Number worksheet — GCSE Higher

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

2.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

3.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

4.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

5.Simplify ⁴√(16a⁸b¹²)

6.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

7.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

8.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

9.2/3 of an amount of money is £30. Work out the amount.

10.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.

11.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.

12.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

13.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

14.Which of these statements about −0.7 and −0.25 is true?

15.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.