Number worksheet — GCSE Higher

1.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.

2.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.

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

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

5.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

6.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

7.Simplify √8 + √18, giving your answer in the form k√2.

8.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

9.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

10.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

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

12.Work out 100 − 4 × 5²

13.√700 lies between which two consecutive integers?

14.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

15.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.