Number worksheet — GCSE Higher

1.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

2.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

3.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

4.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

5.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

6.Write 0.35 as a fraction in its lowest terms.

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.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

9.Work out 3 × (−2)² − 5

10.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

11.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

12.Expand and simplify √3(2 + √12).

13.Write 60 as a product of its prime factors, using index notation.

14.Work out √3 × √12, giving your answer as an integer.

15.Work out 4368 ÷ 12.