Number worksheet — GCSE Higher

1.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.

2.Write 0.005 in standard form.

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

6.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

7.√700 lies between which two consecutive integers?

8.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

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

10.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

11.Work out 5⁰ + 5¹ + 5²

12.Write 12 as a product of its prime factors.

13.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

14.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.

15.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.