Ten advanced tips to achieve the highest grade in maths - Part 1 of 2
Mathematics, often regarded as one of the most challenging subjects, is also one of the most rewarding when truly mastered. In a previous two-part blog series, I shared 10 essential study tips designed to help students improve their maths performance. If you haven’t had the chance to read it yet, I highly recommend starting there — it might be exactly what you need to elevate your grade to a strong and satisfactory level.
This new series, however, is aimed at students who aspire to go above and beyond. If you’re determined to achieve top marks and excel in mathematics, this guide is tailored to help you reach that goal.
The importance of pre-class prep
Preparing for each mathematics class in advance helps you grasp concepts more effectively during lessons. By familiarising yourself with upcoming topics, you can follow explanations more easily and focus on clarifying challenging points. This proactive approach ensures class time reinforces your understanding rather than overwhelming you. In the latter case, many students adopt a passive note-taking approach, leaving the critical task of understanding and processing the material entirely to after-class study sessions.
Additionally, pre-class preparation boosts confidence and engagement. Arriving prepared allows you to participate actively, spot connections between topics, and address doubts in real-time. This habit enhances retention, sharpens problem-solving skills, and leads to better performance in exams.
Ask “Why” and “What If” questions
Mathematics is not just about memorising formulas or procedures; it’s about understanding why they work. For example, instead of simply memorising the quadratic formula, delve into its derivation. Understanding the rationale strengthens your ability to apply concepts in unfamiliar contexts, a skill often tested in advanced maths exams.
“What if” questions such as “What would happen if this number changed?” or “What if this condition was not given? Could I still solve the problem in the same way?” can lead to “aha” moments that strengthen your understanding and help you see maths as logical and interconnected.
Learn to communicate mathematically
High marks in mathematics are often awarded not just for arriving at the correct answer, but for presenting your solutions in a clear, logical, and organised manner. Think of your solution as a teaching tool: communicate your reasoning as if you were explaining it to someone else. This means using proper mathematical notation, clearly stating any assumptions, and showing each step of your process, even if the next step seems obvious. Such an approach ensures that anyone reviewing your work can follow your thought process effortlessly.
Moreover, well-structured solutions convey a deeper understanding of the material and stand out to graders. They demonstrate that you have not only solved the problem but also understood the underlying concepts. In contrast, rushed or messy answers, even when correct, may leave doubts about your comprehension. Taking the time to organise and present your work neatly can make a significant difference in earning top marks.
Use technology wisely
Mathematical tools such as graphing calculators, computer algebra systems, and apps like Desmos or Wolfram Alpha are invaluable for visualising complex problems and verifying solutions. For instance, graphing a function can provide a clearer understanding of its behaviour, offering valuable insights into calculus concepts like limits, derivatives, and integrals.
However, it’s essential to avoid over-reliance on these tools. While they can enhance your learning experience, relying too heavily on them may hinder your ability to solve problems manually. Developing the skill to work through solutions by hand ensures a deeper understanding of the underlying concepts, which is crucial for success in mathematics.
Stay curious and explore beyond the syllabus
Most students rely solely on the course book provided in their class, but exploring alternative resources can significantly deepen your understanding of mathematical concepts. For instance, encountering a definition in another textbook that presents the concept in a more intuitive way may clarify ideas that initially seemed complex in your own course book.
Additionally, mathematics becomes much more engaging and rewarding when you explore its broader applications. For example:
Learn how calculus is used in physics or economics.
Dive into number theory and its role in cryptography.
Experiment with mathematical proofs to build logical reasoning.
By going beyond the syllabus, you not only strengthen your grasp of the material but also develop the confidence to apply concepts in unfamiliar situations, a skill that distinguishes top-performing students.
By applying these five advanced strategies, you’ll develop not only the skills to excel in exams but also a genuine appreciation for mathematics as a subject. Remember, success in maths is less about talent and more about persistence, curiosity, and effective techniques. Good luck!
Continue reading: Ten advanced tips to achieve the highest grade in maths - Part 2 of 2. Subscribe to my maths newsletter at the bottom of this page and never miss an update!
