Number worksheet — GCSE Higher

1.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

2.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

3.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

4.Which of these decimals lies between 1/4 and 2/5?

5.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

6.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

7.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

8.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

9.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

10.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

11.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

12.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

13.Simplify (x⁻²)³, giving your answer as a fraction.

14.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

15.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.