Number worksheet — GCSE Higher

1.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

2.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

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

4.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.

5.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

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

7.Which one of these statements is true?

8.A courier's van has a weight limit of 850 kg for its parcels. The driver's display shows the total mass of the parcels loaded as 850 kg, correct to the nearest 5 kg. Decide whether the parcels are definitely within the weight limit.

9.Write down the symbol that makes this statement true: −2/3 ___ −5/6

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.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.

12.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

13.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.

14.Work out (−2)³ + (−3)² − (−4)

15.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.