MTH 1108/1109 | Department of Mathematical and Computer Sciences | MSU Denver

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Khan Academy MTH 1108/1109

This website shows Khan Academy links for most topics in College Algebra

First find the chapter you want in the menu below.

Scroll down through each section to see some links to Khan Academy videos and practice problems for topics in this section.

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Review Sections

**Review - Polynomials**
Topic	Videos	Practice Problems
Recognize Monomials
Recognize Polynomials	Recognize Terms, Coefficients, and Exponents
Add and Subtract Polynomials	Adding and Subtracting Polynomials 1	Adding and Subtracting Polynomials
Add and Subtract Polynomials	Adding and Subtracting Polynomials 2	Adding and Subtracting Polynomials
Multiply Polynomials	Multiplying Polynomials	Multiplying Polynomials
Know Formulas for Special Products	Special Products of Binomials
Divide Polynomials	Polynomial Division	Dividing Polynomials
Work with Polynomials in Two Variables

**Review - Factoring Polynomials**
Topic	Videos	Practice Problems
Factor Special Products	Factoring Difference of Squares	Factoring Special Products
Factor Perfect Squares	Factoring Perfect Square Trinomials
Factor Second-Degree Polynomials	Factoring Simple Quadratics	Factoring Quadratic Expressions
Factor by Grouping	Factor by Grouping
Complete the Square	Completing the Square

**Review - Rational Expressions**
Topic	Videos	Practice Problems
Reduce a Rational Expression to Lowest Terms	Simplifying Rational Expressions Introduction	Dividing Polynomials by Binomials
Multiply and Divide Rational Expressions	Multiplying and Dividing Rational Expressions
Add and Subtract Rational Expressions	Adding and Subtracting Rational Expressions 2	Adding and Subtracting Rational Expressions
Add and Subtract Rational Expressions	Adding and Subtracting Rational Expressions	Adding and Subtracting Rational Expressions 5
Simplify Complex Rational Expressions

**Review - nth Roots; Rational Exponents**
Topic	Videos	Practice Problems
Work with nth Roots	Radical Expressions with Higher Roots
Simplify Radicals	Simplifying Square Roots
Rationalize Denominators	How to Rationalize a Denominator
Simplify Expressions with Rational Exponents	Fractional Exponent Expressions	Exponents 3

Chapter 1

**1.1 Real Numbers and the Rectangular Coordinate System**
Topic	Videos	Practice Problems
Sets of real numbers	Classifying numbers	Classifying numbers practice
The rectangular coordinate system	Points on the coordinate plane	Plotting points practice
Distance formula	Distance between points	Distance formula practice
Midpoint formula	The midpoint of a line segment	Midpoint practice

**1.2 Introduction to Relations and Functions**
Topic	Videos	Practice Problems
Interval notation	Intervals and interval notation
Domain and range	What is the domain of a function?	Domain practice
Deciding whether relations are functions	Testing if a relationship is a function	Recognizing functions practice
Vertical Line Test	Recognizing functions	Recognizing functions practice
Function notation	What is a function?	Functions practice

**1.3 Linear Functions**
Topic	Videos	Practice Problems
Graphing a linear function	Graph by plotting points	Graphing practice 1
Locating intercepts	Finding intercepts	Intercepts practice
Slope	Finding slope	Slope practice
Graphing using the slope and a point	Graphing from slope-intercept equation	Graphing practice 2

**1.4 Equations of Lines and Linear Models**
Topic	Videos	Practice Problems
Point-slope form	Point-slope and slope-intercept equations	Equations practice
Parallel and perpendicular lines	Writing equations of perpendicular lines	Perpendicular lines practice

**1.5 Linear Equations and Inequalities**
Topic	Videos	Practice Problems
Solving linear equations in one variable	Linear equation	Linear equations practice
Identities	Creating an equation with infinitely-many solutions
Contradictions	Creating an equation with no solution
Solving linear inequalities in one variable	Solving an inequality	Inequalities practice
Compound inequalities	Double inequalities

**1.6 Applications of Linear Functions**
Topic	Videos	Practice Problems
Applications of linear equations	Mixture problems
Formulas	Manipulating formulas

Chapter 2

**2.1 Graphs of Basic Functions and Relations; Symmetry**
Topic	Videos	Practice Problems
Increasing, decreasing, and constant functions	Increasing, decreasing, positive, or negative intervals	Increasing or decreasing practice
Even and odd functions	Intro to function symmetry	Symmetry practice

**2.2 Vertical and Horizontal Shifts of Graphs**
Topic	Videos	Practice Problems
Vertical and horizontal shifts	Shifting functions	Shifting functions practice

**2.3 Stretching, Shrinking, and Reflecting Graphs**
Topic	Videos	Practice Problems
Vertical stretching	Shifting & reflecting functions	Shifting & reflecting practice
Vertical shrinking	Compressing functions
Reflecting	Reflecting & compressing functions

**2.4 Absolute Value Functions**
Topic	Videos	Practice Problems
Solving absolute value equations	Absolute value equations	Absolute value equations practice
Solving absolute value inequalities	Absolute value inequalities

**2.5 Piecewise-defined Functions**
Topic	Videos	Practice Problems
Evaluating piecewise-defined functions	Evaluating piecewise-defined functions	Evaluating piecewise-defined functions practice
Graphing piecewise-defined functions	Graphing piecewise-defined functions	Graphing piecewise-defined functions practice

**2.6 Operations and Composition**
Topic	Videos	Practice Problems
Adding functions	Adding functions
Subtracting functions	Subtracting functions
Multiplying functions	Multiplying functions
Dividing functions	Dividing functions
Composition of functions	Intro to composing functions

Chapter 3

**3.2 Quadratic Functions and Graphs**
Topic	Videos	Practice Problems
Quadratic functions	Forms & features of quadratic functions	Quadratic functions practice
Vertex formula	Finding the vertex of a parabola
Circles in standard form	Features of a circle from standard equation	Equation of a circle practice 1
Circles in expanded form	Features of a circle from expanded equation	Equation of a circle practice 2
Completing the square	Completing the square

**3.3 Quadratic Equations and Inequalities**
Topic	Videos	Practice Problems
Zero-product property	Solving a quadratic by factoring	Solve a quadratic by factoring practice
Square-root method	Solving quadratics by square roots	Solve a quadratic by square roots practice
Completing the square	Solving quadratics by completing the square
The quadratic formula	Using the quadratic formula	Quadratic formula practice
Quadratic inequalities	Quadratic inequalities

**3.4 Applications of Quadratic Functions and Models**
Topic	Videos	Practice Problems
No topics available

Chapter 4

**4.1 Graphs of Polynomial Functions**
Topic	Videos	Practice Problems
Turning points and real zeros	Zeros of polynomials and their graphs	Zeros of polynomials practice
End behavior	End behavior of polynomials	End behavior practice

**4.2 Topics in the Theory of Polynomial Functions Part 1**
Topic	Videos	Practice Problems
Polynomial division	Long division of polynomials
Remainder theorem	Using the remainder theorem to check factors	Remainder theorem practice

**4.3 Topics in the Theory of Polynomial Functions Part 2**
Topic	Videos	Practice Problems
No topics available

**4.4 Polynomial Equations, Inequalities, Applications, and Models**
Topic	Videos	Practice Problems
Solving a polynomial equation	Finding zeros of polynomials	Finding zeros of polynomials practice
Polynomial inequalities	Quadratic inequalities

Chapter 5

**5.1 Rational Functions and Graphs**
Topic	Videos	Practice Problems
No topics available

**5.2 Rational Functions and Graphs part 2**
Topic	Videos	Practice Problems
Vertical and horizontal asymptotes	Rational function end behavior and discontinuities
Graphing a rational function	Graphing rational functions

**5.3 Rational Equations, Inequalities, Models, and Applications**
Topic	Videos	Practice Problems
Solving a rational equation	Equations with rational expressions
Solving a rational inequality	Rational inequalities
Models and Applications	Rational equations word problem

**5.4 Functions Defined By Powers and Roots**
Topic	Videos	Practice Problems
Domain of a root function	Domain of a radical function	Domain practice
Transforming graphs of root functions	Transforming the square root function

**5.5 Equations, Inequalities, and Applications Involving Root Functions**
Topic	Videos	Practice Problems
Solving root equations	Solving radical equations	Radical equations practice

Chapter 6

**6.1 Inverse Functions**
Topic	Videos	Practice Problems
One-to-one functions	Relating invertability to being one-to-one
Finding inverses of one-to-one functions	Introduction to function inverses
Finding equations of inverses	Finding inverse functions	Inverse functions practice

**6.2 Exponential Functions**
Topic	Videos	Practice Problems
Graphs of exponential functions	Exponential function graph	Exponential graphs practice
Solving exponential equations	Solving exponential equations using exponent properties	Solving exponential equations practice
The number e and continuous compounding	e and compound interest

**6.3 Logarithms and Their Properties**
Topic	Videos	Practice Problems
Change exponential statements to logarithmic statements	Logarithms	Logarithms practice
Evaluate logarithmic expressions	Evaluating logarithms	Evaluating logarithm expressions practice
Properties of logarithms	Intro to logarithm properties	Logarithm properties practice
The change of base rule	Change of base rule	Change of base rule practice

**6.4 Logarithmic Functions**
Topic	Videos	Practice Problems
Graph logarithmic functions	Graphing logarithmic functions	Graphing logarithmic functions practice

**6.5 Exponential and Logarithmic Equations**
Topic	Videos	Practice Problems
Solving exponential equations	Solving exponential equations using logarithms	Solving exponential equations with logarithms practice
Solving logarithmic equations	Logarithmic equations

**6.6 Further Applications and Modeling with Exponential and Logarithmic Functions**
Topic	Videos	Practice Problems
Exponential Growth	Exponential model word problem: bacteria growth	Exponential growth practice
Exponential Decay	Exponential model word problem: medication dissolve

Chapter 7

**7.1 Systems of Equations**
Topic	Videos	Practice Problems
Substitution method	Systems of equations with substitution	Substitution method practice
Elimination method	Systems of equations with elimination	Elimination method practice
Special Systems	Number of solutions to a system of equations	Number of solutions practice
Nonlinear systems	Quadratic systems: algebraic solution

**7.2 Solution of Linear Systems in Three Variables**
Topic	Videos	Practice Problems
Solving a system of three equations in three variables	Solving linear systems with three variables
Identifying a system with no solution	Solving linear systems with three variables: no solution

Chapter 12

**12.5 The Binomial Theorem**
Topic	Videos	Practice Problems
Binomial Coefficients	Intro to the binomial theorem
Pascal's Triangle	Pascal's Triangle and binomial expansion
The Binomial Theorem	Expanding binomials	Expanding binomials practice

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