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Question Paper Solutions - Mathematics 2010 - 2011 ICSE Class 10

Year2010 - 2011 (March)

Attempt all questions From Question 1 to Question 4

Attempt any four questions From Question 5 to Question 11

Marks: 80

Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.

Chapter: [2.05] Factorization
Concept: Factor Theorem

if `A = [(3,5),(4,-2)] and B = [(2),(4)]`is the product AB possible? Give a reason. If yes, find AB

Chapter: [2.06] Matrices
Concept: Multiplication of Matrix

Mr Kumar borrowed Rs. 15000 for two years. The rates of interest for two successive years are 8% and 10% respectively. If he repays Rs. 6200 at the end of the first year, find the outstanding amount at the end of the second year.

Chapter: [1.01] Compound Interest
Concept: Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn at random.

1) a face card (King, Jack or Queen)

2) an even-numbered red card

Chapter: [7] Probability
Concept: Simple Problems on Single Events

Solve the following equation:

`x - 18/x = 6` Give your answer correct to two significant figures.

Chapter: [2.02] Quadratic Equations
Concept: Nature of Roots

In the given figure O is the centre of the circle. Tangents A and B meet at C. If ∠ACO = 30°, find

1) ∠BCO

2) ∠AOB

3) ∠APB

Chapter: [2] Circle
Concept: Tangent to a Circle

Ahmed has a recurring deposit account in a bank. He deposits Rs. 2,500 per month for 2 years. If he gets Rs. 66,250 at the time of maturity, find

1) The interest paid by the bank

2) The rate of interest

Chapter: [1.03] Banking
Concept: Computation of Interest

Calculate the area of the shaded region, if the diameter of the semicircle is equal to 14 cm. Take `pi = 22/7`

Chapter: [3.04] Circles
Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle

ABC is a triangle and G(4, 3) is the centroid of the triangle. If A = (1, 3), B = (4, b) and C = (a, 1), find ‘a’ and ‘b’. Find the length of side BC.

Chapter: [2.07] Co-ordinate Geometry
Concept: Distance Formula

Solve the following inequation and represent the solution set on the number line 2x – 5 <= 5x + 4 < 11, where x ∈ I

Chapter: [2.07] Co-ordinate Geometry
Concept: Equation of a Line

Evaluate without using trigonometric tables. 

`2((tan 35^@)/(cot 55^@))^2 + ((cot 55^@)/(tan 35^@)) - 3((sec 40^@)/(cosec 50^@))`

Chapter: [5] Trigonometry
Concept: Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables

A Mathematics aptitude test of 50 students was recorded as follows:

Marks 50 - 60 60 - 70 70 - 80 80 - 90 90 – 100
No. of Students 4 8 14 19 5

Draw a histogram from the above data using a graph paper and locate the mode.

Chapter: [5] Statistics
Concept: Graphical Representation of Histograms

A manufacturer sells a washing machine to a wholesaler for Rs. 15000. The wholesaler sells it to a trader at a profit of Rs. 1200 and the trader in turns sell it to a consumer at a profit of Rs. 1800. If the rate of the VAT is 8% find:

1) The amount of VAT received by the state government on the sale of this machine from the manufacturer and the wholesaler.

2) The amount that the consumer pays for the machine.

Chapter: [1.02] Sales Tax and Value Added Tax
Concept: Introduction to Sales Tax and Value Added Tax

A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.

Chapter: [4] Mensuration
Concept: Area and Volume of Solids - Sphere

ABCD is a parallelogram where A(x, y), B(5, 8), C(4, 7) and D(2, -4). Find

1) Coordinates of A

2) An equation of diagonal BD

Chapter: [2.07] Co-ordinate Geometry
Concept: Mid-point Formula

Use a graph paper to answer the following questions (Take 1 cm = 1 unit on both axes)

1) Plot A(4,4), B(4,-6) and C(8,0), the vertices of a triangle ABC.

2) Reflect ABC on the y-axis and name it A’B’C’.

3) Write the coordinates of the images A’, B’ and C’.

4) Give a geometrical name for the figure AA’ C’ B’ BC.

5) Identify the line of symmetry of AA’ C’ BC’.

Chapter: [3.01] Symmetry
Concept: Lines of Symmetry

Mr Choudhury opened a Saving Bank Account at State Bank of India on 1st April 2007. The entries of one year as shown in his passbook are given below.

Date Particulars Withdrawals (in Rs.) Deposits (in Rs.) Balance (in Rs.)
Ist April 2007 By Cash - 8550.00 8550.00
12th- April 2007 To Self 1200.00 -- 7350.00
24th April 2007 By Cash - 4550.00 11900.00
8th July 2007 By Cheque - 1500.00 13400.00
10th Sept. 2007 By Cheque - 3500.00 16900.00
17th Sept. 2007 By Cheque 2500.00 - 14400.00
11th Oct. 2007 By Cash - 800.00 15200.00
6th Jan. 2008 To Self 2000.00 - 13200.00
9th March 2008 By Cheque - 950.00 14150.00

If the bank pays interest at the rate of 5% per annum, find the interest paid on 1st April 2008. Give your answer correct to the nearest rupee.

Chapter: [1.03] Banking
Concept: Computation of Interest

Using componendo and dividendo, find the value of x

`(sqrt(3x + 4) + sqrt(3x -5))/(sqrt(3x + 4)-sqrt(3x - 5))  = 9`

Chapter: [2.04] Ratio and Proportion
Concept: Componendo and Dividendo Properties

if A = [(2,5),(1,3)], B = [(4,-2),(-1,3)]` and I =  I is the identity matrix of the same order and At is the transpose of matrix A, find At.B + BI.

Chapter: [2.06] Matrices
Concept: Matrices Examples

In the adjoining figure, ABC is a right angled triangle with ∠BAC = 90°.

1) Prove ΔADB ~ ΔCDA.

2) If BD = 18 cm CD = 8 cm Find AD.

3) Find the ratio of the area of ΔADB is to an area of ΔCDA.

Chapter: [3.01] Triangles
Concept: Similarity of Triangles

1) Using step–deviation method, calculate the mean marks of the following distribution.

2) State the modal class.

Class Interval 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 80 - 85 85 – 90
Frequency 5 20 10 10 9 6 12 8
Chapter: [6] Statistics
Concept: Measures of Central Tendency - Mean, Median, Mode for Raw and Arrayed Data

Marks obtained by 200 students in an examination are given below:

Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine

1) The median marks.

2) The number of students who failed if minimum marks required to pass is 40.

3) If scoring 85 and more marks are considered as grade one, find the number of students who secured grade one in the examination.

Chapter: [6] Statistics
Concept: Median from the Ogive

Mr. Parekh invested Rs. 52,000 on Rs. 100 shares at a discount of Rs. 20 paying 8% dividend. At the end of one year, he sells the shares at a premium of Rs. 20. find

1) The annual dividend

2) The profit earned including his dividend.

Chapter: [1.04] Shares and Dividends
Concept: Shares and Dividends

Draw a circle of radius 3.5 cm. Marks a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.

Chapter: [2] Circle
Concept: Tangent to a Circle

Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.

Chapter: [5] Trigonometry
Concept: Trigonometric Identities

6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.

Chapter: [2.04] Ratio and Proportion
Concept: Proportions

In what period of time will Rs. 12,000 yield Rs. 3972 as compound interest at 10% per annum, if compounded on a yearly basis?

Chapter: [1.01] Compound Interest
Concept: Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years

A man observes the angle of elevation of the top of a building to be 30o. He walks towards it in a horizontal line through its base. On covering 60 m the angle of elevation changes to 60o. Find the height of the building correct to the nearest metre.

Chapter: [5] Trigonometry
Concept: Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.

Chapter: [3.04] Circles
Concept: Areas of Sector and Segment of a Circle

Rs. 480 is divided equally among ‘x’ children. If the numbers of children were 20 more then each would have got Rs. 12 less. Find ‘x’.

Chapter: [1.04] Shares and Dividends
Concept: Shares and Dividends

Given the equation of line L, is y = 4.
(1) Write the slope of line L2, if L2, is the bisector of angle O.
(2) Write the co–ordinates of point P.
(3) Find the equation of L2.

Chapter: [2.07] Co-ordinate Geometry
Concept: Equation of a Line