Number worksheet — GCSE Higher

1.Work out √144 − 2 × 3 + √25

2.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

3.Work out (−3) × 4 + 2 × (−5)

4.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

5.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.

6.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

7.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

8.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

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

10.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

11.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.

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

13.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

14.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

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.