Half Yearly Model Question Paper 2019

9th Standard

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Maths

Time : 02:30:00 Hrs
Total Marks : 100

    Part I

    Answer all the questions.

    Choose the most suitable answer from the given four alternatives and write the option code with the corresponding answer.

    14 x 1 = 14
  1. From the adjacent diagram n[P(AΔB)] is

    (a)

    8

    (b)

    16

    (c)

    32

    (d)

    64

  2. The set {x: x ∈ A, x ∈ B, x ∉ A ∩ B} is___________.

    (a)

    A ∩ B

    (b)

    A U B

    (c)

    A - B

    (d)

    A Δ B

  3. The value of  \(0.\bar { 23 } +0.\bar { 22 } \) is 

    (a)

    \(0.\bar { 43 } \)

    (b)

    0.45

    (c)

    \(0.4\bar { 5 } \)

    (d)

    \(0.\bar { 45 } \)

  4. if \(\frac { 1 }{ 7 } \) = \(0.\bar { 142857 } \) then the value of \(\frac { 5 }{ 7 } \)

    (a)

    \(0.\overline { 142857 } \)

    (b)

    \(0.\overline { 714285 } \)

    (c)

    \(0.\overline { 571428 } \)

    (d)

    0.714285

  5. The product of \(2\sqrt { 5 } \) and \(6\sqrt { 5 } \) is_______________.

    (a)

    \(12\sqrt { 5 } \)

    (b)

    60

    (c)

    40

    (d)

    \(8\sqrt { 5 } \)

  6. The root of the polynomial equation 2x + 3 = 0 is

    (a)

    \(\frac{1}{3}\)

    (b)

    \(-\frac{1}{3}\)

    (c)

    \(-\frac{3}{2}\)

    (d)

    \(-\frac{2}{3}\)

  7. The value of the polynomial f(x)=6x-3x2+9 when x=-1 is _____________________

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

  8. Divide x3-4x2+6x by "x" the result is _____________________

    (a)

    \(x^{ 2 }+4x-6\)

    (b)

    \(x^{ 2 }-4x-6\)

    (c)

    \(x^{ 2 }-4x+6\)

    (d)

    \(x^{ 2 }+4x+6\)

  9. The interior angle made by the side in a parallelogram is 90° then the parallelogram is a

    (a)

    rhombus

    (b)

    rectangle

    (c)

    trapezium

    (d)

    kite

  10. Diagonal of which of the following quadrilaterals do not bisect it into two congruent triangles?

    (a)

    rhombus

    (b)

    trapezium

    (c)

    square

    (d)

    rectangle

  11. AD is a diameter of a circle and AB is a chord If AD = 30 cm and AB = 24cm then the distance of AB from the centre of the circle is

    (a)

    10cm

    (b)

    9cm

    (c)

    8cm

    (d)

    6cm

  12. The distance between the two points ( 2, 3 ) and ( 1, 4 ) is ______

    (a)

    2

    (b)

    \(\sqrt { 56 } \)

    (c)

    \(\sqrt { 10 } \)

    (d)

    \(\sqrt { 2 } \)

  13. The centre of a circle is (0, 0). One end point of a diameter is (5, -1), then ______________

    (a)

    \(\sqrt{24}\)

    (b)

    \(\sqrt{37}\)

    (c)

    \(\sqrt{26}\)

    (d)

    \(\sqrt{17}\)

  14. The point (0, -3) lies on _______________

    (a)

    + ve x-axis

    (b)

    + ve y-axis

    (c)

    - ve x-axis

    (d)

    - ve y-axis

  15. Part II

    Answer any 10 questions. Question no. 28 is compulsory.

    10 x 2 = 20
  16. If S = {square, rectangle, circle, rhombus, triangle}, list the elements of the following subset of S.
    The set of shapes which have 5 sides.

  17. In a class of 50 students, each of the students passed either in mathematics or in science or in both. 10 students passed in both and 28 passed in science. Find how many students passed in mathematics only

  18. Express the following in the form 3n\(\sqrt { 27 } \)

  19. Use a fractional index to write \(\left( 5\sqrt { 125 } \right) ^{ 7 }\)

  20. Find any 4 irrational numbers between \(\frac { 1 }{ 4 } \) and \(\frac { 1 }{ 3 } \)

  21. If p(x) = x2– 2\(\sqrt { 2 }\)x +1, find p(2\(\sqrt { 2 }\)) .

  22. Expand: (2a+3b)3

  23. Find the value of s for the following system of equa~on has infinitely many
    solutions. 2x - 3y = 7; (s +2) x - (2s + l)y = 3(2s -1)

  24. Identify which ones are trapeziums and which are not.

  25. In a circle, AB and CD are two parallel chords with centre 0 and radius 5 em such that AB = 8 cm and CD = 6 em determine the distance between the chords?

  26. Find the value of Xo

  27. The centre of a circle is (−4,2). If one end of the diameter of the circle is (−3,7) then find the other end.

  28. If  \(\left( \frac { 3 }{ 2 } ,5 \right) ,\left( 7,\frac { -9 }{ 2 } \right) \)and\((\frac{13}{2},\frac{-13}{2})\) are mid-points of the sides of a triangle, then find the centroid of the triangle.

  29. Find the centroid of the triangle whose vertices are (2, -5), (5, 11) and (9,9)

  30. Part III

    Answer any 10 questions. Question no. 42 is compulsory.

    10 x 5 = 50
  31. In the adjacent diagram, if n(U) = 125, y is two times of x and z is 10 more than x, then find the value of x,y and z.

  32. If A={2,5,6,7} and B={3,5,7,8}, then verify the commulative property of : union sets

  33. Locate an irrational number between two rational numbers\(\frac { 23 }{ 10 } \) and\(\frac { 12 }{ 5 } \)

  34. Express each of the following surds in its simplest form \(\sqrt [ 3 ]{ (1024)^{ -2 } } \) and find its order, radicand and coefficient.

  35. Simplify :\(-2\sqrt [ 4 ]{ 768 } +5\sqrt [ 4 ]{ 1875 } +3\sqrt [ 4 ]{ 48 } \)

  36. Expland the following using identities : (4m-3m)2

  37. Solve by cross multiplication method : 3x + 5y = 21; −7x − 6y = −49

  38. In the figure, AB is parallel to CD, find x

  39. In the figure find x0 and y0.

  40. The angles of quadrilateral are in the ratio 3:5:9:13. Find all the angles of the quadrilateral.

  41. In the given figure, ㄥCAB=25°, find ㄥBDC, ㄥDBAand ㄥCOB

  42. The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.

  43. Show that the following points taken in order form the vertices of a parallelogram. A(–3, 1), B(–6, –7), C (3, –9) and D(6, –1)

  44. Write the coordinates of quadrilateral PQRS as shown in the following figure.

  45. Part IV

    Answer all the questions.

    2 x 8 = 16
    1. Find the quotient and remainder when 4x3 + 6x2 + 7x + 2 is divided by x - 2

    2. Show that the point A (3,7) B (6, 5) and C (15, -1) are collinear.

    1. Find any two irrational numbers between\(\frac { 6 }{ 7 } \) and \(\frac { 12 }{ 13 } \)

    2. Find all the three angles of the ΔABC

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