Number worksheet — GCSE Higher

1.Work out √3 × √12, giving your answer as an integer.

2.Work out 4368 ÷ 12.

3.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

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.Work out the value of √(16 + 9)

6.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

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

8.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.

9.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

10.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

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

12.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

13.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

14.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

15.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.