MS AQA Biology maths skills

Mathematical skills used across AQA A-level Biology, including calculations, data interpretation and quantitative reasoning. Free MCQs include clues and explanations.

Specification route
MS
Question bank
10 questions
Course stage
AS / Year 12

Sample questions

QUESTION 1 · MS 1.9 · LEVEL 2

A researcher wishes to determine if there is a significant difference between the mean lengths of leaves from oak trees growing in a shaded wood compared to those growing in an open field. Which statistical test should they use?

  • Student's t-test
  • Chi-squared ($X^2$) test
  • Spearman's rank correlation coefficient
  • Standard deviation
Show clue

This test is specifically designed to compare the mean values of two sets of normally distributed data.

Show answer and explanation

Answer: Student's t-test

Mathematical Skills (MS 1.9). The Student's t-test is used to compare the means of two different samples to see if the difference between them is statistically significant.

QUESTION 2 · MS 1.9 · LEVEL 2

An ecologist collects data on the concentration of nitrates in the soil and the corresponding biomass of a plant species at various sites. Which statistical test should be used to see if these two variables are related?

  • Spearman's rank correlation coefficient
  • Student's t-test
  • Chi-squared ($X^2$) test
  • Index of diversity
Show clue

This test looks for an association or relationship between two continuous variables.

Show answer and explanation

Answer: Spearman's rank correlation coefficient

Mathematical Skills (MS 1.9). Spearman's rank correlation coefficient is used to determine if there is a significant correlation (positive or negative) between two continuous variables.

QUESTION 3 · MS 1.9 · LEVEL 3

When performing a statistical test, a student calculates a probability ($p$) value of $p < 0.05$. What is the correct conclusion to draw from this result?

  • Reject the null hypothesis; there is a less than $5\%$ probability that the difference or correlation observed is due to chance.
  • Accept the null hypothesis; there is a greater than $5\%$ probability that the results are due to chance.
  • Reject the null hypothesis; there is exactly a $5\%$ error rate in the data collection.
  • Accept the null hypothesis; the data proves that the independent variable caused the change.
Show clue

In biology, a $p$ value of less than 0.05 ($5\%$) is the standard threshold for statistical significance.

Show answer and explanation

Answer: Reject the null hypothesis; there is a less than $5\%$ probability that the difference or correlation observed is due to chance.

MS 1.9. If $p < 0.05$, the probability that the results occurred purely by chance is less than $5\%$. This is deemed statistically significant, so the null hypothesis is rejected.

QUESTION 4 · MS 1.9 · LEVEL 1

A strong positive correlation is found between the sales of ice cream and the number of shark attacks in a coastal town. What biological principle must be remembered when interpreting this data?

  • Correlation does not equal causation; both variables may be influenced by a third independent factor, such as high temperature.
  • A positive correlation proves that eating ice cream biologically attracts sharks.
  • The data must be anomalous and should be discarded because the two variables are completely unlinked.
  • The correlation coefficient must be negative if the relationship is indirect.
Show clue

Just because two things happen at the same time doesn't mean one causes the other.

Show answer and explanation

Answer: Correlation does not equal causation; both variables may be influenced by a third independent factor, such as high temperature.

MS 1.9. A significant correlation only indicates that two variables change together. It does not prove a causal mechanism, as a third variable (e.g., hot weather driving people to the beach and making them buy ice cream) might cause both.

QUESTION 5 · MS 3.3 · LEVEL 2

When plotting the growth of a bacterial population over several days, why might a scientist choose to use a logarithmic scale ($log_{10}$) for the y-axis (number of bacteria)?

  • Because bacterial populations grow exponentially, a logarithmic scale allows a massive range of values to be plotted clearly on a single graph.
  • Because bacteria are too small to be counted using a standard linear scale.
  • Because it automatically converts the data into a standard deviation.
  • Because the rate of bacterial reproduction is always exactly 10 times faster each hour.
Show clue

If a population goes from $10$ to $10,000,000,000$, plotting it on standard graph paper is physically impossible.

Show answer and explanation

Answer: Because bacterial populations grow exponentially, a logarithmic scale allows a massive range of values to be plotted clearly on a single graph.

Mathematical Skills (MS 3.3). Logarithmic scales are used when data covers a vast range of magnitudes, such as the exponential growth of microorganisms, condensing exponential curves into straight, readable lines.

QUESTION 6 · MS 3.6 · LEVEL 3

A student plots a curve showing the volume of product formed over time in an enzyme reaction. How can they calculate the exact rate of reaction at precisely $30$ seconds?

  • Draw a straight tangent line to the curve at the $30$-second mark and calculate the gradient of that tangent ($\Delta y / \Delta x$).
  • Divide the total volume of product at $30$ seconds by $30$.
  • Calculate the mean volume of product from $0$ to $60$ seconds.
  • Draw a line of best fit through the origin and calculate its slope.
Show clue

The rate at a specific instant is the steepness of the curve at that exact point.

Show answer and explanation

Answer: Draw a straight tangent line to the curve at the $30$-second mark and calculate the gradient of that tangent ($\Delta y / \Delta x$).

Mathematical Skills (MS 3.6). To find the rate at a specific point on a curve, you must draw a tangent (a straight line touching the curve at that point) and calculate its gradient.

QUESTION 7 · MS 1.11 · LEVEL 2

A measuring cylinder has scale divisions of $2\ cm^3$. What is the absolute uncertainty of a single measurement taken with this instrument?

  • $\pm 1\ cm^3$
  • $\pm 2\ cm^3$
  • $\pm 0.5\ cm^3$
  • $\pm 4\ cm^3$
Show clue

For an analogue scale, the uncertainty is generally half of the smallest scale division.

Show answer and explanation

Answer: $\pm 1\ cm^3$

MS 1.11. The absolute uncertainty of a single reading on an analogue scale is half the smallest division. Since the smallest division is $2\ cm^3$, the uncertainty is $\pm 1\ cm^3$.

QUESTION 8 · MS 1.11 · LEVEL 3

A student measures $10\ cm^3$ of solution using a pipette with an uncertainty of $\pm 0.1\ cm^3$. What is the percentage error of this measurement?

  • $1\%$
  • $0.1\%$
  • $10\%$
  • $0.01\%$
Show clue

Percentage error = (Absolute uncertainty / Measured value) $\times$ 100.

Show answer and explanation

Answer: $1\%$

MS 1.11. Percentage error is calculated as $(0.1 / 10) \times 100 = 1\%$.

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