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College Algebra · Lessons

College Algebra lessons

8 sections · 77 skills · work through the full outline skill by skill — read the long-form lesson or flip through the slide-style version.
Long-form lessonsSlide-style lessons

College Algebra

Practice 77 skills across this outline.

Recommended next
Solve Systems of Linear Equations: Substitution
Linear Models & Systems · Systems of Equations
Long-form lesson
Weighting distribution
22 categories
Exponential & Logarithmic Functions · Logarithms
10%
Rational Expressions & Functions · Rational Function Graphs
8%
Linear Models & Systems · Lines
7%
Modeling, Word Problems & Quantitative Reasoning · Algebraic Modeling
6%
Modeling, Word Problems & Quantitative Reasoning · Data & Regression
6%
Quadratics & Polynomials · Factoring & Polynomial Algebra
6%

Skills

The comprehensive taxonomy of college algebra — drill into a card to work its skills.

Linear Models & Systems · Systems of Equations

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
Solve Systems of Linear Equations: SubstitutionRecommended
Long-form
2
Solve Systems Graphically and Interpret IntersectionsAvailable
Long-form
3
Systems of Equations in ApplicationsAvailable
Long-form
4
Solve Systems of Linear Equations: EliminationAvailable
Long-form

Linear Models & Systems · Lines

4 core skills7% total weight
0/4 completed
4 skills to mastery
1
Equation of a Line FormatsAvailable
Long-form
2
Slope: Compute and InterpretAvailable
Long-form
3
Linear Modeling from Data/Word ProblemsAvailable
Long-form
4
Parallel and Perpendicular LinesAvailable
Long-form

Exponential & Logarithmic Functions · Exponential Functions

2 core skills3% total weight
0/2 completed
2 skills to mastery
1
Solving Exponential EquationsAvailable
Long-form
2
Exponential Growth and Decay ModelsAvailable
Long-form

Exponential & Logarithmic Functions · Logarithms

5 core skills10% total weight
0/5 completed
5 skills to mastery
1
Log Properties (Product, Quotient, Power)Available
Long-form
2
Change of BaseAvailable
Long-form
3
Logarithmic ModelsAvailable
Long-form
4
Definition of LogarithmsAvailable
Long-form
5
Solving Logarithmic EquationsAvailable
Long-form

Functions & Graphs · Inverse Functions

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Finding and Verifying Inverse Functions AlgebraicallyAvailable
Long-form
2
Graphing Inverse Functions and SymmetryAvailable
Long-form
3
One-to-One FunctionsAvailable
Long-form

Functions & Graphs · Transformations

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Shifts, Stretches/Compressions, and ReflectionsAvailable
Long-form
2
Graphing from Parent FunctionsAvailable
Long-form
3
Combining TransformationsAvailable
Long-form

Functions & Graphs · Function Basics

5 core skills3% total weight
0/5 completed
5 skills to mastery
1
Composition of Functions, Domain of CompositionAvailable
Long-form
2
Function Notation: Evaluate and InterpretAvailable
Long-form
3
Relations and FunctionsAvailable
Long-form
4
Average Rate of ChangeAvailable
Long-form
5
Determine Domain and RangeAvailable
Long-form

Functions & Graphs · Graphing Essentials

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Piecewise Functions: Evaluate and GraphAvailable
Long-form
2
End Behavior (Intro)Available
Long-form
3
Intercepts and SymmetryAvailable
Long-form

Modeling, Word Problems & Quantitative Reasoning · Algebraic Modeling

4 core skills6% total weight
0/4 completed
4 skills to mastery
1
Rate Problems (Work, Motion, and Units)Available
Long-form
2
Dimensional Analysis and Unit ConsistencyAvailable
Long-form
3
Mixture ProblemsAvailable
Long-form
4
Translate Word Problems into Expressions, EquationsAvailable
Long-form

Modeling, Word Problems & Quantitative Reasoning · Data & Regression

3 core skills6% total weight
0/3 completed
3 skills to mastery
1
Exponential Regression Interpretation (Technology-Assisted)Available
Long-form
2
Interpreting Scatterplots and Choosing a ModelAvailable
Long-form
3
Linear Regression Interpretation (Technology-Assisted)Available
Long-form

Rational Expressions & Functions · Rational Expressions

3 core skills2% total weight
0/3 completed
3 skills to mastery
1
Add and Subtract Rational ExpressionsAvailable
Long-form
2
Multiply and Divide Rational ExpressionsAvailable
Long-form
3
Complex FractionsAvailable
Long-form

Rational Expressions & Functions · Rational Function Graphs

4 core skills8% total weight
0/4 completed
4 skills to mastery
1
Slant (Oblique) AsymptotesAvailable
Long-form
2
End Behavior via Degree ComparisonAvailable
Long-form
3
Vertical and Horizontal AsymptotesAvailable
Long-form
4
Domain Restrictions, Holes, and DiscontinuitiesAvailable
Long-form

Rational Expressions & Functions · Rational Equations & Inequalities

2 core skills2% total weight
0/2 completed
2 skills to mastery
1
Rational Inequalities Using Sign ChartsAvailable
Long-form
2
Solve Rational EquationsAvailable
Long-form

Foundations & Algebraic Skills · Exponents & Radicals

4 core skills2% total weight
0/4 completed
4 skills to mastery
1
Exponent RulesAvailable
Long-form
2
Radical Equations and Extraneous SolutionsAvailable
Long-form
3
Rationalizing DenominatorsAvailable
Long-form
4
Simplifying Radicals and Combining Like RadicalsAvailable
Long-form

Foundations & Algebraic Skills · Real Number System & Expressions

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
Real Numbers: Operations & PropertiesAvailable
Long-form
2
Rational Expressions and Domain RestrictionsAvailable
Long-form
3
Factoring Out Greatest Common Factor (GCF)Available
Long-form
4
Simplifying Algebraic ExpressionsAvailable
Long-form

Foundations & Algebraic Skills · Linear Equations & Inequalities

5 core skills5% total weight
0/5 completed
5 skills to mastery
1
Solving Linear Equations (Including Fractions)Available
Long-form
2
Absolute Value EquationsAvailable
Long-form
3
Absolute Value InequalitiesAvailable
Long-form
4
Linear Inequalities and Interval NotationAvailable
Long-form
5
Compound InequalitiesAvailable
Long-form

Quadratics & Polynomials · Factoring & Polynomial Algebra

6 core skills6% total weight
0/6 completed
6 skills to mastery
1
Polynomial Operations: Add, Multiply, and FactorAvailable
Long-form
2
Polynomial Graphs: Turning Points, End BehaviorAvailable
Long-form
3
Graphing Polynomial Functions: Zeros and MultiplicityAvailable
Long-form
4
Factoring Trinomials and Special ProductsAvailable
Long-form
5
Polynomial Long Division and Synthetic DivisionAvailable
Long-form
6
Zeros, Factors, and the Factor TheoremAvailable
Long-form

Quadratics & Polynomials · Complex Numbers

2 core skills1% total weight
0/2 completed
2 skills to mastery
1
Complex Solutions to Quadratic EquationsAvailable
Long-form
2
Imaginary Unit and Complex NumbersAvailable
Long-form

Quadratics & Polynomials · Quadratic Functions

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
Quadratic Models and Optimization (Max/Min)Available
Long-form
2
Graphing Parabolas: Vertex, Symmetry, InterceptsAvailable
Long-form
3
Quadratic Formula and the DiscriminantAvailable
Long-form
4
Vertex Form and Completing the SquareAvailable
Long-form

Sequences, Series & Financial Math · Financial Math

3 core skills6% total weight
0/3 completed
3 skills to mastery
1
Present Value and Future ValueAvailable
Long-form
2
Simple Interest and Compound InterestAvailable
Long-form
3
Annuities and Loan Payments (Intro)Available
Long-form

Sequences, Series & Financial Math · Sequences

2 core skills4% total weight
0/2 completed
2 skills to mastery
1
Arithmetic Sequences: Explicit and Recursive FormsAvailable
Long-form
2
Geometric Sequences: Explicit and Recursive FormsAvailable
Long-form

Sequences, Series & Financial Math · Series

2 core skills2% total weight
0/2 completed
2 skills to mastery
1
Sum of Geometric SeriesAvailable
Long-form
2
Sum of Arithmetic SeriesAvailable
Long-form