European Baccalaureate Mathematics (5-period course) study plan

Classify and manipulate algebraic expressions (polynomials, rational expressions, surds, exponentials, logarithms) without errors.

Solve equations and inequalities (linear, quadratic, rational, exponential, logarithmic, absolute value) and express solution sets correctly.

Compute limits of algebraic, exponential, and logarithmic functions using algebraic manipulation and standard limit laws.

Identify and apply the conditions for continuity and differentiability at a point.

Differentiate polynomial, rational, exponential, logarithmic, and composite functions using product, quotient, and chain rules.

Differentiate trigonometric and inverse trigonometric functions and apply implicit differentiation.

Solve optimisation and related-rates problems by setting up and differentiating appropriate functions.

Determine equations of tangent and normal lines and analyse monotonicity and concavity via first and second derivatives.

Compute indefinite integrals using standard forms, substitution, and integration by parts.

Evaluate definite integrals and apply the Fundamental Theorem of Calculus.

Calculate areas between curves and volumes of revolution about the x-axis.

Solve separable first-order differential equations and interpret the constant of integration.

Sketch graphs of polynomial, rational, exponential, logarithmic, and trigonometric functions, identifying domain, range, intercepts, asymptotes, and symmetry.

Determine inverse functions and their graphs, including domain restrictions.

Transform graphs (translations, reflections, stretches) and relate transformations to function notation.

Solve equations and inequalities graphically and interpret intersection points.

Perform vector operations (addition, scalar multiplication, dot product) in 2D and 3D and interpret them geometrically.

Solve problems involving lines and planes in space using vector and Cartesian equations.

Apply trigonometric identities (Pythagorean, sum/difference, double-angle) to simplify expressions and solve equations.

Solve triangles using the sine and cosine rules and compute areas of triangles.

Compute probabilities using conditional probability, independence, and Bayes' theorem.

Calculate and interpret measures of centre and spread, and analyse discrete probability distributions (binomial, normal approximation).

Work with arithmetic and geometric sequences and series, including sums to infinity.

Apply the binomial theorem and solve counting problems using permutations and combinations.

Complete a full-length timed mock exam under official conditions.

Identify and categorise errors by domain and error type (conceptual, procedural, careless).

Re-teach weak topics using targeted exercises and correct all mock exam mistakes.

Improve time management by practising section timing.

Review weak topics identified in week 7 through focused practice and summary sheets.

Complete a second full-length mock exam and compare performance.

Consolidate all formula sheets into a single reference document.

Practise exam strategy (question selection, checking, calculator use) under timed conditions.