Number worksheet — GCSE Higher

1.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

2.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

3.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

4.Given that 2⁵ = 32, work out 2⁶.

5.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

6.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

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

8.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

9.Write 90 as a product of its prime factors.

10.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

11.Write down the symbol that makes this statement true: −2/3 ___ −5/6

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

13.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.

14.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

15.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%