No-calculator prep for ESAT and TMUA

Simplify first

The fastest no-calculator candidates rarely do impressive arithmetic. They avoid needing it. They cancel early, factorise where possible, keep fractions exact and use the answer options to decide how much precision is required.

Before substituting numbers, ask whether a ratio, sign, parity, unit or limiting case will eliminate options. In multiple choice, the options are part of the problem statement.

Keep a small toolkit automatic

You do not need circus arithmetic. You need a compact set of reliable habits: fractions and percentages, common squares and cubes, powers of ten, rearranging linear and quadratic expressions, and interpreting proportional changes.

Practise these inside mixed questions. A mental-maths worksheet can make you faster, but the exam asks you to decide which calculation is needed while reading unfamiliar wording.

• Estimate before exact calculation.
• Keep fractions until the final step when decimals would get messy.
• Use units to catch impossible answers.
• Check signs and orders of magnitude before selecting an option.

Review arithmetic as behaviour

Do not write 'silly mistake' in your log. It hides the fix. Was the mistake caused by rushing? Rounding too early? Losing a negative sign? Copying the wrong value from the question? Each behaviour needs a different repair.

Noetra's per-question timing helps here. If arithmetic errors cluster late in a module, fatigue may be the problem. If they cluster on one topic, method may be the problem. If they happen on questions answered very quickly, overconfidence may be the problem.