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MATHEMATICS (ICSE Paper 2014)

Two and Half Hour. Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper.

The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions form Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the Answer. Omission of essential working will result in the loss of marks.

The intended marks for questions or parts of questions are given in brackets [ ].

Mathematical tables are provided.

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SECTION A [40 Marks]

(Answer all questions from this Section.)

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Question 1:

(a) Given . Find the matrix such that .   [3]

(b) At what rate p.a. will a sum of yield as compound interest in years?   [3]

(c)   The mediam of the following observation arranged in ascending order is . Find the value of and hence find the mean. [4]

Answers:

(a)  Given

Substituting these values in the given expression we get,

(b)  Given: Principle

Amount

Time

We know that;

Therefore,

(c)  Given observation are and mediam

Since which is odd, therefore

Therefore,

Now, Mean

Question 2:

(a) What number must be added to each of the number to make them proportional?   [3]

(b) If is a factor of the expression  and, when the expression is divided by , it leaves a remainder , find the values of .   [3]

(c) Draw a histogram from the following frequency distribution and find the made from the graph:   [4]

Class	0-5	5-10	10-15	15-20	20-25	25-30
Frequency	2	5	18	14	8	5

Answers:

(a)  Let the number that must be added be , then

The new number 

Since they are proportional,

(b) Let is a factor of the given expression;

Since

In the given expression,  we substitute we get

… … … … … (i)

When given expression is divided by

Similarly, in the given expression,  we substitute we get

   … … … … … (ii)

Solving equation (i) and (ii),

(c)

Question 3:

(a) Without using tables evaluate:    [3]

(b) In the given feature,

, , 

Prove:

(i) AC is the diameter of the circle

(ii) Find    [3]

(c) is a diameter of a circle with center , If , Find;

(i) The length of radius

(ii) The Coordinates of    [4]

Answers:

(a)

(b) Given:

(i) Since  is a cyclic quadrilateral

In

( sum property of a triangle)

Now from ,

Hence makes right angle belongs in semi-circle therefore is a diameter of the circle.

(ii) (Angles in the same segment of a circle)

Therefore

(c)   (i) Length of the radius

(ii) Let the point be

Given is the mid-point of . Therefore

Hence, the co-ordinate of

Question 4:

(a) Solve the following equation and calculate the answer correct to two decimal places. . [3]

(b)  In the given figure, and are perpendicular to

(i) Prove that 

(ii) If , Calculate ,

(iii) Find the ratio of the area of    [3]

(c)  Using graph paper, plot the point and .

(i) Reflect and in the origin to get the images and .

(ii) Write the co-ordinate of and

(iii) State the geometrical name for the figure

(iv) Find its perimeter   [4]

Answers:

(a)   Given :

Comparing this expression with , we get 

(b)   (i)  From

Givem

And

(ii) In

Since

Given: ,

(iii) Since $latex \triangle ABC \sim \triangle DEC,

(c)   (i) Please see graph

(ii) Reflection of and in the origin

(iii) The geometrical name for the figure is a parallelogram

(iv) From the graph,

In

Therefore since is a parallelogram

Perimeter of

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SECTION B [40 Marks]

(Answer any four questions in this Section.)

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Question: 5

(a)   Solve the following inequation, write the solution set and represent it on the number line:   [3]

(b)   Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is of per annum and Mr. Britto gets from the bank after years, find the value of his monthly installment.        [3]

(c) Salman buys shares of face value available at .

(i)  What is his investment?

(ii)  If the dividend is what will be his annual income?

(iii)  If he wants to increase his annual income by . How many extra shares should he buy?      [4]

Answers:

(a) Given;

Taking L.C.M. of 3, 2 and 6 is 6.