Core Mathematics

Question 1

1Find the inverse of f(x) = 3x − 2.

Medium

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

Question 2

2If x − 1/x = 3, find x² + 1/x².

Hard

A. 11 B. 7 C. 10 D. 9

Question 3

3What is the sum of the roots of x² − 9x + 14 = 0?

Medium

A. 7 B. 9 C. −9 D. 14

Question 4

4Form a quadratic equation whose roots are 2 and −3.

Medium

A. x² − x − 6 = 0 B. x² + 5x − 6 = 0 C. x² + x − 6 = 0 D. x² − x + 6 = 0

Question 5

5If 2ˣ = 16, find x.

Easy

A. 4 B. 8 C. 3 D. 2

Question 6

6If a ∗ b = a² − b, evaluate 3 ∗ 4.

Easy

A. 13 B. 5 C. −1 D. 7

Question 7

7If 4^(x) × 2^(x + 1) = 32, find x.

Hard

A. 3/2 B. 2 C. 1 D. 4/3

Question 8

8Solve 2x² + x − 6 = 0.

Medium

A. x = 2 or 3 B. x = 3 or −2 C. x = 3/2 or −2 D. x = −3/2 or 2

Question 9

9If f(x) = x² + 1 and g(x) = 2x, find f(g(3)).

Medium

A. 37 B. 10 C. 19 D. 49

Question 10

10The sum of a number and its reciprocal is 10/3. Find the number.

Hard

A. 2 or 1/2 B. 10 C. 3 only D. 3 or 1/3