If you’re a Sec 3 student taking Additional Mathematics (A Math) in Singapore, you already know it’s not like lower sec math. A Math introduces abstract, multi-step topics that require deep understanding and consistent practice. And to tackle that effectively, you need a strong foundation — starting with high-quality, topic-focused A Math notes.
But not all notes are created equal. Some are missing key chapters, others skip worked examples. In this guide, we’ll show you the 10 essential topics your Sec 3 A Math notes must cover — with examples of what to look out for in each.
1. Quadratic Functions
Quadratic equations form the core of many Sec 3 A Math topics and are tested extensively in school exams and the O-Levels.
What to include in your notes:
- Standard form vs completed square form
- Graph transformations
- Finding vertex and axis of symmetry
- Discriminant and nature of roots
- Example: Sketch the graph of y = -2(x – 3)² + 5
Good notes should include both graphing skills and algebraic manipulation techniques.
2. Polynomials and Partial Fractions
This topic is important for algebra fluency, and sets the foundation for integration and binomial expansion later on.
Must-have content:
- Polynomial long division
- Remainder and factor theorems
- Decomposing proper and improper partial fractions
- Example: Express (2x² + 5x + 3)/(x + 1)(x + 2) in partial fractions
Notes should include step-by-step examples and explain when to use substitution vs comparison methods.
3. Exponential and Logarithmic Functions
One of the most misunderstood chapters in Sec 3 A Math. You’ll need well-explained notes here.
Key subtopics:
- Laws of indices and logs
- Converting between exponential and logarithmic forms
- Solving equations involving logs and exponents
- Example: Solve log₂(x + 1) = 3
Your notes should emphasize solving log equations and common exam pitfalls (e.g. undefined values).
4. Linear Law
This chapter tests your ability to convert nonlinear relationships into straight lines, and it frequently appears in school tests.
Important elements:
- Rearranging into the form y = mx + c
- Using log transformations
- Graph plotting tips
- Example: Convert y = axⁿ into a linear form and find a and n
Good notes should include graph sketching templates and marking scheme hints.
5. Coordinate Geometry
This topic mixes algebra with geometry and comes up in real-world applications.
Covered concepts should include:
- Gradient and midpoint formulas
- Equation of a straight line
- Perpendicular and parallel lines
- Example: Find the equation of the line perpendicular to 2x – y = 5 that passes through (3, 2)
Look for worked examples with diagram illustrations in your notes.
6. Trigonometric Identities and Equations
This is a big leap from lower sec trigonometry. Quality notes are critical to avoid confusion.
Topics to expect:
- Basic identities like sin²x + cos²x = 1
- Using identities to simplify expressions
- Solving trigonometric equations within a given interval
- Example: Solve 2sinx + √3 = 0 for 0° ≤ x ≤ 360°
Your notes should clearly explain ASTC rules and include examples with different trig functions and intervals.
7. Differentiation
One of the most heavily tested and foundational A Math topics — especially for Sec 4 and calculus.
Topics to cover:
- Power rule and basic differentiation
- Finding dy/dx from first principles (with h → 0)
- Tangents and normals
- Finding stationary points and determining nature (max/min)
- Example: Differentiate y = 3x³ – 5x² + 2x
Strong notes will have visual interpretations and applications to curve sketching.
8. Application of Differentiation
This is where you apply what you’ve learned in real-world problems, and where many students lose marks.
Essential elements:
- Rate of change questions
- Maximum and minimum problems
- Problem-solving strategy (draw, differentiate, interpret)
- Example: A rectangle has perimeter 40cm. Find the maximum area it can have.
Look for notes with structured problem-solving frameworks and real exam-style questions.
9. Indices and Surds
Often seen as “easy marks,” but they require strong foundational understanding.
Key content:
- Laws of indices
- Simplifying surds
- Rationalising the denominator
- Example: Simplify (3√5 – √2)(2√5 + √2)
Your notes should include common identities and highlight algebraic manipulation techniques.
10. Binomial Expansion
Often tested in algebra-heavy sections and linked with other chapters like functions or inequalities.
What good notes should cover:
- Expansion using binomial theorem
- Finding general term and specific coefficients
- Handling fractional or negative powers
- Example: Find the term containing x² in the expansion of (2 – x)⁵
Effective notes explain the pattern behind coefficients and guide students through substitutions.
How to Tell If Your A Math Notes Are Good Enough
Now that you know the 10 must-have topics, here’s a quick checklist to evaluate your current A Math notes:
- Do they follow the MOE A Math syllabus for Sec 3?
- Are there step-by-step worked examples for each topic?
- Are difficult concepts clearly explained, not just listed?
- Do they include exam-style questions and common mistake alerts?
If your notes are missing any of these, it may be time to upgrade to a set that’s designed to help you understand and apply, not just memorize.
Final Thoughts: Strong Notes = Strong Results
Your A Math notes are more than just study material — they are your personal reference guide, revision tool, and exam-prep support system. If you want to improve your grades, start by making sure your notes are complete, clear, and exam-focused.
Looking for a full set of Sec 3 A Math notes that includes everything mentioned above? Our curated notes are created by educators who know the syllabus and what schools test — with clean layout, worked examples, and bonus worksheets.