Optional Math 9

Model Question Set for Final Terminal Examination

Group : A [10 × 1 = 10]
1. a. If A × B = {(1, 3), (2, 4), (1, 4), (2, 3)} is the Cartesian product, find the sets

A and B.
b. If an+1 = 2an+2 – an, a0 = 2 and a1 = 4, find the value of a2.
2. a. What is the limit value of the sequence 2.01, 2.001, 2.0001, 2.00001, ........ ?

b. Write down the transpose of a matrix A = <2 1F . What type of matrix is it
according to its transpose? 1 3

3. a. What is centroid of a triangle? Write down the co-ordiante of it.

b. Find the slope and y-intercept of the straight line having equation 3 x – y = 3

4. a. IPWfrAhoav+teBdtho=ayto4rCuo,msP6re0oa0vn°eb=tyh–apt12o:sTitaionnAv+eTctaonrBo=f a1p–oTinatn?A.TanB

b.
5. a.

b. Find the image of a point (1, –2) under translation about T = <–1F .
2

Group : B [13 × 2 = 26]
6. a. If f(x + 2) = 3x – 1, find f(x) and f(2).

b. What must be subtracted from 2x3 – 3x2 + 2x – 1 to get x3 – 2x2 –3x + 2?

c. If R = {(x, y) : 2x + y = 9, x, y ∈ N}, find ‘R’ in ordered pairs.
7. a. If aij = 3i – 2j is the general element of a matrix, find the matrix of order 2 × 2 and

its transpose.

b. If A = < 1 2F , find the value of A2 – 3A + 5I where I is identity matrix of order
2 × 2. –1 3

8. a. Find the equation of locus of a point which moves so that it is equidistant from

b. the points (1, 2) and (2, 1).

9. a. If area of triangle having vertices (1, m), (4, 5) and (–2, 3) is 18 square units, find
b.
c. the value of ‘m’.

Prove that : Cos r + Cos 3r + Cos 5r + Cos 7r =0
8 8 8 8
1
If 1 – CosA = 2 , find the value of Cosec2A – Cot2A.

Find the radius of a circle where an arc of length 13.2cm subtends an angle of

30° at the centre of the circle.

10. a. If a =d 3 n , find the magnitude and direction of a. O
3

b. Find OC in terms of a and b where c is the mid-point a b
of AB. B

c. If R X – X = 200 and ∑f = 20, find the mean deviation c
and its coefficient where ∑X = 400.

A

PRIME Opt. Maths Book - IX 347

Group : C [11 × 4 = 44]
11. If f(x) = 2x2 + 5x – 3, g(x) = x2 + 8x + 7 and f(x) = g(x), find the value of x. [Ans: –2, 5]
12. If p(x) = x2 + 3x – 2 and q(x) = x + 3, find the value of p(x).q(x). Also divide the result

so formed by x – 2.

13. Complete the table given below with limit value.

x 0.9 0.99 0.999 0.9999 0.99999 ......................

f(x) = x –1 .............. .............. .............. .............. .............. ..............
x2 – 1

14. If A = <2 1F , B = <1 –2F and C = <3 1F , prove that A(B + C) = AB + AC.
3 –1 2 3 1 2

15. Prove that y = mx + c as the equation of straight line.

16. The number of sides of two regular polygons are in the ratio 4:3 where difference of
their interior angles is 15°. find the number of sides of the polygons. [Ans: 8, 6]

17. Prove that : Cosq – Sinq + 1 = 1 – Sini
Cosq + Sinq + 1 Cosi

18. Prove that : Cos10° – Sin10° = Tan35°
Cos10° + Sin 10°

19. Find the image of triangle having vertice (–2, –1), (1, 3) and (3, –2) under an

enlargement about E[(1, –1), –2]. Also plot the object and image in graph.

20. Find 7th decile of the observations given below. [Ans: 28]

x 12 16 28 32 20 24 36

f 5 10 12 9 14 15 10
21. Find the standard deviation and its coefficient of: [Ans: 6.015, 0.243]

x 15 20 25 30 35

f 6 8 12 10 4

Group : D [4 × 5 = 20]

22. Find the nth term of the sequence given below and write down in sigma notation.
5
1 2 3 4 5 2n
2 3 5 8 12 [Ans: (–1)n n² – n + 4

n=1
Σ – + – + – ]

23. Find the equation of straight line passes through a point A

(1, 4) which cuts the line intercepted between the axes in

the ratio 2:1. Also prove that it passes through the point

(4, –2). [Ans: 2x + y – 6 = 0] P Q
C
24. Prove that PQ = 1 BC and PQ ||BC from the adjoining
2
diagram.
25. If a point A(2, 1) is translated to A’(5, 3) with a translation B

‘T’, find the value of ‘T’. Also find the image of points

B(3, –2) and C(5, 0) with T followed by rotation about 180° with centre (0, 0) for

DABC. Then plot the object and image in graph.

348 PRIME Opt. Maths Book - IX