Worked Solutions
Module 1: Cells as the Basis of Life — Worked Solutions (Preliminary Biology)
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Worked examples for Preliminary Biology Module 1 — Cells as the Basis of Life. Each shows where the marks are awarded, the key idea, and a full model answer in your choice of tutor — Stella, Ella or Cassie.
How to use these
Attempt each question under exam conditions first, then check your response against the model answers. Use the tutor tabs to read the solution in the style that suits you: Stella is direct and to the point, Ella is warm and explains the why, and Cassie is concise and uses bullet points.
Example 1 — Surface area to volume ratio
Question
Explain why cells must remain small, with reference to their surface area to volume ratio and the exchange of materials. (4 marks)
Solution
As a cell grows, its volume increases faster than its surface area, so the surface area to volume ratio falls.
The cell membrane is the surface across which materials are exchanged. The volume sets the demand — the amount of cytoplasm needing nutrients and producing waste.
If a cell gets too large, its small relative surface area cannot move materials in and out fast enough to meet the demands of its large volume. Wastes build up and nutrients run short.
Staying small keeps a high surface area to volume ratio, so exchange across the membrane is fast enough to service the whole cell. Always link the ratio to the rate of exchange — that is the mark.
Let's think about what happens as a cell gets bigger. Volume grows with the cube of the cell's size, but surface area only grows with the square — so volume races ahead and the surface area to volume ratio gets smaller.
Why does this matter? The cell membrane is the surface across which oxygen, nutrients and wastes are exchanged with the environment. The volume of cytoplasm is what demands those materials and generates waste.
So in a large cell, there is a lot of cytoplasm to supply but comparatively little membrane to supply it through. The rate of exchange can't keep up with the cell's needs — nutrients arrive too slowly and wastes accumulate.
By staying small, a cell keeps a large surface area relative to its volume, so diffusion across the membrane is fast enough to service every part of the cell. That's the reason cells divide rather than simply growing forever.
- As size increases, volume increases faster than surface area
- So the surface area to volume ratio decreases
- Membrane (surface area) = site of exchange of materials
- Volume = demand for nutrients and production of wastes
- Large cell: too little surface area for its volume → exchange too slow → wastes build up, nutrients insufficient
- Small cell: high SA:V ratio → exchange across membrane fast enough to meet demands
Where the marks go
- 1 mark: States that as a cell grows, volume increases faster than surface area, lowering the SA:V ratio
- 1 mark: Identifies the surface (membrane) as the site of exchange of materials
- 1 mark: Identifies the volume as setting the demand for materials and the production of wastes
- 1 mark: Links a low SA:V ratio in large cells to an inadequate rate of exchange to meet the cell's needs
Key idea
Surface area governs the rate of exchange, volume governs the demand; cells stay small to keep a high SA:V ratio so exchange across the membrane keeps up with the cell's needs.
Example 2 — Active vs passive transport
Question
Compare active transport and facilitated diffusion as mechanisms for moving substances across the cell membrane. (5 marks)
Solution
Both move substances across the membrane using membrane proteins, and both move substances that cannot cross the phospholipid bilayer easily, such as ions and glucose.
The key difference is the direction relative to the concentration gradient and the energy cost. Facilitated diffusion is passive: substances move down their concentration gradient (high to low) through a channel or carrier protein, with no ATP required.
Active transport moves substances against the concentration gradient (low to high), so it requires energy from ATP and uses carrier (pump) proteins, for example the sodium–potassium pump.
So: same use of proteins, but facilitated diffusion is passive and down the gradient, while active transport is energy-requiring and against the gradient. Make sure you give both a similarity and the differences.
Let's start with what these two have in common, because a good comparison needs similarities as well as differences. Both move substances across the cell membrane, and both rely on transport proteins — they're used for substances like ions and glucose that can't slip through the fatty phospholipid bilayer on their own.
Now the differences. Facilitated diffusion is a passive process: the substance moves down its concentration gradient, from where it's more concentrated to where it's less concentrated. Because it's moving the "natural" way, no energy is needed — the channel or carrier protein just provides a path.
Active transport is the opposite. It moves substances against the gradient, from low to high concentration — like pushing water uphill. That can't happen for free, so the cell spends energy in the form of ATP, using carrier proteins called pumps (the sodium–potassium pump is the classic example).
So the heart of the comparison is energy and direction: facilitated diffusion is passive and goes down the gradient; active transport needs ATP and goes against it. This is why a cell can maintain concentrations that differ from its surroundings.
Similarities:
- Both move substances across the cell membrane
- Both use membrane transport proteins (substances that can't cross the bilayer)
Differences:
- Facilitated diffusion: passive, no ATP; substance moves down the concentration gradient via channel/carrier proteins
- Active transport: requires ATP; moves substance against the gradient via carrier (pump) proteins, e.g. sodium–potassium pump
Where the marks go
- 1 mark: Identifies a valid similarity (both cross the membrane / both use transport proteins)
- 1 mark: States facilitated diffusion is passive and requires no ATP
- 1 mark: States active transport requires energy (ATP)
- 1 mark: States facilitated diffusion moves substances down the concentration gradient and active transport against it
- 1 mark: Provides a relevant example or correct protein type (e.g. carrier/pump such as the sodium–potassium pump)
Key idea
Both use membrane proteins, but facilitated diffusion is passive and moves substances down the gradient, while active transport uses ATP to move substances against the gradient.