Number worksheet — GCSE Higher

1.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

2.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

3.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

4.Work out 3 × (−2)² − 5

5.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.

6.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

7.3/5 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.

8.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

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

10.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

11.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

12.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

13.Simplify (y³)⁴, giving your answer as a single power of y.

14.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

15.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.