Number worksheet — GCSE Foundation

1.Work out (−2)³ + (−3)² − (−4)

2.Work out 4368 ÷ 12.

3.Work out the value of √49 + ∛27

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

5.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

6.In a box of counters the ratio of red counters to blue counters is 4 : 5. What fraction of the counters are blue?

7.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

8.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

9.Which of these numbers is the largest: −9, −7, −4, −2?

10.Write the fraction 47/50 as a decimal.

11.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

12.Work out 18 − 4 × 2

13.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

14.Write 45,000 in standard form.

15.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.