Printable · GCSE Higher · ages 14-16
Number worksheet — GCSE Higher
Fifteen questions across the number statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
Number worksheet — GCSE Higher
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- 1.Work out the reciprocal of (2 + 3)
- 2.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.
- 3.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.
- 4.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.
- 5.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.
- 6.Expand and simplify √3(2 + √12).
- 7.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.
- 8.Write 5/6 as a decimal, showing clearly which digit recurs.
- 9.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
- 10.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.
- 11.After a price increase of 10%, a laptop costs £330. Work out the original price.
- 12.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?
- 13.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.
- 14.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.
- 15.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.
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