ICSE Board Guess Paper
Subject – Mathematics
Class 10th
1. Solve x2 - 5x = 10 and give your answer correct to 2 decimal places.
2. By selling an article for ` 24 , a trader loses as much percent as the cost price of the article. Calculate the cost price.
3. If p : q = r : s then show that (mp + nq) : q = (mr + ns) : s
4. A ( 0, 0), B ( 4 , 6) , C (8 , 3) are the vertices of triangle ABC. Find the equation of :
(i) The median AM,
(ii) The altitude BN,
(iii) The coordinates of fourth vertex D of the parallelogram ABCD.
5. Find the range of values of x which satisfies
- 2 2/3 ≤ x + 1/3 < 3 1/3 ; x Є R
Graph these values of x on the number line
6. Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, they become in the ratio 4:5. Find the numbers.
7. Find the reminder when polynomial f(x) = x4 - 4x3 + 3x2 + 1 is divided by (x+2).
8. If a sum of money placed at compound interest doubles itself in 4 years, in how many years will be eight times.
9. If a sum of money placed at compound interest doubles itself in 4 years, in how many years will be eight times.
10. Find the mean, median and mode of 2, 4, 6, 3, 8, 9, 6, 3, 8, 3, 10, 12.
11. ABC is a triangle. BE and CD are medians which intersect at O. Find the ratio of the areas of triangles DOE and BOC.
12. A vertical flag staff stands on the top of Raj Bhawan Building. The height of the flagstaff above the building is 6m. The angles of elevation of the top and bottom of the flagstaff at a point on the level grounds are 450 and 300 respectively. Find the height of Raj Bhawan Building.
13. Find the value of “m’ if the lines represented by y = 1 – 2x and 2mx – 3y = 1 are :
(i) perpendicular to each other,
(ii) parallel to each other.
14. Find the equation of a line which has the y- intercept 4, and is parallel to the line 2x – 3y = 7. Find the co-ordinates of the point, where it cuts the x- axis.
15. If sin 3x = cos (x - 6), where 3x and (x – 6) are acute angles in degree. Find the value of x. Hence find the value of tan 2x.
16. The simple interest on a sum of money for 2 years at 4% is Rs450. Find the compound interest on this sum of money at the same rate for 1 year if the interest is reckoned half-yearly.
17. The perimeter of a sheet of tin in the shape of a quadrant of a circle is 12.5 cm. Find the area. (Take π = 22/7).
18. Find the linear relation between the components of the ordered pairs of the relation R where R = {(2, 1), (4, 7), (1, – 2), ……}.
19. Construct a regular hexagon in a circle of radius 3 cm.
20. A solid sphere and a solid hemisphere have the same total surface areas. Find the ratio of their volumes.