SAMPLE ICSE MATHEMATICS QUESTION PAPER, MARCH 2014

1. ICSE MATHEMATICS March,2014 Sample Question Paper, By Rakesh Kushwaha (M.Sc.; B.Ed.)
ICSE March-2014
(MATHEMATICS)
SAMPLE MODEL PAPER
Time: 2 hours
M.M.: 80
Date: 10-03-2014
Instructions: 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 for questions or the parts of questions are given in brackets [ ].
SECTION I (40 Marks)
Attempt all questions from this Section
Question 1
A.
If (x + 1) is a factor of (5x + 8)3 – (a – x) 3, find a.
B.
Find the value of x, given A2 = B, A =
C.
The difference of C.I. payable half-yearly and S.I. on a sum of money lent out at 10% p.a. for
[3 Marks]
and B =
one year was Rs 25. Find the sum.
[3 Marks]
[4 Marks]
Question 2
A.
Solve for x :
+
=
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[3Marks]
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2. ICSE MATHEMATICS March,2014 Sample Question Paper, By Rakesh Kushwaha (M.Sc.; B.Ed.)
B.
A die is rolled once. Find the probability of getting:
i.
a perfect square
ii.
an even prime number
iii.
a number < 5
iv.
not an even number.
[3 Marks]
B
C.
C
In the given figure, AD is diameter of the circle with
centre ‘O’. If
BCD = 125 , calculate:
i)
DAB
ii)
.
ADB
A
O
D
[4 Marks]
Question 3
A.
Mr. Prakash Nagaria opened a Recurring Deposit Account in a bank and deposited Rs. 300 per
month for two years. If he received Rs. 7725 at the time of maturity, find the rate of interest per
annum.
B.
[3 Marks]
A bicycle wheel whose diameter is 77 cm makes 50 revolutions in 20 seconds. Find the speed in
km/h. [Take π = 22/7]
C.
[3 Marks]
KM is a straight line of 13 units. If K has the coordinates (2, 5) and M has coordinates (x, -7), find
the possible values of x.
[4 Marks]
Question 4
A.
Solve: x +
,x
W and graph the solution set.
B.
Without using tables, find the value of:
C.
-
[3 Marks]
- 2sin2 45°.
IQ of 50 students was recorded as follows:
IQ Score 80 - 90 90 - 100 100 - 110 110 - 120
No. of Students
6
9
16
13
Draw a histogram for the above data and estimate the mode.
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[3 Marks]
120 - 130
130 - 140
4
2
[4 Marks]
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3. ICSE MATHEMATICS March,2014 Sample Question Paper, By Rakesh Kushwaha (M.Sc.; B.Ed.)
SECTIONII (40 Marks)
Attempt any four questions from this Section
Question 5
A.
A purchases an article for Rs. 3,100 and sells it to B for Rs. 4,250. B in turn sells it to C for Rs.
5,000. If VAT is 10%, find the VAT levied on A and B.
B.
Find the volume of a right circular conical tent, whose vertical height is 8 m and the area of
whose base is 156 m2.
C.
[3 Marks]
[3 Marks]
ABCD is a rhombus. The coordinates of A and C are (3, 6) and (-1, 2) respectively. Write down
the equation of BD.
[4 Marks]
Question 6
A.
Use a graph paper to answer the following questions:
i.
ii.
Reflect ABC on the y-axis and name it as A B C .
iii.
Write the coordinates of the images A , B and C .
iv.
Give the geometrical name for the figure AA C B BC.
v.
B.
Plot A (4, 4), B (4, -6) and C (8, 0), the vertices of a triangle ABC.
Identify the line of symmetry of AA C B BC.
[5 Marks]
The rate of interest decreases from 5 % to 4% with effect from 01.06.2013. Compute the
interest at the end of the year on a saving bank account for the entries shown in the table if the
interest is payable yearly.
Date , Year 2013
January 1
Balance (in Rs.)
[5 Marks]
600
February 9
1,200
March 11
2,500
June 25
3,500
September 10
1,500
November 5
4,000
December 23
500
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Page: 3

4. ICSE MATHEMATICS March,2014 Sample Question Paper, By Rakesh Kushwaha (M.Sc.; B.Ed.)
Question 7
A.
Find the numbers such that their mean proportion is 14 and third proportion is 112. [3 Marks]
B.
Find x and y, if
C.
In the figure, name three pairs of similar triangle.
=
.
[3 Marks]
D
F
If AB = 2 cm, BC = 4 cm and CD = 9 cm,
E
calculate EB and AF.
[4 Marks]
A
Question 8
A.
B
C
Calculate the mean of the following frequency distribution by step-deviation method:
Classes
80 – 85
85 – 90
90 – 95
95 - 100
100 - 105
105 -110
110 - 105
Frequency
5
8
10
12
8
4
3
[5 Marks]
B.
Draw a cumulative frequency curve (ogive) for the following distribution and determine the
median.
Marks
50 - 60
No. of Students
60 - 70
70 - 80
80 - 90
90 - 100
4
8
12
6
10
[5 Marks]
Question 9
A.
Mr. Nilesh holds 150 shares of face value Rs. 50 each. The company declares a dividend of 15%.
Find his income.
[3 Marks]
B.
Construct a circle in a hexagon of side 3.6 cm.
[3 Marks]
C.
Prove that:
[4 Marks]
+
= sin A + cos A
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5. ICSE MATHEMATICS March,2014 Sample Question Paper, By Rakesh Kushwaha (M.Sc.; B.Ed.)
Question 10
A.
Solve for x :
= 3.
[3 Marks]
B.
A certain sum of money compounded annually becomes Rs 6750 after 1 year and Rs 7873.20
after 3 years. Find the sum.
C.
[3 Marks]
A vertical pole and a vertical tower are on the same level ground. From the top of the pole the
angle of elevation of the top of the tower is 60°and the angle of depression of the foot of the
tower is 30°. Find the height of the tower if the height is of the pole is 20 m.
[4 Marks]
Question 11
A.
The sum of squares of two consecutive natural numbers is 313. Find the numbers. [3Marks]
B.
In the given figure, AP is a tangent to the circle
at P. ABC is a secant such that PD is bisector of
Prove that:
[3 Marks]
P
BPC.
BPD = [ ABP - APB].
C
C.
D
B
A
Find the equation of the altitude AD of the triangle whose vertices are A (7, -1), B (-2, 8) and
C (1, 2).
[4 Marks]
**************
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