Number worksheet — GCSE Higher

1.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.

2.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

3.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

4.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

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

6.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

7.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

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

9.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.

10.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

11.Expand and simplify √3(2 + √12).

12.Write down the symbol that makes this statement true: −2/3 ___ −5/6

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

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

15.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.