Number worksheet — GCSE Higher

1.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

2.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

3.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

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

5.Work out 4368 ÷ 12.

6.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

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

8.Work out (−2)³ + (−3)² − (−4)

9.Work out 5⁰ + 5¹ + 5²

10.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?

11.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?

12.Work out the exact value of √(2² + 3²)

13.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?

14.Which of these is written correctly in standard form?

15.Simplify 2³ × 2⁴, giving your answer as a single power of 2.