CLEP 
College Algebra
College · CLEP College Algebra · Certificate available
263 lessons 2.6h runtime 9 units 0 links between lessons Test yourself · 9 quizzes, a mid exam, and a final
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Begin with Unit 1: Real Numbers, Exponents, and Radicals. It sets the foundation for everything that follows.
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Unit 1: Real Numbers, Exponents, and Radicals 41 lessons, 2 lecture parts
- 001 The Real Numbers
- 002 Natural Numbers and Whole Numbers
- 003 The Integers
- 004 Rational Numbers
- 005 Irrational Numbers
- 007 Classifying a Real Number worked example
- 009 Exponential Notation
- 010 The Order of Operations
- 011 Exponents Before Negation
- 012 The Invisible-Parentheses Error
- 014 The Commutative Properties
- 015 The Associative Properties
- 016 The Distributive Property
- 017 The Identity Properties
- 018 The Inverse Properties
- 022 The Product Rule of Exponents
- 023 The Quotient Rule of Exponents
- 025 The Power Rule of Exponents
- 026 The Power-Product Confusion
- 028 The Zero Exponent Rule of Exponents
- 029 The Zero-Power Error
- 031 The Negative Rule of Exponents
- 032 The Negative-Exponent Sign Error
- 034 The Power of a Product Rule of Exponents
- 035 The Power of a Quotient Rule of Exponents
- 037 Simplifying with the Exponent Rules worked example
- 039 Scientific Notation
- 040 Absolute Value
- 041 The Principal Square Root
- 042 The Square Root of a Square
- 043 The Dropped-Absolute-Value Error
- 045 The Product Rule for Simplifying Square Roots
- 046 The Split-Sum Error
- 048 The Quotient Rule for Simplifying Square Roots
- 050 Simplifying a Square Root worked example
- 052 Like Radicals
- 054 Rationalizing a Denominator worked example
- 056 The Principal nth Root
- 057 Rational Exponents: the 1/n Power
- 058 Rational Exponents: the m/n Power
- 060 From Counting to Rational Exponents review
Unit 2: Polynomials, Factoring, and Rational Expressions 31 lessons, 1 lecture part
Lecture: Watch · 33:41
- 061 Polynomials
- 062 Degree and Leading Coefficient
- 063 Monomials, Binomials, Trinomials
- 065 Adding and Subtracting Polynomials
- 067 Multiplying Polynomials
- 068 FOIL
- 070 Squaring a Binomial
- 071 The Missing-Middle Error
- 073 The Difference of Squares
- 081 Factoring
- 082 The Greatest Common Factor
- 083 Factoring Out the GCF worked example
- 085 Factoring x² + bx + c
- 086 Factoring ax² + bx + c by Grouping worked example
- 088 Factoring a Perfect Square Trinomial
- 090 Factoring a Difference of Squares
- 091 The Sum of Squares
- 093 The Sum and Difference of Cubes
- 095 Choosing a Factoring Strategy worked example
- 101 Rational Expressions
- 103 Only Factors Cancel
- 104 The Canceled-Term Error
- 106 Simplifying a Rational Expression worked example
- 108 Multiplying Rational Expressions
- 109 Dividing Rational Expressions
- 111 The Least Common Denominator
- 112 Adding and Subtracting Rational Expressions worked example
- 114 Splitting a Fraction over Its Numerator
- 115 The Denominator-Split Error
- 117 Simplifying a Complex Rational Expression worked example
- 120 The Arithmetic of Polynomials review
Unit 3: Linear Equations, Models, and Inequalities 33 lessons, 1 lecture part
Lecture: Watch · 34:17
- 121 The Cartesian Coordinate System
- 122 Graphing by Plotting Points
- 124 Intercepts
- 126 The Distance Formula
- 127 The Midpoint Formula
- 131 Linear Equations in One Variable
- 132 The Solution of an Equation
- 133 Solving a Linear Equation worked example
- 135 Identity, Conditional, and Inconsistent Equations
- 137 Rational Equations
- 138 Checking in the Original Equation
- 140 Solving a Rational Equation worked example
- 142 The Slope of a Line
- 143 The Slope Formula
- 145 Slope-Intercept Form
- 146 The Point-Slope Formula
- 148 Writing a Line from Two Points worked example
- 150 Parallel Lines
- 151 Perpendicular Lines
- 153 Horizontal and Vertical Lines
- 156 Interval Notation
- 158 Solutions of Linear Inequalities
- 159 The Addition Property of Inequality
- 160 The Multiplication Property of Inequality
- 161 The Kept-Sign Error
- 163 Solving a Linear Inequality worked example
- 165 Compound Inequalities
- 167 Absolute Value as Distance
- 168 Absolute Value Inequalities: Less Than
- 169 Absolute Value Inequalities: Greater Than
- 170 The Swapped-Cases Error
- 172 Solving an Absolute Value Inequality worked example
- 180 The Line and the Balance review
Unit 4: Complex Numbers and Quadratic Equations 28 lessons, 1 lecture part
Lecture: Watch · 31:47
- 181 The Imaginary Unit
- 182 Complex Numbers in Standard Form
- 184 Adding and Subtracting Complex Numbers
- 185 Multiplying Complex Numbers
- 187 The Complex Conjugate
- 188 Dividing Complex Numbers worked example
- 190 Square Roots of Negative Numbers
- 191 The Powers of i
- 196 Quadratic Equations
- 197 The Zero-Product Property
- 198 Solving a Quadratic by Factoring worked example
- 200 Keeping Every Factor
- 201 The Divided-Away Solution
- 203 The Square Root Property
- 204 The Lost-Root Error
- 206 Completing the Square worked example
- 208 The Quadratic Formula
- 209 The Discriminant
- 211 Solving with the Quadratic Formula worked example
- 213 Complex Solutions of Quadratics
- 216 Radical Equations
- 217 Checking After Raising to a Power
- 218 The Unchecked-Squaring Error
- 220 Solving a Radical Equation worked example
- 222 Equations Quadratic in Form
- 224 Equations with Rational Exponents
- 226 Absolute Value Equations
- 230 Every Quadratic Surrenders review
Unit 5: Functions: Definition, Domain, Graphs, Transformations 36 lessons, 1 lecture part
Lecture: Watch · 35:20
- 231 Relations
- 232 Functions
- 234 Function Notation
- 235 Evaluating a Function
- 236 Evaluating at a Sum
- 237 The Assumed-Linearity Error
- 239 Evaluating versus Solving
- 241 One-to-One Functions
- 242 The Vertical Line Test
- 243 The Horizontal Line Test
- 245 Determining Whether a Relation Is a Function worked example
- 249 The Domain of a Function
- 250 The Range
- 252 Finding a Domain from an Equation worked example
- 254 Piecewise-Defined Functions
- 256 The Absolute Value Function
- 263 The Average Rate of Change
- 265 Increasing and Decreasing Functions
- 266 Local Maxima and Minima
- 273 The Algebra of Functions
- 275 Function Composition
- 276 Evaluating a Composite Function worked example
- 278 Composition Order Matters
- 281 Vertical Shifts
- 282 Horizontal Shifts
- 284 Reflections
- 285 Even and Odd Functions
- 287 Vertical Stretches and Compressions
- 288 Horizontal Stretches and Compressions
- 290 Graphing by Transformations worked example
- 293 Inverse Functions
- 294 The Reciprocal-Inverse Error
- 296 The Composition Test for Inverses
- 297 Finding an Inverse Algebraically worked example
- 299 Graphs of Inverse Functions
- 300 The Function Machine review
Unit 6: Linear and Quadratic Functions as Models 19 lessons, 1 lecture part
Lecture: Watch · 25:13
- 301 Linear Functions
- 302 Direction from the Slope
- 304 Slope as a Rate
- 306 Building a Linear Model worked example
- 308 A Linear Model from Two Data Points worked example
- 310 Where Two Lines Meet
- 312 The Zero of a Linear Function
- 321 Quadratic Functions and Parabolas
- 322 The Vertex and Axis of Symmetry
- 324 General Form and Standard Form
- 325 Reading the Vertex from Standard Form
- 326 The Vertex-Sign Error
- 327 The Vertex Formula
- 329 Converting General to Standard Form worked example
- 331 Maximum and Minimum Values
- 333 Zeros, x-Intercepts, Solutions
- 335 The Full Quadratic Workup worked example
- 337 Optimizing with a Quadratic worked example
- 350 The Parabola Dossier review
Unit 7: Polynomial and Rational Functions 24 lessons, 1 lecture part
Lecture: Watch · 29:09
- 351 Power Functions
- 352 End Behavior
- 354 End Behavior from the Leading Term
- 356 Zeros and Multiplicity
- 358 Turning Points
- 360 Sketching a Polynomial worked example
- 364 Polynomial Long Division worked example
- 366 Synthetic Division worked example
- 368 The Remainder Theorem
- 369 The Factor Theorem
- 371 Finding Zeros with the Factor Theorem worked example
- 376 Rational Functions
- 377 Vertical Asymptotes
- 378 Removable Discontinuities
- 379 The Erased-Hole Error
- 381 Horizontal Asymptotes
- 383 Analyzing a Rational Function worked example
- 386 Radical Functions and Their Domains
- 388 Restricting a Domain for an Inverse
- 391 Direct Variation
- 392 Inverse Variation
- 393 Joint Variation
- 395 Solving a Variation Problem worked example
- 410 The Anatomy of Higher Functions review
Unit 8: Exponential and Logarithmic Functions 28 lessons, 1 lecture part
Lecture: Watch · 33:34
- 411 Exponential Functions
- 412 Growth and Decay
- 414 Linear versus Exponential Change
- 416 Evaluating Exponential Functions
- 418 Compound Interest worked example
- 420 The Number e
- 421 Continuous Growth and Decay
- 423 Graphs of Exponential Functions
- 426 The Logarithm
- 427 Logarithms and Exponentials Are Inverses
- 429 Common and Natural Logarithms
- 431 Converting Between Forms worked example
- 433 Evaluating Logarithms Mentally
- 435 Graphs of Logarithmic Functions
- 446 The Product Rule for Logarithms
- 447 The Split-Sum Log Error
- 448 The Multiplied-Logs Error
- 450 The Quotient Rule for Logarithms
- 451 The Divided-Logs Error
- 453 The Power Rule for Logarithms
- 455 Expanding and Condensing Logarithms worked example
- 457 The Change-of-Base Formula
- 463 The One-to-One Property of Exponential Functions
- 465 Solving Exponential Equations with Logarithms worked example
- 467 The One-to-One Property of Logarithms
- 468 Solving Logarithmic Equations worked example
- 473 Doubling Time worked example
- 480 The Inverse Kingdom review
Unit 9: Systems, Counting, the Binomial Theorem + Capstones 23 lessons, 1 lecture part
Lecture: Watch · 34:23
- 481 Systems of Linear Equations
- 482 The Substitution Method
- 484 Solving by Substitution worked example
- 486 The Addition Method
- 488 Solving by Addition worked example
- 490 Independent, Dependent, Inconsistent
- 492 A System from a Story worked example
- 496 Systems in Three Variables
- 498 Solving a Three-Variable System worked example
- 501 Nonlinear Systems
- 503 Solving a Nonlinear System worked example
- 511 The Multiplication Principle
- 513 Factorials
- 515 Permutations
- 516 Combinations
- 518 Binomial Coefficients
- 520 The Binomial Theorem
- 522 Expanding with the Binomial Theorem worked example
- 524 A Single Term of an Expansion
- 530 Many Unknowns, Counted Ways review
- 536 The Error Families review
- 538 The Course, One Thread review
- 540 Where the Numbers End review
Who this subject is for
- Students preparing for the CLEP College Algebra exam
- STEM and business majors needing a strong algebra foundation
- Nursing and healthcare students needing math competency
- Adult learners returning to school
- Homeschool students
- Anyone wanting clear, structured algebra instruction
Why College Algebra matters
College Algebra is a gateway course. It is the foundation for:
- Precalculus
- Calculus
- Statistics
- Chemistry
- Physics
- Economics
- Computer science
Time to complete
- of lessons (263, measured)
- 2.6 h
- of lectures (10)
- 5.1 h
- learning hours on the certificate, with quizzes and the final
- 12 h
Times are measured from the recordings and the exam time limits. Go at your own pace; nothing expires.
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