Number worksheet — GCSE Higher

1.2/3 of an amount of money is £30. Work out the amount.

2.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

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

4.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

5.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

6.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

7.Simplify ⁴√(16a⁸b¹²)

8.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

9.Work out the value of √(16 + 9)

10.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

11.Work out ∛64.

12.Write 0.325 as a fraction in its simplest form.

13.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

14.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.

15.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.