Number worksheet — GCSE Higher

1.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

2.Bella's electricity supplier charges 28.5p per unit (kWh). Last month she used 340 units. Work out the total cost, giving your answer in pounds.

3.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

4.Work out the value of 2⁻²

5.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

6.Expand and simplify √3(2 + √12).

7.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

8.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

9.Work out 3.7 × 24.

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

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

12.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

13.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

14.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.

15.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.