Math III – Glossary | Open Up HS Math (CCSS), Student

A–F

acute angle

Unit 5 Lesson 6

An angle whose measure is between $0 °$ and $90 °$ .

$∠ A B C$ is an acute angle.

acute triangle

Unit 5 Lesson 6

A triangle with three acute angles.

Angles $A$ , $B$ , and $C$ are all acute angles.

Triangle $A B C$ is an acute triangle.

Ambiguous Case of the Law of Sines

Unit 5 Lesson 8

The Ambiguous Case of the Law of Sines occurs when we are given SSA information about the triangle. Because SSA does not guarantee triangle congruence, there are two possible triangles.

To avoid missing a possible solution for an oblique triangle under these conditions, use the Law of Cosines first to solve for the missing side. Using the quadratic formula to solve for the missing side will make both solutions become apparent.

amplitude

Unit 6 Lesson 4

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

Unit 6 Lesson 3

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

Unit 6 Lesson 2, Unit 6 Lesson 4

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

Unit 6 Lesson 7

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

Unit 2 Lesson 1

See logarithmic function.

asymptote

Unit 2 Lesson 2, Unit 4 Lesson 1

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.

base of a logarithm

Unit 2 Lesson 1

See logarithmic function (logarithm).

bimodal distribution

Unit 9 Lesson 1

A bimodal distribution has two main peaks.

The data has two modes.

See also: modes.

binomial

Unit 3 Lesson 4

A polynomial with two terms.

binomial expansion

Unit 3 Lesson 4

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)

Unit 9 Lesson 8

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

Unit 6 Lesson 2

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

Unit 3 Lesson 6

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

Unit 9 Lesson 5

See sample.

common logarithm

Unit 2 Lesson 5

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

composition of functions

Unit 8 Lesson 2, Unit 8 Lesson 4

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

Unit 3 Lesson 8

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

Unit 2 Lesson 6

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

Unit 9 Lesson 6

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

Unit 9 Lesson 5

See sample.

coterminal angles

Unit 6 Lesson 3

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 ( $green$ ) shows a negative rotation of ray $A C$ from $B$ through $D$ to $C$ .

The two angles are coterminal.