Algebra I Worked Examples with Sal Khan

Video Lectures

Displaying all 187 video lectures.
Lecture 1
Example: two-step equation with numerator x | Linear equations | Khan Academ
Play Video
Example: two-step equation with numerator x | Linear equations | Khan Academ
Solve the equation by isolating the term with numerator x.

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Lecture 2
Example 2: Variables on both sides | Linear equations
Play Video
Example 2: Variables on both sides | Linear equations
Solving Equations 2

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Lecture 3
Solving equations with the distributive property | Linear equations
Play Video
Solving equations with the distributive property | Linear equations
Solving Equations with the Distributive Property

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Lecture 4
A clever application of the distributive property to solve a multi-step equation
Play Video
A clever application of the distributive property to solve a multi-step equation
Sal solves the equation (3/4)x + 2 = (3/8)x - 4 using the distributive property

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Lecture 5
Linear systems word problem with substitution | Systems of equations | 8th grade
Play Video
Linear systems word problem with substitution | Systems of equations | 8th grade
Algebraic Word Problem

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8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)





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Lecture 6
Challenge example: Sum of integers | Linear equations
Play Video
Challenge example: Sum of integers | Linear equations
Sum of Consecutive Odd Integers

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Lecture 7
Example: Solving for a variable | Linear equations
Play Video
Example: Solving for a variable | Linear equations
Example of solving for a variable

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Lecture 8
Solving for F in terms of C | Linear equations
Play Video
Solving for F in terms of C | Linear equations
Solving for a Variable 2

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Lecture 9
Absolute value smallest to biggest | Pre-Algebra
Play Video
Absolute value smallest to biggest | Pre-Algebra
Not only will we identify several absolute values in this example, but we will order them from smallest to largest. Content provided by The NROC Project - ©Monterey Institute for Technology and Education

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!





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Lecture 10
Absolute value and number lines | Negative numbers and absolute value | Pre-Algebra
Play Video
Absolute value and number lines | Negative numbers and absolute value | Pre-Algebra
One easy way to think of absolute value is the distance it is from zero. To do that, a number line comes in handy. Watch and learn.

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!





Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub...
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Lecture 11
Absolute value equations 1 | Linear equations
Play Video
Absolute value equations 1 | Linear equations
Absolute Value Equations 1

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Lecture 12
Absolute value equation example 2 | Linear equations
Play Video
Absolute value equation example 2 | Linear equations
Example of solving an absolute value equation

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Lecture 13
Patterns in sequences 1 | Linear equations
Play Video
Patterns in sequences 1 | Linear equations
Patterns in Sequences 1

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Lecture 14
Patterns in sequences 2 | Linear equations
Play Video
Patterns in sequences 2 | Linear equations
Patterns in Sequences 2

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Lecture 15
Equations of sequence patterns | Sequences, series and induction | Precalculus
Play Video
Equations of sequence patterns | Sequences, series and induction | Precalculus
Equations of Sequence Patterns

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 16
Finding the 100th term in a sequence | Sequences, series and induction | Precalculus
Play Video
Finding the 100th term in a sequence | Sequences, series and induction | Precalculus
Finding the 100th Term in a Sequence

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 17
Recognize functions from tables | Functions and their graphs I
Play Video
Recognize functions from tables | Functions and their graphs I
Functional Relationships 1

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 18
Testing if a relationship is a function | Functions and their graphs I
Play Video
Testing if a relationship is a function | Functions and their graphs I
Testing if a relationship is a function

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





Subscribe to Khan Academy’s Algebra II channel:
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Lecture 19
Domain of modeling functions | Functions and their graphs I
Play Video
Domain of modeling functions | Functions and their graphs I
Domain of modeling functions

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 20
Domain and range 2 | Functions and their graphs I
Play Video
Domain and range 2 | Functions and their graphs I
Domain and Range 2

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub...
Lecture 21
Direct variation 1 | Rational expressions I
Play Video
Direct variation 1 | Rational expressions I
Direct Variation 1

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub...
Lecture 22
Basic rate problem | Linear equations
Play Video
Basic rate problem | Linear equations
Basic Rate Problem

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Lecture 23
Basic Linear Function
Play Video
Basic Linear Function
U03_L2_T4_we1 : Basic Linear Function
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 24
Modeling with linear equations example 1 | Linear equations and functions | 8th grade
Play Video
Modeling with linear equations example 1 | Linear equations and functions | 8th grade
Exploring linear relationships

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8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)





Subscribe to Khan Academy’s 8th grade channel:
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Lecture 25
Recognizing linear functions | Linear equations and functions | 8th grade
Play Video
Recognizing linear functions | Linear equations and functions | 8th grade
Recognizing Linear Functions

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8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)





Subscribe to Khan Academy’s 8th grade channel:
https://www.youtube.com/channel/UCq341CBxj87C7AY_zu2qPlQ?sub...
Lecture 26
Exploring nonlinear relationships
Play Video
Exploring nonlinear relationships
U03_L2_T5_we2 : Exploring nonlinear relationships
Lecture 27
Finding the slope of a line from its graph
Play Video
Finding the slope of a line from its graph
Slope of a line

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Lecture 28
Interpreting linear tables word problems example 1
Play Video
Interpreting linear tables word problems example 1
Slope Example

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Lecture 29
Finding intercepts from an equation
Play Video
Finding intercepts from an equation
X and Y intercepts

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Lecture 30
x- and y-intercepts 2 | Linear equations and functions | 8th grade
Play Video
x- and y-intercepts 2 | Linear equations and functions | 8th grade
X and Y intercepts 2

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8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)





Subscribe to Khan Academy’s 8th grade channel:
https://www.youtube.com/channel/UCq341CBxj87C7AY_zu2qPlQ?sub...
Lecture 31
Graph from slope-intercept equation example
Play Video
Graph from slope-intercept equation example
Graphing a line in slope intercept form

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Lecture 32
Equation of a line 2
Play Video
Equation of a line 2
U04_L1_T3_we2 : Equation of a line
Lecture 33
Converting linear equations to slope-intercept form | 8th grade
Play Video
Converting linear equations to slope-intercept form | 8th grade
Converting to slope-intercept form

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8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)





Subscribe to Khan Academy’s 8th grade channel:
https://www.youtube.com/channel/UCq341CBxj87C7AY_zu2qPlQ?sub...
Lecture 34
Writing equations in all forms
Play Video
Writing equations in all forms
Point-slope and standard form

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Lecture 35
Parallel Lines
Play Video
Parallel Lines
U04_L2_T1_we1 : Parallel Lines
More free lessons at: http://www.khanacademy.org/video?v=T-aCweuimis
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 36
Parallel Lines 2
Play Video
Parallel Lines 2
U04_L2_T1_we2 : Parallel Lines 2
More free lessons at: http://www.khanacademy.org/video?v=lOWXZFP8Vuc
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 37
Parallel lines 3
Play Video
Parallel lines 3
U04_L2_T1_we3 : Parallel lines 3
More free lessons at: http://www.khanacademy.org/video?v=y5yNi08cr6I
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 38
Perpendicular Lines
Play Video
Perpendicular Lines
U04_L2_T2_we1 : Perpendicular Lines
More free lessons at: http://www.khanacademy.org/video?v=0671cRNjeKI
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 39
Perpendicular lines 2
Play Video
Perpendicular lines 2
U04_L2_T2_we2 : Perpendicular lines 2
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Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 40
Constructing and solving a two-step inequality | Linear inequalities
Play Video
Constructing and solving a two-step inequality | Linear inequalities
We'll talk you through this fun and challenging inequality problem.

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https://www.khanacademy.org/math/algebra/linear_inequalities...

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Lecture 41
Solving a two-step inequality | Linear inequalities
Play Video
Solving a two-step inequality | Linear inequalities
We're turning up the heat a little and asking you to help us solve a multi-step inequality problem.

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https://www.khanacademy.org/math/algebra/linear_inequalities...

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Lecture 42
Constructing and solving a one-step inequality | Linear inequalities
Play Video
Constructing and solving a one-step inequality | Linear inequalities
Inequalities are more than abstract concepts and exercises. They help solve real life problems. Here's an example.

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Lecture 43
Absolute value inequalities example 1 | Linear equations
Play Video
Absolute value inequalities example 1 | Linear equations
Absolute value inequalities, graph solution on number line

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Lecture 44
Absolute inequalities 2 | Linear equations
Play Video
Absolute inequalities 2 | Linear equations
Absolute Inequalities 2

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Lecture 45
Absolute value inequalities example 3 | Linear equations
Play Video
Absolute value inequalities example 3 | Linear equations
Absolute value inequalities 3

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Lecture 46
Writing and using inequalities | Linear inequalities
Play Video
Writing and using inequalities | Linear inequalities
Writing and using inequalities

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Lecture 47
Constructing and solving a multi-step inequality example
Play Video
Constructing and solving a multi-step inequality example
Learn how to solve an inequality word problem about cell phone texting plans.

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Lecture 48
Constructing, solving two-step inequality example | Linear inequalities
Play Video
Constructing, solving two-step inequality example | Linear inequalities
Let's tackle this word problem together. We'll interpret the information and then construct a linear inequality to solve it.

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Lecture 49
Solving and graphing linear inequalities in two variables 1 | Algebra Basics
Play Video
Solving and graphing linear inequalities in two variables 1 | Algebra Basics
Solving and graphing linear inequalities in two variables. Created by Sal Khan and Monterey Institute for Technology and Education.

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Algebra basics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course





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Lecture 50
Graphing linear inequalities in two variables 2 (old and redone in newer video)
Play Video
Graphing linear inequalities in two variables 2 (old and redone in newer video)
U05_L2_T1_we2 : Graphing linear inequalities in two variables
Lecture 51
Graphing inequalities and checking solutions example
Play Video
Graphing inequalities and checking solutions example
Learn how to graph two-variable linear inequalities and check a solution using the graph.

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Lecture 52
Solving systems by graphing
Play Video
Solving systems by graphing
U06_L1_T1_we1 Solving systems by graphing
Lecture 53
Analyzing solutions to linear systems graphically 1
Play Video
Analyzing solutions to linear systems graphically 1
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Lecture 54
Example 3: Graphically solving systems | Systems of equations | 8th grade
Play Video
Example 3: Graphically solving systems | Systems of equations | 8th grade
Solving systems by graphing 3

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8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)





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Lecture 55
Analyzing solutions to linear systems algebraically
Play Video
Analyzing solutions to linear systems algebraically
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Lecture 56
Example 2: Solving systems by substitution | Systems of equations | 8th grade
Play Video
Example 2: Solving systems by substitution | Systems of equations | 8th grade
Solving systems by substitution 2

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8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)





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Lecture 57
Example 3: Solving systems by substitution | Systems of equations | 8th grade
Play Video
Example 3: Solving systems by substitution | Systems of equations | 8th grade
Solving systems by substitution 3

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8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)





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Lecture 58
Systems of equations word problems example 1
Play Video
Systems of equations word problems example 1
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Lecture 59
Example 2: Solving systems by elimination | Systems of equations | 8th grade
Play Video
Example 2: Solving systems by elimination | Systems of equations | 8th grade
Solving systems by elimination 2

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8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)





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Lecture 60
Example 3: Solving systems by elimination | Systems of equations | 8th grade
Play Video
Example 3: Solving systems by elimination | Systems of equations | 8th grade
Solving systems by elimination 3

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8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)





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Lecture 61
Systems and rate problems
Play Video
Systems and rate problems
U06_L2_T1_we1 Systems and rate problems
More free lessons at: http://www.khanacademy.org/video?v=at4T4n4JYNc
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 62
Systems and rate problems 2
Play Video
Systems and rate problems 2
U06_L2_T1_we2 Systems and rate problems 2
More free lessons at: http://www.khanacademy.org/video?v=H5w55UbIZTw
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 63
Systems and rate problems 3
Play Video
Systems and rate problems 3
U06_L2_T1_we3 Systems and rate problems 3
More free lessons at: http://www.khanacademy.org/video?v=hTBQUibtnBk
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 64
Mixture problems 1
Play Video
Mixture problems 1
U06_L2_T2_we1 Mixture problems 1
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 65
Mixture problems 2 | Linear equations
Play Video
Mixture problems 2 | Linear equations
Mixture problems 2

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Lecture 66
Mixture problems 3 | Linear equations
Play Video
Mixture problems 3 | Linear equations
Mixture problems 3

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Lecture 67
Graphing systems of inequalities
Play Video
Graphing systems of inequalities
U06_L3_T1_we1 Graphing systems of inequalities
Lecture 68
Graphing systems of inequalities and checking solutions example I
Play Video
Graphing systems of inequalities and checking solutions example I
Learn how to graph systems of two-variable linear inequalities and check a solution using the graph.

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 69
Graphing systems of inequalities 3
Play Video
Graphing systems of inequalities 3
U06_L3_T1_we3 Graphing systems of inequalities 3
Lecture 70
Exponent Rules 1
Play Video
Exponent Rules 1
U07_L1_T1_we1 Exponent Rules 1
Lecture 71
Exponent Rules 2
Play Video
Exponent Rules 2
U07_L1_T1_we2 Exponent Rules 2
Lecture 72
Exponent Rules 3
Play Video
Exponent Rules 3
U07_L1_T1_we3 Exponent Rules 3
Lecture 73
Scientific notation 1
Play Video
Scientific notation 1
U07_L1_T2_we1 Scientific notation 1
Lecture 74
Scientific notation 2
Play Video
Scientific notation 2
U07_L1_T2_we2 Scientific notation 2
Lecture 75
U.S. national debt (scientific notation word problem) | Pre-Algebra
Play Video
U.S. national debt (scientific notation word problem) | Pre-Algebra
Ever wonder what your part of the national debt is? It might surprise you. What isn't surprising is that you can use scientific notation and division to figure out the answer.

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!





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Lecture 76
Simplifying expressions with exponents
Play Video
Simplifying expressions with exponents
Simplifying Expressions with Exponents

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Lecture 77
Simplifying expressions with exponents 2
Play Video
Simplifying expressions with exponents 2
Simplifying Expressions with Exponents 2

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Lecture 78
Simplifying expressions with exponents 3
Play Video
Simplifying expressions with exponents 3
Simplifying Expressions with Exponents 3

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Lecture 79
Pythagorean theorem 1 | Right triangles and trigonometry | Geometry
Play Video
Pythagorean theorem 1 | Right triangles and trigonometry | Geometry
Pythagorean Theorem 1

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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.





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Lecture 80
Pythagorean theorem 2 | Right triangles and trigonometry | Geometry
Play Video
Pythagorean theorem 2 | Right triangles and trigonometry | Geometry
Pythagorean Theorem 2

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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.





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Lecture 81
Pythagorean theorem 3 | Right triangles and trigonometry | Geometry
Play Video
Pythagorean theorem 3 | Right triangles and trigonometry | Geometry
Pythagorean Theorem 3

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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.





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Lecture 82
Simplifying a cube root | Exponents, radicals, and scientific notation | Pre-Algebra
Play Video
Simplifying a cube root | Exponents, radicals, and scientific notation | Pre-Algebra
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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!





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Lecture 83
Simplifying Radical Expressions 2
Play Video
Simplifying Radical Expressions 2
U07_L3_T1_we2 Simplifying Radical Expressions 2
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 84
Simplifying Radical Expressions 3
Play Video
Simplifying Radical Expressions 3
U07_L3_T1_we3 Simplifying Radical Expressions 3
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education
Lecture 85
Solving radical equations 1 | Exponent expressions and equations
Play Video
Solving radical equations 1 | Exponent expressions and equations
Solving Radical Equations 1

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Lecture 86
Solving radical equations 2 | Exponent expressions and equations
Play Video
Solving radical equations 2 | Exponent expressions and equations
Solving Radical Equations 2

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Lecture 87
Solving radical equations 3 | Exponent expressions and equations
Play Video
Solving radical equations 3 | Exponent expressions and equations
Solving Radical Equations 3

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Lecture 88
Applying radical equations 1 | Exponent expressions and equations
Play Video
Applying radical equations 1 | Exponent expressions and equations
Applying Radical Equations 1

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Lecture 89
Applying radical equations 2 | Exponent expressions and equations
Play Video
Applying radical equations 2 | Exponent expressions and equations
Applying Radical Equations 2

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Lecture 90
Applying radical equations 3 | Exponent expressions and equations
Play Video
Applying radical equations 3 | Exponent expressions and equations
Applying Radical Equations 3

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Lecture 91
Fractional exponent expressions 1 | Exponent expressions and equations
Play Video
Fractional exponent expressions 1 | Exponent expressions and equations
Fractional Exponent Expressions 1

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Lecture 92
Fractional exponent expressions 2 | Exponent expressions and equations
Play Video
Fractional exponent expressions 2 | Exponent expressions and equations
Fractional Exponent Expressions 2

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Lecture 93
Fractional exponent expressions 3 | Exponent expressions and equations
Play Video
Fractional exponent expressions 3 | Exponent expressions and equations
Fractional Exponent Expressions 3

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Lecture 94
Example 2: Multiplying two monomials with two variables
Play Video
Example 2: Multiplying two monomials with two variables
Express the area of a rectangle with length 4xy and width 2y as a monomial.

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Lecture 95
Multiplying and dividing monomials 2 | Rational expressions I
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Multiplying and dividing monomials 2 | Rational expressions I
Multiplying and Dividing Monomials 2

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 96
Multiplying and dividing monomials 3 | Rational expressions I
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Multiplying and dividing monomials 3 | Rational expressions I
Multiplying and Dividing Monomials 3

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 97
Example 1: Modeling with polynomials
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Example 1: Modeling with polynomials
Write a binomial to express the difference between the area of a rectangle and the area of a circle.

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Lecture 98
Example 2: Modeling with polynomials
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Example 2: Modeling with polynomials
Write a polynomial to express the total value of p twenty dollar bills, q ten dollar bills, and r five dollar bills.

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Lecture 99
Example 2: Adding polynomials
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Example 2: Adding polynomials
Simplify (5x^2 + 8x - 3) + (2x^2 - 7x + 13x)

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Lecture 100
Adding and subtracting polynomials | Algebra Basics
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Adding and subtracting polynomials | Algebra Basics
Add (5x^2+8x-3) + (2x^2 - 7x + 13x). Created by Sal Khan and Monterey Institute for Technology and Education.

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Algebra basics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course





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Lecture 101
Example 4: Adding and subtracting polynomials
Play Video
Example 4: Adding and subtracting polynomials
Simplify (x^3 + 3x - 6) + (-2x^2 + x - 2) - (3x - 4)

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Lecture 102
Multiplying Polynomials1
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Multiplying Polynomials1
U08_L2_T3_we1 Multiplying Polynomials1
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Lecture 103
Example 3: Modeling with polynomials
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Example 3: Modeling with polynomials
Write a polynomial expression that represents the total area of a window made of wood and glass.

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Lecture 104
Example 3: Multiplying a binomial by a polynomial word problem I
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Example 3: Multiplying a binomial by a polynomial word problem I
Find the volume of a tank whose base has an area of 3x^2 + 30x + 5 square feet and whose height is 8x - 5 feet.

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 105
Squaring a binomial | Quadratics and polynomials | Algebra Basics
Play Video
Squaring a binomial | Quadratics and polynomials | Algebra Basics
Squaring a binomial. Created by Sal Khan and Monterey Institute for Technology and Education.

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Algebra basics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course





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Lecture 106
Example 3: Finding the square of a binomial with two variables
Play Video
Example 3: Finding the square of a binomial with two variables
Find the area of a square with side (6x-5y).

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Lecture 107
U08_L2_T4_we3 Special Products of Polynomials 3
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U08_L2_T4_we3 Special Products of Polynomials 3
U08_L2_T4_we3 Special Products of Polynomials 3
Lecture 108
Bay Area CBS Station with Salman Khan
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Bay Area CBS Station with Salman Khan
Bay Area CBS Station with Salman Khan
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Lecture 109
Factoring and the Distributive Property
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Factoring and the Distributive Property
U09_L1_T1_we1 Factoring and the Distributive Property
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Lecture 110
Example 2: Factor a quadratic binomial with two variables by taking a common factor
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Example 2: Factor a quadratic binomial with two variables by taking a common factor
Factor 20u^2v - 10uv^2 as 10uv(2u-v).

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Lecture 111
Example 4: Factor a polynomial with two variables by taking a common factor
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Example 4: Factor a polynomial with two variables by taking a common factor
Factor 4x^4y-8x^3y-2x^2 as 2x^2(2x^2y-4xy).

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Lecture 112
Example 7: Factor a polynomial with two variables by grouping
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Example 7: Factor a polynomial with two variables by grouping
U09_L1_T2_we1 Factoring Trinomials by Grouping 1
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Lecture 113
Factoring Trinomials by Grouping 2
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Factoring Trinomials by Grouping 2
U09_L1_T2_we2 Factoring Trinomials by Grouping 2
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Lecture 114
U09_L1_T2_we3 Factoring Trinomials by Grouping 3
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U09_L1_T2_we3 Factoring Trinomials by Grouping 3
U09_L1_T2_we3 Factoring Trinomials by Grouping 3
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Lecture 115
Example 2: Factoring quadratics by grouping
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Example 2: Factoring quadratics by grouping
Factor 4y^2+4y-15 as (2y-3)(2y+5) by grouping.

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Lecture 116
Example 3: Factoring quadratics by taking a common factor and grouping I
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Example 3: Factoring quadratics by taking a common factor and grouping I
Factor 35k^2+100k-15 as 5(k+3)(7k-1)

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 117
Example 4: Factoring quadratics by taking a negative common factor and grouping
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Example 4: Factoring quadratics by taking a negative common factor and grouping
Factor -12f^2-38f+22 as -2(2f-1)(3f+11).

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 118
Example 3: Factoring quadratics as a perfect square of a sum: (a+b)^2
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Example 3: Factoring quadratics as a perfect square of a sum: (a+b)^2
Factor -4t^2-12t-9 as -1(2t+3)(2t+3), or -(2t+3)^2.

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Lecture 119
Example 5: Factoring a fourth degree polynomial using the
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Example 5: Factoring a fourth degree polynomial using the "perfect square” form
Factor 25x^4-30x^2+9 as (5x^2-3)^2.

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 120
Example 6: Factoring a difference of squares with two variables I
Play Video
Example 6: Factoring a difference of squares with two variables I
Factor 49x^2-49y^2 as (7x+7y)(7x-7y) or as 49(x+y)(x-y).

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 121
Solving a quadratic equation by factoring I
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Solving a quadratic equation by factoring I
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 122
Recognizing a perfect square quadratic I
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Recognizing a perfect square quadratic I
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 123
Dimensions from volume of box | Quadratic equations
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Dimensions from volume of box | Quadratic equations
Solving Quadratic Equations by Factoring 3

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Lecture 124
Quadratic Functions 1
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Quadratic Functions 1
U10_L1_T1_we1 Quadratic Functions 1
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Lecture 125
Parabola vertex and axis of symmetry | Quadratic equations
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Parabola vertex and axis of symmetry | Quadratic equations
Parabola vertex and axis of symmetry

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Lecture 126
Graphing a parabola by finding the roots and vertex | Quadratic equations
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Graphing a parabola by finding the roots and vertex | Quadratic equations
Graphing a parabola by finding the roots and vertex

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Lecture 127
Example 1: Completing the square | Quadratic equations
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Example 1: Completing the square | Quadratic equations
Completing the Square 1

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Lecture 128
Example 2: Completing the square | Quadratic equations
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Example 2: Completing the square | Quadratic equations
Completing the Square 2

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Lecture 129
Completing the square for vertex form | Quadratic equations
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Completing the square for vertex form | Quadratic equations
Completing the Square 3

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Lecture 130
Completing the square for quadratic formula | Quadratic equations
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Completing the square for quadratic formula | Quadratic equations
Completing the Square 4

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Lecture 131
Example 1: Using the quadratic formula | Quadratic equations
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Example 1: Using the quadratic formula | Quadratic equations
Quadratic Formula 1

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Lecture 132
Example 2: Using the quadratic formula | Quadratic equations
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Example 2: Using the quadratic formula | Quadratic equations
Quadratic Formula 2

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Lecture 133
Example 3: Using the quadratic formula | Quadratic equations
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Example 3: Using the quadratic formula | Quadratic equations
Quadratic Formula 3

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Lecture 134
Applying Quadratic Functions 1
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Applying Quadratic Functions 1
U10_L2_T1_we1 Applying Quadratic Functions 1
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Lecture 135
Applying Quadratic Functions 2
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Applying Quadratic Functions 2
U10_L2_T1_we2 Applying Quadratic Functions 2
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Lecture 136
Applying Quadratic Functions 3
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Applying Quadratic Functions 3
U10_L2_T1_we3 Applying Quadratic Functions 3
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Lecture 137
Non-linear systems of equations 1 I
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Non-linear systems of equations 1 I
Non-Linear Systems of Equations 1

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 138
Non-linear systems of equations 2 I
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Non-linear systems of equations 2 I
Non-Linear Systems of Equations 2

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 139
Non-linear systems of equations 3 I
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Non-linear systems of equations 3 I
Non-Linear Systems of Equations 3

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 140
Simplifying rational expressions 1 | Polynomial and rational functions I
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Simplifying rational expressions 1 | Polynomial and rational functions I
Simplifying Rational Expressions 1

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 141
Simplifying rational expressions 2 | Polynomial and rational functions I
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Simplifying rational expressions 2 | Polynomial and rational functions I
Simplifying Rational Expressions 2

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 142
Simplifying rational expressions 3 | Polynomial and rational functions I
Play Video
Simplifying rational expressions 3 | Polynomial and rational functions I
Simplifying Rational Expressions 3

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 143
Multiplying and dividing rational expressions 1 I
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Multiplying and dividing rational expressions 1 I
Multiplying and Dividing Rational Expressions 1

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 144
Multiplying and dividing rational expressions 2 I
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Multiplying and dividing rational expressions 2 I
Multiplying and Dividing Rational Expressions 2

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 145
Multiplying and dividing rational expressions 3 I
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Multiplying and dividing rational expressions 3 I
Multiplying and Dividing Rational Expressions 3

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 146
Adding and Subtracting Rational Expressions 1
Play Video
Adding and Subtracting Rational Expressions 1
U11_L1_T3_we1 Adding and Subtracting Rational Expressions 1
Lecture 147
Adding and subtracting rational expressions 2 I
Play Video
Adding and subtracting rational expressions 2 I
Adding and Subtracting Rational Expressions 2

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 148
Adding and subtracting rational expressions 3 I
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Adding and subtracting rational expressions 3 I
Adding and Subtracting Rational Expressions 3

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 149
Solving rational equations 1 | Polynomial and rational functions I
Play Video
Solving rational equations 1 | Polynomial and rational functions I
Solving Rational Equations 1

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 150
Solving rational equations 2 | Polynomial and rational functions I
Play Video
Solving rational equations 2 | Polynomial and rational functions I
Solving Rational Equations 2

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 151
Solving rational equations 3 | Polynomial and rational functions I
Play Video
Solving rational equations 3 | Polynomial and rational functions I
Solving Rational Equations 3

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 152
Applying rational equations 1 | Polynomial and rational functions I
Play Video
Applying rational equations 1 | Polynomial and rational functions I
Applying Rational Equations 1

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 153
Applying rational equations 2 | Polynomial and rational functions I
Play Video
Applying rational equations 2 | Polynomial and rational functions I
Applying Rational Equations 2

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 154
Applying rational equations 3 | Polynomial and rational functions I
Play Video
Applying rational equations 3 | Polynomial and rational functions I
Applying Rational Equations 3

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 155
Number sets 1 | Fractions | Pre-Algebra
Play Video
Number sets 1 | Fractions | Pre-Algebra
Number Sets 1

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!





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Lecture 156
Number sets 2 | Fractions | Pre-Algebra
Play Video
Number sets 2 | Fractions | Pre-Algebra
Number Sets 2

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!





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Lecture 157
Number sets 3 | Fractions | Pre-Algebra
Play Video
Number sets 3 | Fractions | Pre-Algebra
Number Sets 3

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!





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Lecture 158
Understanding Logical Statements 1
Play Video
Understanding Logical Statements 1
U12_L1_T2_we1 Understanding Logical Statements 1
Lecture 159
Understanding Logical Statements 2
Play Video
Understanding Logical Statements 2
U12_L1_T2_we2 Understanding Logical Statements 2
Lecture 160
Understanding Logical Statements 3
Play Video
Understanding Logical Statements 3
U12_L1_T2_we3 Understanding Logical Statements 3
Lecture 161
Understanding Logical Statements 4
Play Video
Understanding Logical Statements 4
U12_L1_T2_we4 Understanding Logical Statements 4
Lecture 162
Understanding Logical Statements Commentary
Play Video
Understanding Logical Statements Commentary
Understanding Logical Statements Commentary
Lecture 163
Inductive reasoning 1 | Sequences, series and induction | Precalculus
Play Video
Inductive reasoning 1 | Sequences, series and induction | Precalculus
Inductive Reasoning 1

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 164
Inductive reasoning 2 | Sequences, series and induction | Precalculus
Play Video
Inductive reasoning 2 | Sequences, series and induction | Precalculus
Inductive Reasoning 2

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 165
Inductive reasoning 3 | Sequences, series and induction | Precalculus
Play Video
Inductive reasoning 3 | Sequences, series and induction | Precalculus
Inductive Reasoning 3

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 166
Difference between inductive and deductive reasoning | Precalculus
Play Video
Difference between inductive and deductive reasoning | Precalculus
Deductive Reasoning 1

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 167
Deductive reasoning 2 | Sequences, series and induction | Precalculus
Play Video
Deductive reasoning 2 | Sequences, series and induction | Precalculus
Deductive Reasoning 2

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 168
Deductive reasoning 3 | Sequences, series and induction | Precalculus
Play Video
Deductive reasoning 3 | Sequences, series and induction | Precalculus
Deductive Reasoning 3

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 169
Finding probability example 3 | Probability and combinatorics | Precalculus
Play Video
Finding probability example 3 | Probability and combinatorics | Precalculus
Now we're working out the probability of randomly selecting a yellow marble from a bag of multi-colored marbles. Let's practice together.

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 170
Events and Outcomes 2
Play Video
Events and Outcomes 2
U12_L2_T1_we2 Events and Outcomes 2
Lecture 171
Example: Probability through counting outcomes | Precalculus
Play Video
Example: Probability through counting outcomes | Precalculus
The probability of getting exactly 2 heads when flipping three coins. Thinking about this by visualy depicting all of the outcomes.

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 172
Independent or dependent probability event? | Precalculus
Play Video
Independent or dependent probability event? | Precalculus
This time around we're not going to tell you whether we're working on a dependent or independent probability event problem. You tell us!

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 173
Test taking probability and independent events | Precalculus
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Test taking probability and independent events | Precalculus
Have you ever taken a test and discovered you have no choice but to guess on a couple of problems? In this example problem, we are considering the probability of two independent events occurring.

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 174
Die rolling probability with independent events | Precalculus
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Die rolling probability with independent events | Precalculus
We hope you're not a gambler, but if you had to bet on whether you can roll even numbers three times in a row, you might want to figure this probability first.

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 175
Example: Ways to arrange colors | Probability and combinatorics | Precalculus
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Example: Ways to arrange colors | Probability and combinatorics | Precalculus
Thinking about how many ways you can pick four colors from a group of 6

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 176
Example: Ways to pick officers | Probability and combinatorics | Precalculus
Play Video
Example: Ways to pick officers | Probability and combinatorics | Precalculus
How many ways can we pick officers for our organization?

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 177
Example: 9 card hands | Probability and combinatorics | Precalculus
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Example: 9 card hands | Probability and combinatorics | Precalculus
Thinking about how many ways we can construct a hand of 9 cards

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 178
Example: Lottery probability | Probability and combinatorics | Precalculus
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Example: Lottery probability | Probability and combinatorics | Precalculus
What is the probability of winning a 4-number lottery?

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 179
Example: Different ways to pick officers | Precalculus
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Example: Different ways to pick officers | Precalculus
Thinking about the different ways we can pick officers in order to find the probability of one situation in particular.

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 180
Example: Combinatorics and probability | Probability and combinatorics | Precalculus
Play Video
Example: Combinatorics and probability | Probability and combinatorics | Precalculus
Probability of getting a set of cards

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 181
Absolute value equations | Linear equations
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Absolute value equations | Linear equations
Absolute Value Equations

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Lecture 182
Systems of linear inequalities word problems example I
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Systems of linear inequalities word problems example I
Sal models a real-world context into an algebraic system of linear inequalities and graphs it.

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!





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Lecture 183
U06_L1_T1_we1 Solving Systems by Graphing
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U06_L1_T1_we1 Solving Systems by Graphing
U06_L1_T1_we1 Solving Systems by Graphing
Lecture 184
Finding the inequality representing the graph example
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Finding the inequality representing the graph example
Learn how to fit an algebraic inequality to its appropriate graph.

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Lecture 185
U03_L2_T1_we2 Representing Functions as Graphs
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U03_L2_T1_we2 Representing Functions as Graphs
U03_L2_T1_we2 Representing Functions as Graphs
Lecture 186
Inductive patterns | Sequences, series and induction | Precalculus
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Inductive patterns | Sequences, series and induction | Precalculus
Inductive Patterns

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!





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Lecture 187
Multiplying monomials
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Multiplying monomials
Learn how to multiply monomials like 5x² * 4x⁶ or 4p³ * p.

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