group of students in a class.

Find (a) the mode,

(b) the median,

(c) the percentage of students that have at least 3 pets,

Answer(a)[1]

(b)[1]

(c).. % [1]

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15 (a) Factorise completely 3 6 8 4px qx qy py .

(b) Simplify 22 )34(916 xx

Answer(a).[2]

(b).[2]

_______________________________________________________________________

16 (a) Each interior angle of a regular polygon is eight times the corresponding exterior

angle. Find the number of sides of the polygon.

(b) A regular polygon has an interior angle of 140o. Calculate the number of sides of the

polygon.

Answer(a)..sides [2]

(b)..sides [2]

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17 (a) Given that three school bells ring at intervals of 25 minutes, 30 minutes and 1 hour

respectively, calculate the next time they will ring together if they first ring together

at 7.45 am.

(b) Express the numbers 480 and 576 as the products of their prime factors. Find the

smallest positive integer value ofn for which 480n is a multiple of 576.

Answer(a)..[2]

(b) 480 = ...[1]

576 =[1]

n = ...[1]

___________________________________________________________________________

18 (a) Find the largest integer kwhich satisfies 2 4 5k k .

(b) Solve the simultaneous equations

.yx

,yx

332

1325

Answer(a) k=... [2]

(b)x = .....................,y = .....................[3]

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19 Two spherical containersA and B used for storing chemicals has a capacity of 80cm3 and

270cm3 respectively. The curve surface area of container A is given as 90cm2.

(a) Find, in its simplest integer form, the ratio of the radius of the container A to the

radius of the containerB.

(b) Calculate the surface area of containerB.

(c) A manufacturer charges $20 to paint container A. Find the cost of painting the

containerB.

Answer(a) Ratio = .. : ..[1]

(b) cm2 [2]

(c) $ [2]

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20

P Q

6n V

U

S 4m R T

PQRS is a parallelogram such that SR = 4m, SP = 6n. The line PTcutsRQ at U. It is

also given that RU=1

3RQ.

(a) Express the following vectors in terms ofm and n:

(i) RU

(ii) QU

,

(iii) PU,

(b) Vis a point on QTsuch that UV=5

31 m +

5

4n, find SU

and explain why S, Uand

Vare collinear points.

Answer(a)(i) RU

=..... [1]

(ii) QU

= .[1]

(iii) PU

= .[1]

(b) ................................................................................................................................................

......................................................................................................................................................

...............................................................................................................................................[2]

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21 (a) (i) Sketch the graph of (7 2 )y x x .

(ii)Write down the equation of the line of symmetry of (7 2 )y x x .

[2]

Answer(a)(ii ) [1]

(b) (i) Sketch the graph of 1)3( 2 xy .

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

[2]

Answer(b)(ii ) (. , . ) [1]

O x

y

O x

y

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22 The diagram below is the speed-time graph of a lorry. The lorry starts from rest and

steadily accelerates to a speed of 15m/s in 10 seconds. Its speed then remains constant

for some time before it steadily decreases at4

3m/s 2 until it stops. The whole journey

takes one minute.

(a) Given that the speed afterx seconds is v m/s, express v in terms ofx.(b) For how long does the lorry travel at the maximum speed ?

(c) Calculate the total distance travelled by the lorry during this 1 minute.

Answer(a) v = .[2]

(b).... s [2]

(c). . m [2]

15

v

0 x 10 60 t(s)

V m/s

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23 The diagram below shows the map of a triangular fieldABC. The scale of the map is

unknown. The bearing ofCfromA is 090o and D is a point on the sideAB.

(a) A pointElies on the angle bisector ofBACand is such that area ofADC= areaof AEC. Locate and label the position of point E in the diagram, showing your

method of construction clearly.

(b) A point Fis due south ofA and is such that Fis equidistant fromB and C.Locate and label the point Fin the diagram. Write down the bearing of Cfrom F.

(c) The actual distance ofCfromA is 172 m. Make use of this information to find an

estimation for the actual area ofABC in m2.

B

D

North

A C

[3]

Answer(b) Bearing ofCfrom F=.. [1]

(c) ....m2

[2]

2009 RV EM P1

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