Number worksheet — GCSE Higher

1.Work out (−6) + (−4) × 3

2.Simplify x⁶ ÷ x²

3.Work out √(4 × 9)

4.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

5.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.

6.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

7.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

8.Work out 5⁰ + 5¹ + 5²

9.Find the missing number: ▢ ÷ 15 = 24

10.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

11.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

12.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

13.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

14.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

15.Work out 36 ÷ (2 × 3)