2026 O Level Additional Mathematics Syllabus
Singapore-Cambridge O Level Additional Mathematics (4049)
Access the official examination syllabus, learning objectives, and assessment structure.
View / Download SyllabusAdditional Mathematics · Syllabus 4049 · Jurong West
O Level A-Math Tuition in Jurong West
Build strong mathematical foundations, master problem-solving techniques, and gain confidence in O Level Additional Mathematics.
Meet Your A-Math Tutor
Peng Rong
Teacher Peng Rong focuses on helping students understand mathematical concepts, recognise question patterns and develop the confidence to solve problems independently.
A-Math Resources & Downloads
A-Math Formula List
A consolidated reference of key formulae for revision and exam preparation.
View / Download Formula List2026 O Level A-Math Paper 1 & 2 with Solutions
Paper 1, Paper 2 and worked solutions for revision. Separate downloads will be provided when available.
Coming SoonExplore the O Level A-Math Syllabus
Topics follow the official Additional Mathematics syllabus (4049, 2026). Learning objectives below are paraphrased for revision—refer to the official syllabus PDF for the complete list.
Quadratic functions
Parabolas, completing the square, and using discriminants to analyse roots and graphs.
Key learning objectives
- Identify the graph of y = ax² + bx + c and its key features (vertex, axis of symmetry, intercepts).
- Complete the square to convert quadratic expressions to vertex form.
- Use the discriminant to determine the nature of roots of a quadratic equation.
- Form and solve quadratic equations and inequalities arising from problems.
- Apply the relationship between roots and coefficients where required.
Equations and inequalities
Simultaneous equations, linear and quadratic inequalities, and algebraic methods for solving systems.
Key learning objectives
- Solve simultaneous linear equations in two unknowns algebraically and graphically.
- Solve simultaneous equations involving one linear and one quadratic equation.
- Solve linear inequalities and represent solution sets on a number line.
- Solve quadratic inequalities using graphs or sign analysis.
- Form equations from word problems and interpret solutions in context.
Surds
Simplifying surds, rationalising denominators, and operating with irrational roots.
Key learning objectives
- Simplify surds and express answers in simplest surd form.
- Add, subtract and multiply surds where appropriate.
- Rationalise denominators involving surds.
- Solve equations involving surds and check for extraneous solutions.
- Apply surds in exact length and area calculations.
Polynomials and partial fractions
Polynomial division, factor and remainder theorems, and decomposing rational expressions.
Key learning objectives
- Perform division of polynomials and interpret remainder.
- Apply the factor and remainder theorems to factorise polynomials.
- Solve cubic equations where one factor is known or found.
- Resolve proper rational expressions into partial fractions for distinct and repeated linear factors.
- Use partial fractions to simplify integration problems later in the course.
Binomial expansions
General term in binomial expansion and approximations using the first few terms.
Key learning objectives
- Use (a + b)ⁿ for positive integer n and find specific terms.
- Find the general term in a binomial expansion using nCr notation.
- Use expansions for simplification and approximate numerical values when appropriate.
- Apply binomial coefficients in counting arguments at syllabus depth.
- Check validity of approximations by considering the size of neglected terms qualitatively.
Exponential and logarithmic functions
Laws of indices and logarithms, exponential and logarithmic graphs, and solving equations.
Key learning objectives
- Sketch and interpret graphs of exponential and logarithmic functions.
- Apply laws of indices and logarithms to simplify expressions.
- Solve equations involving exponential and logarithmic terms.
- Use change of base where needed for numerical work.
- Model growth and decay problems using exponential functions.
Trigonometric functions, identities and equations
Radians, graphs of trig functions, identities, and solving trigonometric equations.
Key learning objectives
- Use radians and convert between degrees and radians.
- Sketch graphs of sin, cos and tan over specified intervals.
- Prove and apply standard trigonometric identities.
- Solve trigonometric equations in a given interval.
- Apply addition and double-angle formulae where required.
Coordinate geometry in two dimensions
Straight lines, circles, and coordinate proofs using gradients and distances.
Key learning objectives
- Find the equation of a straight line given points, gradient or parallel/perpendicular conditions.
- Determine the intersection of lines and interpret geometrically.
- Use the equation of a circle in standard and general form.
- Find tangents and normals to circles where required.
- Apply coordinate geometry to prove simple geometric results.
Proofs in plane geometry
Logical deduction using properties of triangles, circles, and parallel lines.
Key learning objectives
- Use properties of angles, triangles and parallel lines in deductive proofs.
- Apply congruence and similarity in geometric arguments.
- Use circle theorems (syllabus set) to justify steps in proofs.
- Present proofs clearly with stated reasons for each step.
- Combine coordinate and pure geometry methods when helpful.
Differentiation
First principles, standard derivatives, chain/product/quotient rules, and applications to gradients and rates.
Key learning objectives
- Differentiate xⁿ for rational n and simple combinations of functions.
- Apply product, quotient and chain rules to composite functions.
- Find equations of tangents and normals to curves.
- Locate and classify stationary points using the second derivative or gradient tests.
- Solve problems involving connected rates of change and optimisation.
Integration and applications
Indefinite and definite integrals, area under curves, and kinematics applications.
Key learning objectives
- Integrate standard forms and simple combinations of functions.
- Evaluate definite integrals and interpret as area under a curve.
- Find the area between curves where required.
- Apply integration to kinematics problems linking displacement, velocity and acceleration.
- Use given substitutions or partial fractions from earlier topics when integrating rational expressions.
Our 4-Step A-Math Mastery Journey
Understand the concept. Watch it in action. Try it yourself. Make it stick.
Break each chapter into manageable concepts. Teacher Peng Rong explains the underlying Mathematics, important formulas and reasoning behind each method before moving forward.
Tuition Fees
Secondary 3
$280/month
$35/hour
Secondary 4
$320/month
$40/hour
Monthly fees are calculated based on 4 lessons per month, with each lesson lasting 2 hours (8 hours total).
Frequently Asked Questions
Who are the A-Math classes for?
Our O Level A-Math tuition classes are designed for Secondary 3 and Secondary 4 students.
Where and when are the classes held?
Our classes are held at Tuition @ Pioneer, located just a 2-minute walk from Pioneer MRT. For specific class schedules and availability, please WhatsApp Teacher Peng Rong at 9650 8879.
How are A-Math lessons conducted?
Lessons are structured around understanding one mathematical concept at a time. Students first learn the concept, watch a guided worked example, attempt questions independently, and reinforce their understanding through homework.
Ready to Build Confidence in A-Math?
Strengthen your mathematical foundations, master problem-solving methods, and prepare confidently for your O Level Additional Mathematics examinations.
Small-group classes near Pioneer MRT, Jurong West.
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