Number worksheet — GCSE Higher

1.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

2.Work out 3 × (−2)² − 5

3.Work out (−2)² − 3

4.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

5.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

6.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.

7.Simplify x⁶ ÷ x²

8.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

9.4ˣ = 64. Work out the value of x.

10.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

11.Work out how many factors 36 has.

12.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

13.Work out √25 + 4² − 12 ÷ 3

14.Work out how many factors 100 has.

15.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.