Number worksheet — GCSE Higher

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

2.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.

3.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

4.Write 90 as a product of its prime factors.

5.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

6.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

7.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

8.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.

9.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.

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

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

12.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

13.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

14.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

15.Work out 3 + 4 × (−2).