Elective Mathematics

Question 1

1The inverse of f(x) = (2x + 1)/(x − 3), x ≠ 3, is

Hard

A. (x − 3)/(2x + 1) B. (x + 1)/(2x − 3) C. (3x − 1)/(x + 2) D. (3x + 1)/(x − 2)

Question 2

2Express log₃ 81 as a whole number.

Easy

A. 9 B. 4 C. 27 D. 3

Question 3

3Solve the equation 2^(2x) − 5(2^x) + 4 = 0.

Medium

A. x = 0 or x = 2 B. x = 1 or x = 4 C. x = 0 or x = 4 D. x = 2 only

Question 4

4If f(x) = (2x + 1)/(x − 3), x ≠ 3, find f⁻¹(x).

Hard

A. (3x + 1)/(x − 2) B. (3x − 1)/(x + 2) C. (2x − 1)/(x + 3) D. (x − 3)/(2x + 1)

Question 5

5The remainder when x³ − 2x + 5 is divided by (x − 1) is

Easy

A. 2 B. 6 C. 5 D. 4

Question 6

6If f(x) = 3x + 2, find f⁻¹(11).

Hard

A. 11 B. 3 C. 35 D. 4

Question 7

7Express 3/((x − 1)(x + 2)) in partial fractions.

Hard

A. 2/(x − 1) − 1/(x + 2) B. 1/(x − 1) + 1/(x + 2) C. 3/(x − 1) − 3/(x + 2) D. 1/(x − 1) − 1/(x + 2)

Question 8

8Find the remainder when x³ − 2x² + 4 is divided by (x − 2).

Medium

A. 4 B. 0 C. 2 D. 8

Question 9

9Find the range of f(x) = x² + 4x + 7.

Hard

A. f(x) ≥ 7 B. all real numbers C. f(x) ≤ 3 D. f(x) ≥ 3

Question 10

10Find the sum of the roots of 2x² − 7x + 3 = 0.

Easy

A. 7/2 B. −7/2 C. 3/2 D. 7