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.
01Functions: Domain, Codomain, and Range
Students explore the properties of various functions and their transformations to model physical phenomena.
Students will understand functions as rules that assign a unique output to each input, using tables, graphs, and simple equations.
Students will sketch graphs of linear and quadratic functions, identifying key features like intercepts and turning points.
Students will apply vertical and horizontal translations to quadratic graphs and sketch the resulting graphs.
Students will apply reflections across the x-axis to quadratic graphs and sketch the resulting graphs.
02Equations and Inequalities
Mastering the manipulation of complex algebraic expressions and the logic of solving systems of equations.
Students will solve systems of two linear equations using substitution, elimination, and graphical methods.
Students will solve linear inequalities and represent solutions on a number line and in interval notation.
Students will solve quadratic inequalities using graphical methods and sign diagrams.
Students will define the modulus function and evaluate expressions involving absolute values.
Students will solve equations involving modulus functions algebraically and graphically.
Students will solve inequalities involving modulus functions using algebraic and graphical techniques.
03Sequences and Series
Investigating patterns of numbers and the conditions under which an infinite sum converges.
Students will identify and describe simple number patterns and sequences, finding the next few terms.
Students will derive and apply formulas for the nth term and sum of the first n terms of an AP.
Students will derive and apply formulas for the nth term and sum of the first n terms of a GP.
Students will understand the conditions for convergence and calculate the sum to infinity of a geometric series.
04Differential Calculus
Exploring the concept of rates of change and their applications in optimization and approximation.
Students will apply basic differentiation rules to find derivatives of polynomial functions.
Students will find equations of tangents and normals to curves at given points.
Students will solve problems involving related rates of change in various contexts.
Students will find stationary points and determine their nature (maxima, minima, points of inflexion) using first and second derivative tests.
Students will apply differentiation to solve optimization problems in various real-world contexts.
05Integral Calculus
Mastering the process of accumulation and the fundamental relationship between differentiation and integration.
Students will integrate polynomial functions and use standard integral forms for common functions.
Students will calculate the area bounded by a curve and the x-axis or y-axis.
06Vectors in Three Dimensions
Applying vector algebra to represent points, lines, and planes in 3D space.
Students will define vectors as quantities with magnitude and direction, and represent them graphically and as column vectors in 2D.
Students will perform addition and subtraction of 2D vectors graphically (triangle/parallelogram rule) and algebraically.
Students will multiply 2D vectors by a scalar and understand the effect on magnitude and direction.