Number worksheet — GCSE Higher

1.Work out (−2)³ + (−3)² − (−4)

2.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

3.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.

4.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.

5.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

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

7.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

8.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

9.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

10.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.

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

12.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

13.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

14.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

15.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.