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MATHEMATICS (ICSE Paper 2011)

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) Find the value of if is a factor of  . Hence determine whether is also a factor.    [3]

(b) If   and , is the product possible ? Give a reason. If yes, find .     [3]

(c) Mr. Kumar borrowed for two years. The rate of interest  for the two successive years are and respectively. If the repays at the end of the first year, find the outstanding amount at the end of the second year.    [4]

Answer:

(a)  Let .

Since given that  is a factor

Substituting the value of in the above function we get:

For  to be a factor

Substituting the value of in the above function we get:

Hence ) is a factor of 

(b)  The order of matrix  and the order of matrix  .

Since the Number of columns in  is equal to the number of rows in  , the product   is possible.

(c)   Principal

The rate of interest  for the two successive years are and respectively.

Formula:

Therefore Amount after year

Principal at the start of year after repayment

Amount outstanding at the end of second year

Question 2: 

(a) From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn at random.What is the probability that the card drawn is;

(i) a face card (King, Jack, or Queen)

(i) an even number red card    [3]

(b) Solve the following equation:    Give your answer correct to two significant figures.    [3]

(c) In the given figure is the center of the circle Tangent of and meet at if , find (i) (ii) (iii)     [4]

Answer:

(a) Total number of cards

Number of cards which are multiples of

Total number of cards left

(i) Number of face cards

Probability (of a face card)

(ii) Even numbered red cards

Probability (of a even number red card)

(b) Given 

Simplifying:

Compare with equation , we get and

We know,

Therefore

Answer correct to two significant figures: 

(c)  Consider and

is common

  (two tangents drawn from a point on a circle are of equal lengths)

Therefore  (RHS postulate)

(i)

(ii)

(iii) (chord subtends twice the angle at the center than that it subtends on the circumference)

Question 3:

(a) Ahmed has a recurring deposit account in a bank. He deposits per month for years. If he gets at the time of maturity, find; 

(i) The interest paid by the bank

(ii) The rate of interest    [3]

(b) Calculate the area of the shaded region, if the diameter of the semi circle is equal to .   (Take )     [3]

(c)  is a triangle and is the central of the triangle. If and find and find the length of side .       [4]

Answer:

(a)   

(b) Area of shaded portion = Total area – area of the two quadrants

(c)  Since is the centroid

Therefore

Therefore units.

Question 4:

(a) Solve the following in equation and represent the solution set on the number line:

    [3]

(b) Evaluate without using trigonometric tables:

    [3]

(c) A mathematics aptitude test of 50 students was recorded as follows:

Marks	50-60	60-70	70-80	80-90	90-100
No. of students	4	8	14	19	5

Draw a histogram for the above data using a graph paper and locate the mode.   [4]

Answer:

(a)  

or   or 

 or   or  

Therefore

(b) 

 

 

(c) 

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SECTION B [40 Marks]

(Answer any four questions in this Section.)

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Question 5:

(a) A manufacturer sells a washing machine to a wholesaler for . The wholesaler sells it to a trader at a profit of and the trader in turn sells it to a consumer at a profit of . If the rate of VAT is find:

(i) The amount of VAT received by the state government on the sale of this machine from the manufacture and the wholesaler.

(ii) The amount that the consumer pays for the machine.    [3]

(b) A solid cone of radius and height is melted and made into small spheres of radius . Find the number of sphere formed.     [3]

(c)  is a parallelogram where and Find

(i) Coordinates of

(ii) Equation of diagonal      [4]

Answer:

(a)  (i) Tax received by the manufacturer

For the trader the price  

Tax paid by the trader

Therefore VAT received from wholesaler

Price for the consumer

(ii) Tax paid by the consumer

Hence the total price paid by the consumer

(b)  Cone: Radius : and Height

Sphere: 

Number of sphere

 

(c)  (i) Mid point of

Therefore we have and

is the mid point of as well  (diagonals of a parallelogram bisect each other)

Hence

and 

Hence

(ii) Equation of

Question 6:

(a) Use a graph paper to answer the following (Take on both axes)

(i) Plot and the vertices of a

(ii) Reflect on the