Secondary 4 Mathematics-Science Option Ministerial Examination - Québec study plan

Simplify and factor polynomial expressions, including common factors, difference of squares, and trinomials of the form ax² + bx + c

Solve first-degree equations and inequalities in one variable, and express solution sets on a number line

Solve systems of two linear equations in two variables by substitution and by elimination, and interpret the solution graphically

Translate a short word problem into an algebraic equation and verify the solution in context

Solve second-degree equations by factoring, by completing the square, and by the quadratic formula

Determine the number of real roots of a quadratic equation using the discriminant

Isolate a variable in a literal equation and in a rational equation, stating the restrictions on the variable

Solve inequalities involving a quadratic expression by using a sign table

Sketch and analyze linear functions, identifying slope, y-intercept, and the meaning of each in a context

Determine the rule of a linear function from two points, from a point and the slope, and from a graph

Model a real situation with a linear function and use the model to make a prediction

Compare two linear situations represented in different registers (table, graph, rule, text)

Determine the rule of a quadratic function in standard, factored, and vertex form, and convert between forms

Identify the vertex, axis of symmetry, zeros, and y-intercept from each form of a quadratic function

Solve an optimization problem modeled by a quadratic function and justify the maximum or minimum

Sketch a quadratic function from its rule and describe its variation (increasing and decreasing intervals)

Determine the rule of an exponential function from a table, a graph, or two points, and identify the asymptote

Distinguish growth from decay and interpret the base in a contextual problem

Graph and analyze step functions, including the greatest-integer function, and model a situation such as a parking rate

Determine the rule of a rational function of the form y = k/x and describe its asymptotes and domain

Analyze a periodic function by identifying period, amplitude, and the equation of the axis of symmetry from a graph or table

Model a periodic situation with a sinusoidal-type rule and use it to predict a value

Apply similarity and congruence criteria to prove that two triangles are similar or congruent

Use ratios of similarity to compute missing lengths, perimeters, and areas

Compute the perimeter, area, and volume of plane and solid figures, including composite figures, decomposing them into known shapes

Apply the Pythagorean theorem and trigonometric ratios (sine, cosine, tangent) to solve right-triangle problems

Compute and interpret measures of central tendency and dispersion for a data set, including mean deviation or standard deviation

Compute the probability of an event and of a complement, using equally likely outcomes and counting methods

Solve multi-step situational problems by identifying the type of function or figure involved and choosing an appropriate strategy

Write complete solutions that show the approach, the calculations, and a justified conclusion in the required format

Manage time on a full-length simulation by allocating minutes according to the weighting of the domains

Identify and correct recurring errors from earlier weeks using a personal error log