ICSE Maths Previous Year Question Paper 2012 Solved for Class 10

ICSE Paper 2012
MATHEMATICS

(Two hours and a half)
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 the 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:
ICSE Maths Question Paper 2012 Solved for Class 10 1
(b) The monthly pocket money of Ravi and Sanjeev are in the ratio 5 : 7. Their expenditures are in the ratio 3 : 5. If each saves Rs. 80 every month, find their monthly pocket money. [3]
(c) Using the Remainder Theorem factorise completely the following polynomial:
3x3 + 2x2 – 19x + 6

Solution:
ICSE Maths Question Paper 2012 Solved for Class 10 2
(b)
ICSE Maths Question Paper 2012 Solved for Class 10 3
(c)
ICSE Maths Question Paper 2012 Solved for Class 10 4
ICSE Maths Question Paper 2012 Solved for Class 10 5

Question 2:
(a) On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.? [3]
(b) ABC is an isosceles right angled triangle with ∠ABC = 90°. A semi-circle is drawn with AC as the diameter. If AB = BC = 7 cm, find the area of the shaded region. (Take n = 22/7) [3]
ICSE Maths Question Paper 2012 Solved for Class 10 6
(c)
Given a line segment AB joining the points A (-4, 6) and B (8, -3). Find:
(i) the ratio in which AB is divided by the y-axis.
(ii) find the coordinates of the point of intersection.
(iii) the length of AB.

Solution:
ICSE Maths Question Paper 2012 Solved for Class 10 7
ICSE Maths Question Paper 2012 Solved for Class 10 8

(b)
ICSE Maths Question Paper 2012 Solved for Class 10 9

(c)
ICSE Maths Question Paper 2012 Solved for Class 10 10

Question 3:
(a) In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the radius of the circle. [3]
ICSE Maths Question Paper 2012 Solved for Class 10 11

(b) Evaluate without using trigonometric tables: [3]
ICSE Maths Question Paper 2012 Solved for Class 10 12
(c) Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data.

Marks 5 6 7 8 9
No. of students 6 a 16 13 6

If the mean of the distribution is 7.2, find a and b. [4]

Solution:
(a
ICSE Maths Question Paper 2012 Solved for Class 10 13
(b
ICSE Maths Question Paper 2012 Solved for Class 10 14

(c) 
ICSE Maths Question Paper 2012 Solved for Class 10 15.1

Question 4:
(a) Kiran deposited Rs. 200 per month for 36 months in a bank’s recurring deposit account. If the bank pays interest at the rate of 11% per annum, find the amount she gets on maturity. [3]
(b) Two coins are tossed once. Find the probability of getting:
(i) 2 heads
(ii) at least 1 tail.  [3]
(c) Using graph paper and taking 1 cm = 1 unit along both x-axis and y-axis.
(i) Plot the points A(-4, 4) and B (2, 2)
(ii) Reflect A and B in the origin to get the images A’ and B’ respectively.
(iii) Write down the co-ordinates of A’ and B’.
(iv) Give the geometrical name for the figure ABA’B’.
(v) Draw and name its lines of symmetry.   [4]

Solution:
(a)
ICSE Maths Question Paper 2012 Solved for Class 10 16
(b)
ICSE Maths Question Paper 2012 Solved for Class 10 17
(c)
ICSE Maths Question Paper 2012 Solved for Class 10 18

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

Question 5:
ICSE Maths Question Paper 2012 Solved for Class 10 19
(c) A page from the Savings Bank Account of Mr. Prateek is given below:
ICSE Maths Question Paper 2012 Solved for Class 10 20
If he receives ₹ 198 as interest on 1st January, 2007, find the rate of interest paid by the bank. [4]
Solution:
(a)
ICSE Maths Question Paper 2012 Solved for Class 10 21
(b)
ICSE Maths Question Paper 2012 Solved for Class 10 22
ICSE Maths Question Paper 2012 Solved for Class 10 23
(c)

Months Minimum Balance
January 3,580
February 3,580
March 1,580
April 7,780
May 7,780
June 3,280
July 3,280
August 5,910
September 5,910
October 2,690
November 4,190
December 3,240
Total Rs. 52,800

ICSE Maths Question Paper 2012 Solved for Class 10 24

Question 6:
(a) The printed price of an article is ₹ 60,000. The wholesaler allows a discount of 20% to the shopkeeper. The shopkeeper sells the article to the customer at the printed price. Sales tax (under VAT) is charged at the rate of 6% at every stage. Find:
(i) the cost to the shopkeeper inclusive of tax.
(ii) VAT paid by the shopkeeper to the Government.
(iii) the cost to the customer inclusive of tax. [3]
(b) Solve the following inequation and represent the solution set on the number line:
ICSE Maths Question Paper 2012 Solved for Class 10 25
(c) Without solving the following quadratic equation, find the value of ‘m’ for which the given equation has real and equal roots.
x2 + 2 (m – 1) x + (m + 5) = 0         [3]

Solution:
(a)
ICSE Maths Question Paper 2012 Solved for Class 10 26
(b)
ICSE Maths Question Paper 2012 Solved for Class 10 27

(c)
ICSE Maths Question Paper 2012 Solved for Class 10 28

Question 7:
(a) A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones. [3]
(b) Solve the following equation and give your answer correct to 3 significant figures:
5x2 – 3x – 4 = 0                 [3]
(c) As observed from the top of a 80 m tall lighthouse, the angles of depression of two ships on the same side of the light house in horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest metre. [4]
Solution:
(a)
ICSE Maths Question Paper 2012 Solved for Class 10 29

(b)
ICSE Maths Question Paper 2012 Solved for Class 10 30

(c)
ICSE Maths Question Paper 2012 Solved for Class 10 31

Question 8.
(a) A man invests Rs. 9,600 on Rs. 100 shares at Rs. 80. If the company pays him 18% dividend find:
(i) the number of shares he buys.
(ii) his total dividend.
(iii) his percentage return on the shares.
ICSE Maths Question Paper 2012 Solved for Class 10 32
Solution:
(a)
ICSE Maths Question Paper 2012 Solved for Class 10 33
(b)
ICSE Maths Question Paper 2012 Solved for Class 10 34
ICSE Maths Question Paper 2012 Solved for Class 10 35
(c)
ICSE Maths Question Paper 2012 Solved for Class 10 36

Question 9:
(a) The line through A (-2, 3) and B (4, b) is perpendicular to the line 2x – 4y = 5. Find the value of b. [3]
ICSE Maths Question Paper 2012 Solved for Class 10 37
(c) A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car. [4]

Solution:
(a)
ICSE Maths Question Paper 2012 Solved for Class 10 38
ICSE Maths Question Paper 2012 Solved for Class 10 39
(b)
ICSE Maths Question Paper 2012 Solved for Class 10 40
(c)
ICSE Maths Question Paper 2012 Solved for Class 10 41

Question 10:
(a) Construct a triangle ABC in which base BC = 6 cm, AB = 5.5 cm and ∠ABC = 120°.
(i) Construct a circle circumscribing the triangle ABC.
(ii) Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.   [3]
(b) The following distribution represents the height of 160 students of a school.

Height (in cm) 140-145 145-150 150-155 155-160 160-165 165-170 170-175 175-180
No. of Students 12 20 30 38 24 16 12 8

Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:
(i) The median height.
(ii) The interquartile range.
(iii) The number of students whose height is above 172 cm. [6]

Solution:
ICSE Maths Question Paper 2012 Solved for Class 10 42
(a)
(i) Steps of constructions:
(1) Draw a line segment BC = 6 cm.
(2) Construct ∠CBP = 120°.
(3) Cut BA = 5.5 cm from BP.
(4) Join A to C.
(5) Construct perpendicular bisectors of AB and BC, intersecting at O. Join AO.
(6) Taking as the centre and OA as radius draw a circle, passing through, A, B, and C.
(ii) (1) Extend the right bisector of BC intersecting the circle at D.
(2) Join A to D and C to D.
(3) ABCD is required cyclic
(b)
ICSE Maths Question Paper 2012 Solved for Class 10 43

Question 11:
(a) In triangle PQR, PQ = 24 cm, QR = 7 cm and ∠PQR = 90°. Find the radius of the inscribed circle. [3]
ICSE Maths Question Paper 2012 Solved for Class 10 44
(b)
Find the mode and median of the following frequency distribution:  [3]

x 10 11 12 13 14 15
f 1 4 7 5 9 3

(c) The line through P(5, 3) intersects y axis at Q.
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the co-ordinates of Q. [4]
ICSE Maths Question Paper 2012 Solved for Class 10 45
Solution:

(a)
ICSE Maths Question Paper 2012 Solved for Class 10 46

(b) Mode is the value of the highest frequency.
∴ Mode = 14
For Median, we write the data in ascending order,
10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15.
∵ Median is the middle most value.
ICSE Maths Question Paper 2012 Solved for Class 10 47

(c)
ICSE Maths Question Paper 2012 Solved for Class 10 48

ICSE Class 10 Maths Previous Years Question Papers

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