Number worksheet — GCSE Higher

1.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

2.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

3.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?

4.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

5.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

6.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

7.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

8.Write ∛(x²) as a single power of x.

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

10.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

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

12.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.

13.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.

14.Simplify x⁶ ÷ x²

15.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.