H2 Math: How to Study for Exams – The Way I Studied Math as a Top Student

Whenever a student tells me that they did not do as well as expected in an H2 Math examination, one of the first things I ask is:

“How did you revise for the exam?”

Very often, the answer is something along the lines of, “I practised questions,” or “I did some questions and looked at the solutions when I got stuck.”

Then I ask, “Did you actually study your notes?”

The answer is surprisingly often no.

Some students tell me that they feel practising questions works better for them. Others say that they refer to their notes when they cannot proceed with a question. To them, this feels like revision. After all, they are spending hours doing Math.

But there is an important difference between practising questions and studying the subject.

I have been teaching Math for more than two decades, but I also remember very clearly what it was like to be a student myself. I was a student who consistently did very well academically, and one of the reasons was that I was extremely thorough in the way I studied.

In this article, I want to share exactly how I used to study Math, because I believe this is something many H2 Math students today are missing.

I Did Not Jump Straight into the Questions

Let me use Vectors as an example.

When I was preparing for an examination, I would sit down with my lecture notes and go through the topic from the beginning to the end. I would spend hours doing this if necessary.

I did not simply skim through the notes. I would read them carefully, line by line, making sure that I understood what I was reading.

I would pay particular attention to the key concepts, definitions and explanations, and make sure that I remembered the things that needed to be remembered.

But there was an important part of this process:

I was constantly testing myself.

After studying a section, I would put the notes aside and take a blank piece of paper. Then I would try to scribble down the important concepts I had just studied, almost as if I were explaining the topic to myself.

Could I remember the key idea?

Could I explain it?

Could I reproduce the important points without looking at the notes?

If I couldn’t, I would go back and study that section again.

This was my way of making sure that I was not simply recognising the information because it was sitting in front of me. I wanted to know that I could actually retrieve it from my own memory.

I would repeat this section by section, page by page, until I reached the end of the lecture notes.

That, to me, was revision.

Understanding the Whole Story Matters

One reason I believe students should study their notes from beginning to end is that a mathematical topic is often not just a collection of unrelated formulas and techniques.

There is usually a build-up in concepts.

It is like a story that is unfolding.

One concept is introduced, which leads to another concept, which then allows you to understand a particular method or result.

When you study only by doing individual questions, you can sometimes learn isolated techniques without really understanding how the ideas fit together.

This becomes particularly important in H2 Math, where examination questions may not look exactly like the examples you have practised.

You need to understand the underlying mathematics well enough to recognise what is happening in an unfamiliar question.

That is why I have always believed that thorough understanding has to come before extensive practice.

Then I Would Go Back to Questions I Had Already Done

Once I had properly revised the notes, I would start practising.

But even here, I did not feel that I needed to find endless new worksheets.

I would first redo my tutorial questions, test questions and examination questions.

In particular, I would pay attention to questions that I had struggled with previously.

For a straightforward question that I knew I could do, I did not necessarily spend a long time writing out every line again. I could look at it, think through the method and check the solution.

But if it was a difficult question that had previously caused me problems, I would put the solution aside and work through it again from scratch.

I would scribble my working on paper and only look at the solution after I had genuinely attempted it.

This is an important distinction.

There is a big difference between looking at a solution and thinking, “Yes, I understand this,” and actually being able to produce the solution yourself.

I also liked redoing questions because I knew that I could not possibly remember every question I had done months earlier.

A question that once seemed familiar may feel surprisingly unfamiliar when you return to it later.

Redoing it therefore gives you another opportunity to test whether the knowledge has really stayed with you.

I Did Not Keep Chasing New Questions

Students sometimes think that the more new questions they do, the better prepared they must be.

I don’t necessarily agree.

Of course, once your understanding is strong, you should expose yourself to a wide variety of examination questions.

I would practise Ten-Year-Series questions and past-year school papers closer to the A-Levels.

But I did not think that every revision session had to involve a brand-new worksheet.

There is a lot of value in going back to material you have already encountered and asking yourself:

“Can I still do this now?”

In fact, this was part of what made my revision so efficient as examinations approached.

The First Time Takes a Long Time. The Next Time Gets Faster.

When I revised Vectors for one examination, I might have spent a considerable amount of time going through the notes carefully.

When I came back to Vectors for the next examination, I would still go through the notes from beginning to end.

But it was much faster.

I would read something and think, “Yes, I know this.”

I would recognise the concept immediately and move on.

Another section might require a little more thought, so I would slow down there.

Each time I revisited the topic, the knowledge became more familiar.

This process continued throughout my JC years.

By the time I was preparing for my A-Levels, I found that I could revise many topics very quickly because I had already built that foundation through repeated, thorough revision.

That meant that I could spend much more time doing past-year and preliminary examination papers closer to the actual A-Levels.

And I had time to go for my runs and cycles. Fitness is important too.

The Thorough Work You Put In Earlier Makes Revision Faster Later

Interestingly, I still experience this process today.

I read higher-level mathematics textbooks daily in my own free time because I enjoy learning mathematics beyond what I teach. Topics like Real Analysis, Complex Analysis, Number Theory, etc.

When I open a new chapter, I am once again a student.

The material is unfamiliar.

I cannot simply turn to the questions at the back of the chapter and expect to be able to solve them.

I need to go back to the beginning, reread the explanations, understand the definitions and concepts, work through the examples and sometimes reread the material several times before it becomes familiar.

Only then do the practice questions become much more manageable.

This has reminded me that what I ask my students to do is not some abstract theory about studying.

It is genuinely how learning works when you encounter unfamiliar material.

You first have to build the knowledge internally.

Then you practise applying it.

Then you revisit it so that the knowledge becomes increasingly familiar and accessible.

So What Should You Do When You Sit Down to Study H2 Math?

If you are preparing for an H2 Math examination, I would suggest starting with your notes rather than immediately reaching for a worksheet.

Go through the topic from the beginning.

Read carefully.

Make sure you understand the concepts and definitions, and identify the important points that you need to remember.

Then close the notes and test yourself.

Take a blank piece of paper and see whether you can explain or reproduce the important ideas without looking.

Once you have established that foundation, move on to your questions.

Redo your tutorial questions, particularly the ones you struggled with previously.

Revisit difficult test and examination questions.

For questions you know well, you can revise them more quickly.

For questions that have challenged you before, work through them properly without looking at the solution.

Then, when your foundation is secure, broaden your practice with Ten-Year-Series and past examination papers.

At Debbie’s Learning Cove

This is also why I place considerable emphasis on the quality of revision notes given to my students at Debbie’s Learning Cove.

I have designed my notes to make revision as easy and systematic as possible while still being thorough.

For students who join my H2 Math Tuition classes after their school has already covered a topic, I still encourage them to review their school notes where necessary and, importantly, to ensure they understand the topic’s full development.

My advice to students is simple:

Don’t try to skip the studying part of studying Math.

Practice is essential, but practice is where you apply your understanding.

If the understanding is not there in the first place, doing more and more questions may not solve the underlying problem.

When you sit down to prepare for your next H2 Math examination, give yourself the time to properly learn the material, test yourself, revisit what you have forgotten, and then practise applying what you know.

That is how I studied Math as a student.

And after all these years of teaching, it is still the approach I believe in.

Study thoroughly first. Practise purposefully after. Then revisit until the knowledge becomes your own.

That is when H2 Math revision becomes much more effective.