Number worksheet — GCSE Higher

1.Work out the value of 2⁻²

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

3.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

4.Work out √25 + 4² − 12 ÷ 3

5.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.

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

7.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

8.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

9.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

10.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.

11.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.

12.Write 5,000,000 in standard form.

13.Simplify √8 + √18, giving your answer in the form k√2.

15.Simplify ⁴√(16a⁸b¹²)