Ask any math student what cost them marks in an exam and the honest answer is often the same: “I knew how to do it, but I made a silly mistake.” Careless mistakes are not random. They follow patterns, which means you can find them and fix them. Here is how.
Know your own mistakes first
Before you try to fix anything, find out what you actually get wrong. After every past paper question where you lose marks, write down which kind of mistake it was:
- Misreading: you answered a slightly different question from the one asked.
- Sign slips: a minus sign lost when expanding brackets or moving a term across.
- Arithmetic: a wrong multiplication, a dropped fraction, a copied number that changed.
- Method gaps: not a slip at all, but a topic you have not fully understood yet.
- Time pressure: rushing the last questions.
After a few papers, one or two categories will dominate your list. Those are the ones to work on.
Habits that remove the most mistakes
- Read the question twice, and underline what it asks for. Words such as “exact”, “in terms of”, “to 3 significant figures” and “show that” change what a correct answer looks like.
- Write one step per line. Squeezing three steps into one line is where signs and brackets go missing. It also protects your method marks.
- Expand brackets and negatives slowly. Put a bracket around any negative number you substitute, such as (−3)², so you do not forget the sign.
- Keep exact values until the end. Rounding in the middle of a question quietly damages the final answer.
- Check units and the form of the answer. Is it asking for degrees or radians? A decimal or a fraction? A value or an equation?
Quick checks that take under a minute
- Substitute back. If you solved an equation, put your answer back in. If it does not work, you know before the examiner does.
- Ask if the answer is sensible. A probability above 1, a negative length or a speed far beyond what the situation could allow all signal an error.
- Look at the marks. A question worth 1 mark should not need a page of working, and one worth 6 marks should not be finished in two lines.
- Re-read the question one last time after you finish, and tick off everything it asked for.
Use time as a tool, not a threat
Many careless mistakes come from rushing, and rushing usually comes from poor time planning. In practice papers, note how long each page takes you. If you are running behind, skip a question, mark it, and return later rather than racing through everything. Finish with a few minutes in hand to re-check the questions where a slip is most likely: those with long algebra or several steps.
Practise being careful
Carefulness is a habit, and habits come from practice. Do some past paper questions slowly and deliberately, with full working and a check at the end, even when the topic feels easy. Then do timed papers and notice whether the habits survive the pressure. If they do not, keep practising until they do.