Elective Mathematics

Question 1

1Differentiate y = 5x³ − 2x.

Easy

A. 15x³ − 2 B. 5x² − 2 C. 15x² − 2x D. 15x² − 2

Question 2

2Evaluate lim (x→3) (x² − 9)/(x − 3).

Easy

A. 9 B. 6 C. 3 D. 0

Question 3

3Differentiate from first principles: the derivative of x² is found from lim (h→0) of

Hard

A. ((x + h)² − x²)/h B. (x + h)/h C. x²/h D. (x² − h²)/h

Question 4

4Evaluate the limit of (x² − 4)/(x − 2) as x → 2.

Medium

A. 4 B. 2 C. 0 D. it does not exist

Question 5

5Differentiate 3x⁴ with respect to x.

Easy

A. 3x³ B. 12x³ C. 4x³ D. 12x⁴

Question 6

6Differentiate y = 4/x.

Easy

A. −4/x² B. −4x C. 4 D. 4/x²

Question 7

7Differentiate 5x² − 3x + 7 with respect to x.

Easy

A. 10x B. 10x − 3 C. 5x − 3 D. 10x + 7

Question 8

8The gradient of y = x² at x = 3 is

Easy

A. 3 B. 6 C. 9 D. 2

Question 9

9Find the gradient of the curve y = x³ at x = 2.

Easy

A. 12 B. 6 C. 3 D. 8

Question 10

10Evaluate lim (x→0) (sin 3x)/x.

Hard

A. 0 B. 1 C. 1/3 D. 3