How to excel in maths

Mathematics is a subject that can be both daunting and rewarding. While some individuals seem to effortlessly grasp mathematical concepts, most of us need to put in extra effort to excel. This article is dedicated to the majority—the ones willing to work hard to achieve success in their A-level maths exams and beyond. By following a structured approach and embracing a growth mindset, you can unlock your mathematical potential and reach heights you may have never thought possible.

Understanding the concepts

Fundamentally, to be able to get anywhere in mathematics, you need to understand what you are doing with numbers and why. There is no point in knowing how to differentiate if you don’t know why you want to differentiate and why it works.

Now, I am a strong believer that anyone can learn anything if they approach it with an open mind and determination to succeed. This is called having a growth mindset. However, there is a caveat with how maths is taught at school.

When maths is taught, it is taught by someone who understands a concept in a particular way. We are all inherently different, and similarly, our minds all work slightly differently. So when your teacher explains how they understand something, it does not mean that you should also understand it as you both think differently. Now for some, they manage to grasp what their teacher is saying easily as they think similarly, but for others this may need an alternative approach.

Some examples could be supplementary lessons with a tutor, buying a subscription to online lessons or asking for some 1-on-1 time with your teacher. But sometimes this may still not even work.

If my teacher can’t help me, how can I learn? Well, for A-Levels and GCSEs, we are extremely blessed that there is a plethora of different resources that we can use, both written and in video format! Some of my favourites include, but are not limited to, TLMaths (Youtube), BBC Bitesize (GCSE only), and Khan Academy. (Also see: Extra Resources for more maths resources).

YouTube really can be your best friend. There are thousands of videos explaining mathematical concepts, and they are not all as trivial as those shared by Numberphile. By simply searching for a topic that you are stuck on, you can get many different professionals to explain the same problem; with enough grit and determination, you’ll be able to find a video that you can easily understand!

If, however, that does not seem to work, it may be an indicator that you need to step back and learn the fundamentals a bit better. There is little point in using the integral to calculate the area under a line graph if you don’t know what a line graph actually shows.

Practice the concepts

Once you’ve got the concepts down to the tee, there is only one option to go with. Practice. Practice. Practice.

I foolishly made the mistake during my year 10 final exams, where instead of doing practice questions, I made notes from watching videos and thought that was enough. Not only is this not engaging, but when it comes to maths, practice is the only way to revise. Truthfully, I would never recommend taking notes in maths as it is not only quicker to look something up, but I believe the time spent making notes could be spent better elsewhere.

The best way to practice for an exam is through practice papers. You may now be dashing off to find practice papers for your exam board; however, I would recommend not touching these until you are around 1 month away from your exam. If you are as crazy as I am, you could even leave it until the last week and complete 2 or 3 per day, but maybe for your sanity, I’d advise against this. Instead, use all of the resources that you are fortunate enough to have available to you thanks to the internet. Complete every question in your textbook and revision guide; complete predicted papers; do it all! This is the surefire way to get top marks and become a competent mathematician.

But maybe you’re not studying for a big A-level exam just yet. By completing the questions that you may not have done in class and researching topic-specific questions (Math’s Genie and Physics and Maths Tutor are both excellent resources for this), you will, with time, start to develop your skills and put the theory into practice. By better applying these concepts, you begin to understand them and maybe even start to enjoy them.

(Bonus tip: do your homework. It’s given out for a reason.)

Apply the concepts to unfamiliar situations

Now that you have mastered the concepts and put them to the test by answering every question you can get your hands on, comes the trickiest part of mathematical mastery: These are the questions that separate the A’s and the A*’s. The geniuses and the sedulous, but more importantly, those who can do maths, and those who understand maths.

By applying the mathematical concepts that you’ve learned to unfamiliar situations, you start to develop an extremely sought-after skill. Problem solving. By using maths in an unfamiliar context, most students are hasty to give up, and this is why the last question on the test is so ‘difficult’, but in fact it's the same as the prior questions but in disguise.

To conquer these questions, you have to be able to decipher what the question is asking and then apply the appropriate techniques to solve it. The only way that you will know which techniques to use is by attempting similar questions that push you, and in time, your brain's pattern recognition will kick in and you’ll start to find that you just know what to do. You can't explain it; you just want to differentiate here, factor out here, and expand these brackets here, and bam! You’ve got the answer.

But the only way you can get there is by putting in the hours and attempting questions that are outside your comfort zone.

At the beginning of the article, I said it would be tough, but maths does not require you to spend 4 hours every night (until you are smack in the middle of your A-level exams), but instead a mere 20 minutes, maybe only 5 days a week, but I promise you that this small amount of time after school, before bed, or during break, if uninterrupted and follows the rules that I have just suggested, will work absolute wonders on your mathematical ability.

Imagine the impact of dedicating just 20 minutes a day to math starting right now. If you're in year 13, with your first math paper 38 weeks away on June 4th, time will fly. By committing to 20 minutes daily, five days a week, you'll accumulate over 63 hours of revision. Bump it up to half an hour, and you'll hit almost 100 hours. This early start saves you precious time closer to exams, allowing you to focus on other subjects. Unlike some subjects, math doesn't require rote memorisation. Building these skills gradually pays off.

Yes, 20 minutes daily may seem modest, but consistency can be challenging. Skipping just one day can turn into a week, then a month. Dedication, determination, and discipline are essential for success. If you maintain this routine, you can achieve remarkable results, even surpassing natural mathematical geniuses.

Now with the three steps to mathematical freedom: Understand the concepts. Practice the concepts. Apply the concepts to unfamiliar situations. Go out there and give it your best shot!

I wish you all the best of luck in your journey to mathematical mastery!

Written by George Chant

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