Keystone Algebra 2 Vocab

Front 1

Absolute Value

Back 1

A number’s distance from zero on the number line. It is written |a| and is read “the absolute value of a.” It results in a number greater than or equal to zero (e.g., |4| = 4 and |–4| = 4).

Front 2

Additive Inverse

Back 2

The opposite of a number (i.e., for any number a, the additive inverse is –a). Any number and its additive inverse will have a sum of zero (e.g., –4 is the additive inverse of 4 since 4 + –4 = 0; likewise, the additive inverse of –4 is 4 since –4 + 4 = 0).

Front 3

Arithmetic Sequence

Back 3

An ordered list of numbers that increases or decreases at a constant rate (i.e., the difference between numbers remains the same). Example: 1, 7, 13, 19, … is an arithmetic sequence as it has a constant difference of +6 (i.e., 6 is added over and over).

Front 4

Asymptote

Back 4

A straight line to which the curve of a graph comes closer and closer. The distance between the curve and the asymptote approaches zero as they tend to infinity. The asymptote is denoted by a dashed line on a graph. The most common asymptotes are horizontal and vertical.

Front 5

Bar Graph

Back 5

A graph that shows a set of frequencies using bars of equal width, but heights that are proportional to the frequencies. It is used to summarize discrete data.

Front 6

Binomial

Back 6

A polynomial with two unlike terms (e.g., 3x + 4y or a3 – 4b2). Each term is a monomial, and the monomials are joined by an addition symbol (+) or a subtraction symbol (–). It is considered an algebraic expression.

Front 7

Box-and-Whisker Plot

Back 7

A graphic method for showing a summary and distribution of data using median, quartiles, and extremes (i.e., minimum and maximum) of data. This shows how far apart and how evenly data is distributed. It is helpful when a visual is needed to see if a distribution is skewed or if there are any outliers.

Front 8

Circle Graph (or Pie Chart)

Back 8

A circular diagram using different-sized sectors of a circle whose angles at the center are proportional to the frequency. Sectors can be visually compared to show information (e.g., statistical data). Sectors resemble slices of a pie.

Front 9

Coefficient

Back 9

The number, usually a constant, that is multiplied by a variable in a term (e.g., 35 is the coefficient of 35x2y); the absence of a coefficient is the same as a 1 being present (e.g., x is the same as 1x).

Front 10

Combination

Back 10

An unordered arrangement, listing or selection of objects (e.g., two-letter combinations of the three letters X, Y, and Z would be XY, XZ, and YZ; XY is the same as YX and is not counted as a different combination). A combination is similar to, but not the same as, a permutation.

Front 11

Common Logarithm

Back 11

A logarithm with base 10. It is written log x. The common logarithm is the power of 10 necessary to equal a given number (i.e., log x = y is equivalent to 10y = x).

Front 12

Complex Number

Back 12

The sum or difference of a real number and an imaginary number. It is written in the form a + bi, where a and b are real numbers and i is the imaginary unit (i.e., i = −1). The a is called the real part, and the bi is called the imaginary part.

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Composite Number

Back 13

Any natural number with more than two factors (e.g., 6 is a composite number since it has four factors: 1, 2, 3, and 6). A composite number is not a prime number.

Front 14

Compound (or Combined) Event

Back 14

An event that is made up of two or more simple events, such as the flipping of two or more coins.

Front 15

Compound Inequality

Back 15

When two or more inequalities are taken together and written with the inequalities connected by the words and or or (e.g., x > 6 and x < 12, which can also be written as 6 < x < 12).

Front 16

Constant

Back 16

A term or expression with no variable in it. It has the same value all the time.

Front 17

Coordinate Plane

Back 17

A plane formed by perpendicular number lines. The horizontal number line is the x-axis, and the vertical number line is the y-axis. The point where the axes meet is called the origin.

Front 18

Cube Root

Back 18

One of three equal factors (roots) of a number or expression; a radical expression with a degree of 3. The cube root of a number or expression has the same sign as the number or expression under the radical.

Front 19

Line of Best Fit (for a Scatter Plot)

Back 19

A line or curve drawn on a scatter plot to best estimate the relationship between two sets of data. It describes the trend of the data. Different measures are possible to describe the best fit. The most common is a line or curve that minimizes the sum of the squares of the errors (vertical distances) from

Front 20

Degree (of a Polynomial)

Back 20

The value of the greatest exponent in a polynomial.

Front 21

Dependent Events

Back 21

Two or more events in which the outcome of one event affects or influences the outcome of the other event(s).

Front 22

Dependent Variable

Back 22

The output number or variable in a relation or function that depends upon another variable, called the independent variable, or input number (e.g., in the equation y = 2x + 4, y is the dependent variable since its value depends on the value of x). It is the variable for which an equation is solved. Its values make up the range of the relation or function.

Front 23

Domain (of a Relation or Function)

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The set of all possible values of the independent variable on which a function or relation is allowed to operate. Also, the first numbers in the ordered pairs of a relation; the values of the x-coordinates in (x, y).

Front 24

Elimination Method

Back 24

A method by which a system of linear equations can be solved. It uses addition or subtraction in combination with multiplication or division to eliminate one of the variables in order to solve for the other variable.

Front 25

Equation

Back 25

A mathematical statement or sentence that says one mathematical expression or quantity is equal to another (e.g., x + 5 = y – 7). An equation will always contain an equal sign (=).

Front 26

Estimation Strategy

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An approximation based on a judgment; may include determining approximate values, establishing the reasonableness of answers, assessing the amount of error resulting from estimation, and/or determining if an error is within acceptable limits.

Front 27

Exponent

Back 27

The power to which a number or expression is raised. When the exponent is a fraction, the number or expression can be rewritten with a radical sign.

Front 28

Exponential Equation

Back 28

An equation with variables in its exponents. It can be solved by taking logarithms of both sides.

Front 29

Exponential Expression

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An expression in which the variable occurs in the exponent (such as 4x rather than x4). Often it occurs when a quantity changes by the same factor for each unit of time (e.g., “doubles every year” or “decreases 2% each month”).

Front 30

Exponential Function (or Model)

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A function whose general equation is y = a • bx where a and b are constants.

Front 31

Exponential Growth/Decay

Back 31

A situation where a quantity increases or decreases exponentially by the same factor over time; it is used for such phenomena as inflation, population growth, radioactivity or depreciation.

Front 32

Expression

Back 32

A mathematical phrase that includes operations, numbers, and/or variables (e.g., 2x + 3y is an algebraic expression, 13.4 – 4.7 is a numeric expression). An expression does not contain an equal sign (=) or any type of inequality sign.

Front 33

Factor (noun)

Back 33

The number or expression that is multiplied by another to get a product.

Front 34

Factor (verb)

Back 34

To express or write a number, monomial, or polynomial as a product of two or more factors.

Front 35

Factor a Monomial

Back 35

To express a monomial as the product of two or more monomials.

Front 36

Factor a Polynomial

Back 36

To express a polynomial as the product of monomials and/or polynomials (e.g., factoring the polynomial x2 + x – 12 results in the product (x – 3)(x + 4)).

Front 37

Frequency

Back 37

How often something occurs (i.e., the number of times an item, number, or event happens in a set of data).

Front 38

Function

Back 38

A relation in which each value of an independent variable is associated with a unique value of a dependent variable (e.g., one element of the domain is paired with one and only one element of the range). It is a mapping which involves either a one-to-one correspondence or a many-to-one correspondence, but not a one-to-many correspondence.

Front 39

Fundamental Counting Principle

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A way to calculate all of the possible combinations of a given number of events. It states that if there are x different ways of doing one thing and y different ways of doing another thing, then there are xy different ways of doing both things. It uses the multiplication rule.

Front 40

Geometric Sequence

Back 40

An ordered list of numbers that has the same ratio between consecutive terms (e.g., 1, 7, 49, 343, …is a geometric sequence that has a ratio of 7/1 between consecutive terms; each term after the first term can be found by multiplying the previous term by a constant, in this case the number 7 or 7/1).

Front 41

Greatest Common Factor (GCF)

Back 41

The largest factor that two or more numbers or algebraic terms have in common. In some cases the GCF may be 1 or one of the actual numbers.

Front 42

Imaginary Number

Back 42

The square root of a negative number, or the opposite of the square root of a negative number. It is written in the form bi, where b is a real number and i is the imaginary root.

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Independent Event(s)

Back 43

Two or more events in which the outcome of one event does not affect the outcome of the other event(s) (e.g., tossing a coin and rolling a number cube are independent events). The probability of two independent events (A and B) occurring is written P(A and B) or P(A ∩ B) and equals P(A) • P(B) (i.e., the product of the probabilities of the two individual events).

Front 44

Independent Variable

Back 44

The input number or variable in a relation or function whose value is subject to choice. It is not dependent upon any other values. It is usually the x-value or the x in f(x). It is graphed on the x-axis. Its values make up the domain of the relation or function.

Front 45

Inequality

Back 45

A mathematical sentence that contains an inequality symbol (i.e., >, <, ≥, ≤, or ≠). It compares two quantities. The symbol > means greater than, the symbol < means less than, the symbol ≥ means greater than or equal to, the symbol ≤ means less than or equal to, and the symbol ≠ means not equal to.

Front 46

Integer

Back 46

A natural number, the additive inverse of a natural number, or zero. Any number from the set of numbers represented by {…, –3, –2, –1, 0, 1, 2, 3, …}.

Front 47

Interquartile Range (of Data)

Back 47

The difference between the first (lower) and third (upper) quartile. It represents the spread of the middle 50% of a set of data.

Front 48

Inverse (of a Relation)

Back 48

A relation in which the coordinates in each ordered pair are switched from a given relation. The point (x, y) becomes (y, x), so (3, 8) would become (8, 3).

Front 49

Irrational Number

Back 49

A real number that cannot be written as a simple fraction (i.e., the ratio of two integers). It is a nonterminating (infinite) and non-repeating decimal. The square root of any prime number is irrational, as are π and e.

Front 50

Least (or Lowest) Common Multiple (LCM)

Back 50

The smallest number or expression that is a common multiple of two or more numbers or algebraic terms, other than zero.

Front 51

Like Terms

Back 51

Monomials that contain the same variables and corresponding powers and/or roots. Only the coefficients can be different (e.g., 4x3 and 12x3). Like terms can be added or subtracted.

Front 52

Line Graph

Back 52

A graph that uses a line or line segments to connect data points, plotted on a coordinate plane, usually to show trends or changes in data over time. More broadly, a graph to represent the relationship between two continuous variables.

Front 53

Linear Equation

Back 53

An equation for which the graph is a straight line (i.e., a polynomial equation of the first degree of the form Ax + By = C, where A, B, and C are real numbers and where A and B are not both zero; an equation in which the variables are not multiplied by one another or raised to any power other than 1).

Front 54

Linear Function

Back 54

A function for which the graph is a non-vertical straight line. It is a first degree polynomial of the common form f(x) = mx + b, where m and b are constants and x is a real variable. The constant m is called the slope and b is called the y-intercept. It has a constant rate of change.

Front 55

Linear Inequality

Back 55

The relation of two expressions using the symbols <, >, ≤, ≥, or ≠ and whose boundary is a straight line. The line divides the coordinate plane into two parts. If the inequality is either ≤ or ≥, then the boundary is solid. If the inequality is either < or >, then the boundary is dashed. If the inequality is ≠, then the solution contains everything except for the boundary.

Front 56

Logarithm

Back 56

The exponent required to produce a given number (e.g., since 2 raised to a power of 5 is 32, the logarithm base 2 of 32 is 5; this is written as log2 32 = 5). Two frequently used bases are 10 (common logarithm) and e (natural logarithm). When a logarithm is written without a base, it is understood to be base 10.

Front 57

Logarithmic Equation

Back 57

An equation which contains a logarithm of a variable or number. Sometimes it is solved by rewriting the equation in exponential form and solving for the variable. It is an inverse function of the exponential function.

Front 58

Mapping

Back 58

The matching or pairing of one set of numbers to another by use of a rule. A number in the domain is matched or paired with a number in the range (or a relation or function). It may be a one-to-one correspondence, a one-to-many correspondence, or a many-to-one correspondence.

Front 59

Maximum Value (of a Graph)

Back 59

The value of the dependent variable for the highest point on the graph of a curve.

Front 60

Mean

Back 60

A measure of central tendency that is calculated by adding all the values of a set of data and dividing that sum by the total number of values. Unlike median, the mean is sensitive to outlier values. It is also called “arithmetic mean” or “average”.

Front 61

Measure of Central Tendency

Back 61

A measure of location of the middle (center) of a distribution of a set of data (i.e., how data clusters). The three most common measures of central tendency are mean, median, and mode.

Front 62

Measure of Dispersion

Back 62

A measure of the way in which the distribution of a set of data is spread out. In general the more spread out a distribution is, the larger the measure of dispersion. Range and interquartile range are two measures of dispersion.

Front 63

Median

Back 63

A measure of central tendency that is the middle value in an ordered set of data or the average of the two middle values when the set has two middle values (occurs when the set of data has an even number of data points). It is the value halfway through the ordered set of data, below and above which there are an equal number of data values. It is generally a good descriptive measure for skewed data or data with outliers.

Front 64

Minimum Value (of a Graph)

Back 64

The value of the dependent variable for the lowest point on the graph of a curve.

Front 65

Mode

Back 65

A measure of central tendency that is the value or values that occur(s) most often in a set of data. A set of data can have one mode, more than one mode, or no mode.

Front 66

Monomial

Back 66

A polynomial with only one term; it contains no addition or subtraction. It can be a number, a variable, or a product of numbers and/or more variables.

Front 67

Multiplicative Inverse

Back 67

The reciprocal of a number (i.e., for any non-zero number a, the multiplicative inverse is 1.

Front 68

Mutually Exclusive Events

Back 68

Two events that cannot occur at the same time (i.e., events that have no outcomes in common). If two events A and B are mutually exclusive, then the probability of A or B occurring is the sum of their

Front 69

Natural Logarithm

Back 69

A logarithm with base e. It is written ln x. The natural logarithm is the power of e necessary to equal a given number (i.e., ln x = y is equivalent to e y = x). The constant e is an irrational number whose value is approximately 2.71828….

Front 70

Natural Number

Back 70

A counting number. A number representing a positive, whole amount. Any number from the set of numbers represented by {1, 2, 3, …}. Sometimes, it is referred to as a “positive integer”.

Front 71

Negative Exponent

Back 71

An exponent that indicates a reciprocal that has to be taken before the exponent can be applied. It is used in scientific notation for numbers between –1 and 1.

Front 72

Number Line

Back 72

A graduated straight line that represents the set of all real numbers in order. Typically, it is marked showing integer values.

Front 73

Odds

Back 73

A comparison, in ratio form (as a fraction or with a colon), of outcomes. “Odds in favor” (or simply “odds”) is the ratio of favorable outcomes to unfavorable outcomes (e.g., the odds in favor of picking a red hat when there are 3 red hats and 5 non-red hats is 3:5). “Odds against” is the ratio of unfavorable outcomes to favorable outcomes (e.g., the odds against picking a red hat when there are 3 red hats and 5 non-red hats is 5:3).

Front 74

Order of Operations

Back 74

Rules describing what order to use in evaluating expressions:
(1) Perform operations in grouping symbols (parentheses and brackets),
(2) Evaluate exponential expressions and radical expressions from left to right,
(3) Multiply or divide from left to right,
(4) Add or subtract from left to right.

Front 75

Ordered Pair

Back 75

A pair of numbers used to locate a point on a coordinate plane, or the solution of an equation in two variables. The first number tells how far to move horizontally, and the second number tells how far to move vertically; written in the form (x-coordinate, y-coordinate). Order matters: the point (x, y) is not the same as (y, x).

Front 76

Origin

Back 76

The point (0, 0) on a coordinate plane. It is the point of intersection for the x-axis and the y-axis.

Front 77

Outlier

Back 77

A value that is much greater or much less than the rest of the data. It is different in some way from the general pattern of data. It directly stands out from the rest of the data. Sometimes it is referred to as any data point more than 1.5 interquartile ranges greater than the upper (third) quartile or less than the lower (first) quartile.

Front 78

Pattern (or Sequence)

Back 78

A set of numbers arranged in order (or in a sequence). The numbers and their arrangement are determined by a rule, including repetition and growth/decay rules. See arithmetic sequence and geometric sequence.

Front 79

Perfect Square

Back 79

A number whose square root is a whole number (e.g., 25 is a perfect square since 25 = 5). A perfect square can be found by raising a whole number to the second power.

Front 80

Permutation

Back 80

An ordered arrangement of objects from a given set in which the order of the objects is significant (e.g., two-letter permutations of the three letters X, Y, and Z would be XY, YX, XZ, ZX, YZ, and ZY). A permutation is similar to, but not the same as, a combination.

Front 81

Point-Slope Form (of a Linear Equation)

Back 81

An equation of a straight, non-vertical line written in the form y – y1 = m(x – x1), where m is the slope of the line and (x1, y1) is a given point on the line.

Front 82

Polynomial

Back 82

An algebraic expression that is a monomial or the sum or difference of two or more monomials (e.g., 6a or 5a2 + 3a – 13 where the exponents are natural numbers).

Front 83

Polynomial Function

Back 83

A function of the form f(x) = anxn + an–1xn–1 + … + a1x + a0, where an ≠ 0 and natural number n is the degree of the polynomial.

Front 84

Positive Exponent

Back 84

Indicates how many times a base number is multiplied by itself. In the expression xn, n is the positive exponent, and x is the base number.

Front 85

Power

Back 85

The value of the exponent in a term. The expression an is read “a to the power of n.” To raise a number, a, to the power of another whole number, n, is to multiply a by itself n times.

Front 86

Power of a Power

Back 86

An expression of the form (am)n. It can be found by multiplying the exponents.

Front 87

Powers of Products

Back 87

An expression of the form am • an. It can be found by adding the exponents when multiplying powers that have the same base.

Front 88

Prime Number

Back 88

Any natural number with exactly two factors, 1 and itself (e.g., 3 is a prime number since it has only two factors: 1 and 3). [Note: Since 1 has only one factor, itself, it is not a prime number.] A prime number is not a composite number.

Front 89

Probability

Back 89

A number from 0 to 1 (or 0% to 100%) that indicates how likely an event is to happen. A very unlikely event has a probability near 0 (or 0%) while a very likely event has a probability near 1 (or 100%). It is written as a ratio (fraction, decimal, or equivalent percent). The number of ways an event could happen (favorable outcomes) is placed over the total number of events (total possible outcomes) that could happen. A probability of 0 means it is impossible, and a probability of 1 means it is certain.

Front 90

Probability of a Compound (or Combined) Event

Back 90

There are two types:
1. The union of two events A and B, which is the probability of A or B occurring. This is represented as P(A ∪ B) = P(A) + P(B) – P(A) • P(B).
2. The intersection of two events A and B, which is the probability of A and B occurring. This is represented as P(A ∩ B) = P(A) • P(B).

Front 91

Quadrants

Back 91

The four regions of a coordinate plane that are separated by the x-axis and the y-axis.

Front 92

Quadratic Equation

Back 92

An equation that can be written in the standard form ax^2 + bx + c = 0, where a, b, and c are real numbers and a does not equal zero. The highest power of the variable is 2. It has, at most, two solutions. The graph is a parabola.

Front 93

Quadratic Function

Back 93

A function that can be expressed in the form f(x) = ax^2 + bx + c, where a ≠ 0 and the highest power of the variable is 2. The graph is a parabola.

Front 94

Quartile

Back 94

One of three values that divides a set of data into four equal parts:
1. Median divides a set of data into two equal parts.
2. Lower quartile (25th percentile) is the median of the lower half of the data.
3. Upper quartile (75th percentile) is the median of the upper half of the data.

Front 95

Radical Expression

Back 95

An expression containing a radical symbol .The expression or number inside the radical is called the radicand, and the number appearing above the radical is the degree. The degree is always a positive integer. When a radical is written without a degree, it is understood to be a degree of 2 and is read as “the square root of a.” When the degree is 3, it is read as “the cube root of a.” For any other degree, the expression is read as “the nth root of a.” When the degree is an even number, the radical expression is assumed to be the principal (positive) root

Front 96

Range (of a Relation or Function)

Back 96

The set of all possible values for the output (dependent variable) of a function or relation; the set of second numbers in the ordered pairs of a function or relation; the values of the y-coordinates in (x, y).

Front 97

Range (of Data)

Back 97

In statistics, a measure of dispersion that is the difference between the greatest value (maximum value) and the least value (minimum value) in a set of data.

Front 98

Rate

Back 98

A ratio that compares two quantities having different units (e.g., 168 miles/3.5 hours or 122.5 calories/5 cups ). When the rate is simplified so that the second (independent) quantity is 1, it is called a unit rate (e.g.,48 miles per hour or 24.5 calories per cup).

Front 99

Rate (of Change)

Back 99

The amount a quantity changes over time (e.g., 3.2 cm per year). Also the amount a function’s output changes (increases or decreases) for each unit of change in the input.

Front 100

Rate (of Interest)

Back 100

The percent by which a monetary account accrues interest. It is most common for the rate of interest to be measured on an annual basis (e.g., 4.5% per year), even if the interest is compounded periodically (i.e., more frequently than once per year).

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Ratio

Back 101

A comparison of two numbers, quantities or expressions by division. It is often written as a fraction, but not always (e.g., 2/3, 2:3, 2 to 3, 2 ÷ 3 are all the same ratios).

Front 102

Rational Expression

Back 102

An expression that can be written as a polynomial divided by a polynomial, defined only when the

Front 103

Rational Number

Back 103

Any number that can be written in the form a/b, where a is any integer and b is any integer except zero. All repeating decimal and terminating decimal numbers are rational numbers.

Front 104

Real Number

Back 104

The combined set of rational and irrational numbers. All numbers on the number line. Not an imaginary number.

Front 105

Regression Curve

Back 105

The line or curve of best fit that represents the least deviation from the points in a scatter plot of data. Most commonly it is linear and uses a “least squares” method.

Front 106

Relation

Back 106

A set of pairs of values (e.g., {(1, 2), (2, 3) (3, 2)}). The first value in each pair is the input (independent value), and the second value in the pair is the output (dependent value). In a relation, neither the input values nor the output values need to be unique.

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Repeating Decimal

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A decimal with one or more digits that repeats endlessly (e.g., 0.666…, 0.727272…, 0.08333…). All repeating decimals are rational numbers.

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Rise

Back 108

The vertical (up and down) change or difference between any two points on a line on a coordinate plane (i.e., for points (x1, y1) and (x2, y2), the rise is y2 – y1).

Front 109

Run

Back 109

The horizontal (left and right) change or difference between any two points on a line on a coordinate plane (i.e., for points (x1, y1) and (x2, y2), the run is x2 – x1).

Front 110

Scatter Plot

Back 110

A graph that shows the “general” relationship between two sets of data. For each point that is being plotted there are two separate pieces of data. It shows how one variable is affected by another.

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Simple Event

Back 111

When an event consists of a single outcome (e.g., rolling a number cube).

Front 112

Simplest Form (of an Expression)

Back 112

When all like terms are combined (e.g., 8x + 2(6x – 22) becomes 20x – 44 when in simplest form).The form which no longer contains any like terms, parentheses, or reducible fractions.

Front 113

Simplify

Back 113

To write an expression in its simplest form (i.e., remove any unnecessary terms, usually by combining several or many terms into fewer terms or by cancelling terms).

Front 114

Slope (of a Line)

Back 114

A rate of change. The measurement of the steepness, incline, or grade of a line from left to right. It is the ratio of vertical change to horizontal change. More specifically, it is the ratio of the change in they-coordinates (rise) to the corresponding change in the x- coordinates (run) when moving from one

Front 115

Slope-Intercept Form

Back 115

An equation of a straight, non-vertical line written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front 116

Square Root

Back 116

One of two equal factors (roots) of a number or expression; a radical expression ( a ) with an understood degree of 2. The square root of a number or expression is assumed to be the principal (positive) root. The square root of a negative number results in an imaginary number.

Front 117

Standard Form (of a Linear Equation)

Back 117

An equation of a straight line written in the form Ax + By = C, where A, B, and C are real numbers and where A and B are not both zero. It includes variables on one side of the equation and a constant on the other side.

Front 118

Stem-and-Leaf Plot

Back 118

A visual way to display the shape of a distribution that shows groups of data arranged by place value; a way to show the frequency with which certain classes of data occur. The stem consists of a column of the larger place value(s); these numbers are not repeated. The leaves consist of the smallest place value (usually the ones place) of every piece of data; these numbers are arranged in numerical order

Front 119

Substitution

Back 119

The replacement of a term or variable in an expression or equation by another that has the same value in order to simplify or evaluate the expression or equation.

Front 120

System of Linear Equations

Back 120

A set of two or more linear equations with the same variables. The solution to a system of linear equations may be found by linear combination, substitution, or graphing. A system of two linear equations will either have one solution, infinitely many solutions, or no solutions.

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System of Linear Inequalities

Back 121

Two or more linear inequalities with the same variables. Some systems of inequalities may include equations as well as inequalities. The solution region may be closed or bounded because there are lines on all sides, while other solutions may be open or unbounded.

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Systems of Equations

Back 122

A set of two or more equations containing a set of common variables.

Front 123

Term

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A part of an algebraic expression. Terms are separated by either an addition symbol (+) or a subtraction symbol (–). It can be a number, a variable, or a product of a number and one or more variables (e.g., in the expression 4x^2+ 6y, 4x^2 and 6y are both terms).

Front 124

Terminating Decimal

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A decimal with a finite number of digits. A decimal for which the division operation results in either repeating zeroes or repeating nines (e.g., 0.375000… = 0.375, 0.1999… = 0.2). It is generally written to the last non-zero place value, but can also be written with additional zeroes in smaller place values as needed (e.g., 0.25 can also be written as 0.2500). All terminating decimals are rational numbers.

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Trinomial

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A polynomial with three unlike terms (e.g., 7a + 4b + 9c). Each term is a monomial, and the monomials are joined by an addition symbol (+) or a subtraction symbol (–). It is considered an algebraic expression.

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Unit Rate

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A rate in which the second (independent) quantity of the ratio is 1 (e.g., 60 words per minute,

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Variable

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A letter or symbol used to represent any one of a given set of numbers or other objects (e.g., in the equation y = x + 5, the y and x are variables). Since it can take on different values, it is the opposite of a constant.

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Whole Number

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A natural number or zero. Any number from the set of numbers represented by {0, 1, 2, 3, …}. Sometimes it is referred to as a “non-negative integer”.

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x-Axis

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The horizontal number line on a coordinate plane that intersects with a vertical number line, the y-axis; the line whose equation is y = 0. The x-axis contains all the points with a zero y-coordinate (e.g., (5, 0)).

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x-Intercept(s)

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The x-coordinate(s) of the point(s) at which the graph of an equation crosses the x-axis (i.e., the value(s) of the x-coordinate when y = 0). The solution(s) or root(s) of an equation that is set equal to 0.

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y-Axis

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The vertical number line on a coordinate plane that intersects with a horizontal number line, the x-axis; the line whose equation is x = 0. The y-axis contains all the points with a zero x-coordinate (e.g., (0, 7)).

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y-Intercept(s)

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The y-coordinate(s) of the point(s) at which the graph of an equation crosses the y- axis (i.e., the value(s) of the y-coordinate when x = 0). For a linear equation in slope-intercept form (y = mx + b), it is indicated by b.