BQA Grade 12 key terms

A number that can be written as a fraction of two integers, with a nonzero denominator. Its decimal form either stops or repeats a fixed block of digits forever.

A real number that cannot be expressed as a fraction of two integers. Its decimal expansion never ends and never settles into a repeating pattern, such as the square root of two.

A straight line where every point matches exactly one real number, ordered by position. Distance along the line measures absolute value and supports inequalities and intervals.

The distance of a number from zero on the number line, always nonnegative. It removes any sign, so the absolute value of negative seven equals seven.

A number written as a real part plus a real multiple of the imaginary unit i. It extends the real numbers so that every polynomial equation has a solution.

The symbol i, defined so that its square equals negative one. Powers of i cycle through four values, which simplifies many algebraic computations.

A way of writing numbers as a coefficient between one and ten multiplied by a power of ten. It makes very large or very small quantities easier to compare and compute.

A rough scale of size expressed as the nearest power of ten. Comparing orders of magnitude shows how many times larger one quantity is than another.

A quantity with both magnitude and direction, often drawn as an arrow. Vectors can be added, subtracted, and scaled, and they model forces, velocity, and displacement.

A measurement described by size alone, with no direction attached. Mass, temperature, and elapsed time are familiar examples used alongside vectors.

The single vector that produces the same overall effect as two or more vectors combined. It is found by adding components or by placing arrows head to tail.

An expression formed by adding terms that are constants or products of a constant and whole-number powers of a variable. Its degree is the highest power present.

A statement that a polynomial has a factor of x minus c exactly when substituting c gives zero. It links division, remainders, and roots of equations.

A function whose rule is a polynomial of degree two, graphed as a parabola. Its vertex, axis of symmetry, and intercepts describe the shape and its real solutions.

The part of the quadratic formula under the square root, computed as b squared minus four ac. Its sign reveals whether a quadratic has two, one, or no real solutions.

The turning point of a parabola where it reaches its maximum or minimum value. Its coordinates appear directly in the vertex form of a quadratic equation.

A line that divides a figure into two mirror-image halves. For a parabola, it passes through the vertex and is vertical when the parabola opens up or down.

A rule that assigns exactly one output to each allowed input. The set of allowed inputs is the domain, and the resulting outputs form the range.

The domain is the full set of inputs for which a function is defined; the range is the set of outputs it actually produces. Both can be described with inequalities or interval notation.

A function that reverses another function's effect, so applying both returns the original input. It exists only when each output comes from exactly one input.

Shifts, stretches, compressions, and reflections that change a parent graph's position or shape. Each change corresponds to a specific alteration of the function's rule.

Change in which a quantity is multiplied by a constant factor over equal intervals. Growth factors exceed one; decay factors lie between zero and one.

The exponent to which a base must be raised to produce a given number. Logarithms reverse exponential rules and turn multiplication into addition.

A line that a graph approaches ever more closely without necessarily touching. Rational and exponential functions commonly show vertical or horizontal asymptotes.

An input value that makes the function's output equal zero. Zeros correspond to x-intercepts of a graph and to solutions of the associated equation.

Two or more equations that must be satisfied at the same time by shared variables. Solutions are the points or values that satisfy every equation simultaneously.

A statement comparing two expressions with symbols such as less than or at least. Its solution is a range of values rather than a single number.

A method for finding the best value of a linear objective subject to linear constraints. The optimum typically occurs at a corner of the feasible region.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It underlies distance formulas and many measurement problems.

A ratio comparing two sides of a right triangle, such as sine, cosine, or tangent. These ratios connect angle measures with side lengths and extend to all angles.

An angle measure defined by the arc length it cuts on a circle of radius one. A full turn equals two pi radians, linking angles to arc and sector formulas.

The distance along a circle's edge between two points, and the area of the pie-shaped region bounded by two radii and that arc. Both scale with the central angle.

Shapes with identical angles whose corresponding side lengths share a constant ratio. Areas of similar figures compare as the square of that ratio.

The constant multiplier relating corresponding lengths in two similar figures or a scale drawing. It converts measurements between a model and the real object.

The mean is the sum of values divided by their count; the median is the middle value when data are ordered. The median resists extreme values more than the mean does.

A measure of how far data values typically spread from their mean. A larger value indicates more variability within the data set.

A data value that lies far from the rest of the observations. Outliers can strongly affect the mean and should prompt a check of the data source.

A symmetric, bell-shaped pattern of data centered on the mean. Fixed percentages of values fall within one, two, and three standard deviations of that mean.

A numerical measure of how strongly two variables move together in a linear pattern. Correlation does not by itself establish that one variable causes the other.

A straight line drawn through a scatterplot to summarize the overall trend. It supports predictions, which are most reliable near the middle of the observed data.

Using a model to predict values outside the range of the observed data. Such predictions are riskier because the pattern may not continue beyond that range.

A value added to and subtracted from a sample estimate to form an interval likely to contain the true population value. Larger samples generally shrink it.

A flaw in how a sample is chosen that makes it unrepresentative of the population. Random selection is the main safeguard against this problem.

Solving problems by recognizing that two quantities change at a constant ratio. It supports unit conversion, scaling, and rate comparisons across many contexts.

The time required for a decaying quantity to fall to half its starting amount. Repeated halving produces an exponential decay model with a constant multiplier per interval.

The digits in a measurement that carry meaningful information about its precision. They govern how a computed result should be rounded and reported.

A standard for comparison in an investigation that is treated the same as the experimental group except for the variable being tested. It helps isolate cause and effect.

The independent variable is the factor deliberately changed or selected; the dependent variable is the measured response. Clear identification guides both experimental design and graph reading.

A structure for written scientific arguments that states a position, presents supporting data, and explains why the data justify the position. It is common in constructed responses.

The trustworthiness of information based on the author's expertise, the publisher, and the evidence offered. Evaluating it is essential when reading informational passages.

The main point a passage develops and supports throughout. Identifying it requires distinguishing key information from illustrative details and examples.