Number worksheet — GCSE Higher

1.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

3.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

4.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

5.Estimate the value of √45, giving your answer to the nearest whole number.

6.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.

7.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

8.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

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

10.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

11.Work out how many factors 100 has.

12.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

13.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

14.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

15.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.