Clep College Mathematics Exam - Algebra & Functions

Prepare to earn college credit with the CLEP College Mathematics exams by conquering the Algebra & Functions topic.

What you'll learn

How to solve for an unknown variable in an algebraic equation, how to solve equations in fractional form, and how to solve exponential equations.

How to solve logarithms, what is a common logarithm, and what are the logarithm rules.

Define linear equation, solve linear equations with one unknown variable, and graph linear equations using slope-intercept form.

Model real-world problems using linear functions.

Find a linear equation using point-slope form and intercept form.

Solve simultaneous linear equations.

Solve absolute value equations, solve inequality equations, and graph linear inequalities.

Define and solve quadratic equations.

Use the quadratic formula and understand the impact of the discriminant on the nature of the roots of a quadratic equation.

Identify relations and find their domain and range.

Identify and evaluate functions, including piecewise functions.

Find the domain of a function and the inverse of a function.

Solve and graph exponential functions.

Solve compositions of functions and combine functions algebraically.

Understand how to transform the graph of a function and represent the a graphical transformation of a function in functional notation.

Requirements

This is a college math course, so it is advised that students have taken at least 10th grade math before attempting this course.

Description

This course will teach the concepts related to the Algebra & Functions topic of the College Mathematics CLEP exam. The College Mathematics CLEP exam can be taken for college credit. The exact courses that the college credit can be applied to are determined by your university, please consult your university for details. The Algebra & Functions topic covers approximately 20% of the material on the College Mathematics CLEP exam, according to the College Board website. Mastering the Algebra & Functions topic will help you win points on the College Mathematics CLEP exam which will help you pass the exam. The following lectures are included:Equations - how to solve for unknown variable in equations, how to solve equations in fractional form, and how to solve exponential equationsLogarithms - how to find logarithms, common logarithm, and logarithm rulesLinear equations - define linear equation, solve linear equations with one unknown, general format for linear equations with two unknowns, slope-intercept form, and how to graph linear equationsModeling real-world problems - modeling linear functions and using tabular form to write an equation for a linear functionPoint-Slope and Intercept Form - point-slope form, how to find linear equation given two points using point-slope form, intercept form, how to find linear equation given the x and y intercepts using intercept form, horizontal lines, and vertical linesSimultaneous linear equations - how to solve simultaneous linear equations using substitution, addition or subtraction, and graphingOther systems of equations - dependent equations, consistent vs inconsistent system of linear equations, parallel lines and perpendicular linesInequality and absolute value equations - how to solve inequalities, graphing linear inequalities, and solving absolute value equationsQuadratic equations - define quadratic equations, quadratic equations with one unknown, quadratic equations with two unknowns, and solving quadratic equations with one unknown using factoring, difference of two squares, and quadratic formulaQuadratic formula - quadratic formula examples, discriminant definition, and impact of the discriminant on the nature of the roots of a quadratic equationRelations - ordered pairs, relations, and domain and range of a relationFunctions - function definition, the three ways that functions can be represented, numerical representation of functions,  how to identify relations that are functions, graphical representation of functions, the vertical line test, symbolic representation of functions, evaluating functions to find y with a given x value, and piecewise functionsDomain of functions - 5 options for specifying domain of a function, domain of function rules, and domain of function examplesOther functions- inverses of a function and exponential functionsCombining functions - Composition of functions and combining functions algebraicallyTransformation of graphs - common graph transformations and their impact on the function in functional notation

Overview

Section 1: Algebra

Lecture 1 Equations

Lecture 2 Logarithms

Lecture 3 Linear Equations

Lecture 4 Modeling Real-World Problems

Lecture 5 Point-Slope and Intercept Form

Lecture 6 Simultaneous Linear Equations

Lecture 7 Other Systems of Equations

Lecture 8 Inequality and Absolute Value Equations

Lecture 9 Quadratic Equations

Lecture 10 Quadratic Formula

Section 2: Functions

Lecture 11 Relations

Lecture 12 Functions

Lecture 13 Domain of Functions

Lecture 14 Other Functions

Lecture 15 Combining Functions

Lecture 16 Transformations of Graphs

This course is intended for students that want to earn college credit using the College Mathematics CLEP exam.