Secondary 4 Mathematics-Science Option Ministerial Examination - Québec key terms

A letter or symbol that stands for a number which can change or is not yet known. It lets you write a rule that works for many values at once, such as the x in y = 3x + 5.

The numerical factor multiplied by a variable in a term. In 7x² the coefficient is 7, and in −x it is −1. It tells how many copies of the variable part are taken.

A combination of numbers, variables and operations with no equals sign, such as 4x − 9 or (a + b)². It can be simplified, expanded or factored, but not solved.

A sum of terms in which every variable has a whole-number non-negative exponent, such as 5x³ − 2x + 1. Its degree is the largest exponent present.

The highest exponent on the variable in a polynomial, after simplification. It predicts the maximum number of solutions of the related equation and the general shape of its graph.

Rewriting a sum or polynomial as a product of simpler expressions, for example x² − 9 = (x − 3)(x + 3). It is the main tool for solving polynomial equations by the zero-product rule.

If a product of factors equals zero, then at least one factor equals zero. Solving (x − 2)(x + 5) = 0 therefore gives x = 2 or x = −5.

A statement that two expressions are equal, such as 2x + 7 = 15. Solving it means finding every value of the variable that makes the statement true.

A statement comparing two expressions with <, ≤, > or ≥, such as 3x − 4 ≤ 11. Its solution is a set of values, often shown on a number line or as an interval.

The collection of all values that satisfy an equation or inequality. For x² = 16 it is {−4, 4}; for x < 3 it is every number below 3.

The values of the variable that make an equation true, also called its solutions or zeros. Graphically they are the x-intercepts where the curve meets the horizontal axis.

Two or more equations that must be satisfied at the same time by the same variables. Its solution is the ordered pair or pairs common to all equations, found by substitution or elimination.

A solving technique in which one equation is rearranged to express a variable, and that expression replaces the variable in the other equation, leaving a single equation in one unknown.

A relation that assigns exactly one output value to each input value. Passing the vertical-line test on a graph confirms that a relation is a function.

Any set of ordered pairs linking values of two variables. A relation may or may not be a function, depending on whether an input repeats with different outputs.

The domain is the set of all allowed input values of a function; the range is the set of all outputs it actually produces. Both can be read from a graph or a rule.

An input value for which the function's output equals zero, so the graph crosses or touches the x-axis there. For f(x) = x² − 4 the zeros are 2 and −2.

The measure of a line's steepness, calculated as the change in y divided by the change in x between two points. It appears as the parameter a in y = ax + b.

How much one quantity changes per unit change of another. For a linear function it is constant and equals the slope; for other functions it varies between points.

A function whose rule can be written y = ax + b and whose graph is a straight line. The parameter a gives the slope and b gives the y-intercept.

The output value where a graph crosses the vertical axis, occurring when the input is zero. In y = ax + b it equals b, the function's starting value.

A function of the form f(x) = ax² + bx + c with a ≠ 0, whose graph is a parabola opening upward when a is positive and downward when a is negative.

The highest or lowest point of a parabola, where the function reaches its maximum or minimum value. It lies on the axis of symmetry and is read from the standard or factored form.

The vertical line through a parabola's vertex that divides the curve into two mirror-image halves. Its equation is x = −b/(2a) for f(x) = ax² + bx + c.

A function of the form f(x) = a·bˣ where the base b is positive and not 1. It models growth when b > 1 and decay when 0 < b < 1.

A function whose graph is a series of horizontal segments, staying constant over each interval and jumping at the boundaries. It models rates such as parking fees or postage.

A function defined by different rules on different parts of its domain, such as a different formula for daytime and nighttime rates. Each part is graphed on its own interval.

A function written as one polynomial divided by another, such as f(x) = 1/(x − 3). It is undefined where the denominator equals zero, producing a vertical asymptote.

A line that a curve approaches more and more closely as it extends, without necessarily touching it. Rational and exponential functions often have horizontal or vertical asymptotes.

A function that repeats the same pattern of values at regular intervals called its period. Sine, cosine and many real-world cycles such as tides are periodic.

The length of the smallest interval after which a periodic function's values repeat exactly. It is measured along the horizontal axis, in the units of the input variable.

Half the difference between the maximum and minimum values of a periodic function. It measures how far the curve swings above and below its central horizontal axis.

Figures with the same shape but not necessarily the same size, whose corresponding angles are equal and whose corresponding sides are proportional. The scale factor links their measurements.

Figures that have exactly the same shape and size, so all corresponding sides and angles are equal. One can be superimposed on the other by translations, rotations or reflections.

The ratio between a length in an image and the matching length in the original figure. Areas scale by its square and volumes by its cube.

A transformation that preserves all distances and angles, such as a translation, rotation or reflection. It always produces a figure congruent to the original.

The number of square units needed to cover a plane figure. Formulas differ by shape, and for similar figures areas compare as the square of the scale factor.

The amount of space a solid occupies, measured in cubic units. For similar solids, volumes compare as the cube of the scale factor.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c² = a² + b². It is used to find missing lengths and distances.

A ratio of two sides of a right triangle that depends on an acute angle, namely sine, cosine and tangent. It allows a missing side or angle to be calculated.

The arithmetic average of a data set, found by adding all values and dividing by how many there are. 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. Unlike the mean, it resists distortion by outliers.

A measure of how spread out data values are around the mean. A small value means values cluster near the mean; a large value means they are widely scattered.

A number from 0 to 1 expressing how likely an event is. It is calculated by dividing the number of favourable outcomes by the total number of equally likely outcomes.

A set of one or more outcomes of a random experiment, such as rolling an even number. Its probability is the sum of the probabilities of its outcomes.

Two events that together cover every possible outcome and cannot both occur. Their probabilities add to 1, so P(not A) = 1 − P(A).

A single case that shows a general statement is false. One triangle with angles not adding to 180° would disprove the claim that all triangles behave that way.

A general statement proposed as true after observing patterns, but not yet proven. It must be tested against many cases and can be destroyed by one counterexample.

Reaching a conclusion from statements already accepted as true, using definitions, properties and valid logical steps. Unlike inductive reasoning, it can establish certainty.

The length of the straight segment joining two points in the plane, computed from their coordinates with the Pythagorean theorem: √((x₂−x₁)² + (y₂−y₁)²).

A triangle containing one 90° angle. Its longest side, opposite the right angle, is the hypotenuse, and the other two sides are the legs.