Number worksheet — GCSE Higher

1.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

2.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

3.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

4.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

5.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

6.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

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

8.Write 90 as a product of its prime factors.

9.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.

10.Write 5,000,000 in standard form.

11.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

12.Simplify √8 + √18, giving your answer in the form k√2.

13.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.

14.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

15.Work out −(−3)⁴ + (−3)³