#### Term 3 SA Mock Test 2019

9th Standard

Reg.No. :
•
•
•
•
•
•

Maths

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

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.