JC Mathematics study plan

Sketch and classify the standard function families (polynomial, rational, exponential, logarithmic, trigonometric, absolute value) by hand, stating domain, range, asymptotes and key intercepts for each

Apply transformations in the correct order (vertical/horizontal stretches and reflections before translations) and write the equation of a graph from a described transformation sequence

Construct and solve modulus and inequality problems graphically, expressing solution sets in interval notation

Compute dot and cross products fluently and use them to find angles between vectors, projections, and areas of triangles and parallelograms

Write lines and planes in vector, parametric and Cartesian form and convert between the three representations

Determine intersections of lines and planes in 3D (line-line, line-plane, plane-plane) and classify each system as unique, parallel, coincident or skew with justification

Compute distances from a point to a line and to a plane using vector methods, and derive the formula rather than memorising it

Perform matrix addition, multiplication, transposition and inversion on 2x2 and 3x3 matrices, and verify inverses by multiplication

Interpret determinants geometrically as area/volume scale factors and use them to test invertibility and solve linear systems by elimination or inverse methods

Model one applied 3D problem (e.g. shortest distance between two skew pipes) end to end

Differentiate from first principles for at least three function types and state the limit definition precisely

Apply the chain, product and quotient rules to composite and implicit functions, including logarithmic differentiation for variable-base powers

Solve optimisation and related-rates problems by setting up the model, identifying the constraint, and checking endpoints and physical validity

Integrate standard forms, use substitution and integration by parts, and choose the technique deliberately by inspecting the integrand

Evaluate definite integrals and apply them to areas between curves, volumes of revolution and average values, handling regions that cross the axis correctly

Sketch curves completely using first and second derivatives: stationary points, inflection, concavity, asymptotes and behaviour at infinity

Solve separable first-order differential equations and apply them to exponential growth/decay and Newton's law of cooling with initial conditions

Set up a differential equation from a written rate description and interpret the constant of integration in context

Solve first-order linear ODEs using an integrating factor, and verify any solution by back-substitution

Use slope fields or qualitative reasoning to predict long-term behaviour without solving explicitly

Compute probabilities using conditional probability, independence tests and Bayes' theorem, drawing tree or table diagrams for every problem

Model discrete and continuous random variables, deriving means and variances from definitions and from E(X^2) - [E(X)]^2

Apply binomial, geometric, Poisson and normal distributions, including continuity corrections and normal approximation conditions

Count arrangements and selections with permutations, combinations, repetition and restriction constraints, using complementary counting where cleaner

Apply the pigeonhole principle and simple recurrence counting arguments to justify combinatorial claims

Prove statements by mathematical induction, including divisibility, inequality and summation forms, writing the base case, assumption and inductive step explicitly

Analyse arithmetic and geometric sequences and series: nth terms, sums, convergence conditions and sum to infinity

Expand binomial expressions with positive, negative and fractional indices and state validity ranges

Perform arithmetic on complex numbers in Cartesian and polar form, convert between them, and compute powers and roots using de Moivre's theorem

Interpret complex operations geometrically (rotation, scaling, loci) and solve simple polynomial equations over the complex numbers

Structure a formal proof: state assumptions, define notation, justify each step and distinguish proof by contradiction, contraposition and exhaustion

Construct and critique mathematical models, identifying simplifying assumptions and their effect on conclusions

Solve unstructured multi-step problems by decomposing them into sub-goals and recording the strategy before calculating

Interpret statistical output critically, including sampling bias, correlation versus causation and the limits of a fitted model

Practise explaining a solution aloud in under three minutes to expose gaps in reasoning

Complete two full timed mock papers under exam conditions and mark them against official-style mark schemes

Re-derive the ten formulas you most often misapply (chain rule, integration by parts, de Moivre, Bayes, induction step, integrating factor) from memory

Rework every item in your error log until each is solved correctly without notes

Build a one-page formula and strategy card limited to what you can reproduce, not copy

Simulate exam pacing: allocate minutes per mark and practise abandoning and returning to a stalled question