kerala SSLC

Sample Paper – 2010
Class – X
Subject – Mathematics

Section – I [ 40 Marks]

Q.1(a) When the rate of sales tax is increased from 4.5% to 7%, a car dealer sells a car for Rs.3,750 more. Find the quoted price of the car. (3)

(b) Find the mean proportion of x – y and x³ – x²y. (3)

(c) Ram borrowed Rs.2,500 from Shankar at 12% per annum C.I. After 2 years, he gave Rs.2936 and a radio to Shankar to clear the account. Find the cost of the radio. (4)

Q.2(a) Find the value of p and q, if x² – 1 is a factor of x⁴ + px + 2x² – 3x + q. (3)

(b) Find the median of :

19, 25, 59, 48, 35, 31, 30, 32, 51. If 25 is replaced by 52, find the new median . (3)

(c) In a quadrilateral ABCD, AB = AC = AD. Show that :

∟BAD = 2 (∟CBD + ∟CDB). (4)

Q.3(a) Anupam deposits Rs.1,600 per month in a recurring deposit accountfor three years at the rate of 9% p.a. simple interest. Find the amount she will get at the time of maturity.

(3)

(b) In the given fig., ABC is an equilateral triangle inscribed in a circle of radius 4 cm. Find the area of the shaded region. (3)

Fig

(c) (i) Plot A (2,3) and B (4,5) on a graph paper.

(ii) Reflect A, B in the y-axis to A’, B’. Plot these points on the same graph.

(iii) Write down :

(p) the geometrical name of the figure ABB’A’.

(q) the measure of the angle ABB’

(r) the image B” of B when B is reflected in the point (0,0). (4)

Q.4(a) Evaluate :

Sin²(90º – A) + cos²(90º – A) + sec²(90º – A) – tan²(90º – A). (3)

(b) x + 1/2 ≤ 5 – x /2 ≤ 7/2, x є R. (3)

(c) The mean of the following frequency table is 50. But the frequencies f₁ and f₂ in the classes 20 – 40 and 60 – 80 are missing. Find the values of f₁ and f₂.

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100	Total
Frequency	17	f₁	32	f₂	19	120

(4)

Section – II (40 Marks)

Donot panic ,choose ANY FOUR options correctly

Q.5 (a) In the given fig., O is the center of the bigger circle and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm, find the area of the shaded region. (3)

Fig

(b) If cosec θ – sin θ = a, sec θ – cos θ = b, show that a²b² (a² + b² + 3) = 1. (3)

(c) Mr. Mohan Chand had a Saving Bank Account in a bank. His passbook had the following entries :

Date 2006	Particulars	Withdrawals (in Rs.)	Deposits (in Rs.)	Balance (in Rs.)
Jan. 07	By cash	−	500.00	500.00
Mar. 18	To cheque	100.00	−	400.00
May 22	By cheque	−	1,500.00	1,900.00
July 28	To cash	200.00	−	1,700.00
Sept. 03	By cash	−	1,300.00	3,000.00

He closes the account on 30^th Oct. 2006 and receive Rs.3,043.75. Find the rate of interest per annum. (4)

Q.6.(a) In the given fig., ABC is an isosceles triangle in which AB = AC. A circle through B touches the side AC at D and it intersects the side AB at P. If D is the mid-point of AC, prove AB = 4AP. (3)

fig

(b) If 2my – 3x = 4 and 3my + 8x = 10 are perpendicular to each other, find m. (3)

(c) Find X and Y, if X + Y = [7 0 5] and X – Y = [3 6 9] (4)

Q.7.(a) find the HCF & LCM of (x³ -8) and (x⁴+4x²+4x²) (3)

(b) A bag contain 4 white balls , 3red balls , 5 green balls. if you select a ball in random Find the probability of

(i) one green ball (ii) not a green ball (iii) neither green nor red (3)

(b) From the top of a church spire 96 m high, the angles of depression of two vehicle on a road, at the same level as the base of the spire and on the same side of it are xº and yº, where tan xº = 3/4 and tan yº = 1/3. Calculate the distance between the vehicles. (4)

Q.8.(a) In given fig. ABC is a right angled triangle, right angle at B, AB = 6 cm and BC = 8 cm. A circle with centre O has been inscribed inside the triangle. Find the value of x.

(3)

fig

(b) A (0, 0), B (6, 0), C (4, 2) and D (2, 2) are the vertices of a trapezium ABCD and E and F are the mid-points of AD and BC respectively. Prove that EF = 1/2(AB + CD). (3)

(c) A company with 10,000 shares of nominal value of Rs.100 declares an annual dividend of 8% to the shareholders.

(i) Calculate the amount of dividend paid by the company.

(ii) Raju had bought 90 shares of the company at Rs.150 per share. Calculate the dividend he receives and the percentage return on his investment. (4)

Q.9.(a) A man takes a loan of Rs 50000 from a bank at 5% p.a.in CI. He repays Rs 20000 at the end of first year, Rs 24125 at the end of second year. Find how much money he has to pay at the end of second year in order to clear the loan. (4)

(b) Check whether x = 4 and x = 5 are solutions of the given equation :

√(x² – 16) – (x – 4) = √(x² – 5x + 4). (3)

(c) A cone of height 15 cm and diameter 7 cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed. (3)

10.(a) Draw an Ogive for the following frequency distribution by “Less than” method :

Marks	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Number of students	7	10	23	51	6	3

(6)

(b) If O is the centre of the circle

Prove that

< x + < y = < z

11. (a) The midpoint of the line joining (2a, 4) and (-2, 3b) is (1, 2a + 1). Find the values of ‘a’ and ‘b’.

(b) Find the range of values of ‘x’ which satisfies

< x +

< 3

, x E R

represent your solution on a number line (3)

+ 3cos²30 = 3k . Find k.

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SAMPLE PAPER- 2010

CLASS – X th

MATHEMATICS

SECTION A (40 MARKS )

Answers all questions.

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

is double the remainder left by the polynomial x²-10x + 2k when divided

by x-2 . Find the value of k. (3)

(b) Given X =

, Y=

(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)

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 to the

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

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

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

kilometers. (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) If

, prove that

. (3)

(iii) If cos A=

and cos B =

, evaluate (i) cosec² A (ii) cot A + cot B. (4)

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

2x-5 £ 5x + 4 < 11, xÎ R. (3)

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

marked price. (3)

(iii) Komal deposited Rs. 1,500 per month in a bank for 8 months under the

recurring 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 the

end 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 Ð ATB = 32° and that the Ð APT = 78° , calculate

the 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 which

passes through P, where P divides the line segment joining A ( -2, -3) and B

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

additional discount % must be offered to a customer to bring the actual

selling 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 , and

passes through D. (3)

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

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

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

dividend percentage per share . (4)

(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=6

and y= 2. Complete the figure on the graph . write down the geometrical

name of the figure. (3)

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

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 = ¼ . Calculate the height CD of the tower

in meters. (4)

( c) Solve y -

=2 (3)

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

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

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-ordinates of

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 90-100 100-110 110-120 120-130 130-140

No. 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 a

circular 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 to a

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

of Rs.600. The retailer sells it to the customer at a price of Rs.800. If the

sales tax charged is 5%. Find the tax charged under VAT by :

(i) manufacturer, (ii) wholesaler and (iii) retailer. Find the tax paid by the

customer (4)

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 sin³ A. (3)

(b) The total amount collected for the picnic by certain number of students is Rs. 19,200. If there were 10 more students , the amount 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 from the 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 had the following entries :

Date 2009	Particulars	Withdrawals (in Rs.)	Deposits (in Rs.)	Balance (in Rs.)
Jan. 21	By cash	−	500	500.00
Mar. 18	To cheque	100.00	−	400.00
May 22	By cheque	−	1,500.00	1,900.00
July 28	To cash	200.00	−	1,700.00
Sept. 03	By cash	−	1,300.00	3,000.00

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

(b) The perpendicular AD on the base BC of

ABC intersects BC in D such that BD = 3 CD. Prove that 2 AB² = 2 AC² + BC² (3)

(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)

Saturday, December 4, 2010

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