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CAIE A-Level Biology A2 Mathematical and Statistical Skills Questions

Practise the calculations, graph interpretation and statistical decisions required across CAIE A-Level Biology investigations.

Syllabus
2028–2030
Course
Biology 9700
Level
A2

Covered syllabus points

AS and A Level mathematical requirementsA Level only mathematical and statistical requirementsA Level formula reference and statistics notes

Question 1

[Maximum number: 1]

In 2014, scientists published a phylogenetic (evolutionary) tree diagram showing how and when different groups of insects developed from ancestral groups.

To construct the diagram, the scientists compared nucleotide and amino acid sequence data for 1478 genes from each of 103 different insect species. The 103 species represented all 32 orders of the class Insecta.

The data were used to arrange the species in related groups according to their degree of molecular similarity and to track how sequences changed over time.

For this study, new software for processing large quantities of data was developed.

Calculate the total number of sequences that were compared, considering both the nucleotide and amino acid sequences for each gene.

Question 2

[Maximum number: 2]

Fig. 6.1 is a diagram of mitochondrion.

Fig. 6.1

Fig. 6.1

Assume that the mitochondrion in Fig. 6.1 is a cylinder.

Calculate the surface area of this mitochondrion.
Use the formula: Surface area of cylinder =2πr2+2πrh=2 \pi r^{2}+2 \pi r h
Show your working.

surface area = ‾ μm2\text{surface area = }\underline{\hspace{4cm}}\,\mu\mathrm{m}^{2}

Question 3

[Maximum number: 7]

Phenotypic variation exists in natural populations. There are many causes of variation. Natural selection determines which phenotypes are advantageous.

Question (a)

(a)

There is variation in the quantity of vitamin D stored in the body.

Vitamin D has an important role in keeping bones healthy. The main storage form of vitamin D in the body is serum 25-hydroxyvitamin D (serum 25-OHD).

A study was carried out on 262 healthy women to investigate if the concentration of serum 25-OHD varied between summer and winter. The women had taken no vitamin D supplements. The age range of the women in the sample was 40 to 72 years old.

Table 5.2 shows the results of the study.

Table 5.2

Table 5.2

Additional analysis showed that there was no significant correlation between age and serum 25-OHD concentration.

[ 7 ]

Question (i)

(i)

Explain what is meant by standard deviation.

[ 1 ]

Question (ii)

(ii)

The t-test was used to compare the mean concentration of serum 25-OHD when sampled during the summer with the mean concentration of serum 25-OHD when sampled during the winter, as shown in Table 5.2.

Calculate the value of t using the formula provided.

t=∣xˉ1−xˉ2∣(s12n1+s22n2)t=\frac{\left|\bar{x}_{1}-\bar{x}_{2}\right|}{\sqrt{\left(\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}\right)}}

key to symbols:
xˉ=\bar{x}= mean
s= sample standard deviation
n = sample size (number of observations)

Give your answer to four significant figures.
There is space for your working.

[ 3 ]

Question (iii)

(iii)

The critical value at the 0.0001 probability level is 3.773 .

State the conclusion that can be made about the results of the study shown in Table 5.2 and explain how the result of your calculation in (b)(ii) can be used to support this conclusion.

[ 3 ]

Question 4

[Maximum number: 3]

The glomerular filtration rate (GFR) is the rate at which fluid filters from the blood in the glomerulus into the Bowman's capsule.

Fig. 6.2 shows the mean GFR values for healthy males and females of different age groups.

Fig. 6.2 shows the mean GFR values for healthy males and females of different age groups.

Use Fig. 6.2 to calculate the yearly rate of decrease in mean GFR from the 20-29 age group to the 80-89 age group for females.

Show your working.
Give your answer to one decimal place and include units.
answer

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