Number worksheet — GCSE Higher

1.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

2.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

3.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.

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

5.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

6.Work out ⁴√81

7.Write 0.06 as a fraction in its simplest form.

8.Work out √25 + 4² − 12 ÷ 3

9.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

10.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.

11.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

12.Work out the value of 2⁻⁴

13.Work out 5⁰ + 5¹ + 5²

14.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

15.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.