SMC Tips and Tricks

Anyone doing it this year? Any tips from ppl who’ve done it in the past? I’m in y11 and doing it bc my maths teacher wants everyone doing additional maths doing the smc and really quite nervous about it! I was a mark off a silver on a paper and consistently bronze in all of them and I’d really like a silver but preferably a gold lol - any tips/tricks would be highly appreciated! Thanks :smile:

Reply 1

mqb2766

21

Original post by bicompton

Anyone doing it this year? Any tips from ppl who’ve done it in the past? I’m in y11 and doing it bc my maths teacher wants everyone doing additional maths doing the smc and really quite nervous about it! I was a mark off a silver on a paper and consistently bronze in all of them and I’d really like a silver but preferably a gold lol - any tips/tricks would be highly appreciated! Thanks :smile:

Tbh, Id not be that worried especially in y11. The usual advice is to do a couple of past papers and carefully check the (extended) model solutions that you can download from the ukmt. If necessary, do it timed, then spend a bit of time, open book, thinking about the questions you didnt manage to get done before looking at the model solutions.

Realistically, there are too many different question types to simply give a few tips. There are some slides at drfrost https://www.drfrostmaths.com/resources/page.php?id=6 but they're probably overkill given the time available. Similarly there is an old ukmt tips guide for smc if you pm me. But at the end of the day, the smc is not that much more than gcse, but asked in an unusual way, so sometimes its better to try some problem solving (so estimate ans, simplify problem, try extreme cases, sketch it, work backwards, sub magic numbers, ...) and rely on your existing gcse knowledge with some practice.

Reply 2

mqb2766

21

Original post by bicompton

Anyone doing it this year? Any tips from ppl who’ve done it in the past? I’m in y11 and doing it bc my maths teacher wants everyone doing additional maths doing the smc and really quite nervous about it! I was a mark off a silver on a paper and consistently bronze in all of them and I’d really like a silver but preferably a gold lol - any tips/tricks would be highly appreciated! Thanks :smile:

As youve done a few papers, a few tips (certainly not complete ...). The old one about the prime factors of the year idoes occur now and again, but its very specific and usually an easy question so it can usually be done without any prior learning. So

Problem solving
* Sketch the geometry (and other) questions yourself
* Consider extreme cases, so if a question is asked about the propreties of an irregular shape, can you transform it to make it regular or some of the angles/sides equal to zero in order to answer the simpler question.
* Can you simplify the problem or substitute numbers in order to spot a pattern
* Rather than working out problems algebraically, can you work it out in terms of specific number and rescale the answer.
* If the answers are sufficiely different, can you approximately/roughly solve the problem quickly.
* Think about what the question is asking for, so if its finding a+b+c+d from a set of equations, there is usually no need to find a, b, c and d individually, rather you sould be able to find a+b+c+d directly.

Geometry:
* Recognise how to set up pythagoras with the same unknown on two different sides
* Know the side ratios / trig values for 30-60-90 and 45-45-90 triangles.
* Always draw extra radiii/lines on problems involving circle tangents, inscribed shapes, ... so connect important points to calc lengths and/or angles.
* Recognise pythagorean triples in (circle) problems which may not immediately look like a pythagorean solution
* If the problem involves areas of triangles, think about bases and peppendicular heights
* If its the area of a complex shape, can it be decomposed into simpler trianges
* Be confident with similar triangles and scale factors (length and area)
* Know your gcse circle theorems
....

Numbers
* Know your divisibility rules for 3/9/11 especially.
* If the question involving equations requires an integer solution, always think about prime factorisation at some point
* digit problems occur reasonably often (related to proving divisibility rules) so understand the place value representation
* Know your triangular numbers and similar sums/series.
* Compare expressions by squaring to get rid of surds or comparing fractions in novel ways.

Algebra
* Dots (difference of two squares) is an old favourite
* Be confident with handing simple binomials, especially (a+b)^2 and (a-b)^2 which lead onto am-gm inequality and babylonean multiplication.
* If you see a quadratic, almost the first thought should be to complete the square
* Spot how to solve "unusual" simultaneous equations, so something like a+b=3, b+c=2, c+a=5, by summing them to get a+b+c=... then subtracting one to get a varaible of interest.
* Inequality questions may require completing the square or ....

There are many others, but there is little in the above which isnt ~gcse, and its good to reflect on the quesrtions/solutions after doing a paper and thinking about the underlying principles - did you do it efficiently, what in the question hinted about the solution, .... Most questions can be answered with few lines of working at most (sometimes a good sketch/simpllify the problem is all thats required) so if youre doing "pages" of algebra, then youve gone badly wrong and wasting time. Something like https://www.openbookpublishers.com/books/10.11647/obp.0168 is good to work through if you have the time as is a decent maths history book and if youre ~bronze/silver sometimes doing a few imc papers is worthwhile as the difference between intermediate and senior is more about level of difficulty rather than the topics and if you can do well on the imc, you should do well on the smc as well.

(edited 7 months ago)

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