Number worksheet — GCSE Higher

1.Work out (2/3)² + (1/2)². Give your answer as a fraction.

2.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

3.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

4.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

5.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

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

7.Simplify (y³)⁴, giving your answer as a single power of y.

8.Simplify √45.

9.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.

10.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

11.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

12.Write 200 as a product of its prime factors, using index notation.

13.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.

14.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

15.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.