Maths and Science Exam Technique

Maths and science exams have their own set of technique requirements that are quite different from essay-based subjects. Calculation errors, unit mistakes, incomplete working, and diagram errors cost students thousands of marks every year — and most of these losses are entirely preventable with the right approach.

The Non-Negotiable Rules

Before we discuss specific techniques, here are the universal rules for maths and science exams:

Rule	Why It Matters
Always show your working	Method marks are available even when the final answer is wrong. No working = no method marks.
Always include units	A correct number without units often loses a mark. "15" is incomplete. "15 m/s" earns the mark.
Always check your answer makes sense	If you calculate that a human runs at 500 m/s, something has gone wrong.
Write clearly	If the examiner cannot read your numbers, they cannot give you marks. A "6" that looks like a "0" costs you marks.
Use a sharp pencil for diagrams	Neat, accurate diagrams earn marks. Rough sketches may not.

Maths Exam Technique

Show Your Working: A Detailed Guide

In maths, "show your working" is not optional advice — it is a marking instruction. Here is why:

Question: "Solve the simultaneous equations: 2x + 3y = 12 and 4x - y = 5." (4 marks)

Approach	What They Write	Marks Awarded
No working	x = 1.5, y = 3	0 marks (if wrong) or 1 mark (if correct — but only the answer mark)
Partial working	4x - y = 5, so y = 4x - 5. Sub into first equation... x = 27/14	2-3 marks for correct method steps even if the final answer has an arithmetic error
Full working	All steps shown clearly, final answer circled	4 marks (even if there is a minor arithmetic slip, method marks are protected)

The lesson: Full working protects you from losing all marks due to a single arithmetic error. If you show 4 correct steps and make an error on step 5, you might still earn 3 out of 4 marks. If you show no working and get the final answer wrong, you earn 0.

The Layout Matters

Poor Layout	Good Layout
All working crammed into one line	Each step on a new line
Equals signs scattered randomly	Equals signs aligned vertically
No indication of what you are calculating	Each step labelled if it is part of a multi-step problem
Answer buried in the working	Final answer clearly boxed or underlined

Common Maths Mistakes and How to Avoid Them

Mistake	How Common	Prevention
Sign errors (positive/negative)	Very common	Write out each step. When you subtract a negative, write the double negative explicitly: 5 - (-3) = 5 + 3 = 8
Forgetting to apply an operation to both sides of an equation	Common	Write each operation next to the equation: "divide both sides by 3"
Rounding too early	Common	Keep at least 4 significant figures in intermediate steps. Only round the final answer to the required degree of accuracy.
Misreading the question	Very common	Underline what the question actually asks for. If it says "find the area," do not calculate the perimeter.
Calculator errors	Common	Type the calculation twice. If you get different answers, try a third time.
Incorrect use of formula	Common	Write the formula first, then substitute the values. Do not try to do both in one step.

Checking Your Answers

For maths, always check by asking:

Does the answer make sense? A negative length, an angle greater than 180° in a triangle, or a probability greater than 1 are all impossible.
Does the answer match the units? If the question asks for cm² and you get a number in cm, you have likely forgotten to square something.
Can you substitute back? For equations, put your answer back into the original equation. Does it balance?

Science Exam Technique

Calculations in Science

Science calculations follow the same principles as maths but with additional considerations: