optional mathmateicsa question collection

Opt. Math
Class:- Eight (8)

Group ‘A’ [9x2=18]

Q.1 a) In given right angled triangle ABC, find the ratios of Sec & Cosec .
A
C


θ
B
b) Prove: CosA.
Q.2 a) If Sec = ,find Sin and tan .
b) Find the value of: Sin 900 + Cos600 + Tan 450.

Q.3) a) Find the value of: x and y if (x-2, y-3) = (2, 3).
b) Let R = {(0, 0), (1, 1), (2, 8), (3, 27)} be a relation from A B; find the domain
and range of R .
Or
If A = {a, b} and B = {1, 2}. Find A x B.

Q.4) a) If P(x) = 4x2 – 3x +2 and Q(x) = 2x2 + 6x – 7. Find P(x) + Q(x).
b) If the mid-point of the line joining A (7, b) and B (a, 2) is (-1, 4) then find the
values of a & b .
Or
Find the co-ordinates of point which divides internally the line joining C(-3,-4) and D(2,5) in the ratio 2:3.
c) If
Group -B [8x4=32]

Q.5) A pole stands in a horizontal plane and makes an angle of elevation of the top of the pole from a point
Is 45o and the distance between a point and the pole is 45m, find its height.

Q.6) If 5 tan = 4, find the value of
Q.7) Prove:
Q.8) If A = { 1,2,3) and B = { 1, 4, 9} and R= { {x,y) : y = x2 } , find R .
Q.9) Use synthetic division to find quotient & the remainder if: 4a3 – 3a2 + 2a + 1 is
divided by a-1 .
Q.10) Find the ratio and the point at which the line joining M(2,-4) and N(-3,6) is divided
by x-axis .
Or
Prove that the points A(-1,0), B(3,1), C(2,2) and D(-2,1) are the vertices of a parallelogram.
Q.11) Prove that the points A (2, 3), B (2, 0) & C (-1, 0) are the vertices of an isosceles
triangle.
Q.12) If
THE END
Class: Eight (8)
Subject: Opt. Math
MARKING SCHEME

Group – A
1.a →

1.b L.H.S = Cos A . SecA + Sin A . Cosec A → 1

= 1 + 1
= 2
= R.H.S proved 1

2.a. Here , Sec = Sec = = h/b
then, P =
= 1 1

Now,
1
b.


3.a. Equating corresponding components ,
x – 2 = 3 1
x = 5

again , y – 3 = 3 1
y = 6

b. Domain = { 0,1,2,3} 1
Range = { 0 , 1, 8, 2 } 1

Or
A x B = { a,b} x { 1,2} 1
= {(a,1), (a,2), (b,1), (b,2)}…………..1

4.a. P(x) + Q(x)
= 4x2 + 3x + 2 + 2x2 + 6x – 7 1
= 6x2 + 3x – 5 1


b. We know ,
-1 =
-2 = 7 + 9 1
-2-7 = 9
a = - 9

again ,
4 =
8 = b + 2
8 – 2 = b 1
b = 6


Or



c.



Group B
5. 1 marks for figure and description 1

Let , AB be a pole , A





C 300 B
45m



6.


7. L.H.S. =



8. AxB = { 1,2,3} x { 1,4,9}
= {(1,1) , (1,4), (1,9) , (2,1) , (2,4) , (2,9) , (3,1) , (3,4) , (3,9) } 2
R = {(1,1) , (2,4) , (3, 9) } 2


9. 4 -3 2 1
4 1 3
4 1 3 4 3
Q(x) = 4x2 + a + 3 &
Remainder = 4
10. O =
O = 6m1 – 4m2 2
4m2 = 6m1 1

m1 : m2 = 2 :3 1

Or,
Mid Point of diagonal AC =
= (½,1) ………………1.5
Mid Point of diagonal BD =
= (1/2,1) ……..………….1.5

Mid point of diag. AC = Mid point of diag.BD.
Hence, ABCD is a parallelogram. Proved. …………..1

11.


12.


The End