Number worksheet — GCSE Higher

1.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

2.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.

3.Work out 4368 ÷ 12.

4.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.

5.Work out 3³ + 2⁴.

6.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

7.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

8.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.

9.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.

10.Simplify (y³)⁴, giving your answer as a single power of y.

11.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

12.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

13.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.

14.Write 5,000,000 in standard form.

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