Core Mathematics

Question 1

1For what values of k does 2x² + kx + 8 = 0 have real roots?

Hard

A. all k B. k = 8 only C. k ≤ −8 or k ≥ 8 D. −8 < k < 8

Question 2

2Solve x² + 2x − 15 = 0.

Easy

A. x = 5 or x = 3 B. x = 3 or x = −5 C. x = −3 or x = 5 D. x = 15 or x = −1

Question 3

3Find the range of x for which 5 − 2x < 1.

Easy

A. x > −2 B. x > 2 C. x < 2 D. x < 3

Question 4

4Solve 3x² − 5x − 2 = 0.

Hard

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

Question 5

5Solve x² − 9 = 0.

Easy

A. x = 81 B. x = 9 C. x = 3 or x = −3 D. x = 3 only

Question 6

6Complete the square: x² + 6x = (x + 3)² − k. Find k.

Medium

A. 9 B. 6 C. 3 D. 36

Question 7

7Five pens and two books cost GH¢41; one pen and one book cost GH¢13. What does a book cost?

Medium

A. GH¢9 B. GH¢5 C. GH¢8 D. GH¢4

Question 8

8Solve (x − 2)(x + 3) ≥ 0.

Hard

A. x ≥ 2 only B. x ≤ −3 or x ≥ 2 C. −3 ≤ x ≤ 2 D. x ≤ −3 only

Question 9

9Solve the simultaneous equations 3x − 2y = 4 and 2x + 3y = 7.

Hard

A. x = 2, y = 1 B. x = 0, y = −2 C. x = 3, y = 2.5 D. x = 1, y = 2

Question 10

10Solve 2x + y = 7 and x − y = 2.

Easy

A. x = 1, y = 5 B. x = 4, y = −1 C. x = 2, y = 3 D. x = 3, y = 1