Equation A mathematical sentence formed by setting two expressions equal to each other Example 1: 3 6 = 18 Example 2: 7 + x = 12
Variable A symbol, usually a letter, that is used to represent one or more numbers Example: In the expression m + 5, the letter m is the variable
Solution of an Equation A number that produces a true statement when substituted for the variable in an equation. The number 3 is a solution of the equation 8-2x = 2, because 8-2(3) = 2
Properties of Equality Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality a = b a + c = b + c a = b a - c = b - c a = b a c = b c a = b a c = b c c 0
Ratio A comparison of two numbers by division. Example: if there is 1 boy and 3 girls you could write the ratio as: 1:3 (for every one boy there are 3 girls) 1:3 can also be represented or written as 1 to 3 OR 1/3
Proportion An equation that states two ratios (or fractions) are equal.
Scale Drawing A drawing that uses a scale to represent an object as smaller or larger than the original object.
Scale The ratio of the length in a drawing (or model) to the length of the real thing. Example: in the drawing anything with the size of "1" would have a size of "10" in the real world, so a measurement of 150mm on the drawing would be 1500mm on the real horse.
Scale Model A three-dimensional model that uses a scale to represent an object as smaller or larger than the actual object.
Dimensional Analysis A process that uses rates to convert measurements from one unit to another. Example: 12 pints is equivalent to how many quarts? 1 qt 12 pt ( 2 pt ) = 12 qt = 6 qt 2
Rate A ratio that compares two quantities measured in different units. Example: 55 miles 1 hour = 55 mi/h
Conversion Factor The ratio of two equal quantities, each measured in different units. Example: 12 inches 1 foot
Precision The level of detail of a measurement, determined by the unit of measure. Example: A ruler marked in millimeters has a greater level of precision than a ruler marked in centimeters.
Accuracy The closeness of a given measurement or value to the actual measurement or value. Example: You can find the accuracy of a measurement by finding the absolute value of the difference between the actual and measured values.
Significant Digits The digits used to express the precision of a measurement. Examples: 0.0481 has 3 significant digits 12,000 has 2 significant digits 150.000 has 6 significant digits
Expression A mathematical phrase that contains operations, numbers, and/or variables. Example: 6x + 1
Term of an Expression In Algebra a term is either: * a single number, or * a variable, or * numbers and variables multiplied together.
Coefficient In any term, the coefficient is the numeric factor of the term or the number that is multiplied by the variable. Example: 3x 3 is the coefficient of x
Constant A fixed value. In algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.
Numerical Expression A mathematical phrase that contains only numbers and operations. Example: 9-3
Algebraic Expression An expression that includes at least one variable. Also called a variable expression. Examples: 5n, 6 + c, and 8 - x
Equivalent Expressions Two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same. Example: 3(x + 3) = 3x + 9
Literal Equations An equation that contains two or more variables. Examples: d = rt A = 1 2 h(b 1 + b 2 )
Inequality An inequality says that two values are not equal. Symbol Meaning < is less than > is greater than is less than or equal to is greater than or equal to is not equal to
Solution of an Inequality A number that produces a true statement when substituted for the variable in an inequality. The number 5 is a solution of the inequality 8-2x < 2 because 8-2(5) < 2 8 10 < 2-2 < 2 True
Continuous Graph A graph made up of connected lines or curves.
Discrete Graph A graph made up of unconnected points.
Domain The set of all inputs of a function.
Range The set of all outputs of a function.
Set Notation Notation that includes braces to describe the elements in a set. Example: Another way of saying x < 3, is to use the set notation: {x x is a real number and x < 3} or {x x, x < 3}
Function A rule or correspondence which associates each number x in a (set A) to a unique number f(x) in a (set B).
Vertical Line Test If a vertical line intersects the relation's graph in more than one place, then the relation is a NOT a function.
Independent Variable The input variable of a function. Example: In the function equation y = x + 3, x is the independent variable.
Dependent Variable The output variable of a function. Example: In the function equation y = x + 3, y is the independent variable.
Function Notation A way to name a function using the symbol f(x) instead of y. The symbol f(x) is read as the value of f at x or as f of x. Example: The function y = 2x 9 can be written in function notation as f(x) = 2x 9.
Combine Like Terms Combine all constants into one term and all terms with the same variable into one term. Example: 3x + 2-2x + 9 is simplified as x + 9
Distributive Property A property can be used to find the product of a number and a sum or difference. Example: 3(x + 4) = 3(x) + 3(4) a(b + c) = ab + ac (b + c)a = ba + ca a(b c) = ab ac (b c)a = ba ca
Sequence A list of numbers in a specific order Example: that often form a pattern.
Term of a Sequence Example: An element or number of a sequence.
Explicit Rule A formula that defines the nth term a n, or general term, of a sequence as a function of n. Explicit rules can be used to find any specific term in a sequence without finding the previous terms. Example: f(n) = 2n 9.
Recursive Rule A formula for a sequence in which one or more previous terms are used to generate the next term. Example: f(1) = 4, f(n) = f(n 1) + 10 The sequence for this recursive rule is created using the sum of the previous term f(n 1) and 10.
Arithmetic Sequence A sequence whose successive terms differ by the same nonzero number d, called the common difference. It can be described by an explicit or recursive rule. Example: f(n) = 2000 + 500(n 1) or f(1) = 2000, f(n) = f(n 1) + 500 for n 2; both have a common difference of 500 and the first term is 2000.
Common Difference In an arithmetic sequence, the nonzero constant difference of any term and the previous term. Example: The arithmetic sequence: 5, 9, 13, 17, has a common difference of 4.
x-intercept (Zero) Location where a straight line crosses the x- axis of a graph; the location is represented by an ordered pair (x, y).
y-intercept Location where a straight line crosses the y- axis of a graph; the location is represented by an ordered pair (x, y).
Rate of Change A comparison of a change in one quantity with a change in another quantity. In real-world situations, you can interpret the slope of a line as a rate of change. Example: change in cost change in time
Slope The slope of a non-vertical line is the ratio of the vertical change (the rise) to the horizontal change (the run) between any two points (x 1, y 1 ) and (x 2, y 2 ). Slope is indicated by the letter m m = rise = y 2 y 1 = y run x 2 x 1 x = change in y change in x
Slope Example: the slope is 3/5 y x = Number of units up or down Number of units left or right The change in y means you will move up 3 units since 3 is positive; The change in x means you will move right 5 units since 5 is positive.
Slope Facts 1. Horizontal lines have a slope of zero; m=0 2. Vertical lines have undefined slope 3. Parallel lines have the same slope 4. Perpendicular lines have slopes that are opposite reciprocals. Their product is -1. If m 1 and m 2 are the slopes of two perpendicular lines, then m 1 m 2 =-1
Direct Variation Two variables x and y show direct variation provided that y = ax, where a is a nonzero constant. The variable y is directly proportional to x. Example: Speed and Distance d = 60t The distance traveled is directly proportional to the amount of time traveled.
Constant of Variation The number that relates two variables that are directly proportional. The nonzero constant a in a direct variation equation y = ax. Example: y = -2x constant of variation
Slope-Intercept Form Used when you have the slope and the y-intercept. y = mx + b slope y-int.
Linear Function The equation Ax + By = C represents a linear function provided B 0. Example: The equation 2x y = 3 represents a linear function. The equation x = 3 does not represent a function.
Linear Equation An equation that makes a straight line when it is graphed. y = mx + b m = slope b = y-intercept
Standard Form of a Linear Equation A linear equation written in the form Ax + By = C, where A and B are not both zero. Example: The linear equation y = -3x + 4 can be written in standard form as 3x + y = 4.
Solution of a Linear Equation in Two Variables An ordered pair that produces a true statement when the coordinates of the ordered pair are substituted for the variables in the equation. Example: (1, -4) is a solution of 3x y =7, because 3(1) (-4) = 7.
Discrete Function A function with a graph that consists of isolated points.
Continuous Function A function with a graph that is unbroken.