CBSE - IX

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Term 2 - Summative Assessment

Mathematics

Question Paper Set - 2

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. If x = 1 and y = 3 is a solution of 3x + 5y = k, then k =
  2. A. 16

    B. 15

    C. 18

    D. 17

  3. Pencils cost Rs 2 each; pens cost Rs 7 each. John spends Rs 20 on these items. Then the linear equation for the given data is:
  4. A. 2x + 7y = 20

    B. x + 7y = 20

    C. 2x + y = 20

    D. 2x – 7y = 20

  5. In a quadrilateral, if the opposite sides are equal and the diagonals are also equal, then the quadrilateral is a:
  6. A. Square

    B. Rectangle

    C. Parallelogram

    D. Rhombus

  7. If three angles of a quadrilateral measure 100°, 50° and 70°, then the fourth angle measures:
  8. A. 125°

    B. 135°

    C. 140°

    D. 132°

  9. The base of a parallelogram is 14 cm, and its distance from the opposite side is 8 cm. Then its area is:
  10. A. 144 cm2

    B. 64 cm2

    C. 76 cm2

    D. 112 cm2

  11. The part of a plane enclosed by a simple closed figure is called:
  12. A. Volume of the figure

    B. Planar region

    C. Angular region

    D. Area of the figure

  13. In the figure given here, the value of x is:
  14. A. 120°

    B. 100°

    C. 105°

    D. 102°

  15. In the figure given here, ABCD is a parallelogram. A circle through A, B and C meets CD produced at E. Then AE = A. ED

    B. AD

    C. CD

    D. AC

  16. The total surface area of a hemisphere of radius 14 cm is:
  17. A. 942 cm2

    B. 2464 cm2

    C. 1375 cm2

    D. 2104 cm2

  18. If the mean of 25, 27, 19, 29, 21, 23, p, 30, 28 and 20 is 24.7, then p =
  19. A. 25

    B. 31

    C. 22

    D. 26

    SECTION B

  20. In the equation 3(x – 3) – 3(y – 1) = 10, if x = 3, then find the value of y.

  21. ABCD is a parallelogram. Diagonals AC and BD intersect at O. If ∠ADB = 40°, ∠ABD = 25° and ∠DAC = 30°, then find ∠DOC.


  22. In the figure given here, if ABCD, ABFE and CDEF are parallelograms, then prove that ar(ΔADE) = ar(ΔBCF).

  23. Diagonals AC and BD of quadrilateral ABCD intersect at O such that ar (ΔBOC) = ar (ΔAOD). Then show that ABCD is a trapezium.
  24. Prove that equal chords of a circle subtend equal angles at its centre.
  25. Find the area of a triangle whose sides measure 20 cm, 30 cm and 40 cm.
  26. A rectangular sheet of paper 44 cm × 18 cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder.
  27. A dice is thrown once. Find the probability of getting
  28. (i) a number greater than 2 (ii) a number less than 4.

    SECTION C

  29. Draw the graph of the equation 3x – 2y = 4. From the graph, find the coordinates of the point when:
  30. (i) x = 2

    (ii) y = 7

  31. A railway half ticket costs half the full fare. The reservation charges are the same for both half and full tickets. A family of three adults and five children pay Rs 1200 for their travel from Hyderabad to Bengaluru. If the basic fare is Rs x and reservation charge is Rs y, then find the linear equation that represents the given information.
  32. In the figure given here, ABCD is a parallelogram. Compute the values of x and y.


  33. In the figure given here, ABCD is a parallelogram. AE ⊥ DC and CF ⊥ AD. If CD = 12 cm, AE = 8 cm and CF = 10 cm, find AD.


  34. Construct a triangle ABC in which BC = 8 cm, ∠B = 45° and AB – AC = 3.5 cm.
  35. Find the area of quadrilateral ABCD in which AB = 7 cm, BC = 6 cm, CD = 12 cm, DA = 15 cm and AC = 9 cm.
  36. The thickness of a hollow wooden cylinder is 2 cm. It is 35 cm long and its inner radius is 12 cm. Find the volume of the wood required to make the cylinder, assuming it is open at either end.
  37. Radhika scored 75, 82 and 90 in three Mathematics tests. How many marks must she obtain in the next test to get an average of exactly 85 for the four tests?
  38. The weather forecast from a news channel shows that out of the past 300 consecutive days, its weather forecast was correct 210 times.
  39. (i) What is the probability that on a given day, it was correct?

    (ii) What is the probability that on a given day, it was not correct?

  40. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
  41. 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.

    SECTION D

  42. Draw the graph of the equation 2x + y = 8. Read two solutions from the graph and verify the same by actual substitution. Also find the points where the line meets the two axes.
  43. Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus.
  44. Diagonals AC and BD of cyclic quadrilateral ABCD intersect at right angles at E. Line l through E and perpendicular to AB meets CD at F. Prove that F is the mid-point of CD.


  45. E, F, G and H are the mid-points of the sides of parallelogram ABCD. Show that .
  46. A cone of height 24 cm has a curved surface area of 550 cm2. Find its volume (take ).
  47. A die is thrown 500 times with the frequencies for the outcomes 1, 2, 3, 4, 5, 6 as given in the following table:
  48. Outcome

    1

    2

    3

    4

    5

    6

    Frequency

    80

    50

    90

    85

    100

    95

    Find the probability of getting each outcome.

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