Number worksheet — GCSE Higher

1.Write 5,000,000 in standard form.

2.Simplify x⁷ × x⁴, giving your answer as a single power of x.

3.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

4.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

5.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

6.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

7.Work out (2/3)² + (1/2)². Give your answer as a fraction.

8.Write 5/6 as a decimal, showing clearly which digit recurs.

9.Last year a company made a profit of £5,200,000. Write this amount in standard form.

10.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

11.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

12.Work out the value of √49 + ∛27

13.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.

14.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

15.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.