Secondary 4 Mathematics-Technical and Scientific Option Ministerial Examination - Québec study plan

Review and consolidate the properties of the main function families (polynomial, rational, exponential, logarithmic, trigonometric) by producing a one-page reference sheet for each family.

Solve 15 algebraic manipulation problems (simplifying, factoring, solving equations and inequalities) without a calculator and verify each answer.

Write a 200-word explanation of how to determine the domain of a function from its rule, using two contrasting examples.

Set up a personal error log template with columns for domain, error type, correction, and date.

Graph at least 12 functions by hand, identifying asymptotes, intercepts, and intervals of increase/decrease.

Solve 10 real-world modelling problems that require choosing an appropriate function model and justifying the choice.

Derive the inverse of five invertible functions and verify graphically.

Explain in writing how transformations (translation, scaling, reflection) affect the rule and graph of a function.

Solve 12 optimization problems that reduce to quadratic or rational functions, clearly defining variables and constraints.

Use the concept of vertex and completing the square to find optimal values in at least five contexts.

Interpret the meaning of the optimal value in the problem context and state it in a complete sentence.

Compare two solution methods (algebraic vs. graphical) for three optimization problems.

State and apply the properties of geometric transformations (translations, rotations, reflections, dilations) to figures in the Cartesian plane.

Solve 10 problems involving congruence and similarity, including proofs of triangle similarity.

Construct a concept map linking transformations, congruence, similarity, and metric relations in triangles and circles.

Write a 250-word explanation of how transformations can be used to prove geometric properties.

Apply metric and trigonometric relations in right triangles (Pythagorean theorem, sine, cosine, tangent) to solve 15 problems.

Use the sine and cosine laws to solve 10 oblique triangle problems, including the ambiguous case.

Calculate the area of triangles using multiple formulas and justify the choice.

Solve 5 problems that combine geometric transformations with trigonometric ratios.

Model 6 real-world situations (e.g., heights, distances, navigation) using trigonometric functions and solve for unknown quantities.

Graph sine and cosine functions with amplitude, period, and phase shift, and interpret these parameters in context.

Solve 8 optimization problems that involve trigonometric constraints or objectives.

Verify solutions using a second method (e.g., scale drawing or technology) for three problems.

Organize and interpret data using tables, histograms, and box plots; calculate measures of central tendency and dispersion.

Solve 12 probability problems involving independent and dependent events, conditional probability, and Venn diagrams.

Distinguish between experimental and theoretical probability and explain the law of large numbers.

Design and conduct a small simulation (e.g., using random numbers) to estimate a probability.

Complete two full-length practice exams under timed conditions, simulating the ministerial format.

Review all error log entries and re-solve each incorrect problem correctly.

Create a one-page summary sheet of key formulas and procedures for each domain.

Practice written communication by explaining solutions to three multi-step problems in clear, complete sentences.