Number worksheet — GCSE Higher

1.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.

2.Work out (−6) + (−4) × 3

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

4.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

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

6.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

7.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.

8.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

9.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.

10.2/3 of an amount of money is £30. Work out the amount.

11.Simplify x⁷ × x⁴, giving your answer as a single power of x.

12.Find the missing number: 17 × ▢ = 391

13.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

14.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

15.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.