First Terminal Examination 2073

Class: 9 F.M. 100

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

Attempt all the questions.

  1. a) If (x +2, y) = (5, 4x – 8), find x and y.

b) Identify (a, b) and (b, a) ordered is equal.

  1. If A = {2, 3, 4} and B = {5, 6, 7}, find AxB and BxA and represent them mapping.
  2. Find the domain, co-domain, range, image and pre-images of the function,

f= {(a, 2), (b, 4), (c, 5), (d, 7)}

  1. Simplify: a) b)
  2. Simplify:
  3. Arrange in ascending order:
  4. Find the square root of
  5. Find the value of
  6. If a = , find the value of
  7. If x, y are real numbers and , find x and y.
  8. a) From the given figure, find the trigonometric ratios of sinθ and cosβ.

A

θ

B β C

b) Find the product of: (sinθ – cosθ)(sin2θ + sinθcosθ + cos2θ)

  1. Prove that: (3 - 4sin2θ)(1 - 3tan2θ) = (3 – tan2θ)(4cos2θ – 3)
  2. Prove that:
  3. If tanθ = , find the value of
  4. If sinθ = , show that
  5. If 4cos2θ + 4sinθ – 5 = 0, show that sinθ =
  6. Show that xcosθ - ysinθ = p and xsinθ+ycosθ=9, prove that x2 + y2 = p2 + q2.
  7. In ΔABC, right angled at C, if tanA = and tanB=, show that sinAcosB + cosAsinB = 1
  8. Prove that
  9. Prove
  10. Prove that 2(sin6θ + cos6θ) – 3(sin4θ + cos4θ) + 1 = 0
  11. Express all the trigonometric ratios in terms of secθ.
  12. If cosθ + sinθ = , show that
  13. If and xy = 1, find the value of x2 + y2.
  14. If and , find the value of m2 + mn + n2.

-O-