SECOND SUMMATIVE EXAM 2018

9th Standard

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Maths

Time : 02:30:00 Hrs
Total Marks : 60
    I. Choose the best answer
    15 x 1 = 15
  1. For any three sets P, Q and R, P-(Q\(\\ \cap \)R) is

    (a)

    P-(Q\(\cup \)R)

    (b)

    (P\(\\ \cap \)Q)-R

    (c)

    (P-Q)\(\cup \)(P-R)

    (d)

    (P-Q)\(\\ \cap \)(P-R)

  2. Which of the following is true?

    (a)

    A-B=A\(\cap \)B

    (b)

    A−B = B −A

    (c)

    (A\(\cup \)B)'=A'\(\cup \)B'

    (d)

    (A\(\cap \)B)'=A'\(\cup \)B'

  3. If A and B are two non-empty sets, then (A-B)U(A⋂B) is

    (a)

    A

    (b)

    B

    (c)

    ф

    (d)

    U

  4. When (2\(\sqrt{5}\)-\(\sqrt{2}\))2 is simplified, we get

    (a)

    4\(\sqrt{5}\)+2\(\sqrt{2}\)

    (b)

    22-4\(\sqrt{10}\)

    (c)

    8-4\(\sqrt{10}\)

    (d)

    2\(\sqrt{10}\)-2

  5. \(\frac { \sqrt [ 3 ]{ 18 } }{ \sqrt [ 3 ]{ 2 } } \) is same as

    (a)

    3

    (b)

    \(\sqrt [ 3 ]{ 9 } \)

    (c)

    9

    (d)

    \(\sqrt [ 6 ]{ 3 } \)

  6. Which is the best example of a number written in scientific notation?

    (a)

    0.5 x 105

    (b)

    0.1254

    (c)

    5.367 x 10-6

    (d)

    12.5 x 102

  7. (x+y)(x2−xy+y2) is equal to

    (a)

    (x+y)3

    (b)

    (x-y)3

    (c)

    x3 + y3

    (d)

    x3 - y3

  8. Cubic polynomial may have maximum of ___________ linear factors

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  9. GCD of any two prime numbers is __________

    (a)

    -1

    (b)

    0

    (c)

    1

    (d)

    2

  10. A chord is at a distance of 15cm from the centre of the circle of radius 25cm. The length of the chord is

    (a)

    25cm

    (b)

    20cm

    (c)

    40cm

    (d)

    18cm

  11. In a cyclic quadrilaterals ABCD, ㄥA=4x,ㄥC=2x the value of x is

    (a)

    30°

    (b)

    20°

    (c)

    15°

    (d)

    25°

  12. In the given figure, If OP=17cm PQ=30, cm and OS is perpendicular to PQ, then RS is

    (a)

    10cm

    (b)

    6cm

    (c)

    7cm

    (d)

    9cm.

  13. For which set of numbers do the mean, median and mode all have the same values?

    (a)

    2,2,2,4

    (b)

    1,3,3,3,5

    (c)

    1,1,2,5,6

    (d)

    1,1,2,1,5

  14. If the mean of five observations x, x+2, x+4, x+6, x+8, is 11, then the mean of first three observations is

    (a)

    9

    (b)

    11

    (c)

    13

    (d)

    15

  15. The mean of the first 10 prime numbers is

    (a)

    12.6

    (b)

    12.7

    (c)

    12.8

    (d)

    12.9

  16. II. Answer any 8 questions
    8 x 2 = 16
  17. If A = {2, 3, 4, 5}, B = {2, 3, 5, 7} and C = {1, 3, 5}, then verify \(A\cup (B\cup C)=(A\cup B)\cup C\).

  18. If P = {1,2,5,7,9}, Q = {2, 3, 5, 9, 11}, R = {3, 4,5 7, 9} and S = {2, 3, 4, 5, 8}, then find
    (i) \((P\cup Q)\cup R\)
    (ii) \((P\cap Q)\cap S\)
    (iii) \((Q\cap S)\cap R\)

  19. Use a fractional index to write: \(\left( \sqrt [ 3 ]{ 49 } \right) ^{ 5 }\)

  20. Simplify: (1.598 x 1017) - (4.58 x 1016)

  21. Write the following in scientific notation: (4000000)3 ÷ (0.00002)4

  22. Find the expansion of the following: (x+4)(x+5)(x+6)

  23. By using identity evaluate the following: 73-103+33

  24. Factorise the following: 4x2+9y2+25z2+12xy+30yz+20xz

  25. Find all the angles of the given cyclic quadrilateral ABCD in the figure.

  26. In a rice mill, seven labours are receiving the daily wages of Rs.500, Rs.600, Rs.600, Rs.800, Rs.800, Rs.800 and Rs.1000, find the modal wage

  27. III. Answer any 8 questions in the following 
    8 x 3 = 24
  28. If K = {a,b,d e f }  L = {b,c,d,g} and M = {a,b,c,d,h}, then find the following:
    (i) K \(\cup \)(L \(\cap \) M)
    (ii) K \(\cap \)(L \(\cup \) M)
    (iii) (K\(\cup \)L)\(\cap \)(K\(\cup \)M)
    (iv)
    (K\(\cap \)L)\(\cup \)(K\(\cap \)M)

  29. Verify \(\left( A\cup B \right) '\)=\(A'\cap B'\) using Venn diagrams

  30. U={x:x ∈Z, -2 ≤ x ≤ 10}, A={x : x =2p +1, p ∈Z, -1≤ p ≤ 4}, B = {x : x =3q + 1,q∈Z, -1 ≤ q< 4} verify De Morgan’s laws for complementation.

  31. Rationalise the denominator and simplify \(\frac { 5\sqrt { 3 } +\sqrt { 2 } }{ \sqrt { 3 } +\sqrt { 2 } } \)

  32. Find the value of a and b if \(\frac { \sqrt { 7 } -2 }{ \sqrt { 7 } +2 } \)=a\(\sqrt{7}\)+b

  33. Find the value of m, if (x -2) is a factor of the polynomial 2x2-6x2+mx+4.

  34. If 2x −3y −4z = 0 , then find 8x3-27y3-64z3

  35. Factorise x3+13x2+32x+20 into linear factors.

  36. Draw the \(\triangle \)ABC , where AB = 6 cm, B = 110° and AC = 9 cm and construct the centroid.

  37. Construct the ΔPQR such that PQ = 5cm, PR= 6cm and ㄥQP = ° R 60 and locate its centroid

  38. In a week, temperature of a certain place is measured during winter are as follows 26oC, 24oC, 28oC, 31oC, 30oC, 26oC, 24oC. Find the mean temperature of the week.

  39. The following table represents the marks obtained by a group of 12 students in a class test in Mathematics and Science

    Marks
    (Mathematics)
    52 55 32 30 60 44 28 25 50 75 33 62
    Marks
    (Science)
    54 42 48 49 27 25 24 19 28 58 42 69

    Indicate in which subject, the level of achievement is higher?

  40. A researcher studying the behavior of mice has recorded the time (in seconds) taken by each mouse to locate its food by considering 13 different mice as 31, 33, 63, 33, 28, 29, 33, 27, 27, 34, 35, 28, 32. Find the median time that mice spent in searching its food.

  41. IV. Answer the following 
    1 x 5 = 5
    1. In the concentric circles, chord AB of the outer circle cuts the inner circle at C and D as shown in the diagram. Prove that, AB−CD=2AC

    2. Construct the incentre of ΔABC with AB = 6 cm, ㄥB=65° and AC = 7 cm Also draw the incircle and measure its radius.

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