Singapore · MOE Syllabus Outcomes
JC 2 Mathematics
This course prepares students for university level STEM studies by integrating complex calculus, vector geometry, and statistical modeling. Students develop rigorous logical reasoning and the ability to apply abstract mathematical structures to solve sophisticated real world problems.
The Geometry of Space: Vectors
Exploration of three dimensional space using vector algebra and the geometric relationships between points, lines, and planes.
Understanding the geometric significance of dot and cross products in determining orthogonality and area.
Defining positions and orientations of geometric objects using vector equations.
Calculating the shortest distances and points of intersection between complex geometric entities.
Complex Systems: Complex Numbers
Extending the number system to include imaginary components and exploring their algebraic and geometric representations.
Mastering operations in the complex plane and the properties of complex conjugates.
Representing complex numbers using modulus and argument for efficient multiplication and division.
Using complex numbers to describe paths and regions in a two dimensional coordinate system.
Advanced Calculus: Integration Techniques
Developing sophisticated integration strategies to solve area, volume, and differential problems.
Applying advanced methods to integrate products and composite functions.
Using integration to find areas between curves and volumes of revolution.
Solving first order differential equations and modeling real world rate changes.
Discrete Structures: Sequences and Series
Analyzing patterns, sums of progressions, and the behavior of infinite series.
Exploring the properties of sequences with constant differences or ratios.
Techniques for finding the sum of various series using algebraic manipulation.
Approximating complex functions using power series expansions.
Probability and Discrete Distributions
Quantifying uncertainty and modeling discrete random variables in various scenarios.
Using permutations, combinations, and conditional probability to solve complex counting problems.
Modeling scenarios with a fixed number of independent trials and two possible outcomes.
Modeling the number of events occurring within a fixed interval of time or space.
Statistical Inference and Modeling
Drawing conclusions about populations from sample data using normal distributions and hypothesis testing.
Understanding the properties of the bell curve and its role in the Central Limit Theorem.
Making decisions about population parameters based on sample evidence and significance levels.
Analyzing the strength of relationships between variables and predicting outcomes.