Number worksheet — GCSE Higher

1.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.

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

3.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

4.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

5.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

6.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

7.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

8.Write 7/12 as a decimal, showing clearly which digit is recurring.

9.Work out (−2)² − 3

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

11.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

12.Work out −(−3)⁴ + (−3)³

13.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

14.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.

15.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.