Maths is not a subject you learn by reading. The student who reads the chapter three times and the one who reads it once and solves thirty problems both feel they studied, and the gap between their scores is large. Knowledge in maths settles by being used.
So the question is always the same: theory or problems? The answer is a ratio and an order.
Theory or problems?
Theory once, problems many times. Roughly a fifth of your study time goes to understanding the topic and the rest to solving. Instead of rereading the chapter, go back to the section where a problem defeated you, which makes the revision targeted rather than general.
Order matters too. On a new topic, follow two or three worked examples step by step, then solve similar problems alone. Skip the worked examples and problem-solving turns into trial and error, which locks in the wrong method. Keep a pencil moving during the examples; a solution you read is not a solution you can produce.
How many problems a day?
Around twenty while learning a topic, around forty in revision. What matters more than the count is that they are not all from the same topic. Fifty problems on one topic consolidate that topic, but the exam arrives mixed, and one mixed session a week closes that gap.
Difficulty needs a spread as well. A session of only easy problems feels good and teaches little; a session of only hard ones does the opposite. As a rough mix, half at a level you handle comfortably, a third where you struggle, the rest above your current reach.
Timing yourself belongs to the revision phase. While a topic is new, time pressure interferes with learning; once it is solid, there is no other way to get used to exam pace.
How do you use your mistakes?
By sorting them into four kinds, because each has a different fix: did not know it, knew it but could not set it up, arithmetic slip, misread the question. Students who skip this sorting apply topic revision to all four, when only the first one is a knowledge gap.
An error log works, but most people keep it badly. Copying the problem and writing out the solution takes long enough that nobody returns to it. A lighter version: one line per mistake, with the topic, the cause and the correct step. "Powers, multiplied the exponents with equal bases, should have added them." Reading those lines once a week does more than resolving the whole notebook.
If I read the solution, have I solved it?
No, and this is where maths fools people most. Reading a solution produces a genuine feeling of understanding, because understanding does happen; what is missing is production. If you cannot build the method two days later, you still cannot do that problem.
The practical rule: mark every problem whose solution you read, and solve it again two days later with the solution covered. That second attempt shows your real position. Resolving five of the twenty you looked up earns more marks than twenty fresh problems.
Video lessons carry the same illusion. A fluent explanation feels easy, and ease gets mistaken for learning. Our piece on understanding a topic but not solving problems goes into that difference.
With many gaps, where do you start?
At the start of the chain. Maths topics stack: powers do not hold without factors and multiples, roots do not hold without powers, percentage problems wobble without ratio, and almost everything wobbles without the basics. So you start not with the weakest topic but with the most basic weak topic.
The quick way to build that list is a ten-question test per topic, with results sorted into known, shaky and missing. The shaky group pays best; those topics are usually one missing rule from being solid.
Should you memorise formulas?
Yes, but after learning to derive them. Memorising a formula without knowing where it comes from leaves you stuck when the question is phrased differently; deriving it every time costs minutes you do not have. Derive once, then memorise.
For the memorising itself, spaced repetition works well: review formula cards at growing intervals rather than daily. The method is in spaced repetition and active recall.
What actually reduces careless errors?
Tidier writing. Most arithmetic slips come from a crowded margin rather than from a gap in knowledge: lines running into each other, a minus sign vanishing, a bracket never closed. Writing line by line, aligned on the equals sign, removes a large share of them by itself.
The second method is checking steps rather than results. Substituting the answer back is not always possible, but glancing at the previous line for a second after writing each step catches the error where it is born.
Speed helps too, and mental arithmetic is the cheapest place to gain it. Fast mental math techniques covers the methods, and our brain games include a three-minute daily drill for it.