Sec 3 Math Syllabus: Complete Overview for Parents (2026)
Secondary 3 math significantly advances from fundamental concepts in lower secondary. Students will tackle harder questions involving equations, graphs, and problem-solving. Advanced topics like indices, coordinate geometry, and sine & cosine rules will also be taught.
Mastering the mathematical concepts learnt in Sec 3 will help students in both the O-Level exams and Additional Mathematics.
Sec 3 is your child’s final year to build a strong foundation before O-Levels. Our secondary math tuition teaches students to apply mathematical concepts and develop the critical thinking and logical reasoning skills required for both E-Math and A-Math success
Mastering the Sec 3 Math syllabus not only helps to strengthen your skills for A-Math, but most importantly, it builds the foundation for the O-Level exams.
Consider downloading this revision note as a PDF for printing or reading. It will be delivered to your email inbox.
✅ Key Topics Covered in Sec 3
1. Quadratic Equations
Building on Sec 2 foundations, students now learn three main solving techniques:
Completing the square
Quadratic formula
Solving fractional equations
You are also taught to sketch quadratic graphs by identifying turning points, axes intercepts, and symmetry. Word problems now often require students to model and solve quadratic inequalities.
2. Simultaneous Linear Inequalities
Students move beyond equations to systems of inequalities. They learn to:
Solve simultaneous equations
Indicate solutions on the number line
Solve related real-world word problems, such as constraints in budgeting etc.
3. Indices and Standard Form
In this topic, students explore:
Laws of indices (product, quotient, power rules)
Solving equations involving indices
Applications like compound interest
Writing large and small numbers using standard form, useful for scientific notation
4. Coordinate Geometry
Students revisit graphs, this time with more depth. They learn to:
Calculate the length of a line segment
Determine gradients, midpoints, and equations of straight lines
Apply coordinate geometry to problem-solving, especially with geometric shapes
5. Graphs of Functions
This topic introduces non-linear graphs, including:
Cubic functions
Reciprocal functions
Exponential functions
Students learn to sketch, interpret, and analyse these graphs, with an emphasis on:
Shape and symmetry
Asymptotes
Intersections
Gradient of a curve at a point (an intro to Differentiation under A-Math)
6. Further Trigonometric Functions
Trigonometry extends into more complex applications:
Sine and Cosine of obtuse angles
Area of triangle
Sine Rule and Cosine Rule for non-right-angled triangles
Real-world applications
7. Applications of Trigonometry
Students now solve 3D and angular problems involving:
Angles of elevation and depression
Finding Bearings
3-Dimensional trigonometry, applying skills in pyramids, cones, and spatial reasoning
8. Radian Measure
Students are introduced to:
Radian as an alternative angle measure
Calculating arc length and area of sectors
Applications involving composite figures
9. Congruence and Similarity
Students review:
Congruence tests (SSS, SAS, ASA, RHS)
Similarity tests (AAA, SSS, SAS)
Applying these to solve geometrical proofs and finding unknowns.
10. Area and Volume of Similar Figures and Solids
This builds upon similarity to compare:
Areas and volumes of similar figures/solids
Real-world applications in scaling models, packaging, and construction
11. Circle Properties
This topic introduces elegant geometrical reasoning through:
Symmetric properties of circles
Angle properties (e.g. angle in a semicircle, angle in same segment etc)
Solving complex circle geometry problems
Common Challenges Faced by Sec 3 Students
1. Different Law of Indices
Indices is a killer topic for many Sec 3 students as they often mix up the laws of indices (e.g., multiplying vs raising powers) and make mistakes in simplifying expressions. Questions that involve fractional or negative indices can be especially confusing without solid basics.
2. More Methods for Quadratic Equations
Many students struggle with remembering and applying different methods: completing the square, quadratic formula, and factorisation. Choosing the right method for a given question and avoiding calculation errors can be challenging.
3. Sine and Cosine Rule
Many students tend to forget the formulas or when to use the right formula.
4. Radian Measure
Because students are more used to degrees, many forget to switch their calculator to Radian mode when solving Circular questions involving radians.
5. Circle Properties
With so many different angle properties and symmetry properties under Circles, students often get confused about when to use the right property.
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