Quantitative practice: read the quantity before calculating

Name what is being asked

Before calculation, identify the target quantity and its unit. Is the question asking for a rate, a total, a difference or a percentage of a base? Write a short expression for the relationship. This prevents a familiar-looking problem from pulling you into the wrong method.

For a percentage increase from A to B, the base is A and the increase is B − A. Percentage-point differences compare two percentages directly. Moving from 20% to 25% is a five-percentage-point increase, but a 25% relative increase. Keep the labels distinct.

Use an easy internal check

Estimate the order of magnitude before precise arithmetic. If a speed is in kilometres per hour and a time is in minutes, convert one unit so they agree. An answer that is numerically neat but dimensionally wrong is still wrong.

For ratios, use a concrete total where convenient. If two groups are in the ratio 2:3, there are five equal parts. A total of 100 would mean 40 and 60. Choosing a convenient base is useful when only a proportion matters; it is unsafe when the problem supplies an absolute amount that must be preserved.

Practise in two modes

Untimed work should expose every step and check. Timed work should use only methods you can explain and reproduce. After a timed set, return to the slow or incorrect questions and compare methods. A shortcut that fails when wording changes is not yet a reliable skill.

Create small mixed sets rather than repeating one template for an hour. Interleaving forces you to recognise which relationship applies. Increase speed only when your accuracy remains stable.

Keep a compact formula sheet

Include the meaning of each symbol, an example and one limitation. A formula with no conditions encourages mechanical substitution. Review the sheet by rebuilding the relationship from memory, then checking it. When you discover a repeated error, add a reminder beside the relevant formula.