Algebra
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The Beauty of Algebra
by Khan Academy 980,825 views
Learn more: http://www.khanacademy.org/video?v=kpCJyQ2usJ4
Why the abstraction of mathematics is so fundamental -
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Origins of Algebra
by Khan Academy 490,159 views
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Where did the word "Algebra" and its underlying ideas come from -
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Abstract-ness
by Khan Academy 251,497 views
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The general idea behind the word 'abstract' -
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Descartes and Cartesian Coordinates
by Khan Academy 365,911 views
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Bridging algebra and geometry. What makes linear equations so linear. -
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Variables Expressions and Equations
by Khan Academy 353,112 views
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Introduction and examples of variables, expressions and equations -
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Simple Equations
by Khan Academy 1,505,336 views
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Introduction to basic algebraic equations of the form Ax=B -
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Equations 2
by Khan Academy 638,888 views
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slightly more complicated equations -
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Equations 3
by Khan Academy 479,703 views
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Equations with the variable on both sides. -
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Algebra: Linear Equations 4
by Khan Academy 688,220 views
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Solving linear equations with variable expressions in the denominators of fractions -
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Algebra: graphing lines 1
by Khan Academy 362,918 views
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Graphing linear equations -
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Algebra: Slope and Y-intercept intuition
by Khan Academy 303,054 views
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Getting a feel for slope and y-intercept -
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Algebra: Slope
by Khan Academy 369,413 views
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Figuring out the slope of a line -
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Algebra: Slope 2
by Khan Academy 199,009 views
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Second part of determining the slope of a line -
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Algebra: Slope 3
by Khan Academy 135,984 views
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Part 3 of slope -
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Algebra: Equation of a line
by Khan Academy 258,975 views
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Determining the equation of a line -
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Slope and Y-intercept Intuition
by Khan Academy 209,070 views
Learn more: http://www.khanacademy.org/video?v=8sz1IPjBRS8
Using the "Graph of a line" module to understand how a line's graph changes when its slope or y-intercept is changed. -
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Averages
by Khan Academy 209,426 views
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Introduction to averages and algebra problems involving averages. -
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Integer sums
by Khan Academy 199,851 views
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Adding sums of consecutive integers -
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Taking percentages
by Khan Academy 324,656 views
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Taking a percentage of a number. -
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Growing by a percentage
by Khan Academy 196,841 views
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Growing a quantity by a percentage -
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Another Percent Word Problem
by Khan Academy 164,696 views
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Finding the full price when you know the discount price -
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More percent problems
by Khan Academy 124,871 views
Learn more: http://www.khanacademy.org/video?v=4oeoIOan_h4
Slightly harder percent problems -
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systems of equations
by Khan Academy 253,842 views
Learn more: http://www.khanacademy.org/video?v=nok99JOhcjo
systems of equations -
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Introduction to Ratios (new HD version)
by Khan Academy 471,908 views
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What a ratio is. Simple ratio problems. -
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Ratio problem with basic algebra (new HD)
by Khan Academy 129,167 views
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A slightly more involved ratio problem with algebra -
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More advanced ratio problem--with Algebra (HD version)
by Khan Academy 77,423 views
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More advance ratio problem with algebra. -
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Alternate Solution to Ratio Problem (HD Version)
by Khan Academy 42,655 views
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An alternate solution to the advanced ratio problem in the last video. -
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Advanced ratio problems
by Khan Academy 89,034 views
Learn more: http://www.khanacademy.org/video?v=PASSD2OcU0c
More advanced ratio problems -
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Age word problems 1
by Khan Academy 224,517 views
Learn more: http://www.khanacademy.org/video?v=bAUT_Pux73w
Age word problems -
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Age word problems 2
by Khan Academy 107,537 views
Learn more: http://www.khanacademy.org/video?v=pPqPj8CAPvI
Second set of age word problems -
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Age word problems 3
by Khan Academy 98,934 views
Learn more: http://www.khanacademy.org/video?v=DplUpe3oyWo
Part 3 of the presentation on age word problems -
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Level 1 multiplying expressions
by Khan Academy 111,137 views
Learn more: http://www.khanacademy.org/video?v=Sc0e6xrRJYY
(Ax+By)(Ax+By) -
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Solving a quadratic by factoring
by Khan Academy 244,154 views
Learn more: http://www.khanacademy.org/video?v=N30tN9158Kc
factoring quadratics -
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Introduction to i and Imaginary Numbers
by Khan Academy 177,579 views
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Introduction to i and imaginary numbers -
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Calculating i Raised to Arbitrary Exponents
by Khan Academy 98,359 views
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Calculating i raised to arbitrarily high exponents -
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i as the Principal Root of -1 (a little technical)
by Khan Academy 66,876 views
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i as the principal square root of -1 -
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Complex Numbers (part 1)
by Khan Academy 421,510 views
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Introduction to complex numbers. Adding, subtracting and multiplying complex numbers. -
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Complex Numbers (part 2)
by Khan Academy 230,498 views
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Dividing complex numbers. Complex conjugates. -
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Introduction to the quadratic equation
by Khan Academy 275,450 views
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Introduction to using the quadratic equation to solve 2nd degree polynomials -
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Quadratic Equation part 2
by Khan Academy 166,577 views
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2 more examples of solving equations using the quadratic equation -
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Completing the square
by Khan Academy 395,808 views
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Solving a quadratic by completing the square. -
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Quadratic Formula (proof)
by Khan Academy 133,995 views
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Deriving the quadratic formula by completing the square. -
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Quadratic Inequalities (Visual Explanation)
by Khan Academy 93,100 views
How to solve a quadratic inequality. Visual intuition of what a quadratic inequality means.
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Introduction to functions
by Khan Academy 558,560 views
Learn more: http://www.khanacademy.org/video?v=VhokQhjl5t0
An introduction to functions. -
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Functions Part 2
by Khan Academy 338,796 views
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More examples of solving function problems -
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Functions (Part III)
by Khan Academy 206,746 views
Learn more: http://www.khanacademy.org/video?v=5fcRSie63Hs
Even more examples of function exercises. Introduction of a graph as definition of a function. -
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Functions (part 4)
by Khan Academy 163,264 views
Learn more: http://www.khanacademy.org/video?v=rbt51hXmzig
An example of a functions problem submitted by a youtube viewer -
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Domain of a function
by Khan Academy 387,201 views
Learn more: http://www.khanacademy.org/video?v=U-k5N1WPk4g
Figuring out the domain of a function -
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Proof: log a + log b = log ab
by Khan Academy 158,558 views
Learn more: http://www.khanacademy.org/video?v=FP2arCfAfBY
Proof of the logarithm property: log a + log b = log ab -
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Proof: A(log B) = log (B^A), log A - log B = log (A/B)
by Khan Academy 84,075 views
Learn more: http://www.khanacademy.org/video?v=yEAxG_D1HDw
Proofs of the logarithm properties: A(log B) = log (B^A) and log A - log B = log (A/B) -
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Proof: log_a (B) = (log_x (B))/(log_x (A))
by Khan Academy 53,829 views
Learn more: http://www.khanacademy.org/video?v=cKOtT4WnZb4
Proof of the logarithm property
log_a (B) = (log_x (B))/(log_x (A)) -
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Algebraic Long Division
by Khan Academy 140,305 views
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Dividing one polynomial into another -
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Introduction to Conic Sections
by Khan Academy 246,164 views
Learn more: http://www.khanacademy.org/video?v=0A7RR0oy2ho
What are conic sections and why are they called "conic sections"? -
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Conic Sections: Intro to Circles
by Khan Academy 158,741 views
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Introduction to the Circle -
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Conic Sections: Intro to Ellipses
by Khan Academy 167,219 views
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Introduction to the ellipse. -
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Conic Sections: Intro to Hyperbolas
by Khan Academy 149,010 views
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Introduction to the hyperbola -
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Conic Sections: Hyperbolas 2
by Khan Academy 74,289 views
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Continuation of the intro to hyperbolas -
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Conic Sections: Hyperbolas 3
by Khan Academy 60,313 views
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Part 3 of the intro to hyperbolas -
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Identifying Conics 1
by Khan Academy 95,160 views
Learn more: http://www.khanacademy.org/video?v=LSJuu4Qm2qQ
Part 1 of identifying and graphic conic sections -
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Identifying Conics 2
by Khan Academy 51,465 views
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Part 2 of identifying and graphing conic sections -
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Conic Identification 3
by Khan Academy 44,834 views
Learn more: http://www.khanacademy.org/video?v=Dru0RHgfp2g
Let's identify (and graph) a couple of more conics! -
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Foci of an Ellipse
by Khan Academy 126,130 views
Learn more: http://www.khanacademy.org/video?v=QR2vxfwiHAU
Calculating the foci (or focuses) of an Ellipse. -
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Foci of a Hyperbola
by Khan Academy 72,379 views
Learn more: http://www.khanacademy.org/video?v=S0Fd2Tg2v7M
Introduction to the foci (focuses) of a hyperbola -
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Proof: Hyperbola Foci
by Khan Academy 35,785 views
Learn more: http://www.khanacademy.org/video?v=HPRFmu7JsKU
Proof of the hyperbola foci formula -
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Partial Fraction Expansion 1
by Khan Academy 249,167 views
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Introduction to partial fraction expansion -
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Partial Fraction Expansion 2
by Khan Academy 130,287 views
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A more complex problem -
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Partial Fraction Expansion 3
by Khan Academy 96,584 views
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Dealing with repeated factors -
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Parabola Focus and Directrix 1
by Khan Academy 210,739 views
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Parabola as the locus of all points equidistant from a point and a line -
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Focus and Directrix of a Parabola 2
by Khan Academy 99,602 views
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Finding the focus and directrix of a parabola -
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Two Passing Bicycles Word Problem
by Khan Academy 53,108 views
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Algebra word problem involving two bicycles passing each other. -
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Passed Bike Word Problem
by Khan Academy 30,321 views
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Fun algebra word problem involving a train passing a bike. -
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Passing Trains
by Khan Academy 51,471 views
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Trains passing at different rates. -
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Overtaking Word Problem
by Khan Academy 35,926 views
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3 people overtaking each other at different rates -
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Early Train Word Problem
by Khan Academy 53,453 views
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Fun word problem that is almost a brain teaser. -
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Officer on Horseback
by Khan Academy 46,472 views
Learn more: http://www.khanacademy.org/video?v=IPJAi5zWu9U
Not quite a brain teaser but fun nonetheless! -
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Rational Inequalities
by Khan Academy 67,172 views
Two ways to solve a rational inequality (or an inequality involving a fractional expression)
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Rational Inequalities 2
by Khan Academy 43,669 views
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Slightly harder rational inequality problem -
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Interesting Polynomial Coefficient Problem
by Khan Academy 64,245 views
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Finding the coefficients of a third degree polynomial given 2 roots and the y-intercept -
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Geometric series sum to figure out mortgage payments
by Khan Academy 40,759 views
Figuring out the formula for fixed mortgage payments using the sum of a geometric series
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Introduction to Function Inverses
by Khan Academy 184,559 views
Learn more: http://www.khanacademy.org/video?v=W84lObmOp8M
Introduction to Function Inverses -
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Function Inverse Example 1
by Khan Academy 168,994 views
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Function Inverse Example 1 -
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Function Inverses Example 2
by Khan Academy 85,596 views
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Function Inverses Example 2 -
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Function Inverses Example 3
by Khan Academy 71,761 views
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Function Inverses Example 3 -
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Direct and Inverse Variation
by Khan Academy 118,413 views
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Understanding direct and inverse variation -
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Recognizing Direct and Inverse Variation
by Khan Academy 38,218 views
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Examples of variables varying directly and inversely -
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Recognizing Odd and Even Functions
by Khan Academy 121,304 views
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Even and odd functions -
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Connection between even and odd numbers and functions
by Khan Academy 33,497 views
Learn more: http://www.khanacademy.org/video?v=jFazrvLodrA
A possible reason why even functions are called "even" and odd functions are called "odd" -
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New Operator Definitions
by Khan Academy 73,584 views
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Getting comfortable with evaluating newly defined function operators -
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Proof by Induction
by Khan Academy 135,386 views
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Proving an expression for the sum of all positive integers up to and including n by induction -
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Alternate Proof to Induction for Integer Sum
by Khan Academy 21,338 views
Another way to prove the expression for the sum of all positive integers up to and including n
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Writing Proportions
by Khan Academy 127,985 views
Learn more: http://www.khanacademy.org/video?v=96ZEmUbnuU8
Setting up proportions to solve a word problem -
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Coverting Repeating Decimals to Fractions 1
by Khan Academy 153,386 views
Learn more: http://www.khanacademy.org/video?v=FPNhCVZlbJs
Examples of how to convert basic repeating decimals to fractions -
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Coverting Repeating Decimals to Fractions 2
by Khan Academy 85,543 views
Learn more: http://www.khanacademy.org/video?v=Ihws0d-WLzU
Converting more interesting repeating decimals to fractions