Number worksheet — GCSE Higher

1.Work out −(−3)⁴ + (−3)³

2.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

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

4.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

5.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

6.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

7.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

8.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

9.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

10.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

11.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

12.Write 0.35 as a fraction in its lowest terms.

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

14.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

15.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.