Share

# Mathematics Set 1 2012-2013 ICSE Class 10 Question Paper Solution

SubjectMathematics
Year2012 - 2013 (March)
Mathematics [Set 1]
Marks: 80Date: 2012-2013 March

1
1.1

Given A = [(2,-6),(2,0)], B = [(-3,2),(4,0)], C = [(4,0),(0,2)]

Find the matrix X such that A + 2X = 2B + C.

Concept: Addition and Subtraction of Matrices
Chapter: [0.0208] Matrices
1.2

At what rate % p.a. will a sum of Rs. 4000 yield Rs. 1324 as compound interest in 3 years?

Concept: Conept of Compound Interest - Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
Chapter: [0.011000000000000001] Compound Interest
1.3

The median of the following observations
11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24.
Find the value of x and hence find the mean.

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
2
2.1

What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?

Concept: Proportions
Chapter: [0.0204] Ratio and Proportion
2.2

If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.

Concept: Factor Theorem
Chapter: [0.0203] Factorization
2.3

Draw a histogram from the following frequency distribution and find the mode from the graph:

 Class 0-5 5-10 10-15 15-20 20-25 25-30 Frequency 2 5 18 14 8 5
Concept: Measures of Central Tendency - Mean, Median, Mode for Raw and Arrayed Data
Chapter: [0.06] Statistics
3
3.1

Without using tables evaluate:
3cos 80°. cosec 10° + 2sin 59° sec 31°

Concept: Trigonometry Problems and Solutions
Chapter: [0.05] Trigonometry
3.2

In the given figure, ∠BAD = 65°, ∠ABD = 70°, ∠BDC = 45°

1) Prove that AC is a diameter of the circle.

2) Find ∠ACB

Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle
Chapter: [0.032] Circles
3.3

AB is a diameter of a circle with centre C = (–2, 5). If A = (3, –7). Find

1) the length of radius AC

2) the coordinates of B.

Concept: Lines of Symmetry
Chapter: [0.034] Symmetry
4
4.1

Solve the following equation and calculate the answer correct to two decimal places:

x2 – 5x – 10 = 0.

4.2

In the given figure, AB and DE are perpendicular to BC. 1) Prove that ΔABC ∼ ΔDEC

2) If AB = 6 cm; DE = 4 cm and AC = 15 cm. Calculate CD.

3) Find the ratio of area of ΔABC: area of ΔDEC

Concept: Similarity of Triangles
Chapter: [0.035] Similarity
4.3

Using a graph paper, plot the points A(6,4) and B(0,4).
(1) Reflect A and B in the origin to get the images A' and B'.
(2) Write the co-ordinates of A' and B'.
(3) State the geometrical name for the figure ABA' B'.
(4) Find its perimeter.

Concept: Simple Applications of All Co-ordinate Geometry.
Chapter: [0.021] Co-ordinate Geometry Equation of a Line
5
5.1

Solve the following inequation, write the solution set and represent it on the number line -x/3 <= x/2 - 1 1/3 < 1/6, x ∈ R

Concept: Representation of Solution on the Number Line
Chapter: [0.020499999999999997] Linear Inequations
5.2

Mr Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. It the rate of interest is of 8% per annum and Mr Britto gets Rs. 8088 from the bank after 3 years, find the value of his monthly instalment.

Concept: Computation of Interest
Chapter: [0.013000000000000001] Banking
5.3

Salman buys 50 shares of face value Rs. 100 available at Rs. 132.
(1) What is his investment?
(2) If the dividend is 7.5%, what will be his annual income?
(3) If he wants to increase his annual income by Rs. 150, how many extra shares

Concept: Shares and Dividends
Chapter: [0.012] Shares and Dividends
6
6.1

Show that sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)

Concept: Trigonometric Identities
Chapter: [0.05] Trigonometry
6.2

In the given circle with centre O, ∠ABC = 100°, ∠ACD = 40° and CT is a tangent to the circle at C. Find ∠ADC and ∠DCT. Concept: Tangent to a Circle
Chapter: [0.032] Circles
6.3

Given below are the entries in a Saving Bank A/c passbook.

 Date Particulars Withdrawals Deposit Balance Feb8 B/F - - Rs. 8500 Feb 18 To self Rs. 4000 - April 12 By cash - Rs. 2230 June 15 To self Rs. 5000 - July 8 By cash - Rs. 6000

Calculate the interest for six months from February to July at 6% p.a.

Concept: Computation of Interest
Chapter: [0.013000000000000001] Banking
7
7.1

In ΔABC, A(3, 5), B(7, 8) and C(1, –10). Find the equation of the median through A.

Concept: General Equation of a Line
Chapter: [0.021] Co-ordinate Geometry Equation of a Line
7.2

A shopkeeper sells an article at the listed price of Rs. 1500 and the rate of the VAT is 12% at each stage of the sale. If the shopkeeper pays a VAT of Rs. 36 to the Government, what was the price, inclusive to TAX, at which the shopkeeper purchased the article from the wholesaler?

Concept: Introduction to Sales Tax and Value Added Tax
Chapter: [0.013999999999999999] Gst (Goods and Services Tax)
7.3

In the figure given, from the top of a building AB = 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to 30o and 60o respectively. Find: 1) The horizontal distance between AB and CD.

2) The height of the lamp post.

Concept: Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables
Chapter: [0.05] Trigonometry
8
8.1

Find x and y if [(x,3x),(y, 4y)] = [(5),(12)]

Concept: Matrices Examples
Chapter: [0.0208] Matrices
8.2

A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.

Concept: Area and Volume of Solids - Sphere
Chapter: [0.04] Mensuration
8.3

Without solving the following quadratic equation, find the value of ‘p' for which the given equation has real and equal roots:

x2 + (p – 3)x + p = 0.

9
9.1

In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region. Concept: Areas of Sector and Segment of a Circle
Chapter: [0.032] Circles
9.2

A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball, find the number of black balls in the box.

Concept: Simple Problems on Single Events
Chapter: [0.07] Probability
9.3

Find the mean of the following distribution by step deviation method:

 Class Interval 20-30 30-40 40-50 50-60 60-70 70-80 Frequency 10 6 8 12 5 9
Concept: Measures of Central Tendency - Mean, Median, Mode for Raw and Arrayed Data
Chapter: [0.06] Statistics
10
10.1

Using a ruler and compasses only:

1) Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ABC = 120°

2) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.

3) Measure ∠BCP.

Concept: Circumscribing and Inscribing a Circle on a Triangle
Chapter: [0.033] Constructions
10.2

The marks obtained by 120 students in a test are given below:

 Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 No. ofstudents 5 9 16 22 26 18 11 6 4 3

Draw an ogive for the given distribution on a graph sheet.

Use a suitable scale for ogive to estimate the following:
(1) The median.
(2) The number of students who obtained more than 75% marks in the test.
(3) The number of students who did not pass the test if minimum marks required to pass is 40

Concept: Median from the Ogive
Chapter: [0.06] Statistics
11
11.1

In the figure given below, the line segment AB meets X-axis at A and Y-axis at B. The point P(-3, 4) on AB divides it in the ratio 2:3. Find the coordinates of A and B. Concept: Equation of a Line
Chapter: [0.021] Co-ordinate Geometry Equation of a Line
11.2

Using the properties of proportion, solve for x, given

(x^4 + 1)/(2x^2) = 17/8

Concept: Componendo and Dividendo Properties
Chapter: [0.0204] Ratio and Proportion
11.3

A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and solve it to find the original cost of the books.

#### Request Question Paper

If you dont find a question paper, kindly write to us

View All Requests

#### Submit Question Paper

Help us maintain new question papers on Shaalaa.com, so we can continue to help students

only jpg, png and pdf files

## CISCE previous year question papers Class 10 Mathematics with solutions 2012 - 2013

CISCE Class 10 Maths question paper solution is key to score more marks in final exams. Students who have used our past year paper solution have significantly improved in speed and boosted their confidence to solve any question in the examination. Our CISCE Class 10 Maths question paper 2013 serve as a catalyst to prepare for your Mathematics board examination.
Previous year Question paper for CISCE Class 10 Maths-2013 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.
By referring the question paper Solutions for Mathematics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of CISCE Class 10.

How CISCE Class 10 Question Paper solutions Help Students ?
• Question paper solutions for Mathematics will helps students to prepare for exam.
• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.
• For finding solution of question papers no need to refer so multiple sources like textbook or guides.
S