First Terminal Examination 2073

Class: 7 F.M. 100

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

Attempt all the questions.

Group 'A'

9*(2+2)

  1. Which of the following ordered pairs are equal?

A = (3, 2) B = (2, -3) C = (4, 3) D = (-3, 4)

E = (4, 3) F = (-3, 4) G = (3, -2) H = (2, -3)

  1. Find the value of a and b is:

a) (a + 2, 3b) = (5, 8) b) (2a+1, 3a) = (5, 7)

  1. a) If A = {a, b} and B = {c, d}, find AxB, BxA and show that AxB≠BxA.

b)If P = {1, 2, 3} and Q = {4, 6}, find PxQ and QxP.

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

a) R1 = {(-1, 3), (-2, 4), (2, 6), (3, 6)}

b) R2 = {(a, 4), (b, v), (c, w), (n, p)}

  1. Find the inverse of the following relations:

a) R1 = {(2, 3), (3, 5), (6, 7), (-1, 4)}

b) R2 = {(a, b), (c, d), (x, y), (m, n)}

  1. a) Find the degree of the following polynomials:

4x2 + xy2 + 4y4

b) Express the following polynomials in the standard form:

2 + 3x – 5x3 + 4x2

  1. Find the order or the size of the following matrices:

a) b)

c) d)

  1. a) If A = , find the elements a23, a33, a13 and a32.

b) Construct a 2x2 square matrix in the following case:

aij = 2i + 4j

  1. a) Find the product of: (sinθ + 2)(sinθ – 3)

b) Simplify:

Group 'B'

8*3

  1. Find the product of: (secθ + tanθ)(secθ – tanθ)
  2. Simplify: (1 – cosθ)(1 + cosθ)(1 + cos2θ)
  3. Resolve into factors: 2cos2A + cosA – 6
  4. Prove that:
  5. Find the values of x, y and z.

  1. If A = and B = , find 3A + 4B.
  2. For the following polynomials, find f(x) + h(x) and f(x) – h(x):

f(x) = x3 + 7x – 8 and h(x) = 2x3 – 7x2 + x – 4

  1. If A = {2, 3} and B = {5, 6, 7}, find AxB, BxA and AxA. Represent them in mapping diagram.

Group 'C'

10*4

  1. Find the value of a and b if:

  1. If A = {1, 5} and B = {2, 3, 4}, find the following relations from set A to B.

i) The first component is less than the second component.

ii) The first component is greater than the second component.

  1. Find the product of the following polynomials:

f(x) = 2x – 3 and g(x) = x2 + 3x – 5

  1. Find the quotient and the remainder in the following when f(x) is divided by d(x). f(x) = 3x2 – 5x – 7 and d(x) = x + 3

Also verify the relation between dividend, divisor, quotient and remainder.

  1. If A = and B = , find the matrix C if

3A + C = B

  1. If A = , B = and C = , prove the following relation:

(A + B) + C = A + (B + C)

  1. In ΔPQR, , find in grades.
  2. Prove that: (1 + tanθ)2 + (1 – tanθ)2 = 2sec2θ
  3. Prove that: cosec2θ(1 – cos2θ) = 1
  4. Resolve into factors: sin3θ + sin2θ + sinθ + 1

-O-