Sample Paper Mathematics CBSE SA 2
SAMPLE PAPER / MODEL TEST PAPER
CBSE SA – 2 (II) 2012
SUBJECT – MATHEMATICS
Question number 1 to 10 carry 1 mark each. For each of the question 1-10, four alternative choices have been provided of which only one is correct. You have to select the correct choice.
1. The sum of the first 15 multiples of 8 is:
(a) 920 (b) 860 (c) 900 (d) 960
2. A target PQ at a point P of a circle of radius 5 meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is:
(a) 12 cm (b) 13 cm (c) 8.5 cm (d) root 119 cm
3. If y =3 is a root of the quadratic equation ky square + 3 – ky = 0, then the value of k is:
(a) ½ (b) -1/2 (c) 2 (d) -2
4. A girl calculates that the probability of her winning the first prize in a lottery is 0. 08. If 6000 tickets are sold, how many tickets has she bought?
(a) 40 cm (b) 240 cm (c) 480 cm (d) 750
5. A tree breaks due to storm and broken part bends so that the top of the tree touches the ground making an angle of 30 degree with ground. If the distance between the foot of the tree to the point where the top touches the ground is 8 m then the height of the tree is:
(a) 8/3 cm (b) 3/8cm (c) 8 root 3 m (d) 8/ root 3 m
6. A point P is 13 cm from the centre of a circle. Radius of the circle is drawn from P to the circle is:
(a) 10 (b) 11 (c) 12 (d) 13
7. If tangents PA and PB from a point P to a circle with centre with O are inclined to each other at angle of 80 degree, angle POA is:
(a) 50 degree (b) 40 degree (c) 70 degree (d) 90 degrees
8. The circular ends of a bucket are of radii 35 cm and 14 cm and height of the bucket is 40 cm. Find the volume.
(a) 50080 cm cub (b) 80080 cm cub (c) 70080 cm cub (d) 60080 cm cub
9. In two concentric circle, the length of tangent to inner circle is 8 cm. Find the radius of outer circle, if the radius of inner circle is 3 cm.
(a) 5 cm (b) 4 cm (c) 3 cm (d) 2 cm
10. The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is:
(i) 56 cm (ii) 42 cm (iii) 28 cm (iv) 16 cm
SECTION – B
11. Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0. 62. What is the probability of Reshma winning the match?
In a lottery there are 20 prizes and 30 blanks. Find the probability of getting a prize
12. An equilateral triangle has two vertices at the points (1, 1) and (-1, -1), Find the coordinates of the third vertex.
13. Find the roots of the quadratic equation 1/ x – 3 – 1/x + 5 = 1/6; x does not equal 3, -5.
14. If 9th term of an A.P. is zero prove that its 29th term is double the 19th tern.
15. Prove that parallelogram circumscribing a circle is a rhombus.
16. a road which is 7 m wide surrounds a circular park whose circumference is 352 m.
Find the area of the road.
17. A drinking glass is in the shape of a frustum of a cone of height 14 cm. the diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. (Use PI = 22/7)
18. Find the coordinates of the points which divide the line segment joining A ( -2, 2) and B ( 2, 8) into four equal parts.
SECTION – C
19. A chord of a circle of radius 15 cm subtends an angle of 60 degree at the centre. Find the area of the corresponding minor and major segments of the circle.
(User PI = 3. 14 and root 3 = 1.73)
20. Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.
21. Find the roots of the quadratic equation:
x+3/x+2 = 3x – 7 / 2x – 3; x does not equal -2, 3/2
The sum of two numbers is 17 and the sum of their squares is 157. Find the numbers.
22. The first and the last term of A.P. are 4 and 81 respectively. If the common difference is 7, how many terms are there in the A.P. and what is their sum?
23. If A (x , 3 ), B ( 3, 0 ) , ( 0, -4 ) and D ( 4, y ) are the vertices of a rhombus, taken in order. Find the value of x and y.
24. Prove that the lengths of tangents drawn from an external point to a circle are equal.
ABC is a right triangle right angled at B, such that BC = 6 cm and AB = 8 CM, find the radius of its in circle.
25. Find the area of square , if coordinates of its vertices are ( 1, 2) , ( 6 , 3), ( 5, 8) and ( 0, 7) taken in order.
26. A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. find the total surface area of the toy.
27. A bunch of 10 books contains 3 books on Mathematics, 2 books on Physics and the remaining are on
Chemistry. One book is selected at random. Find the probability that:
(i) it is a chemistry book (b) it is a physics book.
28. The angle of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.
29. A triangle ABC is drawn to circumscribe a circle of radius 4 cm, such that the segments BD and DC into which BC is divided by the point of contact D are of length 8 cm and 6 cm respectively. Find the sides AB and AC.
30. The angle of elevation of a cloud from a point 60 m above a lake is 30 degree and the angle of depression of n the reflection of the could is 60 degree. Find the height of cloud.
31. Sum of the areas of two squares is 468 m square .If the difference of their perimeters is 24 m, find the sides of the two squares.
32. A right triangle, whose sides are 15 cm and 20 m is made to revolve about its hypotenuse. Find the volume and the surface area of the double one so formed. (Take PI = 3.14)
33. A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is 14/3 m and the diameter of hemisphere is 3.5 m. calculate the volume and the internal surface area of the internal surface area of the solid.
34. A metallic right circular cone 45 cm high and whose vertical angle is 60 degree is cut into two parts in the ratio 1 : 2 from the vertex of the cone by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1 cm, find the length of the wire.
CBSE SA 2 Sample Paper / Model Test Paper