Number worksheet — GCSE Higher

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

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.Which of these decimals lies between 1/4 and 2/5?

4.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.

5.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

6.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

7.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

8.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.

9.Write 0.35 as a fraction in its lowest terms.

10.Write down the exact decimal value of the fraction 1/6.

11.Work out −4.5 + 2.8.

12.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.

13.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

14.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.

15.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?