Number worksheet — GCSE Higher

1.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

2.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

3.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

4.Write 5/6 as a decimal, showing clearly which digit recurs.

5.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

6.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

7.Which of these is written correctly in standard form?

8.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

9.Work out the value of √(16 + 9)

10.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

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

12.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

13.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

14.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

15.Write 0.325 as a fraction in its simplest form.