Number worksheet — GCSE Higher

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

2.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

3.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

4.Work out 4368 ÷ 12.

5.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.

6.Work out the value of √(16 + 9)

7.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

8.Work out the exact value of √(2² + 3²)

9.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

10.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

11.Work out √25 + 4² − 12 ÷ 3

12.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

13.Work out the value of √49 + ∛27

14.Last year a company made a profit of £5,200,000. Write this amount in standard form.

15.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.