Number worksheet — GCSE Higher

1.Work out √25 + 4² − 12 ÷ 3

2.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.

3.Work out the exact value of √(2² + 3²)

4.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

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

6.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

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

8.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.

9.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

10.Last year a company made a profit of £5,200,000. Write this amount in standard form.

11.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

12.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.

13.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

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.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%