Breakdown of the O-Level Additional Mathematics syllabus (Syllabus Code 4049) into its main sections:
1. Algebra
- Quadratic Functions:
- Completing the square to find maximum/minimum values.
- Conditions for a quadratic function to always be positive or negative.
- Using quadratic functions for modeling.
- Equations and Inequalities:
- Solving quadratic equations and inequalities.
- Analyzing conditions for intersections and tangents between lines and curves.
- Representing solutions on a number line.
- Surds:
- Operations on surds, including rationalization.
- Solving equations involving surds.
- Polynomials and Partial Fractions:
- Factor and remainder theorems for solving polynomial equations.
- Partial fractions for specific types of denominators.
- Binomial Expansion:
- Expanding binomials using the binomial theorem for positive integer powers.
- Exponential and Logarithmic Functions:
- Properties and laws of exponents and logarithms.
- Solving equations and using these functions for modeling.
2. Geometry and Trigonometry
- Trigonometric Functions, Identities, and Equations:
- Trigonometric functions for angles of any magnitude (degrees or radians).
- Graphs of trigonometric functions.
- Trigonometric identities and their simplifications.
- Solving trigonometric equations within specified intervals.
- Using trigonometric models for real-world problems.
- Coordinate Geometry in Two Dimensions:
- Conditions for lines to be parallel or perpendicular.
- Midpoints, areas of rectilinear figures, and equations of circles.
- Transforming relationships to linear forms for graph interpretation.
- Proofs in Plane Geometry:
- Properties of parallel lines, triangles, quadrilaterals, and circles.
- Congruent and similar triangles.
- Tangent-chord and midpoint theorems.
3. Calculus
- Differentiation:
- Derivatives as gradients and rates of change.
- Rules for differentiating functions, including products, quotients, and compositions.
- Applications to tangents, normals, and optimization problems.
- Using second derivatives to identify maxima, minima, and inflection points.
- Integration:
- Integration as the reverse process of differentiation.
- Definite integrals for areas under curves.
- Applications to displacement, velocity, and acceleration problems in straight-line motion.
4. Additional Assessment Notes
- The syllabus emphasizes reasoning, problem-solving, and the application of mathematical models.
- Use of calculators is allowed, and candidates are expected to provide accurate solutions with appropriate working.
- The syllabus prepares students for further studies in mathematics, particularly A-Level H2 Mathematics.