BQA Grade 12 flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Rational number

A number that can be written as a fraction a/b where a and b are integers and b is not zero. Its decimal form either terminates or repeats.

Imaginary unit i

The number defined by i squared equals negative one. It allows complex numbers of the form a + bi, where a and b are real numbers.

Complex conjugate

For a complex number a + bi, the conjugate is a minus bi. Multiplying a complex number by its conjugate gives the real number a squared plus b squared.

Logarithm

The exponent to which a base must be raised to produce a given number. The equation log base b of x equals y means b to the y equals x.

Vector magnitude

The length of a vector. For vector (a, b), the magnitude equals the square root of a squared plus b squared, derived from the distance formula.

Quadratic formula

For ax squared plus bx plus c equals zero with a not zero, the solutions are x equals negative b plus or minus the square root of b squared minus four ac, all divided by two a.

Discriminant

The expression b squared minus four ac in a quadratic equation. A positive value gives two real roots, zero gives one, and a negative value gives no real roots.

Extraneous solution

A solution produced by algebraic steps that does not satisfy the original equation. It often arises when both sides are multiplied by an expression that can equal zero.

Exponential growth model

A model of the form A of t equals A zero times the quantity one plus r raised to the power t, where r is the growth rate per period and t counts periods.

Remainder theorem

When a polynomial P of x is divided by x minus k, the remainder equals P of k. The binomial is a factor exactly when P of k equals zero.

Vertical line test

A graph represents a function if and only if no vertical line intersects it more than once. Each input then has at most one output.

Inverse function

A function that reverses another function, swapping inputs and outputs. Its graph is the reflection of the original graph across the line y equals x.

Average rate of change

For a function f on the interval from a to b, it equals f of b minus f of a, divided by b minus a. It is the slope of the secant line.

Even function

A function satisfying f of negative x equals f of x for every input in its domain. Its graph is symmetric about the y-axis.

Horizontal shift

A transformation replacing x with x minus h in a function. The graph moves right by h when h is positive and left when h is negative.

Distance formula

The distance between points (x one, y one) and (x two, y two) equals the square root of the sum of the squared differences of the coordinates.

Perpendicular slopes

Two nonvertical lines are perpendicular exactly when the product of their slopes is negative one. Their slopes are negative reciprocals of each other.

Inscribed angle theorem

An angle whose vertex lies on a circle measures half the measure of its intercepted arc. A central angle intercepting the same arc measures the full arc.

Law of Sines

In any triangle, the ratio of a side length to the sine of its opposite angle is constant: a over sine A equals b over sine B equals c over sine C.

Dilation scale factor

A dilation with scale factor k multiplies all lengths by k and all areas by k squared. Angle measures remain unchanged under the transformation.

Conditional probability

The probability of event A given that event B occurred equals the probability of both events divided by the probability of B, provided B has nonzero probability.

Mutually exclusive events

Two events that cannot occur at the same time. For such events, the probability of either occurring equals the sum of their individual probabilities.

Standard deviation

A measure of how spread out values are around the mean. It is the square root of the average squared deviation from the mean.

Normal distribution rule

In a normal distribution, about 68 percent of values lie within one standard deviation of the mean, about 95 percent within two, and about 99.7 percent within three.

Correlation versus causation

A correlation shows that two variables move together, but it does not prove that one causes the other. A confounding variable may drive both.

Dimensional analysis

A method of converting units by multiplying by fractions equal to one, arranged so that unwanted units cancel and only the desired units remain.

Linear programming vertex principle

When a linear objective is optimized subject to linear constraints, the best value occurs at a vertex of the feasible region, not in its interior.

Extrapolation

Using a model to predict values outside the range of observed data. Such predictions carry more uncertainty than predictions within the observed range.

Thesis statement

A sentence, usually in the introduction, that states the central argument of a text. The rest of the text supports or develops it.

Parallel structure

A writing pattern in which items in a list or comparison share the same grammatical form, such as all verbs or all noun phrases.

Control group

In an experiment, the group that does not receive the treatment. It provides a baseline for judging the effect of the treatment.

Falsifiable hypothesis

A testable statement that could be shown false by evidence. A claim that cannot possibly be disproved is not a scientific hypothesis.