Number worksheet — GCSE Higher

1.Simplify x⁶ ÷ x²

2.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

3.Write 0.325 as a fraction in its simplest form.

4.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

5.Work out √144 − 2 × 3 + √25

6.Work out √3 × √12, giving your answer as an integer.

7.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

8.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

9.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

10.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

11.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

12.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

13.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

14.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.

15.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.