Number worksheet — GCSE Higher

1.Work out √144 − 2 × 3 + √25

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.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.

4.Estimate the value of √45, giving your answer to the nearest whole number.

5.Which of these is written correctly in standard form?

6.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

7.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.

8.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

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

10.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

11.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

13.Work out ∛64.

14.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

15.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.