Number worksheet — GCSE Foundation

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

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

3.Write down the value of 7⁰

4.Work out an estimate for 6.8 × 41, by rounding each number to 1 significant figure.

5.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

6.A student always writes the digits after the decimal point over a denominator of 100, whatever the number of decimal places. Using this wrong rule, they convert 0.9 to a fraction. Work out the correct fraction that 0.9 is equal to, giving your answer in its simplest form.

7.A quiz has 50 questions. Freya answers 10% of them incorrectly. Work out how many questions she answers incorrectly.

8.In the number 3.472, work out the value of the digit 7.

9.Write down the symbol that makes this statement true: −9 ___ −4

10.Work out the value of ∛8.

11.Work out the value of 2⁻²

12.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.

13.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

14.Round 3.947 to 2 decimal places.

15.A red blood cell has a diameter of about 7 × 10⁻⁶ metres. A virus has a diameter about 100 times smaller. Work out the diameter of the virus. Give your answer in standard form.