Magnification (image ÷ actual)
AQA GCSE Biology calculation · part of the free Calculation Climb
How many times bigger the image is than the real object: magnification = image size ÷ actual size. No units — but both sizes must be in the same unit first.
How to do it — step by step
- Put image size and actual size in the same unit (usually convert everything to the smaller unit: 1 mm = 1000 µm).
- magnification = image ÷ actual. (Rearrange: actual size = image size ÷ magnification.)
- Check the answer makes sense: a magnified cell image means magnification is a big number with no unit.
Worked examples — from real AQA papers
Finding the magnification. The image of a cell is 40 mm wide; its real width is 0.1 mm.
magnification = 40 ÷ 0.1 = ×400
Both sizes are already in mm, so it's one division. The mark scheme gave one mark for the working 40 ÷ 0.1 and one for 400 — and it warned markers not to accept the answer if a unit was written after it. Magnification is a ratio: never give it a unit.AQA GCSE Biology Paper 1, Foundation, 2020 — 2 marks
Finding the real size (and converting units). An image of a dividing cell is magnified ×800 and measures 50 mm. Find the real width in micrometres.
real width = 50 ÷ 800 = 0.0625 mm = 62.5 µm
Divide first, convert second (×1000 to go from mm to µm). The examiner report said nearly two-thirds of students got full marks, but some "used the figures the wrong way round" and the mm→µm conversion "proved more difficult for some".AQA GCSE Biology Paper 1, Foundation, 2024 — 3 marks
Higher tier: no equation given. A red blood cell image is magnified ×7200 and its diameter measures 6.3 cm. Find the real diameter in micrometres.
real diameter = 6.3 ÷ 7200 = 0.000875 cm = 8.75 µm
At Higher, marks are awarded for recalling the equation and rearranging it before any numbers go in — this 5-marker gave separate marks for recall, rearrangement, substitution, the answer in cm, and the conversion to µm.AQA GCSE Biology Paper 1, Higher, 2025 — 5 marks
Where students lose marks — from the examiner reports
- Dividing (or multiplying) the wrong way round. On the 2019 Physics version of this calculation, the examiner report noted many students "substituted incorrectly or simply multiplied 9 and 6 to give an answer of 54" instead of dividing. Image goes on top.
- Fumbling the mm → µm conversion. Flagged in both the 2022 and 2024 reports as the step that cost otherwise-correct answers. 1 mm = 1000 µm; convert at the end and show it.
- Writing a unit after the magnification. The 2020 mark scheme explicitly refused "×400 mm". Magnification has no unit.
- Measuring the printed image carelessly. Several papers make you measure a line with your ruler first — the 2022 report blamed "inaccurate measurements of line A-B" for wrong final answers. Mark schemes accept a small range (e.g. 48–50 mm), so measure to the nearest mm.
- Not knowing the equation at Higher. Foundation papers usually print it; Higher papers often don't, and recall is worth a mark on its own.
How often it comes up on AQA papers
From Science Street's database of real AQA questions, magnification calculations have appeared on these papers since 2018 — in Biology with cells and microscopes, and on Physics Paper 2 with lenses (where the image can be smaller than the object, so the magnification is less than 1):
| Paper | Marks | What you had to do |
|---|---|---|
| Biology Paper 1 Foundation 2019 | 3 | Image 24 mm, real 0.06 mm → ×400 |
| Biology Paper 2 Foundation 2019 | 3 | Rearrange for real length, answer in µm → 80 µm |
| Biology Paper 1 Foundation 2020 | 2 | 40 ÷ 0.1 → ×400 (no unit accepted) |
| Combined Science Biology Paper 1 Foundation 2022 | 3 | Real length of a palisade cell → 70 µm |
| Biology Paper 1 Foundation 2022 | 4 | Measure line A–B yourself, convert, then divide |
| Biology Paper 1 Higher 2022 | 5 | Recall + rearrange the equation → 120 µm |
| Biology Paper 1 Foundation 2024 | 3 | Real width at ×800 → 62.5 µm |
| Biology Paper 1 Foundation 2025 | 4 | Measure width W, convert to µm, then calculate → 15 µm |
| Biology Paper 1 Higher 2025 | 5 | Recall + rearrange, cm → µm → 8.75 µm |
| Biology Paper 2 Foundation 2025 | 3 | Scale factor in reverse: real object ×17 bigger, answer in metres |
| Physics Paper 2 Foundation 2018 / 2021 | 4 / 2 | Lens diagrams: image height ÷ object height → ×0.4 |
| Physics Paper 2 Foundation 2019 | 3 | Rearrange for object height → 1.5 mm |
The pattern: Foundation gives you the equation and tests the division plus a unit conversion; Higher makes you recall it, rearrange it and convert — usually for 4–5 marks. It has appeared in every year from 2018 to 2025, so treat it as near-certain to come up.
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