Module 4: Equations and Inequalities in One Variable

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1 Module 1: Relationships between quantities Precision- The level of detail of a measurement, determined by the unit of measure. Dimensional Analysis- A process that uses rates to convert measurements from one unit to another. Significant Digits- The digits used to express the precision of a measurement. Module 2: Exponents and Real Numbers Radical symbol - The symbol used to denote a root. The symbol is used alone to indicate a square root or with an index,, to indicate the nth root. Exponent The number that indicates how many times the base in a power is used as a factor. Module 3: Expressions Associative Property- For all numbers a, b, and c, (a + b) + c = a + (b + c). Distributive Property- For all real numbers a, b, and c, a(b + c) = ab + ac, and (b + c)a = ba + ca. Commutative Property- For any two numbers a and b, a + b = b + a Coefficient- A number that is multiplied by a variable. (The number in front of the variable) Expression- A mathematical phrase that contains operations, numbers, and/or variables. Module 4: Equations and Inequalities in One Variable Equation- A mathematical statement that two expressions are equivalent. Identity An equation that is true for all values of the variables. Solution of an inequality in one variable- A value or values that make the inequality true. Inverse operations Operations that undo each other.

2 Module 5: Equations in Two Variables and Functions Function A relation in which every domain value is paired with exactly one range value. Domain- The set of all first coordinates (or x- values) of a relation or function. Range- The set of all second coordinates (or y- values) of a function or relation. Recursive rule for nth term of a sequence A rule for a sequence in which one or more previous terms are used to generate the next term. Explicit rule for nth term of a sequence- A rule that defines the nth term an, or a general term, of a sequence as a function of n. Module 6: Linear Functions Linear Function- A function that can be written in the form y = mx + b, where x is the independent variable and m and b are real numbers. Its graph is a line. Parent function- The simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function. Rate of change- A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable. Slope- A measure of the steepness of a line. If (x1, y1) and (x2, y2) are any two points on the line, the slope of the one, known as m, is represented by the equation m = Slope intercept form- The slope- intercept form of a linear equation is y = mx + b, where m is the slope and b is the y- intercept x- intercept- The x- coordinate(s) of the point(s) where a graph intersects the x- axis. y- intercept- The y- coordinate(s) of the point(s) where a graph intersects the y- axis.

3 Module 7: Building Linear Functions Boundary line- A line that divides a coordinate plane into two half- planes. Common difference- In an arithmetic sequence, the nonzero constant difference of any term and the previous term. Inverse function- The relation that results from exchanging the input and output values of a function. Module 8:Modeling with Linear Functions Bivariate data- is data that involves two variables. Causation- the action of causing something. Correlation- A measure of the strength and direction of the relationship between two variables or data sets. A common error when interpreting paired data is confusing correlation and causation. If a correlation exists between two variables, this does not necessarily mean that one variable causes the other. Correlation coefficient- A number r, where 1 r 1, that describes how closely the points in a scatter plot cluster around the least- squares line. Interpolation- Making a prediction using a value of the independent variable from within a model s domain Module 9: Systems of Equations and Inequalities Solution of a system of linear equations Any ordered pair that satisfies all the equations in a system. Solution of a system of linear inequalities Any ordered pair that satisfies all the inequalities in a system. System of linear equations - A system of equations in which all of the equations are linear.

4 Module 10: Exponential functions and equations: Common ratio- In a geometric sequence, the constant ratio of any term and the previous term. Exponential growth - An exponential function of the form f(x) = abx in which b > 1. If r is the rate of growth, then the function can be written y = a(1 + r)t, where a is the initial amount and t is the time. Exponential decay exponential decay An exponential function of the form f (x) = abx in which 0 < b < 1. If r is the rate of decay, then the function can be written y = a(1 - r) t, where a is the initial amount and t is the time. Exponential function - A function of the form f(x) = ab x, where a and b are real numbers with a = 0, b > 0, and b = 1. Geometric sequence- A sequence in which the ratio of successive terms is a constant r, called the common ratio, where r = 0 and r = 1. Module 11: Modeling with exponential functions Residual- The signed vertical distance between a data point and a line of fit. Module 12: Descriptive Statistics Categorical data- Data that are qualitative in nature, such as liberal, moderate, and conservative. Quantitative data- Numerical data. Outlier- A data value that is far removed from the rest of the data. Cluster- A set of closely grouped data.

5 Module 13: Data Displays Mean- The sum of all the values in a data set divided by the number of data values. Also called the average. Median- For an ordered data set with an odd number of values, the median is the middle value. For an ordered data set with an even number of values, the median is the average of the two middle values. Normal Curve- The graph of a probability density function that corresponds to a normal distribution; bell- shaped and symmetric about the mean, with the x- axis as a horizontal asymptote. Normal Distribution- A distribution of data that varies about the mean in such a way that the graph of its probability density function is a normal curve. Module 14: Polynomials and Operations Binomial - A polynomial with two terms. Degree of a polynomial FOIL method monomial- A mnemonic (memory) device for a method of multiplying two binomials: Multiply the First terms. Multiply the Outer terms. Multiply the Inner terms. Multiply the Last terms. Polynomial- A monomial or a sum or difference of monomials. Trinomial - A polynomial with three terms. Module 15: Factoring Polynomials Greatest common factor - The largest common factor of two or more given numbers.

6 Module 16: Solving Quadratic Equations Discriminant - the discriminant of the quadratic equation ax 2 + bx + c = 0 is b 2-4ac. Completing the square - A process used to form a perfect- square trinomial. To complete the square of x 2 + bx, add. Quadratic formula- the formula x = ± ", which 2a gives solutions, or roots, of equations in the form ax + bx + c = 0 where a 0 Module 17: Quadratic Functions Parabola- The shape of the graph of a quadratic function. Vertex of a parabola - The highest or lowest point on the parabola. Maximum value- the y- value of the highest point on the graph of the function Minimum value- y- value of the lowest point on the graph of the function. Zero of a function- For the function f, any number x such that f(x) = 0 Axis of symmetry- A line that divides a plane figure or a graph into two congruent reflected halves. Module 18: Piecewise and Absolute Value Functions Absolute value function - A function whose rule contains absolute- value expressions. Greatest integer function- A function denoted by f(x) = [x] in which the number x is rounded down to the greatest integer that is less than or equal to x. Piecewise function- A function that is a combination of one or more functions. Step function- A piecewise function that is constant over each interval in its domain.

7 Module 19: Square Root and Cube Root Functions Cube root function - A number, written as x, whose cube is x. Square root function- A function whose rule contains a variable under a square root sign. Translation- A transformation that shifts or slides every point of a figure or graph the same distance in the same direction. Equations: Linear: y = mx + b Exponential: ab Quadratic: ax + bx + c = 0 Absolute Value: a x h + k Square Root: a x h + k Cube Root a x h + k where a = slope, h = horizontal shift, k = vertical shift Vertex: h, k FLIP THE SIGN ONLY FOR h EVERYTIME