Math Revision Tips That Will Make You A Pro at Integration

One of the most difficult topics in Upper Sec and JC Math is Integration. As students only learn it quite late in the syllabus, they have very little time to grasp the concepts. Yet it is a topic that often (almost always) comes up in the exams, and there are so many techniques to learn and apply, making it definitely very overwhelming.

If you are looking for ways to improve your integration techniques and build up your confidence before your next test, make sure to read on for our practical steps on how to practice and revise for this topic!

List down all the techniques

The word ‘integration’ sounds like just one process, but in actual fact, there are many different techniques for integrating different expressions. It helps to lay out all the techniques into a checklist or cheatsheet so that you can review each of them easily and refer to it during your practice.

Some of the key techniques include:

• Basic integration of algebraic expressions
• Integration of exponentials, logarithms, and surds
• Integrating trigonometric functions
• Integrating using partial fractions
• Integration by parts

Our Math tutors recommend that you also include one example for each technique in your cheatsheet so that you can be clear on how it should be used. Be sure to also mark which formulas you need to memorise and which are given during the exam.

Practise by technique

When you’re first starting out, don’t jump straight into exam papers or mixed review questions. Instead, focus on practising one technique at a time. Work through problems grouped by type, and make sure you can solve them without referring back to your notes.

If you’re unsure where to begin, our secondary level Math assessment books are a good starting point, as the topic is structured by technique. This kind of targeted practice ensures you build a solid foundation before moving on to more complex questions.

While practising, pay attention to common pitfalls. Are you forgetting constants of integration? Are you applying the wrong rule? Keep a log of your frequent mistakes – reviewing these can prevent you from making them again.

Build up speed and confidence

Once you’re comfortable with the individual techniques, the next step is to build up fluency. You want to be able to apply the right method quickly and accurately under exam conditions.

Start doing mixed-question sets or chapter reviews that include a variety of integration problems. The goal here is to train your brain to identify which method to use just by looking at the question.

To simulate exam conditions, time yourself. This not only helps you manage speed but also prepares you to work efficiently under pressure. If you’re taking too long on certain question types, flag them and go back for more targeted practice.

Review your work critically

Practising is not enough – you need to be deliberate about it. Once you’ve completed a set of problems, take time to review your answers carefully. Don’t just look at the final answer – look at the suggested solution and evaluate how your workings can be improved.

Ask yourself:

• Did I show my workings clearly and logically?
• Did I use the correct presentation and units, if any?
• Is there a more efficient method I could have used?
• Did I fully meet the question’s requirements, such as the significant figures required?

If you attend a tuition class with us, our JC Math tutors can also offer their expert perspective and help you identify any blind spots.

Conclusion

Integration may seem like a daunting topic, but it’s worth the effort because it carries a lot of marks in the exams. By breaking the topic down into specific techniques, practising intentionally, and reviewing your work, you can gradually build up both skill and confidence.

Don’t be discouraged by initial mistakes – they’re part of the learning process. And if you find yourself needing extra support or motivation, consider working with a IP math tutor who can guide you through tricky problems and accelerate your learning journey.

With structure, consistency, and the right mindset, you’ll be well on your way to mastering integration – and turning a once-intimidating topic into one of your strengths!

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