UCAT Formulae and Figures: how to solve them
A formulae and figures question gives you a rule, a formula, or a labelled diagram, plus the data to feed it, and asks you to apply that rule rather than read a value off a chart. It’s a Quantitative Reasoning question type, answered as single-best-answer with an on-screen calculator. The stimulus can be a geometric figure, a tariff or rate table with a rule that operates on it, or pure text carrying a chain of ratios. The skill it tests is parsing the formula and the givens, mapping each value to the right variable, and finishing in the unit the question asked for.
What is a formulae and figures question?
You get a short scenario, then the rule and the data it operates on, then a set of questions that apply that rule. Each question is single-best-answer with five options, you have a basic on-screen calculator, and you’re working to roughly 43 seconds per question across the section.
Formulae and figures items come in a few shapes: a geometric figure with labelled dimensions and a volume or area formula, a formula paired with a unit-conversion rule (temperature, speed, capacity), a tariff or rate table with a rule that says how to combine the cells, a plan or map with a bulleted set of rules, or a pure-text chain of percentages with no picture at all. The shape changes what you are reading, but it never changes the discipline: read the rule first, find the values it needs, and apply it.
The arithmetic almost never beats you here. The numbers are usually clean and the calculator does the rest. What beats you is everything around the calculation: plugging a value into the wrong variable, reading the full measurement when the question wanted the leftover, finishing in cubic metres when the answer should be in litres. Get fluent at reading each part of a formula stimulus and most of the traps further down this page stop happening.
Tab through the parts of a formula stimulus. Each one highlights where it lives, and what to check before you compute.
One or two sentences set up what you are working with and what the question is heading toward. Read it for the shape (here, a rectangular tank), the unit the answer wants (litres), and whether you are after a capacity, a difference, or a rate. On a formula item the scenario rarely carries numbers: it tells you which numbers to go and find.
The parts to read, in order: the scenario (a tank, the answer wanted in litres, and a “how much more” to compute), the given formula (volume = length × width × depth, so you need three lengths), the figure (where the measurements live, each labelled against a side or a level), the labelled quantities (the four values, and which is the full depth versus the current level), and the givens block (the unit conversion that turns cubic metres into litres at the end). The worked example below solves on the same figure.
A worked example
Same figure, one sub-question. Every wrong option is a number you can reach from the figure by one specific slip, so read the formula, decide whether you want the whole or the difference, and convert last.
How many more litres of water can the tank hold before it is full?
Common mistakes
The wrong answers on a formula set are almost never bad arithmetic: they’re a number you can reach, spoiled by one wrong move. And most of these slips are not specific to formula items. The same wrong-base or wrong-quantity error bites on tables and charts too, because the trap lives in the operation, not the picture. What changes here is that you are applying a rule rather than reading a value, so a couple of new slips appear (a botched unit conversion, a mis-substitution into the formula) on top of the ones shared across Quantitative Reasoning. Each links to a short worked example.
Shared across all five QR types. Trap guides are being published; links open as each goes live.
A reliable method
Practising formulae and figures
Formulae and figures reward one repeatable habit: read the rule, find its inputs, apply it, convert last. The fastest progress comes from doing enough of them that “what unit does the answer want?” becomes the last thing you check every single time, automatically, before you pick an option.
MedPath drills formula and figure questions trap by trap, with the working revealed step by step for each, and steers your practice toward the ones you keep getting wrong.
Practise formulae and figures adaptively.
MedPath drills formula items trap by trap, with the working revealed step by step, and steers practice toward the unit-conversion and wrong-quantity slips you keep falling for.
Common questions
Do I get a calculator?+
Yes. Quantitative Reasoning and Decision Making both give you a simple on-screen calculator; Verbal Reasoning and Situational Judgement do not. The calculator handles the arithmetic, so the work is reading the rule right, mapping the values to the formula, and finishing in the right unit.
How are formulae and figures questions scored?+
As part of Quantitative Reasoning’s 300–900 scaled score, which contributes to your total cognitive score (900–2700). Each question is single-best-answer, marked right or wrong, with no penalty for a wrong guess, so never leave one blank.
What if the question gives me a formula I do not recognise?+
Everything you need is on the screen. These questions are not a test of formulas you memorised; the rule is supplied, with any abbreviations defined and any unit conversions stated. Read the formula, map each variable to a value in the stimulus, and substitute. The only formulas you are expected to bring yourself are the Year-10 staples (area, volume of a box, percentage-of), and even those are usually spelled out.
What’s the most common mistake?+
Finishing in the wrong unit, or applying the rule to the wrong value. The arithmetic is rarely the problem; the read is. Reading the formula first, mapping each labelled quantity to its variable, and asking “what unit does the answer want?” before you convert is worth drilling until it’s automatic.