Mathematics Model question Papers for ICSE-Xth Standard

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ICSE Sample paper

MATHEMATICS

(Two hours and a half)

Answer to this paper must be written in 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.

Section I is compulsory. Attempt any four questions from Section-II. The intended marks are given in

brackets [ ].

Question 1.

(a) Sachin borrows an amount of Rs.50,000.00 as personal loan at the rate of 10%

interest compounded annually from ICICI bank in the year 2002. He has to repay

it in 36 equal monthly instalments. Calculate his monthly installments. [3]

(b) A disc is thrown once,

(i) What is the probability that the number is odd? [3]

(ii) Number is greater than 2?

(c) Find the roots of the equation: [4]

5x2-6x-7=0 to two decimal places.

Question 2.

(a) Find a and b for the matrix: [3]

a b 3 6

=

2a b 8 8

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(b) In the figure below, calculate the area of the triangle OCD. AB is the diameter of

8cm and angle DAO is equal to angle DCO. [4]

D

C

A B

A

(c) Solve the inequation and represent the solution set on the number line. [3]

-2+x≤ 6x/3+2 ≤ 14/3+x

Question 3.

(a) Find the value of ‘m’ for the lines to be parallel to each other. [3]

3x+4y-7=0 and 4y+mx+8=0.

(b) In a graph, a line meets X axis at X and y-axis at Y. M is the point which

divides XY in the ratio 3:2. Find the co-ordinates of X and Y. The co-ordinate of

M is (-2,2). [4]

(c) Solve the equation for θ (0o <θ< 90o) [3]

2 cosec θ= 3 sec2θ

Question 4.

(a) Find the mean and median of the following distribution: [4]

Class Interval Frequency

O

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0-10 12

10-20 8

20-30 13

30-40 16

40-50 15

(b) Calculate the area of the shaded portion. The circle of diameter 4cm is

embedded in an equilateral triangle. The point of tangency to the circle

bisects the side of the triangle. [3]

(c) Without using tables, evaluate: [3]

Sin 33o/Sec 57o +Cos 430/Cosec 470

SECTION B (40 Marks)

Question 5

(a) A function in x is defined as: [4]

F(θ)= 1/(Sin θ +Cos θ )+1/(Sin θ -Cos θ )-2Sin θ /(1-2Cos2 θ )

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(i) Find the vale of f(300)

(ii) For F(θ)=0, prove that

2Sin θ /(1-2Cos2 θ )- 1/(Sin θ -Cos θ )= 1/(Sin θ +Cos θ )

(b) A shopkeeper bought a DVD player for Rs.2,000. He sells it at a profit of

20%. If the applicable VAT is 12.5% then calculate the following. [3]

(i) Amount paid by the customer.

(ii) VAT to be paid by the shopkeeper.

(c) A sphere and cube of equal volume have equal s volume. What is the rat

in the ratio of their surface areas. (The sphere has radius ‘r’ and the cube

has the side as ‘a’). [2]

Question 6

(a) Solve the following quadratic equation: [4]

6x2-2x-4=0

(b) A company with 3500 shares of nominal value of Rs.110 each declares an

annual dividend of 15%. Calculate: [3]

(i) The total amount of dividend paid by the company.

(ii) The annual income of a shareholder holding 90 shares in the company.

(iii) If the share holder has received 5% on his investment. Calculate the price

he had paid for each share.

(c) Given that in the following matrices : [3]

A= p 3 B = 4 m

5 2 1 0

AB=A2 find the value of p and m.

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Question 7

(a) Mr.Roy deposits Rs.1500.00 every month in a recurring deposit account for

four years at 8% per annum. Find the matured value. [3]

(b) Find the area of a triangle formed by the following equations: [4]

3x+4y-12=0 , 3x+15-5y=0 and y=0

(c) In the given figure, ABC and CEF are two triangles where BA is parallel to CE

and AF:AC=2:4. [3]

(i) Prove that triangle ADF is similar to triangle CEF.

(ii) Find AD if CE = 3 cm.

(iii) If DF is parallel to BC, then find the area of ADF : ABC.

A

D E F

B C

Question 8

(a) A man of height 2.2 mts is standing 20mts away from a flagstaff which is

mounted on a pillar of height 1.2 mt on the same plane ground. The angle of

depression at the base of the flagstaff is 30 degree and the angle of

elevation with the top of the flagstaff is 20 degrees. Calculate the height of

the top of the flagstaff from the plane ground. [3]

(b) Draw an ogive for the following distribution: [4]

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House hold expenses (in thousand Rs) Number of families

5-10 250

10-15 210

15-20 180

20-25 150

25-30 130

30-35 100

35-40 40

(i) The median expenses.

(ii) The number of families whose expenses exceeds 25,000 rupees.

(iii) The lower and the upper quartiles.

(iv) The interquartile range.

(c) Mr.Rajesh has a basic salary of Rs. 22,000 per month and his benefits are 1.2

times of his basic salary. Calculate the income tax paid by Mr.Rajesh per year

in the year 2009-2010. [3]

Question 9

(a) Draw a triangle ABC with AB=6cm and BC=7cm and angle ABC = 105

degrees. Construct a triangle ZBC such that Z is equidistant from the points B

and C and equal in area to triangle ABC. [3]

(b) Construct a histogram with the following distribution. Find the mode and draw

the frequency polygon in the same graph. [4]

Monthly Income in Rs. No of employees

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10,000-18,000 20

18,000-26,000 25

26,000-34,000 20

34,000-42,000 18

42,000-50,000 10

50,000-58,000 6

58,000-66,000 3

(c) Prove that if two tangents are drawn from an external point to a circle, then:

(i) The tangents are equal in length.

(ii) The tangents subtend equal angles at the centre of the circle.

(iii) The tangents are equally inclined to the line joining the point and the

centre of the circle. [3]

Question 10.

(a) Prove the following identity: [3]

Sec4A(1-Sin4a)-2tan2A=1

(b) The height of a cylinder is four times the radius of its base. The cylinder is melt

into ten cubes . What is the ratio of the height of the cylinder to the side of

the cube. Keep your answer in the cube root format only. [4]

(c) Given that , f(x)= 7x2-5x+2 where x={-1,0,1,2,3}. Find [3]

(i) The values of f in roaster form.

(ii) Find x such that f=0