Download Term 2 - Summative Assessment

Term 2 - Summative Assessment
Mathematics
Question Paper Set - 1
Max. Marks: 80 Time: 3 to 31/2 hours
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 to select the correct option from among those given.
SECTION A
1. The roots of the equation
are:
A. 14 and 13
B. -14 and 13
C. 12 and 15
D. -12 and 15
2. The nth term of the AP 10, 7, 4, 1 …is:
A. 3n + 1
B. 10 – n
C. n + 1
D. 13 – 3n
3. The number of tangents that can be drawn from an external point to a circle is:
A. Three
B. Two
C. One
D. Zero
4. The measure of the angle between any tangent and the radius at the point of
contact of a circle is:
A. 900
B. 600
C. 450
D. 300
5. PA and PB are the two tangents drawn to a circle from point P outside the circle.
If PA = 5 cm and ∠ APB = 60°, then the length of AB is:
A. 2 cm
B. 5 cm
C. 7 cm
D. 4 cm
6. A tangent PQ at point P of a circle of radius 6 cm meets a line through centre O at
point Q, so that OQ = 10 cm. Then the length of PQ is:
A. 7 cm
B. 8 cm
C. 9 cm
D. 6 cm
7. The circumference of a circle is 30 cm. The length of an arc of angle 60° is:
A. 5 cm
B. 12 cm
C. 15 cm
D. 10 cm
8. The radii of the top and bottom of a frustum of a cone are 4 cm and 3 cm,
respectively, and the height is 5 cm. Then its slant height is:
A.
B.
C.
D.
9.
=
A. 0
B. -1
C. 1
D. ∞
10. The probability that there will 53 Sundays in a leap year is:
A.
B.
C.
D.
SECTION B
11. Find the value of k for which
is a solution of the equation
12. The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
13. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
14. A copper wire, when bent in the form of a square, encloses an area of 121 cm2. If
the same wire is bent into the form of a circle, what will be the area of the circle?
15. The fez, the cap used by the Turks, is shaped like the frustum of a cone. If its
radius on the open side is 10 cm, the radius of the top is 4 cm, and its slant height
is 15 cm, how much cloth will be needed to make it?
16. Find the values of y for which the distance between the points P (2, -3) and Q (10,
y) is 10 units.
17. Show that the points A (8, 10), B (5, 7) and C (-1, 1) are collinear.
18. Find the probability of getting a tail when a coin is tossed once. Also find the
probability of getting a head.
SECTION C
19.
denotes the sum of n terms of an AP, whose common difference is d and first
term is a. Find
20. Rohit, who is on a tour, has Rs 360 for his expenses. If he extends his tour for
four days, he has to cut down his daily expenses by Rs 3. Find the original
duration of the tour.
21. Draw a right triangle in which the sides (other than hypotenuse) are of lengths 12
cm and 16 cm. Now construct another triangle whose sides are times the
corresponding sides of the given triangle.
22. From point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm
is drawn. Find the radius of the circle.
23. How many silver coins, each 1.75 cm in diameter and of thickness 2 mm, must be
melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?
24. A chord PQ of a circle of radius 10 cm makes a right angle at the centre of the
circle. Find the areas of the major and minor segments. [Take π = 3.14].
25. The angles 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.
26. The vertices of ΔABC are A (4, –6), B (3, –2) and C (5, 2). Verify that a median
of ΔABC divides it into two triangles of equal areas.
27. Find the ratio in which the point (–3, p) divides the line segment joining the points
(–5, –4) and (–2, 3). Hence, find the value of p.
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 sum of the squares of two positive integers is 208. If the square of the larger
number is 18 times the smaller number, find the numbers.
30. Raju saves Re. 1 on the first day and increases his savings by Re. 1 every day.
What will be his savings in 365 days?
31. Prove that the tangents drawn from an external point to a circle are equal in
length.
32. Find the perimeter of the shaded region where ADC, AEB and BFC are semicircles on diameters AC, AB and BC, respectively.
33. 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 and volume of the
toy.
34. The angles of elevation and depression, of an aeroplane and its image in water are
30° and 45°, respectively, from the top of a tree of height 5 m. Find the height at
which the aeroplane is flying from the ground.