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SRI KUALA LUMPUR INTERNATIONAL SCHOOL International General Certificate of Secondary Education
Year 11 CANDIDATE NAME CLASS
ADDITIONAL MATHEMATICS 0606/02
Paper 1 Trial Examination 2 hours Candidates answer on Question Paper. Additional Materials: Electronic calculator, Geometrical instruments
READ THESE INSTRUCTIONS FIRST Write 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 or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an electronic calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. At the end of the examination, fasten all your working securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total marks for this paper is 80.
©SRI KL 2012 This document consists of 20 printed pages. [Turn over
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1 A liquid cools from its original temperature to a temperature of To C in x minutes.
Given that T = 60(0.95)x, find the value of
(i) initial temperature, [1]
(ii) T when x = 10, [2]
(iii) x when T = 27. [2]
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2 The polynomial 3 23 11ax x x b , where a and b are constants, is denoted by f(x).
It is given that (x + 2) is a factor of the polynomial. When f(x) is divided by (x + 1), the
remainder is 12.
(i) Find the values of a and of b. [5]
(ii) When a and b have these values, factorise f(x) completely. [3]
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3 The sets P, Q and U are defined as
U = {Real numbers}, P = {Positive numbers} and Q = {Rational numbers}.
(i) Draw a Venn diagram to represent sets P, Q and U. [2]
(ii) Hence, insert all the 6 numbers given below in the correct region on the Venn diagram
drawn in part (i).
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7 , 25 10 , sin(60 ) , 0 , 3 8 , e [4]
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The diagram shows part of the graph with equation 2y x px q .
The graph cuts the x-axis at – 2 and 3 and cuts the y-axis at – 6.
(i) Find the values of p and of q. [3]
(ii) Find the minimum point of the curve. [2]
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(iii) Hence, express y in the form of 2( )ax b c , stating the values of a, b and c. [2]
(iv) On a separate diagram, sketch the function f ( )x y , showing important details. [2]
(v) The line y = k intersects f(x) at exactly 3 points. Evaluate k. [1]
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5 The function f is such that f(x) = a – b cos x for 0 360x , where a and b are positive
constants. The maximum value of f(x) is 10 and the minimum value is – 2.
(i) Find the values of a and of b. [3]
(ii) Sketch the graph of y = f(x). [2]
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6 A manufacturer produces radio, television and mobile phone, which are shipped to two
distributors. The table below shows the number of units of each type of product that are
shipped to each distributor.
Types of product Distributor 1 Distributor 2
Radio 900 500
Television 450 1000
Mobile phone 600 700
The profits made from each unit of radio, television and mobile phone are $50, $80 and $40
respectively.
(i) Write the information in the table as a matrix M. [2]
(ii) Write a matrix P which represents the profit, per unit, of each type of product. [1]
(iii) Using matrix multiplication, calculate the total profit earned from the sales to the
distributors. [3]
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7
The variables x and y are related in such a way that when lg y is plotted against lg x ,a straight
line graph is obtained as shown in the diagram above.
Given that this line passes through (0, 1) and (8, 5), find
(i) the value of x when lg y = 3, [3]
(ii) the values of a and of n when the relationship between x and y is expressed in the form
y = axn
. [3]
lg y
(8, 5)
(0, 1)
lg x
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8 In a school, six members of a committee are to be selected from 6 male teachers, 4 female
teachers and a male principal. Find the number of different committees that can be formed if
(i) the principal is the chairman of the committee, [2]
(ii) there are exactly 2 females in the committee, [2]
(iii) there are not more than 4 males in the committee. [2]
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9 (i) Find 3d(sin 2 )
dx
x . [2]
(ii) Hence, find π
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0sin 2 cos 2 dx x x . [2]
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(iii) Show that 2 3sin 2 cos2 cos2 cos 2 x x x x . [2]
(iv) Hence or otherwise, evaluate π
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0cos 2 dx x . [4]
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10 A particle P travels in a straight line so that its displacement, s metres, from a fixed point O
is given by s = 6t2 – 2t
3 + 30 , where t is the time in seconds measured from the start of the
motion.
(i) Find the initial distance of P from O, [1]
(ii) Find the acceleration of P when it is first instantaneously at rest. [4]
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(iii) Find the average speed of P over the first 4 seconds. [3]
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11 Answer only one of the following two alternatives.
The diagram shows a circle with centre O and radius 10 cm. The circle is divided into two
regions when a chord AB is drawn as shown in the diagram. The angle AOB is θ radians.
(i) Express and simplify the area of the smaller region, A1, in terms of θ. [3]
(ii) Express and simplify the area of the bigger region, A2, in terms of θ. [2]
Given that θ = π
3 radians,
(iii) Find the percentage of 1
2
A
A. [2]
(iv) Find the length of chord AB. [2]
(v) Hence, find the perimeter of triangle AOB. [1]
The diagram shows an inverted cone of a radius 4 cm and a height of 20 cm.
Oil is poured into the cone. At the instant when the height of the oil level is h cm, the radius
of the oil surface is r cm.
(i) If the height of the oil level increases at the rate of 10.1 cm s , find the rate of change of
the volume of oil when h = 6 cm. [4]
(ii) The volume of the container, V cm3, of height x cm is given by 31
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V x x .
(a) Find the maximum value of V. [3]
(b) If x changes from 9 cm to 8.9 cm, find the approximate change in volume of the
container. [3]
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EITHER
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Start your answer to Question 11 here.
Indicate which question you are answering.
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Continue your answer to Question 11 here if necessary.
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BLANK PAGE
Prepared by: Checked by: Approved by:
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Mr. Ling Sii Nen Ms. Umi Kaltom Dr. Roland
Additional Mathematics Teacher Head of Mathematics Department Senior Assistant
