JC Mathematics study guide
JC Mathematics · Work through your exam, one topic at a time.
JC Mathematics (often called Junior College Mathematics or JC Math) is a pre-university level mathematics credential taken by students completing the junior college stage of schooling, typically as preparation for university admission in quantitative fields. It is intended for candidates who have already mastered secondary-school algebra and who are ready to work with rigour: formal proof, multi-step modelling, and problems that combine several topics in a single item. The JC Mathematics study guide has 11 sections and about 2,108 words.
01Functions, Graphs and Transformations
The Functions, Graphs and Transformations domain tests whether you can describe a function as a rule, a graph and a mapping, and move fluently between these views. Expect domain and range restrictions, inverse and composite functions, modulus and reciprocal graphs, and transformations of standard curves.
236 words, about 1 min02Sequences, Series and Mathematical Induction
Sequences, Series and Mathematical Induction tests recognition and manipulation of arithmetic and geometric progressions, telescoping sums, and formal induction. You must justify convergence and structure induction clearly.
209 words, about 1 min03Vectors and Three-Dimensional Geometry
Vectors and Three-Dimensional Geometry tests algebra with vectors, lines and planes, and geometric reasoning in 3D. Expect dot and cross products, angles, intersections, distances and skew lines.
208 words, about 1 min04Complex Numbers
Complex Numbers tests algebraic, geometric and polar forms. You need fluency with conjugates, modulus-argument form, De Moivre’s theorem, loci and polynomial roots.
192 words, under 1 min05Calculus: Differentiation and Applications
Calculus: Differentiation and Applications tests derivative techniques and their use in curve analysis, optimisation, rates and approximations. Expect chain, product, quotient, implicit and parametric differentiation.
176 words, under 1 min06Calculus: Integration and Applications
Calculus: Integration and Applications tests antiderivatives, definite integrals, areas and volumes. You must choose an effective method and track limits and signs.
179 words, under 1 min07Differential Equations
Differential Equations tests formation, solution and interpretation of first-order models. Expect separable equations, linear first-order equations with integrating factors, and applied growth, decay or cooling models.
169 words, under 1 min08Probability and Statistics
Probability and Statistics tests probability rules, distributions and statistical inference. Expect conditional probability, independence, binomial and Poisson models, normal approximation, sampling and hypothesis tests.
179 words, under 1 min09Discrete Mathematics and Combinatorics
Discrete Mathematics and Combinatorics tests counting, arrangements, selections and recurrence-style reasoning. Expect permutations with restrictions, combinations, inclusion-exclusion and pigeonhole arguments.
186 words, under 1 min10Matrices and Linear Algebra
Matrices and Linear Algebra tests matrix arithmetic, determinants, inverses and solving linear systems, with geometric interpretations of transformations. Addition and multiplication require compatible orders; AB≠BA generally.
166 words, under 1 min11Problem Solving, Modelling and Proof
Problem Solving, Modelling and Proof tests how you construct arguments, choose representations and validate models. Expect direct proof, contradiction, contrapositive, induction, counterexamples, and modelling cycles with assumptions.
208 words, about 1 min