Jurongville Prelim 2009 Em p1

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JURONGVILLE SECONDARY SCHOOLPRELIMINARY EXAMINATION

2009

Elementary Mathematics(PAPER 1)

Secondary 4 Express/ 5 Normal (Academic)

2nd September 2009 (Wednesday) Duration : 2 hours(0745 - 0945)

Name : ________________________________ [ ]

Marks :

Class : 4___ / 5N ___ Parents Signature:

_______________________

INSTRUCTIONS:

Write your name and index 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.Write your answers on the question paper.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 tothree 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 .

The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks for this paper is 80.

*Observe our school values of Integrity and Excellence by not cheating

and doing your best in this paper

DO NOT OPEN THE BOOKLET UNTIL YOU ARE TOLD TO DO SOSetter: Mdm Lucy Wu

This document consists of 18 printed pages and 2 blank pages.


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Mathematical Formulae

Compound interest Total amount =

nr

P

1001

Mensuration Curved Surface area of a cone = rl

Surface area of a sphere = 24 r

Volume of a cone = hr2

3

1

Volume of a sphere = 3

3

4r

Area of triangle ABC = Cab sin2

1

Arc length = r , where is in radians

Sector area = 2

2

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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1) (a) A new car is valued at $55 000. At the end of each year its value is reduced by15% of its value at the start of the year. What will it be worth after6 years?

(b) Throughout his life Mr Beans heart has beat at an average rate of 72 beats perminute. Mr Bean is 60 years old. How many times has his heart beat during hislife? Give your answer in standard form correct to two significant figures.

Ans: (a) $__________________ [1]

(b) ___________________ [1]

2) 6 men take 4 hours to dig a hole. Find the time taken if 8 men are available. If it takes

2

1hour to dig the hole, how many men are there?

Ans: _________________________ h [1]

______________________ men [1]


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3) On a map of scale 1 : 20 000 the area of a forest is 50 cm2. On another map the area ofthe forest is 8 cm2. Find the scale of the second map.

Ans: ___________________________ [2]

4) A group of NCC cadets are marching for their National Day Parade March Past. If theymarched in pairs, one cadet is without a partner. If they marched in 3s, 5s and 7s,there will be one cadet without a partner. Calculate the smallest number of pupils in theMarch Past contingent.

Ans: ___________________________ [2]


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5)

Find a formula for the shaded part in terms ofp, q and r.

Ans: ___________________________ [2]

6) An intelligent fish lays black or white eggs and it likes to lay them in a certain pattern.Each black egg is surrounded by six white eggs.

Here are 3 black eggs and 14 white eggs.

(a) How many eggs does it lay altogether if it lays 200 black eggs?

(b) How many eggs does it lay altogether if it lays n black eggs?

Ans: (a) ___________________ [1]

(b) ___________________ [1]

p

qr


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7) Each packet of Quaker Cereal carries a token and 5 tokens can be exchanged for a freepacket. How many free packets will I receive if I bought 125 packets?

Show clearly your working.

Ans: ___________________________ [2]

8) (a) Simplify28

7

1612 pp

(b) Showing your working clearly, solve the equation

64

1)23( 2

3

x

Ans: (a) ___________________ [1]

(b) x = ________________ [2]


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9) (a) Channel U starts its transmission every evening at 17 30 and finishes at03 45 the following morning. Calculate the duration of its transmission, givingyour answer in hours.

(b) If the minute hand of the clock moves through a duration of 36 minutes, what isthe corresponding angle that the hour hand move?

Ans: (a) _________________ h [1]

(b) _________________ [2]

10) If { x: x is an integer such that }10010 x

A = { x: x when divided 15 leaves a remainder 7}B = { x:x when divided by 17 leaves a remainder 14}

(a) Find the value ofn (A).

(b) Find the value of ).( BAn

(c) State the largest member ofB.

Ans: (a) ___________________ [1]

(b) ___________________ [1]

(c) ___________________ [1]


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11) (a) Write the number 438 pico in standard form.

(b) If it takes

5

1of a second to write a zero and

10

1sec to write an integer other than a

zero, how long does it take to write the number?

Ans: (a) ___________________ [1]

(b) ________________ sec [2]

12) Given that 105 x ,3

x

ky , where kis a constant and the smallest value ofy is 2, find

(a) the value ofk,

(b) the largest value ofy,

(c) the largest value ofxy

yx .

Ans: (a) k= ________________ [1]

(b) ___________________ [1]

(c) ___________________ [1]


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13) During the National Day Celebration, JVS ordered T-shirts of various sizes for the students.The matrices show the order of various sizes of T-shirts and the cost ($) for the various sizes.

SMLXL

Girls

Boys

1352106050

85180240220

S

M

L

XL

20.9

12

50.13

15

(a) Find 11

1352106050

85180240220

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

(c) Using matrix multiplication, find the total amount the school has to pay.

Ans: (a) ___________________ [1]

(b) __________________________________________________________________ [1]

(c) $ __________________ [1]


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14) In the diagram, ABCDEFis a regular hexagon and APQRB is a regular pentagon. PXR

is a straight line. Calculate

(a) BAP,(b) ABX .

(c) Show that PR is parallel toAB. [2]

Ans: (a) __________________ [1]

(b) __________________ [1]

15) John sells cylindrical tins of pet food in his provision shop. The height of a tin is 8 cmand the cost price is $3.20. He intends to sell another type which is geometricallysimilar to the ones he is selling but whose height is 4 cm. Calculate the price to thenearest one cent that he should sell this smaller tin so that he makes a profit of 35%.

Ans: $ _________________________ [4]

D

B

A

E

F

C

Q

R

X

P


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16) In the diagram, O is center and angle PQT = 28o and angle RPT = 40o, find the bearingof

(a) P from T,(b) R from T,

(c) P from R.

Ans: (a) __________________ [1]

(b) __________________ [2]

(c) __________________ [1]

40

28T

P

Q

R

O

N


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17) In a video game, a spot on the screen bounces off the four sides of a rectangular frame. Thespot moves from A to B to C to D, as shown in the diagram below.

(a) What can you say about the angle at which the spot bounces off each side,compared with the angle at which it approached the side?

(b)The column vector describing the part AB of the movement is

3

2

. Write down

the column vector describing BC and CD.

(c) From D the spot moves to E on the fourth side of the frame. Given that the spotcontinues in the same way, write down the vector DE.

(d) Given that the spot bounces off the fourth side at E and continues to move,describe its subsequent path.

Ans: (a) ___________________ [1]

(b) ___________________ [2]

(c) ___________________ [1]

(d) __________________________________________________________________ [1]


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18) A racing car manufacturer makes two models, the Alfa and Beta which are alike in every aspectexcept body design and styling. To determine if the body design of the Alfa has less windresistance, both cars were tested on the Bukit Speedway. The following table gives lap times inminutes on a 5 km track;

Alfa 1.0 0.9 1.0 0.8 0.9 1.0 0.9 1.0Beta 1.3 1.2 1.0 0.9 1.1 0.9 1.4 1.3

(a) Find the mean lap times for the Alfa and the Beta.

(b) Find the standard deviation for each car.

(c) Comment on the performance of each car.

Ans: (a) Alfa _______________Beta _______________ [2]

(b) Alfa _______________Beta _______________ [2]

(c) _________________________________________________________________ [1]

19) Expressy= 31102 xx in the form bax 2)( where a and b are integers. Hence

sketch the graph ofy. State its minimum value and the line of symmetry.

Sketch [1]

Ans: ___________________________ [2]

Min value __________________ [1]

Line of symmetry ____________ [1]


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20)

In the diagram, 090 ADBABC , AD =p andDC= q.

(a) Use similar triangles to show that pzx 2

.

(b) Find a similar expression for 2y .

(c) Add the two expressions for 2x and 2y and hence prove the

Pythagoras Theorem.

Ans:

(a) __________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________ [2]

(b) __________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________[2]

(c) __________________________________________________________________

__________________________________________________________________

__________________________________________________________________ [1]

A C

B

x

p q

y

z

D


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21)The diagram shows a grid of squares. A button is placed on one of the squares. The sixfaces of a fair die are marked 1, 2, 3, 4, 5and 6. The fair die is tossed. If 1 is shown,the button is moved one square upwards followed by one square to the left. If 2 or 3

is shown, the button is moved one square downwards. If 4 is shown, the button ismoved one square to the right. If 5 or 6 is shown, the button is moved two squares tothe left. The table below illustrates the movement.

Numbershown

Direction of movement

1

2 or 3

4

5 or 6

(a) The button is placed on the square I. The die is tossed once. Find the probabilitythat the button finishes at the square U.

(b) On another occasion, the die is tossed once and the button is moved. When the dieis tossed a second time, the button is moved again.

(i) If the button is placed at G, find the probability that the button finishes at

square R.(ii) If the button is placed on the square R, find the probability that the button

finishes at the square U.

Ans: (a) ___________________ [1]

(b)(i) ___________________ [2]

(b)(ii) ___________________ [2]

U G

E

D

I

R

P


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22)

The diagram is the speed-time graph of an object during a period of 15 seconds.

(a) (i) Calculate the retardation during the first 4 seconds.

(ii) Calculate the distance travelled in the first 4 seconds.

(iii) Given that the acceleration of the object between t= 10 and t= 15 is

20 2ms , calculate the speed of the object when t= 15.

Ans: (a)(i) _______________ ms-2 [1]

(a)(ii) ________________ m [1]

(a)(iii) _______________ ms-1

[1]

80

24

04 10 15

Speed in 1ms

Time in sec


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(b) On the axes in the answer space, sketch the distance time graph, indicating thedistance travelled, for the journey.

[2]

4 10 15Time in sec0

Distance in m


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23) (a) Using ruler and compasses, construct XYZ in which XY = 10 cm, YZ = 9 cmand XZ = 8 cm.

(b) Measure, and write down, the size of the smallest angle in the triangle. Give areason for your choice.

(c) A point P is 3.8 cm from X and also equidistant from Y and Z. On your diagramand using suitable constructions find and mark the point P.

Constructions:

(a) XYZ(c)

[2][2]

Ans: (b) __________________ [1]

Reason ___________________________________________________________ [1]


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BLANK PAGE


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No Answer No Answer

1 a) $20743.22b) 2.3 X 109

13 a) 220390300270 b) The total order for XL, L, M andS sized T-shirts respectively.c) $14 804

2 3 hours48 men

14 a) 1080b) 600

c)0

0

0

180

72

36

RBAPRB

PRB

QRF

Since they are interior angles,PR is parallel to AB.

3 1 : 50 000 15 $0.54

4 211 16 a) 3320

b) 2200

c) 01205 q+r-p 17 a) Equally inclined to the

horizontal or negativegradients to each other.

b)

4

6BC ,

6

9CD

c)

4

6

d) E will move to A andcontinue the path in the

same pattern.6 A0 802

b) 4n + 218 a) Mean

Alfa: 0.9375Beta:1.1375

b) Std deviationAlfa: 0.0696Beta: 0.180

c) Alfa is a better performingcar because it has consistentlysmaller lap times.

7 31 19 6)5( 2 xy

Min value = 6Line of symmetry: x = 5.

8a) 3 8

1

p

b) 3

24x

20 a) Proof

b) zqy 2


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c)2

22

)( zqpz

zpqzyx

This is the Pythagoras Theorem.

9a)

4

110 h

b) 180

21a)

6

1

b)i)181

ii)9

1

10 a) 6b) 1c) 99

22 a) i) 14 ms-2b) ii) 208 mc) 124 ms-1

11 a) 4.38 x 10-10

b)10

12 sec

12 a) k = 2000

b) 16c) 0.8

23 b) 00 149 Reason: Angle opposite the shortestside would be the smallest angle.

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Jurongville Prelim 2009 Em p1