Number worksheet — GCSE Higher

1.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

2.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

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

4.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

5.Work out the value of 6² − 4³.

6.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

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

8.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

9.Work out the exact value of √(2² + 3²)

10.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

11.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

12.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.

13.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

14.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

15.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.