Number worksheet — GCSE Higher

1.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

2.Which of these statements about −0.7 and −0.25 is true?

3.Work out 3 + 4 × (−2).

4.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

5.Simplify x⁷ × x⁴, giving your answer as a single power of x.

6.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

7.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

8.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

9.Work out √(4 × 9)

10.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

11.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

12.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

13.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

14.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

15.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.