Number worksheet — GCSE Higher

1.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

2.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

3.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.

4.Work out (−2)² − 3

5.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

6.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

7.Work out the value of 6² − 4³.

8.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.

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

10.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

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

12.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

13.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

14.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

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