Number worksheet — GCSE Higher

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

2.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

3.Simplify (3a²)² × (2a)³

4.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

5.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

6.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

7.Write 0.875 as a fraction in its simplest form.

8.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

9.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

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

11.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.

12.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

13.√700 lies between which two consecutive integers?

14.Write 90 as a product of its prime factors.

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.