Summary of the O-Level Mathematics syllabus (Syllabus Code 4052), broken down into sections and suggested levels of study:
1. Number and Algebra
- Numbers and Their Operations (Sec 1):
- Prime factorization, HCF, LCM, indices, and standard form.
- Ordering numbers on a number line and approximation.
- Ratio, Proportion, and Percentage (Sec 1):
- Simplifying ratios, map scales, direct/inverse proportions, and percentage calculations.
- Rate and Speed (Sec 1):
- Concepts of average speed and unit conversion.
- Algebraic Expressions and Formulae (Sec 1 & Sec 2):
- Simplification, factorization, expansion, and algebraic fractions.
- Changing the subject of a formula and finding nth terms in patterns.
- Functions and Graphs (Sec 2 & Sec 3):
- Linear and quadratic functions, graph plotting, and properties of curves.
- Equations and Inequalities (Sec 2 & Sec 3):
- Solving linear, quadratic, and fractional equations.
- Formulating and solving real-world problems.
- Set Language and Notation (Sec 3):
- Venn diagrams, union/intersection, and complement of sets.
- Matrices (Sec 4):
- Basic matrix operations, scalar multiplication, and interpreting data.
2. Geometry and Measurement
- Angles, Triangles, and Polygons (Sec 1 & Sec 2):
- Properties of angles, parallel lines, polygons, and constructions.
- Congruence and Similarity (Sec 2 & Sec 3):
- Similar triangles, scale drawings, and ratios of areas and volumes.
- Properties of Circles (Sec 3):
- Tangent properties, angle properties in circles, and equal chords.
- Pythagoras’ Theorem and Trigonometry (Sec 2 & Sec 3):
- Applications of Pythagoras’ theorem and trigonometric ratios.
- Sine and cosine rules, and solving 2D/3D problems involving angles.
- Mensuration (Sec 1 to Sec 4):
- Calculating areas, perimeters, volumes, and surface areas of various shapes.
- Sector areas and arc lengths (including radian measure).
- Coordinate Geometry (Sec 2 & Sec 3):
- Gradient, length of a line segment, and equations of straight lines.
- Vectors in Two Dimensions ( Sec 4):
- Operations with vectors, position vectors, and geometric applications.
3. Statistics and Probability
- Data Handling and Analysis (Sec 1 to Sec 4):
- Collecting, representing, and interpreting data through various graphs.
- Measures of central tendency (mean, median, mode) and spread (range, standard deviation).
- Probability (Sec 1 & Sec 4):
- Probability of single and combined events, including tree diagrams and addition/multiplication rules.
Suggested Progression
- Sec 1: Foundational topics like numbers, algebra basics, and simple geometry.
- Sec 2: Intermediate algebra, trigonometry basics, and expanded geometry concepts.
- Sec 3: Advanced algebra, trigonometry, coordinate geometry, and probability/statistics introduction.
- Sec 4: Consolidation of complex topics (e.g., vectors, matrices, probability, advanced trigonometry).