Number worksheet — GCSE Higher

1.Work out the value of (1/3)⁻²

2.Expand and simplify √3(2 + √12).

3.Work out (−6) + (−4) × 3

4.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

5.Write 7/12 as a decimal, showing clearly which digit is recurring.

6.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

7.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

8.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

9.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

10.During one night on a mountain, four hikers each recorded the temperature they felt: Ben −6 °C, Priya −2 °C, Sam −9 °C, Alex 1 °C. Work out the difference between the coldest and the warmest of these four temperatures.

11.Work out (2/3)² + (1/2)². Give your answer as a fraction.

12.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

13.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

14.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

15.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.