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How to learn and revise maths
You learn maths by doing maths. Reading notes or watching a video feels productive, but the progress comes from trying questions, checking them, fixing mistakes and coming back to topics again later. This page is for every year group. The Diploma section at the bottom adds what is specific to the IB Diploma.
Four ideas to start with
Do maths to learn maths
Treat maths like a sport or an instrument. Regular, active practice builds the skill and the intuition. Solve problems, spot patterns and explain your steps.
Understand first, then memorise
A method you understand is easier to remember and easier to adapt to a new question. Only memorise what has to be memorised, such as a definition or a formula you are not given.
Little and often
Short, regular sessions spread through the week work better than one long session the night before. Aim to revisit each topic several times.
Mistakes are the best material
Every wrong answer shows you exactly what to work on next. Correct it, work out why it went wrong, then try a similar question.
Why you need to come back to a topic
New learning fades quickly if you do nothing with it. The German psychologist Hermann Ebbinghaus first measured this in 1885, and the pattern has since been found again in modern experiments: memory falls steeply at first, then more slowly. Each time you recall something, the memory lasts longer, so review at spaced intervals instead of re-reading once.
- Straight after the lessonAnswer a couple of questions or write one line on what you learned.
- The next daySummarise the key points from the last lesson from memory, then check your notes.
- A week later, or soonerTry questions on the topic with nothing to look at.
- A month later, or soonerRepeat. This becomes your regular cycle of recall and retrieval practice.
Study strategies that work
Try two or three, keep what works for you, and keep changing between them.
Practice testing
Close the book and your notes, try questions on the topic from memory, then check and correct in green pen. Note what you could not do and revise that. Testing yourself is one of the most effective study techniques, and it also shows you what you do not know yet.
Worked examples: study, cover, redo
Study a worked example line by line and say why each step works, not just what it is. Then cover the solution and redo the question yourself, and finish with a similar question with new numbers.
Flash cards and the Leitner boxes
Put a question on the front and the answer on the back. Cards you get right move to a box you review less often, and cards you get wrong go back to the first box. For maths, go beyond definitions: put a question up to the point where you made a mistake and ask yourself what the next step is. Keep blank cards with you while you work and make a card whenever you meet something to learn. Printable double-sided flash cards are on the unit pages in Revision, so you can print them, cut them out and keep them in your boxes.
The Feynman technique
Explain the idea to someone who does not know it, such as a parent or a younger brother or sister. If they ask a question you cannot answer, or you have to explain it another way, you have found what to revise. When you can teach it, you understand it.
Revision cards at the end of each topic
Make a short set of cards or a one-page summary at the end of every topic, while it is fresh. You will thank yourself when the test comes.
Mixed practice
Once you have practised a topic on its own, practise it mixed in with others. In a test you have to decide which method to use, so practise that decision.
When you are stuck: four steps
Work through these in order. Only ask for help once you have honestly tried the first three, and take your working with you to show what you have done.
- Test yourselfTry the whole question as if it were a test: no books, no slides, no videos.
- Use resourcesTry again with your notes, the textbook, slides or videos.
- Use the solutionsWork backwards from the answer if you can. If not, read the solution one step at a time and then close it and redo the question.
- Ask for helpAsk your teacher, go to the Maths Clinic or Learning Support at the times they offer, and bring all your working from steps 1 to 3.
After a test: what to do with the result
Every time a test comes back, put each topic into one of four groups. The groups tell you what to do this week.
Priority 4
Went well, and you revised
Great. Dip back in regularly to keep it fresh: review your flash cards or answer a question or two.
Priority 1
Did not go well, and you revised
Something is not understood yet. Ask your teacher for help, so it can be sorted out in class or in a one-to-one.
Priority 3
Went well, but you did not revise
You probably understood it in the unit and kept it. Revise it after Priority 1 and 2 are done.
Priority 2
Did not go well, and you did not revise
Revise this topic this week, then check whether it is really a Priority 1 or a Priority 3 next time a question comes up.
Error analysis (for every question where you lost marks)
- Find your mistake: the exact line where the question went wrong.
- Explain it to yourself in writing: what you did wrong, and what you should have done instead.
- Complete the whole question again, fully and correctly, writing the correct method and reasoning in green pen.
- If you needed help to do step 3, change the numbers in the question and redo it on a separate sheet.
After a revision period, ask yourself: Did I make a timetable? Did I stick to it? What worked well, and what should I do differently next time?
Planning your revision
Write down the date of every test or exam, and work backwards from it.
Give time to every subject, not just maths.
Put time off in the timetable first. A plan with no rest does not get followed.
Choose how you will work: by topic, or through mixed practice, and leave time at the end for exam-style questions.
Use your results from the last test to decide which topics come first (see the four priority groups above).
Check the plan at the end of each week and move things that did not happen, rather than dropping them.
Sleep matters more than another late hour of revision. Drink water, eat well, get some fresh air and exercise, and take time to relax.
Set a target, and notice progress
Revision goes better when you are calm and kind to yourself. After a test, choose one small target for next time and put a learning-zone target sticker in your book to remind you. If maths makes you very anxious, the resilience page has ideas for students and parents.
Diploma Maths (AI SL): extra guidance
Everything above applies in the Diploma too. These points are specific to Diploma Maths.
Personal responsibility
Aim for at least 2.5 to 3.5 hours of maths a week outside lessons, spread over several shorter blocks. Choose the level you are comfortable starting at, move up if it is too easy and back if it is too hard, and try the applied questions at the end of each exercise. Do your work in black or blue pen or pencil and correct it in green pen. Come to the next lesson with any questions you still have.
Always have your formula book and a charged GDC
Do not practise without them. Note what the formula book gives you for a topic, and make short instruction notes on how to use the GDC for it.
Revising a topic, step by step
Pick a topic, such as linear functions. Get your formula book and GDC out and note what the formula book gives you. Watch a video on the topic. Write your GDC instructions. Work on applied problems from the textbook, past papers or Diploma maths questions, trying them with only the formula book and GDC. Correct your work and work through anything difficult. Repeat for each topic, then move to mixed question practice and finally a full IB past paper.
Mind maps
Use the Core content and AI SL mind maps to see what each topic covers and to plan your revision. They are merged into one slideshow in the revision area, topic by topic.
Exam preparation and mocks
Make a revision timetable that includes time off and every subject. Decide whether you will work by topic or through mixed practice, and leave time for exam-style questions. Look at the dates of your mocks and final papers, work backwards from them, and use your last exam analysis to decide which topics come first.
Exploration feedback
You will get your annotated script back with a one-to-one meeting. Take notes. Review the feedback carefully, ask about anything you are unsure of, and finish the final Exploration by the deadline. Tell your teacher straight away if there is a problem.
The research behind this page
Check volume and page details against the originals before you cite them.
- Ebbinghaus, H. (1885). Über das Gedächtnis. Leipzig: Duncker & Humblot. (The forgetting curve.)
- Murre, J. M. J., & Dros, J. (2015). Replication and analysis of Ebbinghaus’ forgetting curve. PLOS ONE, 10(7), e0120644.
- Roediger, H. L., & Karpicke, J. D. (2006). Test-enhanced learning: taking memory tests improves long-term retention. Psychological Science, 17(3), 249–255.
- Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students’ learning with effective learning techniques. Psychological Science in the Public Interest, 14(1).
- Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics practice problems boosts learning. Instructional Science, 35(6), 481–498.
- Moser, J. S., Schroder, H. S., Heeter, C., Moran, T. P., & Lee, Y.-H. (2011). Mind your errors: evidence for a neural mechanism linking growth mind-set to adaptive posterror adjustments. Psychological Science, 22(12), 1484–1489.