Biology 9700/53 — October/November 2012

Background Concept

Every controlled investigation involves three types of variable. The independent variable is the factor the experimenter deliberately changes between treatments (here, between flasks). The dependent variable is the factor that is measured to detect the effect of that change. All other variables must be kept constant (controlled) so that any difference in the dependent variable can be attributed to the independent variable rather than to some other changing factor.

In this investigation the student is interested in how nitrate (a plant nutrient) affects the population growth of Chlorella. The cells need nitrate to make amino acids, proteins and nucleic acids, so a change in nitrate availability is expected to change how fast the population grows.

Understanding the Question

The stem (from the question) describes a student who set up five flasks containing different concentrations of sodium nitrate (5, 10, 15, 20 and 25 $\text{mmol dm}^{-3}$) and then counted the Chlorella cells in each flask every two days for ten days using a haemocytometer. Part (a)(i) simply asks you to name the independent and dependent variables in this investigation.

Approach

Look at the description in Fig. 1.2: identify the factor that was deliberately varied (the independent variable) and the factor that was measured and recorded (the dependent variable).

Step-by-Step Reasoning

1. Independent variable — the factor the student deliberately changed between flasks. From Fig. 1.2, this is the concentration of sodium nitrate (5, 10, 15, 20, 25 $\text{mmol dm}^{-3}$).
2. Dependent variable — the factor the student measured to see the effect. From Table 1.1 and the haemocytometer step in Fig. 1.2, this is the number of Chlorella cells (per $\text{cm}^3$ of culture).

Mark scheme note: the words 'amount' and 'frequency' are rejected for the dependent variable, and the words 'growth' and 'population growth' are ignored (because the data table records actual cell counts, not a derived 'growth' figure). The precise, mark-scheme-aligned term is 'number of cells'.

Key Takeaways

• Independent = what is varied by the experimenter.
• Dependent = what is measured to detect the effect of that variation.
• Use the precise term 'number of cells' rather than 'growth', 'amount' or 'population growth'.

Common Mistakes

• Writing 'amount of nitrate' instead of 'concentration of nitrate' — the mark scheme requires the word concentration.
• Writing 'population growth' or 'amount of Chlorella' for the dependent variable — both are rejected; the precise term is 'number of cells'.
• Confusing independent and dependent — the independent variable is on the x-axis of a results graph, and the dependent variable is on the y-axis.

Things to Be Careful About

The mark scheme explicitly REJECTS 'amount' and IGNORES 'growth' / 'population growth' for the dependent variable. Stick to the literal data: 'number of cells'.

Background Concept

A controlled variable is any factor that is kept the same for every treatment in an investigation. Holding these constant ensures that the only meaningful difference between treatments is the independent variable, so any difference observed in the dependent variable can fairly be attributed to that independent variable.

The procedure in Fig. 1.2 has been deliberately written so that the only factor that changes from flask to flask is the concentration of sodium nitrate. Every other quantity mentioned in the procedure is therefore a controlled variable.

Understanding the Question

Part (a)(ii) asks you to look at Fig. 1.2 and pick out two factors that the student has already kept constant. The phrase 'as shown in Fig. 1.2' is important: you are restricted to factors that are visible in the diagram, not factors you think should have been controlled.

Approach

Read each numbered step in Fig. 1.2 and ask: 'Is this quantity different between flasks, or the same?' Anything the same is a controlled variable. Pick the two that are most clearly stated.

Step-by-Step Reasoning

Going through Fig. 1.2 step by step:

1. Step 1: $250\ \text{cm}^3$ of growth medium in each of five flasks — the volume of growth medium is the same.
2. Step 1: different concentrations of sodium nitrate — this is the independent variable, not a control.
3. Step 2: $1\ \text{cm}^3$ of Chlorella culture is added to each flask using a graduated pipette — the volume of Chlorella culture is the same, and the source of culture (one stock culture) is the same.
4. Step 3: flasks are left in sunlight at room temperature — light and (room) temperature are kept the same.
5. Step 4: cells are counted immediately, then every 2 days for 10 days — the time of sampling is the same for all flasks.
6. The diagram shows five identical conical flasks — the size (and type) of flask is the same.

The mark scheme accepts any two of: source of culture, time of investigation/sampling, volume of growth medium, volume of culture, size of flask, temperature, light.

Key Takeaways

• 'Controlled' means 'kept the same in every treatment'.
• The procedure diagram is the place to look for these.
• The most quantitative, easiest-to-credit answers are volumes and times.

Common Mistakes

• Naming the independent variable (nitrate concentration) as a control — it is the variable being changed, so it is the opposite of controlled.
• Naming vague factors like 'the experimenter' or 'the lab' — these are not biological/physical variables.
• Writing 'amount' or 'quantity' instead of a precise quantity with a unit — the mark scheme ignores 'amount/quantity' and accepts only the quantity with a unit (e.g. $250\ \text{cm}^3$, $1\ \text{cm}^3$, every 2 days).

Things to Be Careful About

The mark scheme only credits the first two suggestions you write. Write your two strongest answers first. Also, give the quantity rather than the vague word 'amount' or 'quantity' — '$250\ \text{cm}^3$ of growth medium' is far safer than 'the same amount of medium'.

Background Concept

A fair test requires that every variable other than the independent variable is held constant. For a culture of photosynthetic single-celled algae such as Chlorella, growth is influenced by many factors besides nitrate: light (intensity, wavelength and daily duration), temperature, pH of the medium, dissolved oxygen, dissolved $\text{CO}_2$, and the even distribution of cells in the culture when each flask is inoculated.

The mark scheme for this part is in the format '2 × 2': two marking points for each variable, one for naming it and one for describing a valid method of standardising it. The variable and its method must be clearly linked.

Understanding the Question

Part (a)(iii) asks you to describe how two other variables could be controlled — i.e. variables that are not among the ones already credited in (a)(ii). The 'method' part of each answer must be specific enough that someone else could carry it out.

Approach

For each variable you choose, state (1) what the variable is and (2) exactly how the student would keep it the same for every flask. Link the method to the variable explicitly.

Step-by-Step Reasoning

The mark scheme lists nine possible variable–method pairs. Two that are easy to credit well:

1. Light — Chlorella photosynthesises, so light intensity, wavelength and daily duration all affect growth. Control by using a lamp of fixed wattage, at a fixed distance from every flask, switched on for a fixed number of hours per day (e.g. 12 h light / 12 h dark). Mark scheme accepts 'filter of known wavelength', 'same wattage bulb', 'lamp at fixed distance' or 'stated fixed duration'.
2. Temperature — enzyme-catalysed reactions in the cell (and the rate of diffusion of nutrients) depend on temperature. Control by placing all flasks in a thermostatically controlled water bath or incubator set to a constant temperature (e.g. $25\ \text{°C}$). The mark scheme accepts 'temperature-controlled room', 'thermostatically controlled water bath' or 'incubator'.

Other valid pairs (any two would do):

• pH — add a buffer to the growth medium. (Reject 'phosphate buffer', 'add $\text{H}^+$' or 'add $\text{OH}^-$' from the mark scheme.)
• Aeration / oxygen — bubble air (or $\text{O}_2$) through each flask using a small pump or air stone, at the same rate. The mark scheme accepts 'pump / oxygen cylinder / bubbler / diffuser / air lift / bubbling of air or oxygen'.
• Carbon dioxide — add sodium hydrogen carbonate ($\text{NaHCO}_3$) to the medium, or bubble $\text{CO}_2$ from a cylinder at a fixed rate. The mark scheme accepts 'bicarbonate' but rejects 'carbonate'.
• Even cell density — swirl or stir the Chlorella stock culture immediately before removing the $1\ \text{cm}^3$ sample, so that each flask receives a representative number of cells.
• Maintaining nitrate concentration — replace the medium at fixed intervals (e.g. every 48 h), so that the cells do not deplete the nitrate and change the independent variable during the experiment.
• Counting method — use a systematic procedure on the haemocytometer (e.g. always count the same five large squares) so that every count is comparable.

A common error is to give a method that could not actually be carried out, or to describe a method without saying which variable it controls. Both variable and method are needed, and they must be linked.

Key Takeaways

• Name the variable and give a workable standardisation method.
• Link the two — 'temperature, controlled by a thermostatically water bath' not 'a water bath' alone.
• Do not repeat factors already credited in (a)(ii).

Common Mistakes

• Naming a variable already credited in (a)(ii) (e.g. light or temperature if you put them in (a)(ii)) — the mark scheme restricts the (a)(iii) credit to factors not already mentioned, except for counting method.
• Giving a vague method — 'control the temperature' is not enough; 'place all flasks in a thermostatically controlled water bath at $25\ \text{°C}$' is.
• Suggesting 'phosphate buffer' to control pH — the mark scheme specifically rejects this because phosphate would interfere with the independent variable in part (f).

Things to Be Careful About

The mark scheme says 'Identifying a variable must be free standing, method must be linked to the variable'. A standalone 'use a buffer' with no variable named scores nothing; 'pH — add a buffer to the medium' scores both marks for that variable.

Background Concept

A solution of a given molarity is prepared by dissolving a known mass of solute in a known volume of solvent. The relationship is:

Once a single concentrated 'stock' solution has been made, lower concentrations are obtained by dilution: mixing a measured volume of the stock with a measured volume of water. For two solutions of the same solute, the dilution equation is:

where $c_1$ and $V_1$ are the concentration and volume taken from the stock, and $c_2$ and $V_2$ are the concentration and total volume of the dilution.

Understanding the Question

The student must (a) make up the highest-concentration solution ($25\ \text{mmol dm}^{-3}$) from solid sodium nitrate, and (b) use that to make the other four concentrations (5, 10, 15 and $20\ \text{mmol dm}^{-3}$). The description must be detailed enough that another person could follow it.

Approach

Work in two stages: (1) calculate and weigh the mass needed for the $25\ \text{mmol dm}^{-3}$ stock; (2) describe the proportional dilutions to give the lower concentrations. Show the calculation, then the practical steps.

Step-by-Step Reasoning

Stage 1 — the $25\ \text{mmol dm}^{-3}$ stock.

$25\ \text{mmol dm}^{-3} = 25 \times 10^{-3}\ \text{mol dm}^{-3} = 0.025\ \text{mol dm}^{-3}$.
For $1\ \text{dm}^3$ of this solution:

So weigh $2.125\ \text{g}$ of solid $\text{NaNO}_3$, dissolve it in (and make up to) $1\ \text{dm}^3$ of deionised water, and stir.

Stage 2 — the lower concentrations (proportional dilutions).

The mark scheme wants the ratios of stock : water (or water : stock) for each of 5, 10, 15 and $20\ \text{mmol dm}^{-3}$ in the order shown in Fig. 1.2. Because each lower concentration is a simple fraction of 25, the dilution can be done by mixing stock and water in the corresponding ratio (e.g. 1 part stock + 4 parts water gives 1/5 of 25 = $5\ \text{mmol dm}^{-3}$):

The mark scheme's notation '4 : 1, 3 : 2, 2 : 3, 1 : 4' refers to the water : stock ratios for the 5, 10, 15 and 20 series. Use a graduated pipette or measuring cylinder for each volume and stir / swirl each dilution thoroughly.

Key Takeaways

• $\text{mass} = \text{molarity} \times \text{volume} \times \text{molar mass}$ is the workhorse calculation for solution preparation.
• Make one stock, then dilute proportionally to save time and weighing errors.
• Always use deionised / distilled water to avoid contaminating the medium.

Common Mistakes

• Forgetting to convert mmol dm⁻³ into mol dm⁻³ — the calculation gives 0.025, not 25.
• Using tap water — ions in tap water can contaminate the medium and affect the growth of Chlorella.
• Saying 'mix' without saying how — the mark scheme rejects 'mix' unqualified and accepts only 'stir', 'swirl', 'mix thoroughly' or 'mix with a glass rod'.
• Omitting the actual dilution ratios — the mark scheme requires the 1:4, 2:3, 3:2, 4:1 series to be visible in the answer.

Things to Be Careful About

The mark scheme accepts 'rounding of decimal places' (so 2.13 g is fine) and 'volumetric flask' for the $1\ \text{dm}^3$ make-up. It rejects 'serial dilution' (because that is a different technique involving repeated ten-fold dilutions) and 'mix' on its own. Always quote the type of water (deionised / distilled) and the method of mixing (stir, swirl, glass rod).

Background Concept

A control in a controlled investigation is a treatment in which the independent variable is absent (or held at a standard value), so that the 'baseline' level of the dependent variable can be measured. Without a control, it is impossible to tell whether any change seen in the experimental flasks is genuinely due to the independent variable, or would have happened anyway.

In a nutrient experiment there are two common controls:

• A negative control with no nutrient added (here, no nitrate).
• A positive control with a known effective amount of nutrient.

For this investigation the mark scheme requires the negative-control idea: nitrate is replaced by water, so the only difference between this flask and the experimental flasks is the absence of nitrate.

Understanding the Question

Part (b)(ii) asks for a 'suitable solution' to use as a control. This must be a single solution (or flask) that allows the student to compare the nitrate-containing flasks against a nitrate-free baseline. The growth medium itself is still required (because the cells need other nutrients to live), but the sodium nitrate is removed and replaced by water.

Approach

Replace the variable being tested (sodium nitrate) with the solvent (deionised water) while keeping everything else the same.

Step-by-Step Reasoning

• The independent variable is sodium nitrate concentration.
• A control must remove this variable while keeping the growth medium otherwise identical.
• So: take $250\ \text{cm}^3$ of growth medium and add deionised water in place of the $25\ \text{mmol dm}^{-3}$ sodium nitrate solution used for the experimental flasks.
• Inoculate with $1\ \text{cm}^3$ of the same Chlorella culture, leave in the same conditions, and count cells in the same way.

The mark scheme accepts 'a flask containing only growth medium and water' or 'a flask with water added in place of (sodium) nitrate (solution)'. The key idea is that nitrate is being replaced by water.

Key Takeaways

• A control replaces the independent variable with the solvent/standard treatment.
• For a nutrient study, the negative control is a flask with no nutrient but otherwise identical conditions.
• The control allows the student to say whether the growth seen in the experimental flasks is actually due to the nitrate, not to the growth medium or the cells themselves.

Common Mistakes

• Suggesting 'distilled water alone' as the control — this would not support Chlorella growth because the cells need the other nutrients in the growth medium.
• Adding a different amount of water to the control than to the other flasks — this would introduce a new variable.
• Using 'no flask' as the control — a control must still be a treated flask measured in the same way as the experimentals.

Things to Be Careful About

The control must differ from the experimental flasks only in the independent variable. Everything else — the volume of growth medium, the volume of culture, the flask, the light, the temperature — must be identical.

Background Concept

A percentage increase expresses a change as a proportion of the starting value, multiplied by 100. It is the standard way of comparing the growth of two populations that started at different sizes: a culture that grew from 100 to 200 cells has increased by 100 %, while a culture that grew from 10 000 to 12 000 cells has increased by only 20 %, even though the absolute increase of 2000 is much larger.

The calculation always has the same three parts:

1. A representative value for the final (new) measurement — here, the mean of the 5 haemocytometer samples on a given day.
2. A representative value for the starting measurement — here, the mean of the 5 samples on day 0 (the 'mean number of cells in $1\ \text{cm}^3$ at the start' column in Table 1.1).
3. The percentage formula:

The subtraction must be the right way round (new minus original) so that a positive answer represents an increase.

Understanding the Question

Table 1.1 records, for each flask, the 'mean number of cells in $1\ \text{cm}^3$ at the start' and then the 'mean percentage increase in number of cells of Chlorella' on days 2, 4, 6, 8 and 10. Part (c)(i) asks you to state how that percentage increase was obtained from the raw haemocytometer counts. The mark scheme gives three marks: one for finding the means, one for finding the difference, and one for dividing by the original and multiplying by 100.

Approach

Walk through the procedure in three clear steps, and finish with the formula.

Step-by-Step Reasoning

1. Find the mean of the 5 haemocytometer samples for each flask on each day. The student took 5 samples per flask; the mean is the sum of the 5 counts divided by 5. The table already shows this mean (under 'mean number of cells in $1\ \text{cm}^3$ at the start' and is implied for the later days).
2. Find the difference between the new (later) mean and the original (day 0) mean for that flask.
3. Divide that difference by the original (day 0) mean and multiply by 100, to express the change as a percentage of the starting value.

The final formula is:

The mark scheme accepts the formula in words or in symbols, and allows 'average' for 'mean'. It applies error carried forward (ecf) if the candidate's earlier work is wrong.

Key Takeaways

• Always average repeated measurements before processing.
• Percentage change is always: (new − original) / original × 100.
• The direction of subtraction matters: new minus original gives a positive number for an increase.

Common Mistakes

• Forgetting to take the mean of the 5 samples first — using a single sample as the 'new' value inflates the uncertainty.
• Dividing by the new value instead of the original — that is percentage decrease relative to the new value, not percentage increase.
• Subtracting the wrong way round (original − new) — this gives a negative number for an increase.
• Multiplying the answer by 1000 instead of 100 (confusing percentage with parts per thousand).

Things to Be Careful About

The mark scheme says 'subtraction must be correct way round if shown' and 'A original described in terms of the control' — so the formula can equivalently use 'control' as the original value, but only if the candidate has set up a control in the same units.

Background Concept

When comparing populations that started at different sizes, raw differences are misleading and percentage change normalises the comparison. For example, an increase of 2000 cells means a great deal in a flask that started with 5000 cells (40 % increase) but very little in a flask that started with 50 000 cells (4 % increase). Percentage removes the effect of the different starting values.

Understanding the Question

Part (c)(ii) asks for the reason the student went to the trouble of computing a percentage increase rather than simply reporting the raw increase in cell number.

Approach

Look at the 'mean number of cells in $1\ \text{cm}^3$ at the start' column of Table 1.1: the values are 10035, 10630, 10128, 10743, 10108 and 10900. They are not identical. Any comparison of growth has to take that variation into account.

Step-by-Step Reasoning

• Each flask was inoculated with $1\ \text{cm}^3$ of Chlorella culture, but the number of cells in that $1\ \text{cm}^3$ was slightly different in every case because the original culture is not perfectly uniform.
• If the student simply reported 'number of cells on day 10', a flask that started with more cells would look like it had grown more, even if its cells had actually grown more slowly in proportion.
• By converting to a percentage increase, the student puts every flask on the same scale: 100 % means the number of cells has doubled, regardless of the starting value.
• This makes a fair comparison possible between flasks that had different starting cell numbers.

The mark scheme accepts 'easier to make comparisons between different samples / different starting numbers', and also 'differences easier to see / cell numbers harder to compare'.

Key Takeaways

• Percentage change is the right tool when starting values differ.
• It normalises the comparison so every flask can be compared on the same scale.

Common Mistakes

• Saying 'to make the numbers smaller' or 'to make the data easier to write down' — these are not the biological reason.
• Saying 'to make the data more accurate' — taking a percentage does not improve accuracy; the means and original counts still have to be accurate.
• Confusing percentage increase with absolute increase — the candidate should make clear why a percentage is used, not just describe what it is.

Things to Be Careful About

The mark scheme is short (1 mark) and rewards the idea of comparison between samples with different starting numbers. The candidate does not need to mention statistics, just the idea that the starting numbers were different and the percentage removes that difference.