Most of the arithmetic in the General Academic Module is not difficult. On the official description, the module asks you to apply reasoning to short academic texts, data and charts, and the numbers that turn up in that kind of material are rarely large or awkward. What they are, very often, is relative: a share of a total, a change over a baseline, a rate per person, an average across groups. Relative figures are where careful candidates lose marks, not because the calculation is hard but because it is easy to do the right calculation on the wrong quantity. This post is about keeping those quantities straight.
Know what each number is relative to
Every percentage, ratio or rate has a hidden denominator, and most errors come from losing track of it. "Thirty per cent of respondents" is thirty per cent of whoever responded, not of everyone who was asked. "Costs rose by a fifth" is a fifth of the earlier cost, not the later one. Before you calculate anything, say to yourself what the figure is a fraction of.
That habit settles the most common trap on its own. If a value rises by 20% and then falls by 20%, it does not return to where it started. The fall is taken from a larger base, so you end up at 96% of the original. Options built on that slip look right because the arithmetic seems symmetrical. The denominator is not.
The same discipline applies when a passage combines two percentages. If 40% of a sample are engineers and 25% of those engineers work abroad, the engineers abroad are 25% of 40%, which is 10% of the sample, not 25% and not 65%. A quick sketch of the nested groups on your rough work, even just two labelled boxes, is often enough to stop you adding figures that should be multiplied.
Percentages and percentage points are different answers
When a share moves from 10% to 15%, it has risen by five percentage points and by fifty per cent. Both statements are true, and they answer different questions. An option that reports one when the question asks for the other is not a careless distractor. It is the most predictable wrong answer the question can have.
Read the question stem for the exact wording. "By how many percentage points" asks for a subtraction. "By what percentage" asks for the change divided by the starting value. If the stem is ambiguous in your head, write both numbers down and check which one the options actually use. Usually only one of them appears, and that tells you what was intended.
This distinction also matters for interpretation questions that have no arithmetic at all. A passage that says a rate "doubled" from 1% to 2% describes a large relative change and a small absolute one. A conclusion that treats the doubling as dramatic in absolute terms has gone further than the data. It is the overreach our guide to research summary passages warns about, carried by a number.
Ratios, rates and per-capita figures
A ratio compares two quantities. A rate compares a quantity to a unit of something else, such as time, people or area. Both are ways of making unequal groups comparable, and questions often check whether you noticed that a raw total was not comparable in the first place.
If one region reports more cases than another, that says nothing about which region is worse off until you know the populations. Dividing by population gives a per-capita figure, and the ranking can reverse. When a table gives totals and the question asks which group is "more likely" or "most affected", that is a signal to convert to a rate before comparing.
Ratios have their own small trap: the order of terms. A ratio of 3:2 between two groups means the first is one and a half times the second, and the second is two-thirds of the first. Both figures may appear among the options. Label each term with what it stands for as you write it down. That costs a second and removes the ambiguity entirely.
Units belong here too. A rate per thousand and a rate per hundred thousand are not comparable until you convert one of them, and a chart and a table in the same question can quietly use different ones. Our guide to interpreting graphs and tables covers reading the frame of a chart. With rates, the frame is half the answer.
Averages of groups do not simply average
When two groups of different sizes each have an average, the combined average is not the midpoint of the two. It sits closer to the average of the larger group, weighted by size. If 80 students average 60 and 20 students average 90, the overall average is 66, not 75.
You rarely need the exact weighted figure. Usually you only need to know which side of the midpoint the answer falls, and that is enough to eliminate options. This is where estimation earns its place: decide roughly where the answer must lie, then look for the option in that range before you commit to full arithmetic.
A related trap is averaging percentages directly. If one class has a 50% pass rate and another has 70%, the combined pass rate is 60% only if the classes are the same size. When sizes are given, weight by them. When they are not given, an option claiming a precise combined figure is often unsupported, and recognising that can be the whole answer.
How to practise this without a textbook
You do not need a new body of mathematics. You need the habit of naming the denominator, applied until it is automatic. Some practical ways to build it:
- When you read any news chart, write one sentence saying what each figure is relative to.
- For every percentage change you meet, work out both the percentage-point and the relative version.
- Take a table of totals and convert it to rates before deciding which row is "largest".
- In your error log, tag every wrong answer that came from using the wrong base. If the tag recurs, it is your main weakness.
What you may bring to the desk, and what writing material the centre provides, is set out in the participant instructions for your sitting, so confirm it there rather than assuming. Either way, practise these calculations mentally and on rough work of the kind you expect to have, not with a calculator you may not be allowed.
From there, work them under time. The mixed sets in our practice questions put relative figures inside short academic contexts, and a run of the free dMAT practice test will show whether the habit survives a clock. Our General Academic Module preparation guide sets out a weekly routine this fits into, and the syllabus overview summarises how the module sits alongside the Core. For the module's current length and format, check the official sources rather than any summary, including ours.
The arithmetic in this module is rarely what goes wrong. Ask "relative to what?" before every calculation, and most of the traps described here go away.
