Math 3 – Glossary | Open Up HS Math (NC), Student

A–F

absolute value

Unit 4 Lesson 3

A number’s distance from zero on the number line.

The symbol $| a |$ means the absolute value of $a$ .

Recall that distance is always positive.

The diagram shows that $| 2 | = + 2$ and $| - 2 | = + 2$ .

absolute value function

Unit 4 Lesson 3

A function that contains an algebraic expression within absolute value symbols. The absolute value parent function, written as:

$f (x) = | x | = x, if x > 0$

$f (x) = | x | = 0, if x = 0$

$f (x) = | x | = - x, if x < 0$

altitude

Unit 3 Lesson 1

Altitude of a triangle:

A perpendicular segment from a vertex to the line containing the base.

Altitude of a solid:

A perpendicular segment from a vertex to the plane containing the base.

amplitude

Unit 8 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 8 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.

angles associated with circles: central angle, inscribed angle, circumscribed angle

Unit 2 Lesson 1, Unit 2 Lesson 4

Central angle: An angle whose vertex is at the center of a circle and whose sides pass through a pair of points on the circle.

Inscribed angle: An angle formed when two secant lines, or a secant and tangent line, intersect at a point on a circle.

Circumscribed angle: The angle made by two intersecting tangent lines to a circle.

angular speed

Unit 8 Lesson 2, Unit 8 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 2 Lesson 5, Unit 2 Lesson 6, Unit 8 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.

arc of a circle, intercepted arc

Unit 2 Lesson 1, Unit 2 Lesson 3

Arc: A portion of a circle.

Intercepted arc: The portion of a circle that lies between two lines, rays, or line segments that intersect the circle.

argument of a logarithm

Unit 5 Lesson 1

See logarithmic function.

asymptote

Unit 7 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 5 Lesson 1

See logarithmic function (logarithm).

bimodal distribution

Unit 10 Lesson 1

A bimodal distribution has two main peaks.

The data has two modes.

See also: modes.

binomial

Unit 6 Lesson 3

A polynomial with two terms.

binomial expansion

Unit 6 Lesson 3

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 angle

Unit 2 Lesson 1

An angle whose vertex is at the center of a circle and whose sides pass through a pair of points on the circle.

Central Limit Theorem (CLT)

Unit 10 Lesson 7

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.

centroid

Unit 1 Lesson 6

The point of concurrency of a triangle’s three medians.

chord of a circle

Unit 2 Lesson 1

A chord of a circle is a straight line segment whose endpoints both lie on the circle. In general, a chord is a line segment joining two points on any curve.

A diameter is a special chord that passes through the center of the circle.

circle: equation in standard form; equation in general form

Unit 2 Lesson 10

The standard form of a circle’s equation is ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ where $(h, k)$ , is the center and $r$ is the radius.

The general form of the equation of a circle has ${(x - h)}^{2}$ and ${(y - k)}^{2}$ and $r^{2}$ multiplied out and then like terms have been collected.

$x^{2} + y^{2} + D x + E y + F = 0$

circumcenter

Unit 1 Lesson 6

The point where the perpendicular bisectors of the sides of a triangle intersect. The circumcenter is also the center of the triangle’s circumcircle—the circle that passes through all three of the triangle’s vertices.