Core Mathematics

Question 1

1Simplify log₃ 81 − log₂ 0.25.

Hard

A. 2 B. 4 C. 6 D. −2

Question 2

2Express the recurring decimal 0.333… as a fraction.

Easy

A. 1/9 B. 3/10 C. 33/100 D. 1/3

Question 3

3Find the product of the HCF and LCM of 12 and 18.

Easy

A. 108 B. 6 C. 36 D. 216

Question 4

4Find the value of x if 2x₅ = 13 in base ten (2x₅ means 2 followed by digit x in base five).

Medium

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

Question 5

5Find the value of 0.36 ÷ 0.012.

Easy

A. 0.3 B. 300 C. 30 D. 3

Question 6

6Find the least number which when divided by 6, 8 and 12 leaves a remainder of 5.

Hard

A. 24 B. 53 C. 19 D. 29

Question 7

7Solve log₁₀(x + 3) + log₁₀(x − 3) = log₁₀ 16.

Hard

A. 5 B. −5 C. ±5 D. 4

Question 8

8Express 0.4̇5̇ (0.454545...) as a fraction in its lowest terms.

Hard

A. 9/20 B. 45/100 C. 5/11 D. 4/9

Question 9

9Simplify 3⁻² × 9.

Easy

A. 1 B. −81 C. 1/81 D. 81

Question 10

10Find the value of x if log x + log 4 = log 20.

Hard

A. 16 B. 24 C. 80 D. 5