Term 3 SA Mock Test 2019

9th Standard

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Maths

Time : 02:15:00 Hrs
Total Marks : 60

    I. Choose the best answer 

    10 x 1 = 10
  1. Which of the following is a solution of the equation 2x − y = 6

    (a)

    (2,4)

    (b)

    (4,2)

    (c)

    (3, −1)

    (d)

    (0,6)

  2. Which condition does not satisfy the linear equation ax + by + c = 0

    (a)

    a \(\neq \) 0 , b = 0

    (b)

    a = 0 , b \(\neq \) 0

    (c)

    a = 0 , b = 0 , c \(\neq \) 0

    (d)

    a \(\neq \)0, b \(\neq \) 0

  3. The coordinates of the point C dividing the line segment joining the points P(2,4) and Q(5,7) internally in the ratio 2:1 is

    (a)

    \((\frac{7}{2},\frac{11}{2})\)

    (b)

    (3,5)

    (c)

    (4,4)

    (d)

    (4,6)

  4. The centroid of the triangle with vertices (−1,−6), (−2,12) and (9,3) is

    (a)

    (3,2)

    (b)

    (2,3)

    (c)

    (4,3)

    (d)

    (3,4)

  5. if sin \(\alpha\) = \(\frac { 1 }{ 2 } \) and \(\alpha\) is a cute, then (3 cos\(\alpha\) - 4cos3 \(\alpha\)) is equal to

    (a)

    0

    (b)

    \(\frac { 1 }{ 2 } \)

    (c)

    \(\frac { 1 }{ 6 } \)

    (d)

    -1

  6. The value of 2tan30° tan60° is

    (a)

    1

    (b)

    2

    (c)

    \(2\sqrt { 3 } \)

    (d)

    6

  7. If the lateral surface area of a cube is 600 cm2, then the total surface area is

    (a)

    150 cm2

    (b)

    400 cm2

    (c)

    900 cm2

    (d)

    1350 cm2

  8. The volume of a cuboid is 660 cm3 and the area of the base is 33 cm2. Its height is

    (a)

    10 cm

    (b)

    12 cm

    (c)

    20 cm

    (d)

    22 cm

  9. A particular result of an experiment is called

    (a)

    Trial

    (b)

    Simple event

    (c)

    Compound event

    (d)

    Outcome

  10. A letter is chosen at random from the word “STATISTICS”. The probability of getting a vowel is

    (a)

    \(\frac { 1 }{ 10 } \)

    (b)

    \(\frac { 2 }{ 10 } \)

    (c)

    \(\frac { 3 }{ 10 } \)

    (d)

    \(\frac { 4 }{ 10 } \)

  11. II. Answer any 8 questions 

    8 x 2 = 16
  12. Draw the graph for the following linear equations
    (i) y = 4
    (ii) x = -2
    (iii) 2x - 4 =0
    (iv) 6 + 2y = 0
    (v) 9 – 3x = 0

  13. Draw the graph of the equations x= 3, x = 5 and 2x – y – 4 = 0. Also find the area of the quadrilateral formed by these lines and the x-axis.

  14. The points A(−3,6) , B(0,7) and C(1,9) are the mid-points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallellogram.

  15. Find the coordinates of the point which divides the line segment joining the points A(4,−3) and B(9,7) in the ratio 3:2.

  16. A boy standing at a point O finds his kite flying at a point P with distance OP=25m. It is at a height of 5m from the ground. When the thread is extended by 10m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios) 

  17. Verify cos3A = 4cos3 A - 3cosA , when A = 300

  18. Using Heron’s formula, find the area of a triangle whose sides are
    (i) 10 cm, 24 cm, 26 cm (ii) 1.8 m, 8 m, 8.2 m

  19. Find the area of a quadrilateral ABCD whose sides are AB = 13cm, BC = 12cm, CD = 9cm, AD = 14cm and diagonal BD = 15cm

  20. You are walking along a street. If you just choose a stranger crossing you, what is the probability that his next birthday will fall on a sunday?

  21. What is the probability of drawing a King or a Queen or a Jack from a deck of cards?

  22. III. Answer any 8 questions in the following 

    8 x 3 = 24
  23. Check whether (5, −1) is a solution of the simultaneous equations x – 2y = 7 and 2x + 3y = 7.

  24. Find the value of k for which the given system of equations kx + 2y = 3; 2x − 3y = 1 has a unique solution.

  25. If the centroid of a triangle is at (−2,1) and two of its vertices are (1,−6) and (−5,2), then find the third vertex of the triangle.

  26. If sec \(\theta\) = \(\frac { 13 }{ 5 } \), then show that \(\frac { 2sin\theta -3cos\theta }{ 4sin\theta -9cos\theta } \) = 3

  27. i) If cosecA = sec340, find A (ii) If tanB = cot 470, find B.

  28. Find the value of cos19059'

  29. Find the TSA and LSA of a cuboid whose length, breadth and height are 7.5 m, 3 m and 5 m respectively.

  30. The length, breadth and height of a hall are 25 m, 15 m and 5 m respectively. Find the cost of renovating its floor and four walls at the rate of \(\triangle\)80 per m2.

  31. The length, breadth and height of a cuboid are in the ratio 7:5:2. Its volume is 35840 cm3. Find its dimensions.

  32. When a dice is rolled, find the probability to get the number greater than 4?

  33. In an office, where 42 staff members work, 7 staff members use cars, 20 staff members use two-wheelers and the remaining 15 staff members use cycles. Find the relative frequencies.

  34. IV. Answer in detail

    2 x 5 = 10
  35. The perimeter of a rectangle is 36 metres and the length is 2 metres more than three times the width. Find the dimension of rectangle by using the method of graph.

  36. In what ratio does the point P(–2, 4) divide the line segment joining the points A(–3, 6) and B(1, –2) internally?

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