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“How To Ace All Your Math Exams. Every. Time.”
Introduction
What you’re about to read is the research and findings that I’ve assembled over the past couple of weeks. These findings have allowed me to discover the best methods to mastering math, despite not originally being as passionate nor motivated to it.
Don’t get me wrong. I’m not a math person. At least, I don’t think I am.
However, I think math is extremely cool. Just acknowledging the fact that the rules and formulas we use everyday, even the most basic ones, are the ones responsible for helping us develop a fundamental understanding of math, problem-solving, and how to tackle the world’s most basic and most complicated problems. It’s because of math that the world’s population can perform mathematical operations in their heads within instants, and build machines that can solve just as complex of problems in shorter time spans.
However, not long ago, I never used to think like this. If you asked me just a few months ago, I probably would’ve told you that I only used to be good at math during my elementary school years when I used to get packets for homework, and solve them all within minutes. Then, I didn’t really like math. I didn’t hate it, but I would never say that it amazed me. It didn’t. Now I share a very different opinion.
The reason for the change in stance and perspective is what I’m going to share with you today. I believe that insight, and that shift has been able to transform me into a person that went from sucking at math, and not being able to grasp mathematical concepts very easily (because it all felt forced) to a person that learns mathematical concepts for the fun and knowledge-stance of it.
Let me explain what I mean.
Please Read (Step Zero)
You need to read this before you go on to acing your math exams. Why? Because this will determine if you are applicable for the insight that I’m soon to share.
What I’m going to share will not apply to everyone. It only applies to a select few; representing those who are interested in math, and interested in actually developing within the subject. Otherwise, none of the information below will work.
I believe that the best way to maximize your guarantee of this is to follow this first, step zero.
Step Zero
This is a piece of advice that likely no other source will share with you. The reason? Because this is something so unheard of, so unrecognized. Sure, everyone knows that if they want to enjoy the job they work, and willing work in that job despite awful pay and disrespect, they need passion. Passion is the motivation that drives them forward.
But, what if I told you that this same passion/motivation is also essential for your learning? Whether that learning is for a course, for an in-school subject, or a personal interest, if you want to learn something faster than anyone else, and solidify it into your long-term memory, you need to find that same internal motivation. It’s what pushes you forward into a position so comfortable, so pleasing, and so wonderful. It’s a position that will finally allow you to realize the true beauty that is learning. Its the same motivation that changed me. So, I hope that it’ll change you too.
Here’s the advice: To do well on any math concept, and do so comfortably (even if you’re not the most excellent in math), you need to find some external meaning in that concept. How can that concept be applied to something you might pursue in the future, and how might be of service to those around you? What history does it have that has made it so important in math records? How might you, an ordinary person, use it to solve some of the world’s most concerning and challenging problems?
Purpose is the driving motivator that will help you make these fundamental steps. If this still doesn’t make sense, read the next section.
Interpretation
Step zero is meant to give you that necessary context for learning, and learning math especially. When you look at the formulas you use, learn its history, who discovered it, and its value in the context of our species today. Acknowledge the fact that someone, somewhere, discovered and created those formulas out of practically nothing; and have, nonetheless, transformed our species for the better – transforming us into a more, advanced, and capable society.
These formulas are more than just formulas. They have allowed us to understand math as a whole, and how it applies to the world itself, space and time, and so much more. Apply this context to any math concept you come across, and it will come far easier than it used to have.
Of course, the important thing to note here is that it can take time to digest these things. Although it might seem pointless and of no (or very little) significance now, it might not appear that way in the future. Your understanding and perspective on the world and its beauties only changes as you age, and as your wisdom grows (not saying that I’m the smartest there is either haha).
Example
If there’s one thing I can really apply into context, it’s Trigonometry. Specifically, the trigonometry I learned in high school pre-calculus. Although it definitely isn’t the easiest thing there is, what really has interested me above everything about the concept is how the concept of the wave (one of the most significant mathematical discoveries in the history of humans).
The wave, or the motion of the ocean, is what formed Trigonometry, what makes a wave, a wave. Applications of sin, cos, phase shifts, amplitude, and other parameters were so basic, seemingly so pointless, but values so essential to what’s formed our understanding of all the waves that surrounds us daily, today.
Additionally, learning trigonometry allowed me to branch out into other math concepts; with Calculus being the key emphasis here. I made this move because the career that I was researching and studying for at the time involved some calculus. And, in my mind, it wasn’t a very hard decision to make. And, in the end, it only made me a better student and learner (being better able to handle advanced math concepts).
Step 1: Difficulty of Current
How difficult is the current subject you’re studying? This is arguably one of the most important questions you can ask yourself. Answering this question will give you an idea of where you are in your current subject, and how far you need to progress in order to exceed your own expectations.
Either you’re struggling, well-off, very well-off, or have no clue what you’re doing. That’s it. There’s only 4. Your goal at this point should be to form some kind of understanding on the material – but not in the traditional way. That won’t work.
Step 2: Understanding
There are quite a decent collection of methods that exist that you can utilize to learn material as fast as possible. Some methods work better than others depending on how you learn, therefore, if you don’t know what you’re learning type is, I suggest checking out this brief post on how to determine your learning type and what kind of learner you are. This is crucial for fast-tracking your road to academic success and a well-crafted understanding on any school subject.
Anyways, here’s the list:
- Your professor.
- Private/Saved lectures.
- Classmate notes.
- YouTube videos.
- Khan Academy.
- Study buddy.
- Simplification/Visualization.
- Real-World Use Case.
- Practice problems.
- Mini-steps.
- Practice until it makes sense.
Notice that there’s actually a few good options. All of these work great (except the last one –> that’s more of a “hopefully it’ll make sense” type of option). Therefore, if you’re willing to put in the work necessary, then all of these should work fantastically.
The Suggestion You Probably Didn’t Expect
However, if you’re trying to fast-track as best as possible, you need something that’s fast, efficient, and will make the most of every minute you dedicate. You need something that will, specifically, do all of these at the same time.
My suggestion? Generative AI.
Specifically, when I say “Generative AI”, I mean AI models like ChatGPT and Gemini. These models do one great thing in particular: a lot of things. If I had artificial intelligence back when I took algebra in middle school, and when going through some of the most challenging concepts in my math career through school, I could’ve saved myself hours of time and unnecessary sacrifice that I had to end up making either way.
And, it’s because of AI that I was able to fly through my personal work long after, while giving in significantly less effort than I had ever put in before. I was able to do just as much, while literally doing less, and still ending up with the same quality and quantity of output in less time. Seriously, I was able to cut the time into thirds or even quarters.
I am not telling you in any way to cheat and use AI to do your homework, because that’s wrong. Never have I ever though that the purpose of AI was to get ahead, having malicious intent. What I am saying instead is to use AI to help you grasp concepts faster and easier than you were ever able to before.
But, Why?
I’ll make this very simple. The reason you should ever use tools like these your rate of thinking, your ability to generate ideas on command, and your speed at reproducing work. Tools like this have existed for years, with the only difference now being that they’re a lot easier and cheaper to find (plus, they work far better).
Chances are: some of you already know or even already implement this suggestion on the daily, while some of the older folks might be resistant to anything else. And as I said previously, we all hold onto our beliefs. But, it’s your choice as for whether or not you want to 10X your working speeds, or just continue moving at the same, slow speed that gets you where you want to be far slower than the faster vehicle does. Slow and steady does not win the game when you get the same quality of work done in more time, and when the due date is slowly (but nevertheless, incrementally) screaming your name.
Step 2: Understanding (cont.)
My Application
I’ll make this as quick and as straightforward as I can. Now that you know why the implementation of artificial intelligence can level up your creative speeds and feats to a level beyond what you’re normally capable of, let’s figure out how you can implement these technologies the right, and fast way.
First, let’s get one thing straight. AI gets things wrong. And since you’re using AI to solve math problems and other algorithmic problems, it’s far from perfect (but still better than the average human); but still good enough to do the job and help you solve even the trickiest math problems on your math homework. The best part of all here is that AI won’t give up on you. It’ll try its best to understand and form an answer, with a well-backed explanation, to the best of its ability.
If you’re taking any high school math, or something even lower, it will almost always be able to solve it. I’d give it about a 90% accuracy, depending on the type of problem – with some problems reaching a comfortable 100% and others reaching a scarily low 20% or less. Yeah, I know. That is absolutely terrible. I hear you. Problems involving diagrams, and 2D models (not all the time however, there are exceptions) especially are some of the trickiest ones, given that not all AI models can read and interpret images very well, meaning that for those problems: you’re on your own.
What to ask
Second, there’s only 1 right way to correctly use AI for any math problem. That is:
- Give it the problem.
- Have it explain, step-by-step, the solution and how it got it.
- In some cases, you might just need one part of an entire set of steps to be explained. In this case, you’d just tailor your request to include this exact detail (or two), and done.
- Repeat the exact steps it follows, following exactly what it does.
- If it misses a tiny step, and just assumes you know it, have it explain that small part. (you might need to repeat yourself for this)
- Repeat this process until you’ve locked it into your brain.
- Optional: Ask it to slightly increment the problem’s difficulty, and repeat steps 2-4 as many times as you want.
Specific Model
If you want a good starting point, and a reliable model that’s free-to-use (and that also offers a really-nice looking and cheap paid plan) and still really useful, then I would recommend Gemini. It’s a model that’s created by Google, and it does really well on mathematical-sort of problems. It, just like any other LLM (large language model), can explain concepts very simply, and it does everything you need it to do. A really good feature that you also might prefer having are image inputs; meaning that you can just give it a picture of a problem, and have it explain.
I personally would recommend other models in this situation; however, given that we’re here to solve math problems, I would have to say that this is a very good starting point.
PhotoMath
“Photomath” is a popular mobile application that you can download (at least on iPhone) to seamlessly take a picture of your work, and have it be explained to you, step-by-step.
In my personal opinion, I wouldn’t recommend Photomath. First off, a majority of people who use applications like these are the same people using these to do their work for them; and find out just how bad they messed up on test day. Sure, you could go for it. But, as I mentioned earlier, this isn’t worth doing by any means. You won’t learn anything, and you’ll miss so much material that could have made sense; but you didn’t allow it to.
And that’s why I recommend LLMs like Gemini. It can offer step-by-step explanations in a way that you want it explained, rather than the automatic way it’s explained by Photomath. If you need analogies, or further explanations on a certain step, you just ask; and the AI provides. Photomath doesn’t offer this luxury.
Khan Academy
Khan Academy is a great resource, and it works greatly; but, as I said for Photomath, it isn’t as good of a resource as people say it is. Although it does have some nice courses and teachers on the platform; it’s nearly impossible to explain something as well as an AI that knows you as well as your classmates.
Step 3: Breakdown & Application
Learn how to break down the problems you’re solving for into smaller, more manageable steps; while simultaneously learning how to apply these steps into practice. Define terms for what they are, develop abstracted understandings of it, with even samples of fictional data for visualization and demonstration.
Step 4: You Aren’t Good Enough
You aren’t good enough. Don’t get ahead of yourself. If you want to really improve your math-solving ability, you need to solve more problems. Repeat this action again and again and again, while simultaneously implementing the steps above, and you’ll fast-track your success rate when solving these kind of problems by a factor of 10.
PRO TIP: If you want to take math seriously, like for a profession (but still hate it), investigate different types of math. Take the extra time to learn how it’s applied to your field of interest. Learn why it’s applied, and how it can be deciphered into plain English for mortals like you to understand. This is a large and more long-term step that takes time to put into effect, and requires your consistent action and ultimate attention.
My Brief Story
I used to be a person that loved math (my favorite subject), to someone that liked it, to a person that despised it, to a person that now appreciates it again. I don’t have the same love for it that I used to; but I don’t dislike it like how I used to in the past 4-5 years. And I consider that a big accomplishment.
The knowledge and intuition I’ve gained have allowed me to grasp an understanding that math is more interesting than it appears on the surface. I’m not saying that you should like it; but what I am saying is that everyone, no matter the profession, should take the time to master (to a certain point) the difficulty of math that has formed our societies today. They are what have permitted us to be as advanced and as powerful as we are. Take that into account, and you’ll advance yourself to levels of deep mental understanding that exceeds anything you’ve ever experienced.
Don’t believe me? Do what I did. Go out there and explore the never-ending forest that is math.
Conclusion
In this post, my goal was to provide as much personally-tested advice as possible; enough to the point that anyone could use it to level their understanding of mathematical concepts by as large of a margin as possible. Maybe there’ll be a more formal, and more research-backed post in the future on doing well in math, but I highly doubt it. After all, there is barely anything you haven’t heard of for learning math; that don’t really suit math learning in the first place.
Implement all of the steps above, in the order that it is, and repeat your new process of learning prior to test day.
