Elective Mathematics

Question 1

1Differentiate y = x²/(x + 1).

Hard

A. (x² + 2x)/(x + 1)² B. 2x/(x + 1) C. (x² − 2x)/(x + 1)² D. 2x(x + 1)

Question 2

2Find the equation of the normal to y = x² at (1, 1).

Hard

A. y = −2x + 3 B. y = 2x − 1 C. y = x D. y = −x/2 + 3/2

Question 3

3∫₀^π cos x dx =

Hard

A. 1 B. −2 C. 0 D. 2

Question 4

4Find dy/dx if y = x² eˣ.

Hard

A. eˣ(x² + 2x) B. x² eˣ C. eˣ(2x + 1) D. 2x eˣ

Question 5

5Differentiate y = (3x − 1)⁴.

Hard

A. 12(3x − 1)⁴ B. 12(3x − 1)³ C. 4(3x − 1)³ D. 3(3x − 1)³

Question 6

6Evaluate ∫₁² (3x² − 2x) dx.

Hard

A. 6 B. 4 C. 3 D. 5

Question 7

7Find the gradient of y = x² − 4x at the point (1, −3).

Easy

A. −2 B. −3 C. 6 D. 2

Question 8

8The derivative of sin x is

Easy

A. −sin x B. tan x C. −cos x D. cos x

Question 9

9If y = e^(2x) sin x, dy/dx is

Hard

A. 2e^(2x) cos x B. e^(2x)(2 sin x + cos x) C. e^(2x) cos x D. 2e^(2x) sin x

Question 10

10If s = 2t³ − 3t², find the acceleration at t = 2.

Medium

A. 6 B. 18 C. 12 D. 24