Number worksheet — GCSE Higher

1.Work out ∛64.

2.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.

3.Work out the value of √(16 + 9)

4.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

5.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

6.Work out the value of 6² − 4³.

7.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

8.Write 0.35 as a fraction in its lowest terms.

9.4ˣ = 64. Work out the value of x.

10.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

11.Estimate the value of √45, giving your answer to the nearest whole number.

12.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

13.Write 0.005 in standard form.

14.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.

15.During one night on a mountain, four hikers each recorded the temperature they felt: Ben −6 °C, Priya −2 °C, Sam −9 °C, Alex 1 °C. Work out the difference between the coldest and the warmest of these four temperatures.