Number worksheet — GCSE Higher

1.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

2.Work out 5⁰ + 5¹ + 5²

3.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

4.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

5.Estimate the value of √45, giving your answer to the nearest whole number.

6.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

7.Work out √144 − 2 × 3 + √25

8.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.

9.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

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

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

12.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

13.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.

14.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

15.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.