ICSE Board Sample Paper
Subject – Mathematics
Class – 10th
Time – 2 ½ Hours Full Marks – 80
SECTION – A (40 Marks)
Answer all questions from this section.
1. a) A man invests Rs 5000 for three years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs 5600. Calculate:
i. The rate of interest per annum.
ii. The interest accrued in the second year.
iii. The amount at the end of the third year. 4
(b) Solve the quadratic equation by using formula: √3 x2 +10x – 8√3 = 0. 3
(c) Prove the following identities: (1- sinA)/(1+sinA) = (secA + tanA)2. 3
2. (a) Find the value of a and b if x – 1 and x – 2 are factors of x3 – ax + b. 3
(b) On a certain sum of money, the difference between the compound interest for a year, payable half yearly, and the simple interest for a year is Rs 16. Find the sum lent out, if the rate of interest in both cases is 8 %. 4
(c) Mr. Jacob has a two years recurring deposit account in State Bank of India and deposits Rs.1500 per month. If he receives Rs.37,875 at the time of maturity, find the rate of interest. 3
3. (a) Plot the points A(9,6) and B(5,9) on the graph paper. These tcwo points are the vertices of a figure ABCD which is symmetrical about x = 5 and y = 6. Complete the figure on the graph. Write down the geometrical name of the figure. 3
(b) A man invests Rs 16800 in buying shares of nominal value Rs 24 and selling at 12% premium. The dividend on the shares is 15% per annum.
i. Calculate the number of shares he buys.
ii. Calculate the dividend he receives annually. 4
(c) Amit deposited Rs. 800 per month in a recurring account for 1 year at the rate of 10% p.a. Find the amount Amit will get on maturity. 3
4. (a) Mrs. Sarojini deposits Rs. 1600 per month in a cumulative account at 9% p.a simple interest. If she gets Rs. 65,592 at the time of maturity, find the total time for which account was held. 4
(b) Saloni deposited Rs 150 per month in a bank for 8 months under the Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum?
(c) Find the mean for the following frequency distribution:
| Class intervals | 84 – 90 | 90 – 96 | 96-102 | 102-108 | 108-114 |
| Frequency | 8 | 12 | 15 | 10 | 5 |
SECTION B (40 Marks)
Attempt any four questions from this Section
5. (a) The following table gives the daily wages of 50 workers of a factory :
| Wages(in Rs) | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 | 50-55 | 55-60 |
| No. of workers | 2 | 1 | 5 | 9 | 21 | 10 | 2 |
Calculate the man daily wages of a worker of the factory. If the daily wages of all the worker are increased by Rs. 8 , what will be the new mean daily wage of a worker. 6
(b) Points (3 , 0) and ( -1 , 0) are invariant points under reflection in the line L1; points (0 , - 3) and ( 0 , 1) are invariant points on reflection in line L2 ;
(i) Write down the equations for the lines L1 and L2.
(ii) Write down the images of points P ( 3 , 4) and Q ( - 5 , - 2) on reflection in line L1 . Name the images as P’ and Q’ respectively.
(iii) Write down the image of P and Q on reflection in line L2 . Name the images as P” and Q” respectively.
(iv) State or describe a single transformation that maps P’ onto P”. 4
6. (a) Solve x2 - 5x = 10 and give your answer correct to 2 decimal places. 3
(b) Prove the following identity: (tan θ + sec θ - 1) /(tan θ – sec θ + 1) = (1 + sin θ)/ cos θ. 3
(c) The angles of elevation of the top of the tower from two points at distances 15 m and 8 m from the base and in the same straight line with it are complementary. Find the height of the tower and give your answer correct to 1/100 of a metre. 4
7. (a) A (5, x ) , B ( -4 , 3) and C (y , -2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y. 3
(b) A right triangle, whose sides are 15 cm and 20 cm, is made to revolve about its hypotenuse. Find the volume and the surface area of the double cone so formed. (take π = 3.14) 4
(c) Two trains X and Y start from a railway station at the same time. The X train travels due west and the Y train due north. The X train travels 5 km/hr faster than the Y train. If after two hours, they are 50 km apart, find the average speed of each train. 3
8. (a) Eight points A1,A2,A3,…. Divides the circumference of the circle in 8 equal arcs. A1 and A5, A3 and A6 are joined. Find the measure of acute angle at the intersection of line segments A1A5 and A3A6. 3
(b) A spherical drop of soap water of radius 1cm is blown into a bubble of outer radius 20 cm. Find approximately the thickness of the bubble. Leave your answer in fraction. 4
(c) Two right ∆s ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and DB intersect at P, prove that AP x PC = BP x PD. 3
9. (a) The equation of line is y = 3x – 5. Write down the slope of this line and the intercept made by it on the Y-axis. Hence or otherwise, write down the equation of a line which is parallel to this line and which passes through the point (0, 5). 4
(b). Use graph paper for this question : 6
The table given below show the monthly wages of some factory worker :
(i) Using the table, calculate th cumulative frequencies of workers.
(ii) Draw the cumulative frequency curve. Use 2 cm = Rs. 500 starting the origin at Rs.6,500 on x-axis and 2 cm= 10 workers on the y-axis.
(iii) Use your graph to write down the median wage in Rs :
| Wages in Rs. Per day | 6500-7000 | 7000-7500 | 7500-8000 | 8000-8500 | 8500-9000 | 9000-9500 | 9500-10000 |
| No. of workers | 10 | 18 | 22 | 25 | 17 | 10 | 8 |
10. (a) Use ruler and compasses to answer this question, show all construction lines and arcs clearly.
(i) Construct triangle ABC such that AB = BC = 7cm and BC = 5 cm.
(ii) Draw a circle with center A and radius 3 cm, let the circle cut AD at Q.
Construct another circle to touch the circle with center A externally at Q, and pass through Band C. 6
(b) The point P (a, b) is first reflected in the origin and then reflected in the x- axis to the point P’ (3, - 4). Find the values of “a” and “b”. Also find the co-ordinates of P”, when P is reflected in the line x =y. 4