sample paper icse maths 2010 class x set 8

7/28/2019 Sample Paper ICSE Maths 2010 Class X Set 8

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SAMPLE PAPER- 2010CLASS X th

MATHEMATICS

SECTION A (40 MARKS )Answers all questions.

1.(a) The polynomial kx3+3x2+8 when divided by x-2 leaves a remainderwhich

is double the remainder left by the polynomial x2-10x + 2k when dividedby x-2 . Find the value of k. (3)

(b) Given X =

43

21, Y=

1

0(i) Find a matrix Z such that X + Z is a zero

matrix.(ii) Find the matrix M such that X + M = X.(iii) Find XY. (4)

(c) A piece of butter 3cm by 5cm by 12 cm is placed in a hemispherical bowlof

radius 3.25 cm. Will the butter overflow when it melts completely . (3)

2. (a) If x2, 4 and 9 are in continued proportion , find the value of x. (3)

(b) Find the equation of a line that passes through (1,3) and is parallel tothe

line y= -3x + 2. (3)

(c) On a map drawn to a scale of 1: 125,000, a triangle plot of land has the

following measurements: AB = 10cm, BC = 8cm, ACB = 90 .Calculate

(i) The actual length of AB in Km. (ii) the area of the lot in squarekilometers. (4)

3. (i) Calculate the mean , median and mode of the following numbers : 12,11,

10. 11, 12, 13, 14, 13, 15, 13. (3)

(ii) Ifdc

ba

dc

ba

58

58

58

58

=

+

+

, prove thatd

c

b

a= . (3)

(iii) If cos A=5

4and cos B =

25

24, evaluate (i) cosec2 A (ii) cot A + cot B.

(4)

4. (i) Solve the following inequation and graph the solution on the numberline:

2x-5 5x + 4 < 11, x R. (3)


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(ii) The price of a T.V set inclusive of sales tax of 9% is Rs. 40,221. Find themarked price. (3)

(iii) Komal deposited Rs. 1,500 per month in a bank for 8 months under therecurring Deposit Scheme .What will be the maturity value of her

deposits ,

if the rate of interest is 12% per annum and interest is calculated at theend of every month. (4)

SECTION B (40 MARKS )Answer any four questions.5. (a) A,B and T are three points on a circle . The tangent at T meets BA

produced at P. Given that ATB = 32 and that the APT = 78 ,

calculatethe angle subtended by BT at the centre of the circle. (3)

(b) Write down the equation of the line whose gradient is 4/3 and whichpasses through P, where P divides the line segment joining A ( -2, -3) and

B(5,4) , in the ratio 2:5. (4)

(c) An electric shaver is listed at Rs. 1500 with a discount of 20% . Whatadditional discount % must be offered to a customer to bring the actualselling price to Rs. 1080 . (3)

6. (a) Construct a triangle ABC, in which AC= 7cm, BC= 8cm, AB= 6cm. (i)Mark

D, the mid point of BC. (ii) Construct the circle which touches AB at A , andpasses through D. (3)

(b) A man invests Rs. 7500 on buying shares of face value of Rs. 100 eachat

a premium of 50% in a company . If he earns Rs. 550 at the end of theyear

as dividend, find (i) the number of shares he has in the company. (ii) whatis

dividend percentage per share . (4)

(c) Show thatA

A

A

A

cos1

sin

cos1

cos1

+

=

+

(3)

7. (a) Use graph paper for this question. Plot the points A(8,2) and B(6,4) .These two points are the vertices of a figure which is symmetrical about

x=6and y= 2. Complete the figure on the graph . write down the geometricalname of the figure. (3)

(b) From a window A, 15m above the ground , the angle of elevation of thetop


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C of a tower is x , where tan x = 5/2 and the angle of depression of the

foot

D of the tower is y , where tan y = . Calculate the height CD of thetower

in meters. (4)C

B D

( c) Solve y - 63 y =2 (3)

8. (a) The perimeter of a rectangular plot is 180m and its area 1800 m2 . Ifthe

length is x m, express the breadth in terms of x . Hence , form an equationin

x. Solve the equation and find the length and the breadth of the rectangle.(3)

(b) Draw the graphs of 3y=12-2x and 2x-3y=4. Write down the co-ordinatesof

the point of intersection. Take 2cm = 1 unit on both the axes. (3)

(c ) The I.Q of 50 people was recorded as follows:

I.Q 80-90 90-100 100-110 110-120 120-130 130-140No. of people 6 9 16 13 4 2

Draw a histogram for the above data and estimate the mod. (4)

9. (a) A circular garden has a circumference of 440m . It is surrounded by acircular path which has been built at the cost of Rs. 63,756 at the rate of

Rs.6 per sq m. Find (i) the area of the path (ii) the radius of the outer circle.

(3)

(b)A manufacturer produces a good which cost him Rs.500. He sells it toa

Wholesaler at a price of Rs.500 and wholesaler sells it to retailer at aprice

of Rs.600. The retailer sells it to the customer at a price of Rs.800. If thesales tax charged is 5%. Find the tax charged under VAT by :(i) manufacturer, (ii) wholesaler and (iii) retailer. Find the tax paid by the


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customer (4)

(c) The centre of a circle is (x + 2, y 1).Find x and y if end points ofdiameter

are (2, - 2) and (8, - 2). Hence find the radius. (3)

10.(a) If 2 sin A 1 = 0, show that : sin 3A = 3 sin A 4 sin 3 A. (3)

(b) The total amount collected for the picnic by certain number ofstudents is Rs. 19,200. If there were 10 more students , theamount each student had to pay would have been reduced by Rs.160. find the total number of students attending picnic. (3)

(c) A bag contains 5 red , 4 black and 7 white balls. A ball is drawn fromthe bag at random. Find the probability that the ball drawn is

(i) black (ii) black or white , (iii) not red. (4)

11. (a) Mr. Aggarwal had a Saving Bank Account in a bank. His passbook hadthe following entries :

Date2009

Particulars Withdrawals(in Rs.)

Deposits(in Rs.)

Balance(in Rs.)

Jan. 21 By cash 500 500.00Mar. 18 To cheque 100.00 400.00May 22 By cheque 1,500.00

1,900.00July 28 To cash 200.00

1,700.00

Sept. 03 By cash 1,300.003,000.00

He closes the account on 30th Oct. 2009 Calculate the amount he received ifthe rate of interest is 6% p.a. (3)

(b) The perpendicular AD on the base BC ofABC intersects BC in D suchthat BD = 3 CD. Prove that 2 AB2 = 2 AC2 + BC2 (3)

(c) Alok invests Rs. 12800 for three years at the rate of 10% perannum compound interest. Find :

(i) The sum due to alok at the end of the first year.(ii) The interest he earns for the second year.(iii) The total amount due to him at the end of the third year. (4)

Contact-PATHAK STUDY CENTRE, MOHALI


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sample paper icse maths 2010 class x set 8

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