Number worksheet — GCSE Higher

1.Work out the value of 2⁻⁴

2.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

3.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

4.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

5.Work out the value of 6² − 4³.

6.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

7.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

8.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

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

10.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

11.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

12.Write 200 as a product of its prime factors, using index notation.

13.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

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

15.Work out 3.7 × 24.