Number worksheet — GCSE Higher

2.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

3.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.

4.Simplify √45.

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

6.Simplify (y³)⁴, giving your answer as a single power of y.

7.Work out 4368 ÷ 12.

8.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

9.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.

10.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

11.Work out the value of √49 + ∛27

12.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?

13.Simplify √8 + √18, giving your answer in the form k√2.

14.Simplify (3a²)² × (2a)³

15.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.