Singapore · MOE Syllabus Outcomes
JC 1 Mathematics
This course bridges secondary mathematics to university-level thinking by emphasizing rigorous proof and abstract modeling. It focuses on developing logical precision and the ability to apply complex functions to real-world scenarios.
Functions and Graphs
Students explore the properties of various functions and their transformations to model physical phenomena.
Understanding the concepts of domain, range, and the conditions for the existence of composite and inverse functions.
Applying translations, reflections, and stretches to parent functions and sketching complex rational functions.
Equations and Inequalities
Mastering the manipulation of complex algebraic expressions and the logic of solving systems of equations.
Solving systems of linear equations in three variables using substitution and elimination methods.
Solving non-linear inequalities and equations involving absolute value signs.
Sequences and Series
Investigating patterns of numbers and the conditions under which an infinite sum converges.
Developing formulas for the nth term and the sum of the first n terms of APs and GPs.
Using the method of differences to find the sum of series and understanding convergence.
Differential Calculus
Exploring the concept of rates of change and their applications in optimization and approximation.
Extending differentiation to include product, quotient, and chain rules for transcendental functions.
Using derivatives to solve problems involving tangents, normals, and optimization in various contexts.
Integral Calculus
Mastering the process of accumulation and the fundamental relationship between differentiation and integration.
Learning integration by substitution and using the standard forms of integrals.
Calculating the area under a curve and the volume of revolution for complex shapes.
Vectors in Three Dimensions
Applying vector algebra to represent points, lines, and planes in 3D space.
Understanding displacement vectors and the use of the scalar product to find angles.
Formulating vector equations for lines and planes and finding points of intersection.