Number worksheet — GCSE Higher

1.Work out ∛(−27) + ∛8

2.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

3.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

4.Work out 100 − 4 × 5²

5.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

6.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.

7.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

8.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

9.Work out √(4 × 9)

10.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

11.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

12.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?

13.Round 0.006482 to 2 significant figures.

14.Simplify x⁷ × x⁴, giving your answer as a single power of x.