Maths SolverThe seven days before a big maths exam are the most over-revised days in the school year. Almost every student I have ever taught has, at some point, sat down on the Sunday before the Friday paper and tried to learn something new from scratch. Almost every one of those students would have done better with a different plan.
The plan I have given to every Year 11 I have ever taught is roughly as follows. It is not magic; it is just a recognition that exam week is a different kind of week from the rest of the term and should be used differently.
The principle: don’t learn new content
By exam week, you have either covered a topic or you haven’t. If you have covered it but it is shaky, the week is for shoring it up. If you have not covered it at all, the week is genuinely too late to learn it from scratch — you would be better off spending the same time on the topics you almost know, where the return per hour is much higher.
The reason this is hard to accept emotionally is that the topics you don’t know feel scarier than the topics you almost do, so the impulse is to attack them. The impulse is wrong. A topic you have spent six months not understanding is unlikely to crystallise in three days; a topic you almost have can become reliable in a single afternoon. Spend your time on the second category.
Days 7 to 5 (the weekend before): diagnostic past papers
Sit two timed past papers under exam conditions on the Saturday and Sunday. Mark them carefully on the same day. The point is not the score; the point is the diagnosis. Each wrong answer goes on a single sheet of paper, organised by topic. By the end of Sunday you should have a list of around $10$–$15$ specific topics or question types that you got wrong.
The list should be specific. “Trigonometry” is too broad to act on; “cosine rule with the obtuse angle” is the right level of detail. The more specific the diagnosis, the faster the remedy.
If your school does mocks late in the year, you have probably already done some of this. Use the same diagnostic list; do not reinvent it.
Days 4 to 3 (Monday and Tuesday): hit the diagnostic list
Pick the top three or four items off your diagnostic list — the ones that came up most in the past papers and that you struggled with most. Spend about an hour per topic, in this order:
- Read the relevant article in your textbook (or on this site, or wherever you usually get explanations from). Focus on the worked examples.
- Do five practice problems on that topic, no calculator if it’s a non-calc paper, with calculator if it isn’t.
- Mark them. Did your accuracy improve from the past paper?
- If yes, that topic moves off the list. If no, do another five problems.
At the end of these two days, your diagnostic list should be shorter. Do not try to clear it. The aim is to fix the most common errors, not to achieve a perfect understanding of every topic on the syllabus.
Day 2 (Wednesday): another past paper, then a single weak topic
Do another full past paper, timed. Mark it. Compare your error pattern to the diagnostic list from the weekend — have the problems you fixed actually stayed fixed?
Then pick one topic from the list (just one) where you still feel shaky. Spend an hour on it. Stop.
Day 1 (Thursday): formula review and an early night
Today is not for new content or for hard problems. The day before the exam should be light.
- Review your formula sheet, and any formulas that aren’t on it but you need to know. Write them out from memory once.
- Do a small number of warm-up problems — ten or fifteen short ones, picked from a variety of topics. The aim is to feel fluent, not to learn anything new.
- Pack your bag. Calculator (with fresh batteries if it takes them), pens, pencils, ruler, eraser, water, watch (most exam halls have a clock but check). Put it by the door.
- Eat properly. Sleep early. The single most underrated piece of exam advice is “get a full night’s sleep before the exam.”
Exam morning
A small routine that has worked well for many of my students:
- Eat breakfast. A real one, not just toast or coffee. Brain function under exam pressure is more dependent on blood sugar than students realise.
- Glance at your formula sheet for two minutes, then put it away. Do not try to do problems on the morning — this is anxious-energy territory and the marginal value is essentially zero.
- Arrive ten minutes early, no more. Sitting in the corridor for forty minutes with other panicking students is contagious anxiety. Show up close to the start time.
- Avoid the “what did you get for question 7?” conversation outside the hall. It accomplishes nothing; if your answer differs you panic, if it agrees you don’t learn anything.
In the exam itself
The first three minutes of any maths exam should be spent reading, not writing. Skim the entire paper, mark the questions that look straightforward and the ones that look hard. Start with the straightforward ones. The reason: easy questions get you marks quickly and warm up your brain; hard questions take time, and you want to give them the time they need with the marks already in the bank.
Time-box. If a question is taking three times longer than it should, leave it. Come back at the end. The most expensive thing in an exam is the question you spent twenty minutes on and still got wrong — you also lost the marks on three other questions you could have done.
Show working. On most maths papers (especially A-Level and free-response sections of AP and IB), you can earn marks for method even when the final answer is wrong. The student who writes “$x = 7$” with no working gets nothing if $x$ is in fact $5$; the student who shows the algebra gets most of the marks and loses one for arithmetic. Show working as if the marker is trying to give you marks, because they are.
Read the question twice. The second read often catches the part of the question you didn’t notice the first time, especially “hence” and “in the form” instructions that specify how the answer should be presented.
After the exam
If you have another paper coming, do not talk about this one with classmates. The conversation will either confirm you got everything right (in which case you don’t need it) or convince you that you got everything wrong (in which case it just makes you anxious for the next paper). Walk away.
If this was your last paper, do whatever you like. The marking is out of your hands now.
What I would not do during exam week
Three patterns I see students fall into that I would actively avoid.
Pulling all-nighters. Tired students score lower than rested students who studied less. The relationship is documented in dozens of studies and visible in every classroom. Your last few hours of late-night studying are worth less than your first few hours of clear-headed studying the next morning.
Memorising worked examples. Memorising a specific worked example is almost zero help on the exam, because the exam will use different numbers. What you want is the method, which only sticks if you do the manipulation yourself, not if you read someone else’s.
“Active recall” on a topic you don’t understand. Flashcards and spaced-repetition systems are great for memorising vocabulary or formulas. They are not the right tool for maths topics, because the topics are not lookup-based; you have to be able to do the maths, not just remember it. Spend exam week doing problems, not reciting cards.
The honest summary
The week before a maths exam is for diagnosis and consolidation, not for learning. Do timed past papers; identify your common errors; spend a focused hour each on the most common ones; sleep properly; eat properly; show up rested. That is the entire system.
Anything more elaborate than that — colour-coded revision schedules, fourteen-hour study days, “ultimate cram guides” from YouTube — is mostly noise. The simple version, executed properly, beats all of them.