Number worksheet — GCSE Higher

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

2.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

3.Work out 36 ÷ (2 × 3)

4.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.

5.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

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 market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

8.Work out 3 + 4 × (−2).

9.Round 592.5 to the nearest 10.

10.Work out the value of 2⁻⁴

11.Simplify (x⁻²)³, giving your answer as a fraction.

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

13.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

14.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?

15.Work out how many factors 100 has.