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Term 2 - Summative Assessment

Mathematics

Question Paper Set - 1

Time: 3 to 3 ½ hours
Max. Marks: 80

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 coordinates of the point of intersection of the lines x = −8 and y = 5 are:
2. A. (8, 5)

B. (-8, 5)

C. (8, -5)

D. (-8, -5)

3. x = 2 and y = 5 is a solution of:
4. A. x + 2y = 12

B. x + y = 12

C. 2x + y = 10

D. x - 2y = 10

5. If the angles of a quadrilateral are in the ratio of 2 : 4 : 5 : 7, then its angles measure:
6. A.

B.

C.

D.

7. In the figure given here, PQRS is a parallelogram with PR = 7.8 cm and QS = 6 cm. If PQ and QS intersect at O, then OP= and OQ=:
8. A. 3.7 cm, 3 cm

B. 4.9 cm, 4 cm

C. 3.9 cm, 3 cm

D. 3 cm, 3 cm

9. The region occupied by a simple closed figure in a plane is called:
10. A. Length

B. Volume

C. Perimeter

D. Area

11. One-fourth of a circular disk is called a:
12. A. Semi-circle

B. Quadrant

C. Sector

D. Arc

13. In the figure given here, if O is the centre of the circle, then x measures:
14. A.

B.

C.

D.

15. In the figure given here, ABCD is a trapezium in which AB || DC. Then ar (∆AOD)= ____.
16. A.

B.

C.

D.

17. The measure of the edge of a cube is 5.5 cm. Its surface area is:
18. A. 172 m2

B. 181.5 m2

C. 160 m2

D. 150.2 m2

19. The probability of getting a number less than 5 in a single throw of a die is:
20. A.

B.

C.

D.

SECTION B

21. Write four solutions of the equation 3x + y = 4.
22. In △ABC, D and E are the mid-points of AC and BC, respectively. If DE = 11.5 cm, then find the length of AB.
23. ABCD is a parallelogram. P is a point on AD such that If Q is a point on BC such that , then show that AQCP is a parallelogram.
24. In ∆ABC, AD is a median. Prove that ar(ΔABD) = ar(ΔACD).
25. In the figure given here, Find

26. The sides of a triangle are 9 cm, 12 cm and 15 cm in length. Find its area.
27. A hemispherical bowl made of stone is 5 cm thick. If its inner radius is 35 cm, then find its total surface area.
28. 18. A coin is tossed 500 times with the following frequencies:

Head: 245, Tail: 255

Compute the probability of each event.

29. SECTION C

30. Draw the graph of the equation 2x + 3y = 13, and determine whether x = 4, y = 2 is a solution or not.
31. A shopkeeper makes a profit of 20 per cent on selling a children’s umbrella, and a loss of 10 per cent on selling a normal umbrella, but gains Rs. 10 on selling one of each. If the cost of a children’s umbrella is Rs. x, and that of a normal umbrella is Rs. y, then frame a linear equation that represents the information given.
32. Two opposite angles of a parallelogram measure (60 – x)° and (3x – 4)°. Find the measure of each angle of the parallelogram.

33. PQRS and ABRS are two parallelograms, and

X is any point on side BR. Show that:

(i) ar(PQRS) = ar(ABRS)

(ii) ar(AXS) =

34. Construct a triangle ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm.
35. A cylinder is 12 cm high, and the circumference of its base is 44 cm. Find its curved surface area and total surface area.
36. A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make ten such caps.
37. This table gives the life of 400 neon lamps:
38.  Life (in hours) Number of lamps 300 – 400 14 400 – 500 56 500 – 600 60 600 – 700 86 700 – 800 74 800 – 900 62 900 – 1000 48

(i) Represent the given information with the help of a histogram.

(ii) How many lamps have a life of more than 700 hours?

39. In a cricket match, a batsman hits a boundary 6 times off the 30 balls that he plays. Find the probability that he does not hit a boundary off a delivery.
40. Three coins are tossed simultaneously 200 times, with the following frequencies of different outcomes:

 Outcome 3 heads 2 heads 1 head No head Frequency 23 72 77 28

If the three coins are tossed simultaneously again, compute the probability of two heads coming up.

41. SECTION D

Use this table to draw a graph.

 x –5 –1 3 b 13 y –2 a 2 5 7

From the graph, find the values of a and b.

42. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
43. In the figure given here, CD∥AB and ∠CBA = 25°. Find x.
44. If each diagonal of a quadrilateral separates it into two triangles of equal areas, then show that the quadrilateral is a parallelogram.
45. The difference between the semi-perimeter and the sides of triangle ABC are 8 cm, 7 cm and 5 cm, respectively. Find its semi-perimeter.
46. The graph given here shows the histogram and frequency polygon of the daily expenses of seven groups of tourists.

Read the graph and answer the following questions:

(i) What is the least daily expense?

(ii) What is the highest daily expense?

(iii) How many tourists spent an average of Rs. 150 every day?

(iv) Determine the average expenditure of the group that had the maximum daily expenses.

(v) How many tourists belong to Group D?

(vi) Determine the lowest and highest expenditure of the tourists from Group F.

(vii) Which group was the largest? How many tourists were there in this group?

(viii) Which group was the smallest? How many tourists were there in this group?

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