Math 1 – Glossary | Open Up HS Math (NC), Student

A–F

acute angle

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

$∠ A B C$ is an acute angle.

arithmetic mean

The arithmetic mean is also known as the average. The arithmetic mean between two numbers will be the number that is the same distance from each of the numbers. It is found by adding the two numbers and dividing by $2$ .

The arithmetic mean of several numbers is found by adding all of the numbers together and dividing by the number of items in the set:

Example: Find the arithmetic mean of ${5, 6, 7, 8} \Rightarrow \frac{5 + 6 + 7 + 8}{4} = \frac{26}{4} = 6.5$

arithmetic sequence

Unit 1 Lesson 2

The list of numbers $3 10 17 24 31$ represents an arithmetic sequence because, beginning with the first term, $3$ , the number $7$ has been added to get the next term. The next term in the sequence will be ( $31 + 7$ ) or $38$ .

The number being added each time is called the constant difference ( $d$ ).

The sequence can be represented by a recursive equation.

In words:

Name the $first term$ . $Next = Previous + d$

Using function notation:

An arithmetic sequence can also be represented with an explicit equation, often in the form $f (n) = d (n - 1) + f (1)$ where $d$ is the constant difference $(d)$ and $f (1)$ is the value of the first term.

The graph of the terms in an arithmetic sequence are arranged in a line.

associative property of addition or multiplication

Unit 4 Lesson 3

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

asymptote

Unit 2 Lesson 4

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.

average rate of change

Unit 2 Lesson 7

See rate of change.

bimodal distribution

Unit 9 Lesson 6

A bimodal distribution has two main peaks.

The data has two modes.

See also: modes.

binomial

Unit 7 Lesson 3

A polynomial with two terms.

bivariate data

Unit 9 Lesson 1

Deals with two variables that can change and are compared to find relationships. If one variable is influencing another variable, then you will have bivariate data that has an independent and a dependent variable (ordered pairs). This is because one variable depends on the other for change.

box and whisker plot (box plot)

Unit 9 Lesson 6

A one-dimensional graph of numerical data based on the five-number summary, which includes the minimum value, the $25 th$ percentile $(Q_{1})$ , the median, the $75 th$ percentile $(Q_{3})$ , and the maximum value. These five descriptive statistics divide the data into four parts; each part contains $25 %$ of the data.

Boxplots can be vertical or horizontal.

categorical data or categorical variables

Unit 9 Lesson 6

Data that can be organized into groups or categories based on certain characteristics, behavior, or outcomes. Also known as qualitative data.

causation

Unit 9 Lesson 1

Tells you that a change in the value of the $x$ variable will cause a change in the value of the $y$ variable.

center (statistics)

Unit 9 Lesson 6

A value that attempts to describe a set of data by identifying the central position of the data set (as representative of a “typical” value in the set). Measure of center refers to a measure of central tendency (mean, median, or mode).

change factor (pattern of growth)

Unit 1 Lesson 3

A change factor is a multiplier that makes each dependent variable grow (or sometimes decrease) as the independent variable increases. Sometimes called the growth factor.

In a geometric sequence it is the common ratio.

In an exponential function it is the base of the exponent.

common ratio (r) (constant ratio)

Unit 1 Lesson 3

The change factor or pattern of growth ( $r$ ) in a geometric sequence. To find it divide any output by the previous output.

Example: $f (n)$ is a geometric sequence.

Output $f (n)$	$37$	$74$	$148$	$296$
Input $n$	$1$	$2$	$3$	$4$

Output

$f (n)$

$37$

$74$

$148$

$296$

Input

$n$

$1$

$2$

$3$

$4$

The common ratio is

$r = \frac{output}{previous output} = \frac{296}{148} = 2 or \frac{148}{74} = 2$

commutative property of addition or multiplication

Unit 4 Lesson 3

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

compound inequality in one variable

Unit 4 Lesson 5

A compound inequality contains at least two inequalities that are separated by either “and” or “or.”

an inequality that combines two inequalities either so that a solution must meet both conditions (and $\cap$ ) or that a solution must meet either condition (or $\cup$ ).

Examples:

$(- 3, 2]$ can be written as ${x | - 3 < x \leq 2}$

(The value of $x$ in this set must meet both conditions, $x > - 3$ and $x \leq 2$ , which is the same as $x > - 3 \cap x \leq 2$ )

$(- \infty, - 3) \cup [2, \infty)$ can be written as ${x | x < - 3 or x \geq 2}$ which is the same as ${x | x < - 3 \cup x \geq 2}$

(The value of $x$ in this set may meet either condition $x < - 3 or x \geq 2$ )

compound inequality in two variables

Unit 5 Lesson 6

The graph of a compound inequality in two variables with an “and $\cap$ ” represents the intersection of the graph of the inequalities. A number is a solution to a compound inequality combined with the word “and” if the number is a solution to both inequalities (where the regions overlap). In a system of inequalities, the word “and” is implied because the solution set must work in each equation.

If the inequalities were combined using “or” the solution would be all of the shaded area.

See feasible region and solution set for a system.

constant difference (d) (common difference)

Unit 1 Lesson 2

Difference implies subtraction: common difference, constant difference, equal difference refer to the same thing. In an arithmetic sequence it is the constant amount of change. To find the difference select any output and subtract the previous output.

Example: $f (n)$ is an arithmetic sequence.

Output $f (n)$	$19$	$25$	$31$	$37$
Input $n$	$1$	$2$	$3$	$4$

The constant difference is:

$d = (37 - 31) = 6$ or $(25 - 19) = 6$

constraint

Unit 5 Lesson 2

A restriction or limitation

continuous function/discontinuous function

Unit 2 Lesson 1, Unit 3 Lesson 1

A function is considered continuous if its graph does not have any breaks or holes.

A function can be continuous on an interval.

A discontinuous function is a function that is not a continuous curve. When you put your pencil down to draw a discontinuous function, you must lift the pencil from the page to continue drawing the graph at least once before it is complete. The image shows a function that is discontinuous, even though the domain is continuous on the interval that is shown.

correlation

Unit 9 Lesson 1

The extent to which two numerical variables have a linear relationship. A correlation gives you a number $r$ , (the correlation coefficient) which can range from $- 1.00$ to $1.00$ . Zero correlation means there is no relation between two variables. A correlation of $1.00$ (either + or -) means perfect correlation.