Number worksheet — GCSE Foundation

1.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

2.A newspaper reports that 48,000 people attended a festival. The figure is correct to the nearest thousand. Which statement about the number of people who attended must be true?

3.A concert hall has 300 seats. 20% of the seats are in the balcony. Work out how many of the seats are in the balcony.

4.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

5.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

6.At midday the temperature in the Lake District was 3 °C. By midnight it had fallen to −6 °C. Work out the fall in temperature.

7.Freya types 4² + 3² into her calculator and writes down 49. Work out the correct value of 4² + 3².

8.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

9.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.

10.Work out −4.5 + 2.8.

11.Work out √144

12.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

13.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

14.Write 5,000,000 in standard form.

15.Write the fraction 9/25 as a decimal.