** 1st mistake: starting to worry about exams too late.**

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!

If you wish to receive automatic e-mails about our new posts (for a quicker chance to answer a riddle and win a prize) or distance courses, please contact us and tick the box “keep me updated”. You can easily unsubscribe at any time by e-mailing “unsubscribe” in the subject line.

My best revision advice is “keep going”. In the past I often felt frustrated by mathematical mistakes. However my teacher always encouraged me to consider this experience as a learning opportunity and I did! I still make some mistakes, but never make the same mistake twice. So I really prefer to make all possible mistakes before important exams.

By the way, the answer to your riddle 1 is Pythagoras theorem: the square of the hypotenuse in a right-angled triangle equals the sum of the squares of the smaller sides. Can you now enrol me on 2 of your web tutorials for the MAT paper? I would prefer the harder topics such as “Tangent lines and areas bounded by cubic parabolas” and “Global extrema of a 2-variable function over a region”.

Dear Learner, thank you for your excellent revision advice!

You have correctly guessed Pythagoras’ theorem in our riddle 1 from the post Introduction to our Master Maths blog: 4 reasons to start. However your correct statement seems incomplete.

Since your answer is the first, we shall give you the hint: does your claim imply that the triangle with the sides 3, 4, 5 is right-angled? If not, can you complete your initial statement to cover our last question?

If you write full Pythagoras’ theorem as a new comment, then we shall certainly enrol you on the requested web tutorials for the MAT paper.

Right now you could self-register at our tutorials web site, simply click on “Create a New Account”. After logging in, navigate to our free web tutorial “Beyond Pythagoras’ theorem and applications”, then click on “Enrol me in this course” in the left-hand side menu.

I was confused for a while by your question, but now I see that my statement doesn’t say that the triangle with sides 3,4,5 should be right-angled. I guess that the opposite claim is also correct: if a^2+b^2=c^2, then the triangle with the sides a,b,c should be right-angled. Is it the second part of Pythagoras’ theorem?

Dear Learner, yes! Full Pythagoras’ theorem consists of two parts and can be stated in one phrase as follows: a triangle with sides a< =bblogger@master-maths.co.uk the title of two web tutorials you would like to access at our Master Maths tutorials website.