Mock Trial Exam Nicely Done

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SRI KUALA LUMPUR INTERNATIONAL SCHOOLInternational General Certificate of Secondary Education

Year 11

CANDIDATENAME

CLASS

ADDITIONAL MATHEMATICS 0606/02

Paper 1 Trial Examination2 hours

Candidates answer on Question Paper.Additional Materials: Electronic calculator, Geometrical instruments

READ THESE INSTRUCTIONS FIRSTWrite in dark blue of black pen.

You may use a soft pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue orcorrection fluid.

Answerall the questions.Give non-exact numerical answers correct to 3 significantfigures, or 1 decimal place in the case of angles in degrees,

unless a different level of accuracy is specified in thequestion.The use of an electronic calculator is expected, whereappropriate.You are reminded of the need for clear presentation in youranswers.

At the end of the examination, fasten all your workingsecurely together.The number of marks is given in brackets [ ] at the end ofeach question or part question.The total marks for this paper is 80.

SRI KL 2012 This document consists of20 printed pages. [Turn over

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2 The straight line 2 3 6x y meets the curve2 2(2 1) 6( 2) 49x y at the pointsA andB.

Calculate the distanceAB. [6]


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3 Solve the simultaneous equations 9 3 243y x ,2 64

22

y

xy . [4]


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4 Let f(x) =x2kx, where kis a real constant, and g x x .

(i) Show that the least value of f(x) is2

4

k and find the corresponding value ofx. [3]

(ii) Find the coordinates of the two intersecting points of the curvesy = f(x) andy = g(x). [3]


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(iii) Suppose k= 3,

(a) In the same diagram, sketch the graphs ofy = f(x) andy = g(x) and label their

intersecting points. [3]

(b) Find the range of values ofx such that f( ) g( )x x .

Hence, find the least value of f(x) within this range of values ofx. [3]


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5 (i) Obtain the expansion, in ascending powers ofp, of 5

2 p . [3]

(ii) Hence, find the coefficient of6

x in the expansion of 5 2

2 22 1x x . [3]


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6 The letters of the word OLYMPIADS are written on 9 different cards.

(i) Find the number of ways of arranging these cards in a row such that

(a) the vowels O, I and A are always together, [2]

(b) the three letters M, I and D are separated from each other. [2]

(ii) If these 9 cards are to be packed into three different envelopes with 3 cards each,

how many ways can this be done? [2]

(iii) If 5 cards are to be selected. Find the number of ways it can be done if the cards with

letters O andL must either be selected together or not at all. [2]


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7 A particle P moves in a straight line so that at time tseconds after leaving a fixed point O its

velocity, v1

ms

, is given by2

5 8et

v

.

(i) Findan expression forthe acceleration of the particle. [2]

(ii) Find an expression for the displacementof the particle from O. [3]


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(iii) Find the distance of the particle from O at the instant at which the particle is

instantaneously at rest. [3]

(iv) Particle Q travels at a constant speed of 51

ms . Explain briefly whether particle P can

travel faster than particle Q. [2]


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8 Given the equations

(i) y = pqx

,

(ii) y =Bxk

, wherep, q,B and kare unknown constants.

Each of the equations may be represented by a straight line. They each need to be expressed in

the form Y= mX+ c, whereXand Yare each functions ofx and/ory, and m and c are constants.

Complete the following table and insert in it an expression for Y,X, m and c for each case.

Equations Y X m c

y = pqx

y =Bxk

[5]


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9 Given that 3cos2y x and sin2y x for 0 x .

(i) Sketch, in a single diagram, the graphs 3cos2y x and sin2y x for 0 x . [4]

(ii) Find the coordinates of the point of intersection of the two curves for

02

x . [4]


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(iii) Calculate the area of the region bounded by the two curves and they-axis. [4]


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10 Answer only one of the following two alternatives.

EITHER

A food company produces cans of instant soup. Each can is in the form of a right cylinder

with a base radius ofx cm and a height ofh cm. Its capacity is Vcm3, where Vis constant.

The cans are made of thin metal sheets.The cost of the curved surface of the can is 1 cent per cm

2and the cost of the plane surfaces

is kcents per cm2. Let Ccents be the production cost of one can.

(i) Express h in terms of,x and V. [3]

(ii) Hence show that 22

2V

C kxx

. [2]

(iii) Ifd

0d

C

x , expressx

3in terms of , kand V. [3]

(iv) Show that Cis a minimum when2

hxk

. [3]

OR

(a) Find thex- coordinate of the first two stationary points of the curve 2e sinxy x ,

wherex is in radian and 0x . Determine the nature of these points. [7]

(b) A sector has radius rcm and angle radians. Given that its area is fixed,

use calculus to find the approximate percentage change in its radius when its angle

decreases by 2%. [4]


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Start your answer to Question 10 here.

Indicate which question you are answering.

EITHER

OR


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Continue your answer to Question 10 here if necessary.


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Continue your answer to Question 10 here if necessary


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Prepared by:

SII NEN

-----------------------------

Mr. Ling Sii Nen

Additional Mathematics Teacher

Mock Trial Exam Nicely Done

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