Number worksheet — GCSE Higher

1.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

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

3.√700 lies between which two consecutive integers?

4.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

5.Simplify (3a²)² × (2a)³

6.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

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

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

9.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

10.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

11.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

12.Which of these statements about −0.7 and −0.25 is true?

13.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?

14.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

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.