Secondary 4 Mathematics-Technical and Scientific Option Ministerial Examination - Québec key terms

A relation that assigns exactly one output value to each input value from a defined set. It can be described by a rule, a table, a graph, or an equation.

The set of all input values for which a function is defined. It excludes values that cause division by zero or a negative expression under an even root.

The set of all output values a function actually produces as the input varies over its domain. It is read from the vertical spread of the graph.

An input value for which the function equals zero. On a graph these are the x-intercepts, found by solving f(x) = 0.

The measure of a line's steepness, computed as the change in y divided by the change in x between two points. It gives the constant rate of change of a linear function.

The point where a graph crosses the vertical axis, occurring where the input equals zero. For a linear function it equals the initial value of the situation.

A function whose graph is a straight line, written in the form y = ax + b. Its rate of change is constant and its rule can be built from two points.

How much the output changes for each unit increase in the input. For a linear function it is constant; for other functions it is computed over an interval.

A function of the form f(x) = ax² + bx + c with a not zero, whose graph is a parabola. Its vertex gives the maximum or minimum value.

The U-shaped curve that is the graph of a quadratic function. It opens upward when the leading coefficient is positive and downward when it is negative.

The highest or lowest point of a parabola, located on its axis of symmetry. It represents the optimal value in many optimization problems.

The vertical line through the vertex that divides a parabola into two mirror-image halves. Its equation is x = −b/(2a) for a quadratic in standard form.

A formula giving the solutions of ax² + bx + c = 0: x equals negative b plus or minus the square root of b² − 4ac, all divided by 2a.

The expression b² − 4ac under the square root in the quadratic formula. Its sign tells whether the equation has two, one, or no real solutions.

Rewriting an algebraic expression as a product of simpler factors. It is used to solve polynomial equations by setting each factor equal to zero.

A function of the form f(x) = a·bˣ where the base b is positive and not equal to one. It models growth or decay at a constant percentage rate.

The multiplier applied to a quantity in each period of an exponential model. A value above one means growth; a value between zero and one means decay.

A function whose graph consists of horizontal segments, staying constant over each interval and jumping at the boundaries. It models rates that change in brackets, such as tiered pricing.

A function defined by different rules on different parts of its domain. Each rule applies only to a stated interval of input values.

The function that reverses another function, sending each output back to its original input. Its graph is the reflection of the original graph in the line y = x.

Two or more equations that must be satisfied at the same time. Its solution is the set of values making every equation true, found graphically or algebraically.

A statement comparing two expressions with symbols such as less than, greater than, or not equal. Its solution is a set of values, often shown as an interval or shaded region.

Figures with the same shape but not necessarily the same size, whose corresponding angles are equal and corresponding sides are proportional. The ratio of similarity links all their lengths.

The ratio between a length in an image and the corresponding length in the original figure. It determines how all lengths, areas, and volumes change under a similarity transformation.

A geometric transformation that enlarges or reduces a figure about a fixed centre by a given scale factor. Angles stay unchanged while lengths are multiplied by that factor.

A transformation that slides every point of a figure the same distance in the same direction. It preserves shape, size, and orientation.

A transformation that turns a figure about a fixed centre point through a given angle and direction. Distances from the centre are preserved.

A transformation that flips a figure across a line, producing a mirror image. The line of reflection is the perpendicular bisector of each segment joining a point to its image.

A transformation that preserves all distances and angles, so the image is congruent to the original. Translations, rotations, and reflections are isometries.

A relationship in which two quantities vary so that their ratio stays constant. It is used to find unknown lengths in similar figures and in scale drawings.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It is used to find missing lengths and distances.

A ratio of two side lengths in a right triangle, named sine, cosine, or tangent depending on which sides are compared. It links an acute angle to side lengths.

A triangle containing one angle of 90 degrees, whose longest side is the hypotenuse. It underlies the trigonometric ratios and the Pythagorean theorem.

A relationship stating that each side of a triangle divided by the sine of its opposite angle is constant. It solves triangles when an angle and its opposite side are known.

A generalized Pythagorean relationship: the square of one side equals the sum of the squares of the other two minus twice their product times the cosine of the included angle.

A unit for measuring angles based on arc length: one radian subtends an arc equal in length to the radius. A full turn equals 2π radians.

The distance measured along a curved portion of a circle. It equals the radius multiplied by the central angle measured in radians.

The arithmetic average of a data set, found by adding all values and dividing by their number. It is sensitive to extreme values.

The middle value of an ordered data set, or the average of the two middle values when the count is even. It is resistant to extreme values.

A measure of how spread out values are around the mean, equal to the square root of the variance. A small value means values cluster near the mean.

A value splitting ordered data into four groups of roughly equal size. The first, second, and third quartiles mark the 25th, 50th, and 75th percentiles.

A diagram showing the minimum, first quartile, median, third quartile, and maximum of a data set. It displays spread and skewness at a glance.

A symmetric bell-shaped distribution of continuous data, described by its mean and standard deviation. Roughly 68 percent of values lie within one standard deviation of the mean.

A number between −1 and 1 measuring the strength and direction of a linear relationship between two variables. A value near zero indicates a weak linear link.

The line of best fit through a scatter plot, used to model a linear trend and make predictions. The correlation coefficient describes how well it fits.

A graph plotting paired data as points on a coordinate plane. It reveals the form, direction, and strength of a relationship between two variables.

A number between 0 and 1 expressing how likely an event is. It equals the number of favourable outcomes divided by the number of equally likely outcomes.

The probability that an event occurs given that another event has already occurred. It restricts the sample space to the outcomes satisfying the given condition.

Events whose outcomes do not affect each other's likelihood. Their combined probability equals the product of their individual probabilities.

Events that cannot occur at the same time, so their intersection is empty. Their combined probability is the sum of their individual probabilities.

The process of finding the input giving the greatest or least value of a quantity under given constraints. It often uses the vertex of a parabola or a system of inequalities.

A restriction on the possible values of the variables in a model, often written as an inequality. Constraints define the feasible region of an optimization problem.

The set of all points satisfying every constraint of an optimization problem. The optimal solution of a linear model occurs at a vertex of this region.

The quantity to be maximized or minimized in an optimization problem, expressed as a function of the variables. It is evaluated over the feasible region.

A mathematical representation of a real situation, using functions, equations, or graphs to describe relationships and support predictions. Its validity is limited to the context it was built for.

Checking whether a model fits the real data and whether its predictions are reasonable. It may involve comparing predicted values with observations or examining the correlation.

A statement believed to be true based on observed patterns but not yet proven. In reasoning tasks it must be supported by examples or a deductive argument.

A single case that shows a general statement to be false. Finding one is enough to disprove a conjecture.

A logical chain of justified steps showing that a statement must be true. Each step relies on definitions, known properties, or previously established results.

A sequence in which each term is obtained by multiplying the previous term by a fixed number. It connects to exponential growth and decay models.