Mathematical problems

Suitable for A/AS-level and Higher biology students.
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1. A shoot grows from 55cm to 59cm. What is this increase in length as a percentage?

2. A muscle contracts from 5cm to 3.5cm. What is this decrease in length as a percentage?

3. A population contains 56 red individuals, 42 orange individuals and 14 yellow individuals. Express these proportions as the simplest whole number ratio.

4. Out of a population of 600 butterflies, 70% are male. How many males are there?

5. Out of a population of 1500 birds, 180 have red crests. What percentage of the birds have red crests?

6. Five areas each contain the following numbers of plant species: 25, 29, 21, 34, 35. What is the mean (average) number of plant species in an area?

7. A breeding experiment produces normal fruit flies and ebony-bodied fruit flies in a 3:1 ratio. If 120 flies are produced in total, how many are expected to be ebony-bodied?

8. A root is originally 12cm long. If its length increases by 25%, what will the new length be?

9. A mouse increases in weight from 140g to 170g. What is this increase as a percentage?

10. A population increases from 28 individuals to 70 individuals. What is this increase as a percentage?

11. A sample decreases in mass from 80g to 74g. What is this decrease as a percentage?

12. A group includes 26 marked individuals and 39 unmarked individuals. Express the proportion of marked to unmarked individuals as the simplest whole number ratio.

13. If air consists of 21% oxygen, what volume of oxygen is there in 40 litres of air?

14. The heights of four people were as follows: 177cm, 185cm, 151cm, 191cm. What was the mean (average) height?

15. If 25 kJ of solar energy strikes a leaf, and 4% of this is absorbed, how much energy is absorbed?

16. In a group of children, 12 had brown eyes and 16 had blue eyes. What percentage of the children had blue eyes?

17. If a stem increases in length from 15cm to 35 m in 8 days, what is its growth rate in centimetres per day?

18. A breeding experiment produces yellow/round peas, yellow/wrinkled peas, green/round peas and green/wrinkled peas in a 9:3:3:1 ratio. If 96 individuals are produced, what number will be expected to have yellow/round peas?

19. In a particular species the sex ratio is 3 females : 2 males. If a group contains 93 females, how many males would be expected?

20. If 55% of a population is male, and 40% of males have moustaches, what percentage of the total population has moustaches?

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