Core Mathematics

Question 1

1If y varies directly as x and y = 12 when x = 3, find y when x = 5.

Easy

A. 15 B. 20 C. 36 D. 4

Question 2

2Solve 3(x − 2) = 2(x + 1).

Easy

A. 4 B. 8 C. −8 D. 1

Question 3

3Find the range of x for which x² − x − 6 < 0.

Hard

A. x < −2 or x > 3 B. −3 < x < 2 C. x > 3 D. −2 < x < 3

Question 4

4Solve the simultaneous equations x + y = 7 and x − y = 1.

Easy

A. x = 3, y = 4 B. x = 5, y = 2 C. x = 6, y = 1 D. x = 4, y = 3

Question 5

5If α and β are roots of 2x² − 5x + 1 = 0, find α² + β².

Hard

A. 21/4 B. 17/4 C. 23/4 D. 25/4

Question 6

6Factorise ab + ac − 2b − 2c.

Medium

A. (a + 2)(b − c) B. a(b + c) − 2 C. (a − 2)(b + c) D. (a − b)(2 + c)

Question 7

7Expand (2x − 3)².

Easy

A. 4x² − 6x + 9 B. 4x² − 12x + 9 C. 4x² − 9 D. 4x² + 9

Question 8

8Make r the subject of the formula V = πr²h.

Medium

A. r = √(V/(πh)) B. r = πh/V C. r = √(Vπh) D. r = V/(πh)

Question 9

9Simplify 1/(x − 1) − 1/(x + 1).

Hard

A. 2/(x² − 1) B. 0 C. −2/(x² − 1) D. 2x/(x² − 1)

Question 10

10Solve x² − 5x + 6 = 0.

Easy

A. x = 1 or 6 B. x = 2 or 3 C. x = −2 or −3 D. x = −1 or 6