- Are you not getting the grades that you think reflect your ability?
- Do you find you have often made several silly mistakes when you get back your assessments?
- Do you find that you 'get' the work, but struggle to get marks for your answers?
Students who get the highest grades are not always the strongest mathematicians. In many cases, student underperform in exams because they have failed to put in sufficient time to learn effective exam technique.
Try to actively work on developing the following strategies when working on exam questions:
Practise Under Exam Conditions
If the only time you answer exam questions in timed conditions is when you are in an exam, you are more likely to have issues with the following:
- Not working at a fast-enough pace (running out of time).
- Feeling anxious and under pressure.
- Making careless mistakes through lack of checking strategies.
- Using poor written communication and losing method marks.
The pressure never completely goes away, but with purposeful practice it gets easier to manage.
Practise completing exam questions in exam conditions.
- Have a time limit - Roughly 1 minute per mark (slightly more for questions that occur later in the paper).
- Remove as many distractions as possible (where possible put away electronic devices).
- Check answers yourself before looking at the mark scheme.
- Do not use your notes when working in exam conditions.
- Answer the questions using full written solutions.
Maths is not just about ‘getting the right answer’. You should aim to express your ideas clearly. Exam markers are only human and do not have an infinite amount of time to search through a disorganised solution to award marks.
- Cross out mistakes – do not write over the top of them.
- Write along the lines of the page.
- Try not to squash your working up into a small space.
- Leave space between questions.
- Start a new page when necessary.
- Use an equals sign to connect two lines of working where approrpriate.
- Do not use arrows (unless you are using the 'implies' symbol).
- Try to ensure one line follows on from the previous line.
- State what you are calculating.
- e.g. "gradient of AB = …"
- Do not just write down calculations or values on their own.
- Mathematics should flow down the page (not across).
- Use connecting statements:
- e.g. "Substituting eqn (1) into (2):"
- e.g. "Since AB is perpendicular to BC..."
Reducing Careless Mistakes
The most common reason students drop marks in exams is by making careless mistakes. Everyone makes mistakes, but the most consistent mathematicians have developed reliable strategies to identify and correct them.
These strategies are unlikely to develop on their own and you must actively work to improve the checking of your work in your day-to-day practice. If you only try to use these strategies in the exams/assessments you will be unlikely to remember to do the majority of them.
Re-read the Question
Often a question takes considerable time to answer. You may have forgotten the details by the time you have finished answering it.
- Check you have properly answered the question.
- Check you have used the required accuracy (e.g. exact value, 1 d.p.).
- Check you have given your answer in the correct form (e.g. \( ax+by=c\).)
Calculator Display Check
After using your calculator, check the calculation on the display for errors.
- When entering a calculation, you are likely only looking at the buttons you press.
- Don't just read the answer!
Use diagrams to help understand questions or to check working.
- Diagrams are particularly useful for coordinate geometry, mechanics and vectors.
- Avoid the temptation to skip drawing diagrams when practising as they take time.
- If you skip them when practising, you’ll skip them in the exam.
Practise using your calculator to speed up calculations and to check answers.
Note: Your calculator is not a substitute for mathematical understanding. Almost any question can be made into a ‘non-calculator’ question using two words: ‘Show that…’.
- Solve quadratics, cubics and simultaneous equations using ‘equations mode’
- You need to practise this to make it a habit.
- Use the gSolve function where possible to check roots, y-intercepts and min/max points.
- Use the derivative and integral calculator when numerical answers are required.
- However, do not forget that graph mode uses decimal approximations.
- Store values in your calculator if they may be useful later (e.g. during trigonometric calculations).
Above all, practise using your calculator to develop fluency. If it doesn’t come naturally you won’t do it when under pressure in the exam (especially if you’re not fast enough).
Line by line checking.
Line-by-line checking means checking each term on your working from one line to the next for mistakes. It is very effective but can be time consuming. However, with practice you can improve your speed. Line-by-line checking may not be possible if you don’t already work at a fast-enough pace to complete the exam.
Reflect on Your Mistakes
Once you have answered the question check/correct your work using the mark scheme.
- Read the mark scheme carefully to ensure you gained the method marks.
- Write down the number of marks you awarded yourself for the question (be harsh).
- Where possible use written/video solutions to see how to improve your communication.
- If you failed to achieve full marks on a question, make a note of it and try it again at a later date.
You may find your teacher regularly mentions the importance of ‘doing your corrections’. Often students make a token effort to copy the mark scheme just to ‘jump through the hoop’. These students are missing out on a significant chance to rapidly improve their progress.
If you don’t try to understand and correct your mistakes, you will continue making them over and over (including in the final exam). If you take the time to understand why the mistake was made, you can take steps to ensure you don’t repeat it.
Firstly, always ensure you check your answers (first by yourself, then using the mark scheme or solutions). If you don’t know you’re making a mistake, you can’t take steps to correct it!
Next try to identify why you made the mistake.
For calculation errors, try to keep a log of which mistakes you frequently make so that you become more mindful of them.
- For example, do you often make sign errors or miss out solutions when square rooting?
- Review your log right before the exam so your common mistakes are fresh in your mind.
For mistakes which occur through a lack of understanding, make sure to take the time to properly understand the mistake.
- Sometimes this will be easy enough by just reading the mark scheme.
- Sometimes you will need to ask for help.
- Try to annotate mistakes as well as writing a correction as this will help when you next review the question.
Make a note of any questions you got wrong first time around. These can then be used again when revising a topic.
- If you are making a lot of mistakes with a particular topic, this is an indication that you should spend considerable time working on it.