Number worksheet — GCSE Higher

1.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

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 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.

4.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

5.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?

6.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

7.Simplify ⁴√(16a⁸b¹²)

8.Work out ⁴√16

9.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

10.Write 5/6 as a decimal, showing clearly which digit recurs.

11.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?

12.Write 7/12 as a decimal, showing clearly which digit is recurring.

13.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.

14.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

15.Rationalise the denominator of 6/√3, giving your answer in its simplest form.