Number worksheet — GCSE Higher

1.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

2.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

3.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.

4.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

5.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.

6.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

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

8.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

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

10.Write 0.005 in standard form.

11.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

12.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

14.Work out ∛64.

15.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.