Number worksheet — GCSE Higher

1.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

2.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

3.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.

4.Work out (−2)³ + (−3)² − (−4)

5.Write 60 as a product of its prime factors, using index notation.

6.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?

7.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

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

9.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

10.Find the missing number: 17 × ▢ = 391

11.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

12.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.

13.Find the missing number: ▢ ÷ 15 = 24

14.Write ∛(x²) as a single power of x.

15.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.