Download Term 2 - Summative Assessment

Term 2 - Summative Assessment
Mathematics
Question Paper Set - 2
Max. Marks: 80 Time: 3 to 31/2hours
1. 1. All questions are compulsory.
2. The question paper consists of 34 questions divided into four sections – A, B, C
and D. Section A consists of 10 questions of 1 mark each, Section B of 8
questions of 2 marks each, Section C of 10 questions of 3 marks each, and Section
D consists of 6 questions of 4 marks each.
3. Question numbers 1 to 10 in Section A are multiple-choice questions, wherein
you have select the correct option from among those given.
Section A
1. If one of the roots of the quadratic equation
of p is:
is 4, then the value
A. 7
B. -7
C. 5
D. 8
2. If the 17th term of an AP exceeds the 10th term by 7, then the common difference
is:
A. 3
B. 2
C. 1
D. 4
3. From a point Q, the length of the tangent to a circle is 15 cm, and the distance of
Q from the centre is 17 cm. The radius of the circle is:
A. 7 cm
B. 12 cm
C. 14 cm
D. 8 cm
4. In the figure given here, PA and PB are tangents to the
circle drawn from an external point P. CD is a third
tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, then the length of
PC is:
A. 5 cm
B. 10 cm
C. 12 cm
D. 8 cm
5. A line segment that intersects a circle at two distinct points is called a:
A. Radius
B. Diameter
C. Tangent
D. Secant
6. The angle between any tangent and the radius at the point of contact of a circle is:
A. 450
B. 900
C. 600
D. 300
7. The area of a sector of a circle with radius 7 cm and angle at centre 600 is:
A.
B.
C.
D.
8. The radius and height of a cylinder are in the ratio 2 : 3, and its volume is 12936
cm3. The height of the cylinder is:
A. 21 cm
B. 14 cm
C. 15 cm
D. 24 cm
9.
A.
B.
C.
D.
10. A bag contains five red balls and three black balls. A ball is drawn at random
from the bag. The probability that the ball drawn is red is:
A.
B.
C.
D.
SECTION B
11. If one root of the quadratic equation 2x2 + kx – 6 = 0 is 2, find the value of k.
Also find the other root.
12. If the second term of an AP is 4 and the seventh term is –11, find its 18th term.
13. If AB, AC and PQ are tangents in the given figure, and AB = 6 cm, find the
perimeter of ΔAPQ.
14. Find the radius of the circle whose perimeter and area are numerically equal.
15. The radius and slant height of a cone are in the ratio 7 : 13, and its curved surface
area is 286 cm2. Find its radius.
16. Find the point on the X-axis that is equidistant from the points (–2, 5) and (2, –3).
17. Find the relation between x and y if the points (x, y), (1, 2) and (7, 0) are
collinear.
18. A letter is chosen at random from a given word. Find the probability that the letter
is a vowel if the word is ‘MATHEMATICS’.
SECTION C
19. Find the sum of all natural numbers between 200 and 1502 that are exactly
divisible by 3.
20. A two-digit number is four times the sum of its digits and twice the product of its
digits. Find the number.
21. From a point P at a distance of 7.5 cm from the centre O of a circle of radius 3
cm, draw tangents to the circle using its centre.
22. Two concentric circles are of radii 10 cm and 8 cm. A chord of the larger circle
touches the smaller circle. Find the length of the chord.
23. A cylindrical bucket, 28 cm high and with the radius of base 7 cm, is field with
sand. This bucket is emptied on the ground and a conical heap of sand is formed.
If the height of the conical heap is 21 cm, find its radius and slant height.
24. Two concentric circles have their areas in the ratio 4 : 9. The radius of the inner
circle is 7 cm. Calculate the diameter of the outer circle.
25. A straight highway leads to the foot of a tower. A man standing at the top of the
tower observes a car at an angle of depression of 30°. The car is approaching the
foot of the tower with a uniform speed. Six seconds later, the angle of depression
of the car is found to be 60°. Find the time taken by the car to reach the foot of the
tower from this point.
26. Find the area of quadrilateral ABCD formed by the points A (–2, –2), B (5, 1), C
(2, 4) and D (–1, 5).
27. The mid-points of sides AB, BC, CA of triangle ABC are D (2, 1), E (1, 0) and F
(-1, 3), respectively. Find the coordinates of the vertices of triangle ABC.
28. A bag contains five white balls and some red balls. If the probability of drawing a
red ball is double that of drawing a white ball, find the number of red balls in the
bag.
SECTION D
29. The denominator of a fraction is one more than twice the numerator. If the sum of
the fraction and its reciprocal is
, find the fraction.
30. The sums of n terms of three arithmetical progressions are S1, S2 and S3. The first
term of each is unity, and the common differences are 1, 2 and 3, respectively.
Prove that S1 + S3 = 2S2.
31. Prove that the line segment joining the points of contact of two parallel tangents
to a circle is a diameter of the circle.
32. Find the area of the shaded region in the figure given here, if BC = BD = 8 cm,
AC = AD = 15 cm, and O is the centre of the circle.
33. Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm
into a rectangular tank that is 50m long and 44 m wide. Find the time in which the
level of water in the tank will rise by 21 cm.
34. From a window p metres high above the ground in a street, the angles of elevation
and depression of the top and the foot of another house on the opposite side of the
street are θand ø, respectively. Show that the height of the opposite house, in
metres, is p (1 + tan θ cot ø).