UCAT Quantitative Reasoning: set up the calculation before reaching for the calculator

Find the quantity the question actually wants

Read the requested unit and comparison before collecting numbers. A table may contain far more information than one answer requires. Decide whether you need a total, a rate, a percentage change or a share of a whole.

Medify's numerical advice focuses on foundations such as percentages, conversions and rates, alongside sensible calculator use. Practise the weak step rather than assuming every slow question is an arithmetic problem.

An original example: two percentages, two bases

A club's membership rises from 240 to 300. The increase is 60, so percentage increase = 60 ÷ 240 × 100 = 25%. A return from 300 to 240 is a 20% decrease because the new calculation uses 300 as its starting base. The same change in people produces different percentages.

Before entering numbers, write ‘change ÷ starting value’. That short note prevents the calculator from efficiently performing the wrong operation. If a question instead asks what percentage of the current 300 members are new, the denominator is again 300.

Estimate, calculate and check the unit

At a constant 72 km h⁻¹, a journey lasting 25 minutes covers 72 × 25/60 = 30 km. Multiplying by 25 without converting minutes would give an implausible result. This original example shows why a unit check belongs before and after the calculation.

Use the official on-screen calculator tutorial to practise entering, clearing and recalling values. Do simple arithmetic mentally when it is reliable; use the calculator when it reduces errors. A mental-maths drill complements interpretation practice but cannot replace it.

• Name the unknown and its unit.
• Select only the necessary data.
• Estimate the order of magnitude.
• Calculate, then check the answer against the question.