Number worksheet — GCSE Higher

1.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.

2.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?

3.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

4.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

5.Work out 4368 ÷ 12.

6.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.

7.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

8.Work out (2/3)² + (1/2)². Give your answer as a fraction.

9.Work out the value of 6² − 4³.

10.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.

11.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

12.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

13.Which one of these statements is true?

14.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

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