One student at a top UK university started to panic about 2 weeks before an exam and e-mailed the lecturer that she is really worried. In our opinion, this worry is a very good sign and 2 weeks are probably the absolute minimum when students should start to worry. Indeed, this student got 83 (of 100) in the exam, while her best mark for any other module was 67. Another student started to e-mail his questions on the course much earlier about 2 months before the exam and then gained 100.
1st tip: regular work wins over last moment rush.
One of the two top revision tips by BBC is distributed practice, namely a continuous training over a long period. Indeed, making many short steps is easier than going up a steep slope. Such a long-term practice is especially important in mathematics, because some concepts often require months or even years to understand properly. That is why we run our distance courses over several months: 12-week courses for the MAT paper and Oxbridge interviews, and 16-week courses for STEP exams.
2nd mistake: reading solutions without trying hard.
Writing rigorously justified solutions to mathematical problems is a time-consuming job even for experts. Most publicly available solutions to past exam questions from MAT or STEP papers are too short and skip important details. If students get solutions for free without making their own efforts, then the learning value is close to 0. On the contrary, if you really tried several approaches and used expert hints, then you are more likely to master key ideas and solve any similar problems.
2nd tip: do problems yourself as in a real exam.
The second (and final) top revision tip by BBC is practice testing, namely doing real (or similar) problems. All other popular tips have either moderate or low value. A long time before these tips were published, we had started our courses by modifying questions from real past exam problems.
Such a modification is especially efficient for checking your understanding. Even changing simple notations does the job. For instance, most students can be confused by a function x(f). Of course, we genuinely modify MAT and STEP problems by changing not only numerical values, but also all forms of given functions keeping essential ideas. Hence reading a past solution can help a little bit, but does not spoil our homework. We often see that students have read a solution to an original past exam question, but have made the same mistakes in proofs that we find in almost every homework.
3rd mistake: paying someone else for your job.
One student surprised us by the following suggestion. He didn’t want to do any STEP-like problems himself, but was keen to pay us money for solving easier problems at A-level. Yes, he was going to train us (and pay us) for A-levels instead of using our guidance for his own exam preparations.
If you are learning to drive, then you will certainly drive yourself under the supervision of an expert driving instructor. So you will not pay for watching how a Formula-1 instructor drives a cheap car, because only watching hardly helps you learn to drive. Similarly in any exam preparations, you may want to do problems yourself and learn from detailed feedback on your regular written attempts.
3rd tip: find an expert to guide your progress.
Some over-ambitious students claim that they can complete our first homework, which we mark for free in any course, but never submit their work. Getting a right answer doesn’t mean a complete solution in mathematics. Actually, the annual STEP examiners’ report highlights that no credit is given for guessing a specific answer without explaining the logic.
So mathematics is not about getting a right answer, but about rigorous justifications how and why you can arrive at a right answer. Even our best students rarely gain the full mark for their first homework. In fact, these students quickly understand that their writing style needs major improvements and start working hard to succeed later.
This time we suggest the following poll instead of a usual riddle.
- Poll 1: what is your best revision technique by your past experience?
- How to submit your vote: to write your answer, submit a comment.
- Prize: if you also submit a first correct answer to one of our open riddles,
then you will get a free 1-year access to two of our interactive web tutorials.
- Restriction: only the first vote with a correct public answer will be rewarded.
- Update: Learner has shared excellent advice and also solved our riddle 1.
Some countries are celebrating the Day of Knowledge today as the start of a new academic year, so our warm congratulations to everyone who learns!
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