First Terminal Examination 2073

Class: 8 F.M. 100

Time: 3 hrs. Subject: Optional Mathematics P.M. 32

Attempt all the questions.

Group 'A'

9*(2+2)

  1. a) If (a, 4) = (-2, a+b), find a and b.

b) If P = {a, b} and Q = {1, 2}, find PxQ and QxP.

  1. Find the domain and range of the following relations:

a) R1 = {(1, 2), (2, 3), (3, 4), (4, 5)}

b) I = {(-2, 0), (0, 7), (-4, 8), (7, -3), (-8, -4)}

  1. If the function g is given by g(x) = 4x – 3, find

a) g(-3) b) g(3+h)

  1. a) Find the degree of the polynomials: 4x4y2 + 2x2y3 + xy3

b) Simplify:

  1. Write the order of the following matrices:

a)

b) Construct a 2x3 matrix in the following condition:

aij = 8 + 2j

  1. a) If , find the value of x and y.

b) Find the distance between the points A(3, -4) and B(-9, -4).

  1. a) Find the distance between the points A(a+b, a-b) and B(a-b, a+b).

b) Express the following angles as indicated:

i) 20020I (into sexagesimal seconds)

ii) 80g (into radians)

  1. a) Find the product of: (1 + cosA)(1 – cosA)(1 + cos2A)

b) Factorize: sin4θ – cos4θ

  1. a) Factorize: sin6θ + cos6θ

b) Prove that: (1 – cos2A)(1 + tan2A) = tan2A

Group 'B'

8*3

  1. Prove that: sec4A – sec2A = tan4A + tan2A
  2. Prove that:
  3. If two angles of a triangle are 400 and 100g, find the remaining angle in radian.
  4. Show that the point P(2, 3), Q(3, 5) and R(6, 1) are the vertices of a right angled triangle.
  5. Find the co-ordinates of a point on X-axis. Which is at distance 5 units from the point (4, 4).
  6. If and , find 2A – B.
  7. Rationalize the denominator of:
  8. If m(x) = 2x3 – x2 + x – 4 and n(x) = 7x3 + 8x + 2 are two polynomials, find m(x) + n(x) and m(x) – n(x).

Group 'C'

10*4

  1. If p(x) = x3 + 3x – 7 and q(x) = x + 2, find p(x).q(x) and its degree.
  2. Simplify:
  3. If A = {2, 3, 4, 5, 9}, construct the Cartesian product AxA and find the following relations:

a) is less than b) is greater than

c) is not equal to d) is the square of

  1. If the function f is given by f(x) = x2, then find the value of
  2. If , find the values of x, y and z.
  3. If and , find the determinant of 2B – 2C.
  4. If the distance between the two points A(a, 2a) and B(4, 3) is units, find the co-ordinate of A.
  5. If a point (x, y) is equidistant from the points (a+b, a+b) and (a-b, a-b), prove that x + y = 2a.
  6. If two angles of a triangle are in the ratio 1:2:7, find the angles in degrees.
  7. Prove that:

-O-