Number worksheet — GCSE Higher

1.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

2.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.

3.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

4.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

5.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

7.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

8.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.

9.Work out 5⁰ + 5¹ + 5²

10.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

11.Work out 6² − 4².

12.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

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

14.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

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