Number worksheet — GCSE Higher

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

2.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

3.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

4.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

5.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

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

7.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

8.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

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

10.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

11.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.

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

13.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

14.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.

15.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.