Mathematical proficiency is not an innate gift; it is a skill built through deliberate practice. No one is born knowing how to prove trigonometric identities or solve differential equations. These concepts require time, patience, and effort.
The most effective way to prepare for A-Levels is not by passively reading notes, but by engaging in active retrieval by solving problems, making mistakes, and learning from them. Consistent practice under exam conditions does more than just test your knowledge. It builds the pattern recognition, automaticity and confidence required to succeed.Β
Here is a strategy based on how the brain actually learns mathematics:
Performing well in single-topic tests often creates a false sense of mastery. This is because you already know which method to use before you read the question. However, an A-Level exam presents a different challenge: you must identify the correct tool from your entire toolkit without any clues. Last-minute cramming won't suffice. Maths proficiency is developed through gradual, consistent practice.
By starting past papers as early as February, you give yourself the time to identify weak areas, refine your skills, and balance revision across all subjects.
Many students fall into the trap of "passive revisionβ. Spending hours creating colourful notes or highlighting textbooks feels productive, but research shows it does little for long-term retention. Maths is learned by doing. You must engage in active retrieval: forcing your brain to recall methods and apply them to problems. Avoid the time-sink of transcribing textbooks or making pretty summaries. Copying is not learning. Instead, use PMTβs excellent Cheat Sheets for reference and dedicate 100% of your study time to answering questions.
Donβt try to revise every individual topic. It will take too long. Review your past tests/quizzes and pinpoint exactly where you lost marks. These gaps are your priorities, not the topics you are already comfortable with.
Attempt full past papers under timed conditions without using notes. Afterwards, mark them using the official mark scheme. List every topic or method you struggled with to create your personal "hit list" for future practice.
Donβt just skim the mark scheme; understanding the answer is not the same as being able to produce it. If you get a question wrong, study the model solution to find your error. Then, hide the solution and re-solve the problem from scratch. Compare your working line-by-line with the official method to ensure your answer is structured exactly as the examiners want.
Once you've identified a gap, you must isolate it. Use question sets grouped by specific topic (e.g. all completing the square). This form of repetition is necessary to build the fluency and automaticity needed to perform the skill without thinking.Β
Tip: Use DrFrost to generate worksheets targeting specific skills.
Your brain doesnβt learn best through cramming: it thrives on repetition over time. Spaced repetition takes advantage of how memory works by forcing you to retrieve information just as it starts to fade. By re-testing yourself on tricky concepts at gradually increasing intervals (e.g. 3 days, 1 week, 2 weeks), you build long-term retention.
Once you have drilled your weak areas, you must verify your progress. Attempt a fresh past paper under timed conditions to test if you can transfer your drilled skills back into a mixed environment. If new gaps appear, rinse and repeat the process. Bring any persistent issues to our next tutorial for review.