Number worksheet — GCSE Higher

1.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

2.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

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

4.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

5.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

6.Work out 5⁰ + 5¹ + 5²

7.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.

8.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

9.Write down the exact decimal value of the fraction 1/6.

10.Last year a company made a profit of £5,200,000. Write this amount in standard form.

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

12.Work out ∛64.

13.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.

14.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

15.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.