Working without a calculator in the ESAT and TMUA

Simplify before you calculate

Neither the ESAT nor the TMUA lets you use a calculator. That sounds like a test of mental arithmetic, but the people who cope best rarely do anything impressive in their heads. They set the question up so that there's very little arithmetic left to do.

In practice that means cancelling early, factorising where you can and keeping fractions exact. If a question gives you a mass, a speed and a time, rearrange the formula in letters first and put the numbers in at the end. Often half of them cancel before you multiply anything.

Let the answer options do some of the work

In a multiple-choice question, the options are part of the question. Read them before you start calculating, because they tell you how precise you need to be.

Before you substitute anything, ask whether something simpler would rule options out. The sign of the answer, whether it's odd or even, its units, a ratio between two quantities or what happens at an extreme value can each cross off one or two options.

If the options are 0.3, 30 and 3000, you only need the size of the answer. A rough estimate is a perfectly good method there, and it's much quicker than working the value out exactly.

The arithmetic worth knowing by heart

You don't need party-trick arithmetic. You need a small set of things you can do quickly and reliably: fractions and percentages, common squares and cubes, powers of ten, rearranging linear and quadratic expressions, and working out what a proportional change does to an answer, such as what happens to an area when a length doubles.

Practise these inside mixed questions. A mental-maths worksheet will make you faster at sums, but in the exam you also have to decide which sum the question needs while reading wording you haven't seen before. A worksheet never asks you to do that.

A few habits help on every question:

• Estimate the answer before you work it out exactly.
• Keep fractions until the last step if decimals would get messy.
• Use units to rule out answers that can't be right.
• Check the sign and the rough size before you choose an option.

When you get a sum wrong

Try not to write 'silly mistake' when you mark a paper. It doesn't tell you what to change. Look at your working and find the actual cause. Did you rush? Round too early? Lose a minus sign? Copy the wrong number from the question?

Each of those has its own fix. Rushing might mean reading the question through once more before you choose. Rounding early means keeping exact values until the end. A minus sign that keeps going missing might mean writing out one extra line at the step where it happens.

Where in the paper your mistakes happen

It also helps to look at where the mistakes came. Noetra records how long you spend on each question, which makes this easier to see, but rough notes on a paper mock work too.

If your arithmetic errors bunch up late in a module, tiredness may be the problem. If they bunch up on one topic, your method for that topic is the more likely cause. If they happen on questions you answered very quickly, you may have been too sure of yourself and skipped a check.