Khan Academy MTH 1310

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Chapter 0: Algebra Review

**Section 0.2**
Topic	Videos	Practice Problems
Real Numbers	Number Sets
Properties of Real Numbers	Arithmetic Properties
Inequalities and Intervals	Inequalities on a Number Line	Inequalities on a Number Line
Absolute Value	Absolute Value and Number Lines	Absolute Value
Order of Operations	Introduction to Order of Operations	Order of Operations

**Section 0.3**
Topic	Videos	Practice Problems
Positive Integer Exponents	Understanding Exponents	Exponents 1
Negative and Zero Exponents		Exponents 2
Operations with Exponents		Properties of Integer Exponents

**Section 0.4**
Topic	Videos	Practice Problems
Roots	Understanding Square Roots
Fractional Exponents	Rational Exponents and Exponent Laws	Exponents 4
Rationalizing Denominators	How to Rationalize a Denominator

**Section 0.5**
Topic	Videos	Practice Problems
Combining Polynomials	Addition and Subtraction of Polynomials	Adding and Subtracting Polynomials
Distributive Law	Distributive Property Example	Distributive Property
Product of Two Polynomials	FOIL for Multiplying Binomials	Multiplying Expressions
Division of Polynomials	Polynomial Division	Dividing Polynomials with Remainders

Chapter 1: Linear Equations and Functions

**Section 1.1: Solutions of Linear Equations and Inequalities in One Variable**
Topic	Videos	Practice Problems
Solving Linear Equations	Algebra:Linear Equations
Solving Fractional Equations	Solving Rational Equations	Solving Rational Equations
Solving an Equation for One of Two Variables	Solving for a Variable	Manipulating Formulas
Profit Example	Linear Equation Word Problem	Linear Equation Word Problems
Solving Inequalities	Multi-step Inequalities	Linear Inequalities

**Section 1.2: Functions**
Topic	Videos	Practice Problems
Functions	Relations and Functions
Graphing Functions
Evaluating Functions		Functions 1
Function Notation	Understanding Function Notation
Domain and Range	Domain of a Radical Function	Domain of a Function
Operations with Functions	Sum of Functions Difference of Functions Product of Functions Quotient of Functions
Composition of Functions	Creating a New Function from Composition

**Section 1.3: Linear Functions**
Topic	Videos	Practice Problems
Intercepts	Graphing with Intercepts
Slope	Slope of a Line
Equations of Lines	Finding a Linear Equation
Writing the Equation of a Line	Constructing the Equation of a Line	Slope-Intercept Form
Slope-Intercept Form	Point-Slope and Standard Form	Converting between Slope-Intercept and Standard Form
Graphing Linear Functions	Graphing in Slope-Intercept Form

**Section 1.4: Graphs and Graphing Utilities**
Topic	Videos	Practice Problems
Graphing with a Graphing Calculator

**Section 1.5: Solutions of Systems of Linear Equations**
Topic	Videos	Practice Problems
Graphical Solution of a System	Solving Linear Systems by Graphing
Solution by Substitution	Solving Linear Systems by Substitution
Solution by Elimination	Solving Systems of Equations by Elimination	Systems of Equations
Inconsistent and Dependent Systems	Special Types of Linear Systems

**Section 1.6: Applications of Functions in Business and Economics**
Topic	Videos	Practice Problems
Cost, Revenue, and Profit Functions
Marginal Cost
Break Even
Market Equilibrium	Market Equilibrium

Chapter 2: Quadratic and Other Special Functions

**Section 2.1: Quadratic Equations**
Topic	Videos	Practice Problems
Quadratic Equations	Quadratics in Standard Form
Solving by Factoring	Solving a Quadratic by Factoring	Solving Quadratics by Factoring
Solving by the Square Root Method	Solving Quadratics by Square Roots	Solving Quadratics by Taking Square Roots
Solving by the Quadratic Formula	How to Use the Quadratic Formula	Quadratic Formula
Nonreal Solutions	How to Use the Quadratic Formula

**Section 2.2: Quadratic Functions: Parabolas**
Topic	Videos	Practice Problems
Vertex and Graph of a Parabola	Parabola Vertex and Axis of Symmetry
Maximization
Graph of a Quadratic Function	Graphing a Parabola
Graph Comparison	Shifting and Scaling Parabolas	Graphing Parabolas 1
Average Rate of Change	Average Rate of Change	Average Rate of Change

**Section 2.3: Business Applications Using Quadratics**
Topic	Videos	Practice Problems
Break-Even Point
Profit Maximization
Market Equilibrium

**Section 2.4: Special Functions and Their Graphs**
Topic	Videos	Practice Problems
Shifted Graphs	Shifting and Reflecting Functions	Shifting and Reflecting Functions
Rational Functions	Rational Functions
Asymptotes	Asymptotes of Rational Functions Another Example

**Section 2.5: Modeling; Fitting Curves to Data with Graphing Utilities**
Topic	Videos	Practice Problems
Curve Fitting

Chapter 3: Matrices

**Section 3.1: Matrices**
Topic	Videos	Practice Problems
Matrices	Intro to the Matrix	Matrix Dimensions
Matrix Sums and Differences	Matrix Addition and Subtraction	Matrix Addition and Subtraction
Scalar Multiplication	Scalar Multiplication	Scalar Matrix Multiplication
Transpose of a Matrix

**Section 3.2: Multiplication of Matrices**
Topic	Videos	Practice Problems
Matrix Product	Matrix Multiplication Intro Multiplying a Matrix by a Matrix Defined and Undefined Matrix Operations	Multiplying a Matrix by a Matrix
Identity Matrix	Identity Matrix

**Section 3.3: Gauss-Jordan Elimination: Solving Systems of Equations**
Topic	Videos	Practice Problems
Gauss-Jordan Method	Reduced Row Echelon Form 1
Matrix Solution of a System	Reduced Row Echelon Form 2
A System with No Solution	Reduced Row Echelon Form 3

**Section 3.4: Inverse of a Square Matrix; Matrix Equations**
Topic	Videos	Practice Problems
Finding an Inverse Matrix	Inverse of a 2x2 Matrix	Inverse of a 2x2 Matrix Inverse of a 3x3 Matrix
Solutions with Inverse Matrices	Matrix Equations and Systems
Determinant of a 2x2 Matrix	Finding the Determinant of a 2x2 Matrix	Matrix Determinant

Chapter 4: Inequalities and Linear Programming

**Section 4.1: Linear Inequalities in Two Variables**
Topic	Videos	Practice Problems
Graphing an Inequality	Graphing Linear Inequalities in Two Variables	Graphing Inequalities
Graphical Solution of a System of Inequalities	Graphing Systems of Inequalities	Graphing Systems of Inequalities

**Section 4.2: Linear Programming: Graphical Methods**
Topic	Videos	Practice Problems
Maximization
Minimization

Chapter 5: Exponential and Logarithmic Functions

**Section 5.1: Exponential Functions**
Topic	Videos	Practice Problems
Exponential Functions	Exponential Growth Functions
Graphing an Exponential Function	Graphing Exponential Functions
Exponential Functions with Base e
Exponential Growth	Exponential Growth and Decay Word Problems

**Section 5.2: Logarithmic Functions and their Properties**
Topic	Videos	Practice Problems
Logarithms and Exponential Functions	Comparing Exponential and Logarithmic Functions
Graphing a Logarithmic Function	Graphing Logarithmic Functions
Graphing the Natural Logarithm	Natural Logarithm with a Calculator
Logarithm Properties	Using Multiple Logarithm Properties to Simplify	Logarithms
Change of Base Formula	Change of Base Formula

**Section 5.3: Solutions of Exponential Equations**
Topic	Videos	Practice Problems
Solving an Exponential Equation	Solving an Exponential Equation	Using Logarithms to Solve Exponential Equations
Solving a Logarithmic Equation	Solving Logarithmic Equations

Chapter 6: Mathematics of Finance

**Section 6.1: Simple Interest; Sequences**
Topic	Videos	Practice Problems
Simple Interest	Introduction to Interest
Arithmetic Sequences	Arithmetic Sequences

**Section 6.2: Compount Interest; Geometric Sequences**
Topic	Videos	Practice Problems
Compound Interest	Interest Part 2
Future Value
Present Value
Continuous Compounding
Annual Percentage Yield	Annual Percentage Rate
Geometric Sequences	Geometric Sequences Introduction

**Section 6.3: Future Values of Annuities**
Topic	Videos	Practice Problems
Future Value	Time Value of Money
Payment for an Ordinary Annuity
Future Value for an Annuity Due

**Section 6.4: Present Values of Annuities**
Topic	Videos	Practice Problems
Present Value	Time Value of Money
Payments from an Annuity
Present Value of an Annuity Due
Present Value of a Deferred Annuity

**Section 6.5: Loans and Amortization**
Topic	Videos	Practice Problems
Payments to Amortize a Debt
Amortization Schedule
Unpaid Balance

Chapter 7: Introduction to Probability

**Section 7.1: Probability; Odds**
Topic	Videos	Practice Problems
Probability	Basic Probability	Probability 1
Probability of Events	Example: Probabilities
Sample Spaces	Example: Sample Space
Odds

**Section 7.2: Unions and Intersections of Events: One Trial Experiments**
Topic	Videos	Practice Problems
Unions and Intersections of Events	Intersection and Union of Sets Probability with Venn Diagrams
Inclusion-Exclusion Principle	Addition Rule for Probability
Mutual Exclusivity

**Section 7.3: Conditional Probability: The Product Rule**
Topic	Videos	Practice Problems
Conditional Probability	Introduction to Dependent Probability	Identifying Dependent and Independent Events
Product Rule		Dependent Probability
Independent Events	Compound Probability of Independent Events	Compound Events
Product Rule for Independent Events	Product Rule with Independence	Independent Probability
"At Least One" Probability Rule	At Least One

**Section 7.4: Probability Trees and Bayes' Formula**
Topic	Videos	Practice Problems
Probability Tree	Example: Bag of Unfair Coins
Bayes' Formula

**Section 7.5: Counting: Permutations and Combinations**
Topic	Videos	Practice Problems
Fundamental Counting Principle	Permutations 1
Factorials
Permutations	Example: Ways to Arrange Colors	Permutations
Combinations	Example: 9 Card Hands	Combinations

**Section 7.6: Permutations, Combinations, and Probability**
Topic	Videos	Practice Problems
Applications	Example: Different Ways to Pick Officers Example: Combinatorics and Probability Example: Lottery Probability	Probability with Permutation and Combination

**Section 7.7: Markov Chains**
Topic	Videos	Practice Problems
Probability Vector
Regular Markov Chain

Chapter 8: Further Topics in Probability; Data Description

**Section 8.1: Binomial Probability Experiments**
Topic	Videos	Practice Problems
Binomial Experiments	Binomial Distribution

**Section 8.3: Discrete Probability Distributions; The Binomial Distribution**
Topic	Videos	Practice Problems
Discrete Probability Distribution	Constructing a Probability Distribution
Expected Value	Expected Value	Expected Value

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Department of Mathematical and Computer Sciences