Elective Mathematics

Question 1

1Find the distance from the point (3, 4) to the line 3x + 4y − 5 = 0.

Medium

A. 3 B. 25 C. 4 D. 5

Question 2

2Solve cos 2x = cos x for 0° ≤ x ≤ 360°.

Hard

A. 0°, 120°, 240°, 360° B. 90°, 270° C. 60°, 300° D. 180° only

Question 3

3Simplify (1 − cos²θ)/sin θ.

Easy

A. sin θ B. tan θ C. 1 D. cos θ

Question 4

4cos(A − B) =

Easy

A. sin A cos B − cos A sin B B. cos A cos B + sin A sin B C. cos A cos B − sin A sin B D. cos A − cos B

Question 5

5The gradient of the line joining (1, 2) and (3, 8) is

Easy

A. 3 B. 6 C. 1/3 D. 2

Question 6

6Find the equation of the tangent to the circle x² + y² = 25 at (3, 4).

Hard

A. 3x + 4y = 25 B. 3x − 4y = 25 C. 4x − 3y = 0 D. x + y = 7

Question 7

7Find the gradient of the line perpendicular to y = 2x + 5.

Easy

A. −1/2 B. 2 C. −2 D. 1/2

Question 8

8Find the acute angle between the lines y = x and y = −x.

Easy

A. 60° B. 45° C. 30° D. 90°

Question 9

9Given sin 3θ = 3 sin θ − 4 sin³θ, find sin 3θ when sin θ = 1/2.

Hard

A. 1/2 B. 1 C. 0 D. −1

Question 10

10Two perpendicular lines have gradients m₁ and m₂. Then

Easy

A. m₁ + m₂ = 0 B. m₁m₂ = −1 C. m₁m₂ = 1 D. m₁ = m₂