Algebra 2 – Glossary | Open Up HS Math (CCSS), Family

A–F

amplitude

The height from the midline (center line) to the maximum (peak) of a periodic graph. Half the distance from the minimum to the maximum values of the range.

For functions of the form $y = A \sin b θ$ or $y = A \cos b θ$ , the amplitude is $| A |$ .

angle of rotation in standard position

To represent an angle of rotation in standard position, place its vertex at the origin, the initial ray oriented along the positive $x$ -axis, and its terminal ray rotated $θ$ degrees counterclockwise around the origin when $θ$ is positive and clockwise when $θ$ is negative. Let the ordered pair $(x, y)$ represent the point where the terminal ray intersects the circle.

angular speed

Angular speed is the rate at which an object changes its angle in a given time period. It can be measured in $(\frac{degrees}{second})$ . Typically measured in $(\frac{radians}{second})$ .

arc length

The distance along the arc of a circle. Part of the circumference.

Equation for finding arc length:

$s = r θ$

Where $r$ is the radius and $θ$ is the central angle in radians.

argument of a logarithm

See logarithmic function.

associative property of addition or multiplication

See properties of operations for numbers in the rational, real, or complex number systems.

asymptote

A line that a graph approaches, but does not reach. A graph will never touch a vertical asymptote, but it might cross a horizontal or an oblique (also called slant) asymptote.

Horizontal and oblique asymptotes indicate the general behavior of the ends of a graph in both positive and negative directions. If a rational function has a horizontal asymptote, it will not have an oblique asymptote.

Oblique asymptotes only occur when the numerator of $f (x)$ has a degree that is one higher than the degree of the denominator.

augmented matrix

An augmented matrix for a system of equations is a matrix of numbers in which each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign) and each column represents all the coefficients for a single variable.

Given the system:

$3 x + 1 y = 14$

$5 x - 3 y = 0$

Here is the augmented matrix for this system:

base of a logarithm

See logarithmic function (logarithm).

bimodal distribution

A bimodal distribution has two main peaks.

The data has two modes.

See also: modes.

binomial

A polynomial with two terms.

binomial expansion

When a binomial with an exponent is multiplied out into expanded form.

Example:

${(a + b)}^{2} = (a + b) (a + b) = 1 a^{2} + 2 a b + 1 b^{2}$

Pascal’s triangle (shown) can be used to find the coefficients in a binomial expansion. Each row gives the coefficients to ${(a + b)}^{n}$ , starting with $n = 0$ . To find the binomial coefficients for ${(a + b)}^{n}$ , use the $n th$ row and always start with the beginning variable raised to the power of $n$ . The exponents in each term will always add up to $n$ . The binomial coefficients for ${(a + b)}^{5}$ are $1$ , $5$ , $10$ , $10$ , $5$ , and $1$ — in that order or $1 a^{5} + 5 a^{4} b + 10 a^{3} b^{2} + 10 a^{2} b^{3} + 5 a b^{4} + 1 b^{5}$

Central Limit Theorem (CLT)

This theorem gives you the ability to measure how much your sample mean will vary, without having to take any other sample means to compare it with.

The basic idea of the CLT is that with a large enough sample, the distribution of the sample statistic, either mean or proportion, will become approximately normal, and the center of the distribution will be the true parameter.

clockwise / counterclockwise

clockwise: Moving in the same direction, as the hands on a clock move.

counterclockwise: Moving in the opposite direction, as the hands on a clock move.

closure

A set is closed (under an operation) if and only if the operation on any two elements of the set produces another element of the same set.

cluster sample

See sample.

common logarithm

A logarithm with base $10$ , written $\log x$ , which is shorthand for $\log_{10} x$ .

commutative property of addition or multiplication

See properties of operations for numbers in the rational, real, or complex number systems.

complex conjugates

A pair of complex numbers whose product is a nonzero real number.

The complex numbers $(a + b i)$ and $(a - b i)$ form a conjugate pair.

The product $(a + b i) (a - b i) = a^{2} + b^{2}$ , a real number.

The conjugate of a complex number $a + b i$ is the complex number $a - b i$ .

The conjugate of a complex number is represented with the notation $\overset{―}{a + b i}$ .

complex number

A number with a real part and an imaginary part. A complex number can be written in the form $a + b i$ , where $a$ and $b$ are real numbers and $i$ is the imaginary unit.

When $a = 0$ , the complex number $0 + b i$ can be written simply as $b i .$ It is then referred to as a pure imaginary number.

complex plane

A coordinate plane used for graphing complex numbers, where the horizontal axis is the real axis and the vertical axis is the imaginary axis.

The diagram shows the complex numbers

$2 + 2 i$ , $- 1 + 1 i$ , $- 2 - 1 i$ , and $1 - 2 i$ graphed in the complex plane.

composition of functions

The process of using the output of one function as the input of another function.

$f (x) = 3 x - 1; g (x) = 5 x + 1$

Replace $x$ with $5 x + 1$ .

$f (g (x)) = 3 (5 x + 1) - 1$

$f (g (x)) = 15 x + 3 - 1 = 15 x + 2$

conjugate pair

A pair of numbers whose product is a nonzero rational number.

The numbers $(a + \sqrt{b})$ and $(a - \sqrt{b})$ form a conjugate pair.

The product of $(a + \sqrt{b}) (a - \sqrt{b}) = a^{2} - {(\sqrt{b})}^{2} = a^{2} - b$ , a rational number.

continuous compound interest

Continuously compounded interest means that the account constantly earns interest on the amount of money in the account at any time, which includes the principal and the interest earned previously.

control group

The control group is used in an experiment as a way to ensure that your experiment actually works. It is a baseline group that receives no treatment or a neutral treatment. To assess treatment effects, the experimenter compares results in the treatment group to results in the control group.

convenience sample

See sample.

coterminal angles

Two angles in standard position that share the same terminal ray but have different angles of rotation.

The diagram shows a positive rotation ( $blue$ ) of ray $A C$ from $B$ through $F$ to $C$ . The dotted arc (