Number worksheet — GCSE Higher

1.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

2.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

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

4.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

5.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

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

7.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

8.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.

9.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

10.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

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

12.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

13.Bella's electricity supplier charges 28.5p per unit (kWh). Last month she used 340 units. Work out the total cost, giving your answer in pounds.

14.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

15.Work out 5/6 × 2/9, giving your answer in its simplest form.