#### Class 9 Term 3 SA Model Question

9th Standard

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Maths

Time : 02:30:00 Hrs
Total Marks : 60

I. Choose the best answer

10 x 1 = 10
1. The linear equation in one variable is

(a)

2x + 2 = y

(b)

5x − 7 = 6 − 2x

(c)

2t(5 − t) = 0

(d)

7p − q = 0

2. The value of k for which the pair of linear equations 4x + 6y −1 = 0 and 2x + ky − 7 = 0 represents parallel lines is

(a)

k = 3

(b)

k = 2

(c)

k = 4

(d)

k = -3

3. If $P(\frac{a}{3},\frac{b}{2})$is the mid-point of the line segment joining A(−4,3) and B(−2,4) then (a,b) is

(a)

(-9, 7)

(b)

$(-3, \frac{7}{2})$

(c)

(9, -7)

(d)

$(3, -\frac{7}{2})$

4. The ratio in which the x-axis divides the line segment joining the points (6,4) and (1, −7) is

(a)

2:3

(b)

3:4

(c)

4:7

(d)

4:3

5. The value of $\frac { 2tan30° }{ 1-{ tan }^{ 2 }30° }$ is equal to

(a)

cos600

(b)

sin600

(c)

tan600

(d)

sin300

6. The value of 2tan30° tan60° is

(a)

1

(b)

2

(c)

$2\sqrt { 3 }$

(d)

6

7. The lateral surface area of a cube of side 12 cm is

(a)

144 cm2

(b)

196 cm2

(c)

576 cm2

(d)

664 cm2

8. The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is

(a)

280 cm2

(b)

300 cm2

(c)

360 cm2

(d)

600 cm2

9. Probability lies between

(a)

−1 and +1

(b)

0 and 1

(c)

0 and n

(d)

0 and $\infty$

10. If A is any event in S then its complement P(A′) is equal to

(a)

1

(b)

0

(c)

1-A

(d)

1-P(A)

11. II. Answer any 8 questions

8 x 2 = 16
12. The monthly income of A and B are in the ratio 3:4 and their monthly expenditures are in the ratio 5:7. If each saves Rs 5,000 per month, find the monthly income of each.

13. Five years ago, a man was seven times as old as his son, while five year hence, the man will be four times as old as his son. Find their present age.

14. Using section formula, show that the points A(7, −5), B(9, −3) and C(13,1) are collinear.

15. Find the centroid of the triangle whose vertices are
(i) (2,−4), (−3,−7) and (7,2) (ii) (−5,−5), (1,−4) and (−4,−2)

16. Evaluate:
(i)sin300 +cos 300
(ii) tan600.cot600
(iii) $\frac { tan45° }{ tan30°+tan60° }$
(iv)sin2450 +cos2450

17. Find the value of 8sin2x.cos 4x.sin6x , when x =150

18. The sides of the triangular ground are 22 m, 120 m and 122 m. Find the area and cost of levelling the ground at the rate of Rs.20 per m2.

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

20. What is the probability of throwing an even number with a single standard dice of six faces?

21. The probability of guessing the correct answer to a certain question is $\frac { x }{ 3 }$. If the probability of not guessing the correct answer is $\frac { x }{ 5 }$, then find the value of x.

22. III. Answer any 8 questions in the following

8 x 3 = 24
23. Solve by cross-multiplication method
(i) 8x − 3y = 12 ; 5x = 2y + 7
(ii) 6x + 7y −11 = 0 ; 5x + 2y = 13
(iii) $\frac { 2 }{ x } +\frac { 3 }{ y } =5;\frac { 3 }{ x } -\frac { 1 }{ y } +9=0$

24. Find the value of k, for the following system of equation has infinitely many solutions. 2x − 3y = 7;(k + 2)x − (2k +1)y = 3(2k −1)

25. Find the centroid of the triangle whose veritices are A(6,−1), B(8,3) and C(10,−5).

26. Express (i) sin74° in terms of cosine (ii) tan12° in terms of cotangent (iii) cosec39° in terms of secant

27. Find the value of sin 64034'.

28. Find the value of (i) sin38036' + tan12012' (ii) tan60025' - cos 49020'

29. The lengths of sides of a triangular field are 28 m, 15 m and 41 m. Calculate the area of the field. Find the cost of levelling the field at the rate of ₹ 20 per m2

30. cube has the total surface area of 486 cm2. Find its lateral surface area.

31. The total surface area of a cube is 864 cm2. Find its volume

32. 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.

33. The probability that it will rain tomorrow is $\\ \frac { 91 }{ 100 }$. What is the probability that it will not rain tomorrow?

34. IV. Answer in detail

2 x 5 = 10
35. Use graphical method to solve the following system of equations y = 2x + 1; −4x + 2y = 2

36. Find the points of trisection of the line segment joining (−2,−1) and (4, 8)