# ICSE Board Class 10 Math Sample Papers 2011

## ICSE Board Sample Papers 2011 for Class 10 Math

SAMPLE  PAPER
MATHEMATICS

CLASS 10

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 from 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 loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ].
Mathematical tables are provided.

SECTION A (40 Marks)
Attempt all questions from this Section
Question 1
(a) Find the value of a and b if  x −1 and  x − 2 are factors of 3x ax b − + .  [3]

(b) In the figure given below, ABCD is a parallelogram. E is a point on AB.
CE intersects the diagonal BD at G and EF is parallel to BC.
If AE : EB = 1 : 2 find
(ii)  area of triangle BEF : area of triangle ABD  [3]

(c)        On a certain sum of money, the difference between the compound interest
for a year, payable half yearly, and the simple interest for a year is Rs 16.
Find the sum lent out, if the rate of interest in both cases is 8 % . [4]

Question 2

(a) Plot the points A(9,6) and B(5,9) on the graph paper. These two points are
the vertices of a figure ABCD which is symmetrical about x = 5 and y = 6.
Complete the figure on the graph.  Write down the geometrical name of
the figure.  [3]

(b) In the diagram given below ∠EDC. The tangent drawn to the circle at C
makes an angle of 50 with AB produced. Find the measure of ∠ACB.  [3]

(c) PQRS is a square piece of land of side 56 m.  Two semicircular grass
covered lawns are made on two of its opposite .

(b) A point P(a, b) is reflected in the Y-axis to P
Write down the values of a and b.

(c) Given :  A x x x R = < − < ∈ { : 3 2 1 9, } , B x x x R = ≤ + ≤ ∈ { :11 3 2 23, }
where R is the set of real numbers.
(i)  Represent A and B on number lines
(ii) On the number line also mark A B ∩ . [4]

Question 4
(a)     Mr. Jacob has a two years recurring deposit account in State Bank of India
and deposits Rs.1500 per month. If he receives Rs.37,875 at the time of
maturity, find the rate of interest.       [3]
(b) Calculate the arithmetic mean, correct to one decimal place, for the
following frequency distribution of marks obtained in a Geometry test.
Marks            0-10 10-20 20-30 30-40 40-50
No of students 7      13       15         12      3           [4]

SECTION B (40 Marks)
Attempt any four questions from this Section
Question 5

(a) In the diagram given below if AF = 21 cm, CE =  30 cm and FB = 7 cm.
Find the volume of the figure.  [3]
(b) A man bought 200 shares each of face value Rs.10 at Rs. 12 per share.  At
the end of the year, the company from which he bought the shares declares
a dividend of 15%. Calculate:
(i) the amount of money invested by the man
(ii) the amount of dividend he received
(iii) the percentage return on his outlay.     [4]

Question  6
to three significant figures:

(b)  An integer is chosen at random from 1 to 50. Find the probability that the
number is:
(i)   divisible by 5
(ii)   a perfect cube
(iii) a prime number.  [3]

Question 7
(a) Bosco wishes to start a 200 m2  rectangular vegetable garden. Since he has
only 50 m barbed wire, he fences three sides of the rectangular garden
letting his house compound wall act as the fourth side of the fence. Find the
dimensions of the garden.  [3]

(b) Construct a triangle ABC, with AB = 6 cm, BC = 7 cm and ∠ABC = 60°.
Locate by construction the point P such that
(i) P is equidistant from B and C.
(ii) P is equidistant from AB and BC
(iii) Measure and record the length of PA. [3]
(c)  Mr. A. Ramchander has an account with Central  Bank of India.  The
following entries are from his pass book:
Date Particulars Withdrawal Deposits Balance
05.01.2009 B/F   8000
20.01.2009 To self 2500
04.02.2009 By cash  9000
20.02.2009 By cash  3000
04.03.2009 To self 1000
15.04.2009 By cash  12000

Complete the above page of his passbook and calculate the interest
accumulated in four months, January to April at the rate of 3.5% per
annum. If the interest is added on 30 th
April, find his balance on that date. [4]

Question 8
(a) Prove that
1/secx-tanx+1/secx+tanx=2/cosx .[3]

(b) In the figure given below, CD is the diameter of the circle which meets the
chord AB at P such that AP = BP = 12 cm. If DP = 8 cm, find the radius
of the circle.   [3]

(c) Prove that A(2, 1), B(0,3) and  C(-2,1) are the three vertices of  an
isosceles right angled triangle.  Hence find the coordinates of a point D, if
ABCD is a square.  [4]
Question 9
(a) A fair dice is rolled. Find the probability of getting
(i)  3 on the face of the dice
(ii)  an odd number on the face of the dice
(iii)  a number greater than 1 on the face of the dice.  [3]
(b) A (4,2), B(6,8) and C (8,4) are the vertices of a triangle ABC. Write down
the equation of the median of the triangle through A. [3]
(c) The angle of elevation of an aeroplane from a point P on the ground is 60
After 12 seconds from the same point P, the angle of elevation of the same
plane changes to 30 . If the plane is flying horizontally at a speed of
600 3 km / h, find the height at which the plane is flying. [4]

Question 10
(a) The following table shows the distribution of the heights of a group of
students:
Height
(cm)
140-145 145-150 150-155 155-160 160-165 165-170 170-175
No of
students
8 12 18 22 26 10 4
Use a graph sheet to draw an Ogive for the distribution.
Use the Ogive to find:
(i) the inter quartile range
(ii) the number of students whose height is more than 168 cm
(iii) the number of students whose height is less than 148 cm. [6]
(b) The manufacturer sold a TV to a wholesaler for Rs.7000. The wholesaler
sold it to a trader at a profit of Rs.1000. If the trader sold it to the customer
at a profit of Rs.1500, find:
(i) the total VAT (value added tax) collected by the state
government at the rate of 5% .

Question 11
(a) In the diagram given below, equation of AB is  x y − + = 3 1 0 and equation
of AC is  x y − − = 2 0
(i) Write down the angles that the lines AC and AB make with the
positive direction of  X- axis.
(ii)    Find ∠BAC.  [3]
(b) In the figure given below, O is the center of the circle. Chord CD is parallel
to the diameter AB.  If ∠ABC = 35°, calculate ∠CED. [3]
(c) Construct a triangle ABC, given that AB = 6 cm, BC = 8 cm and median
AD = 5 cm. Construct an incircle to triangle ABC and measure its radius. [4]

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