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Algebra

Publicat: 19 Apr 2011 00:00

By Salman Khan - Khan Academy
Course Description:
Topics covered from very basic algebra all the way through algebra II. This is the best algebra playlist to start at if you've never seen algebra before. Once you get your feet wet, you may want to try some of the videos in the "Algebra I Worked Examples" playlist.
Lectures:








Lecture 1 - Simple Equations



Introduction to basic algebraic equations of the form Ax=B.












Lecture 2 - Equations Part 2



Slightly more complicated equations.












Lecture 3 - Equations Part 3



Equations with the variable on both sides.












Lecture 4 - Linear Equations



Solving linear equations with variable expressions in the denominators of fractions.












Lecture 5 - Graphing Lines Part 1



Graphing linear equations.












Lecture 6 - Slope and Y-intercept Intuition



Getting a feel for slope and y-intercept.












Lecture 7 - Slope Part 1



Figuring out the slope of a line.












Lecture 8 - Slope Part 2



Second part of determining the slope of a line.












Lecture 9 - Slope Part 3



Part 3 of slope.












Lecture 10 - Averages



Introduction to averages and algebra problems involving averages.












Lecture 11 - Integer Sums



Adding sums of consecutive integers.












Lecture 12 - Taking Percentages



Taking a percentage of a number.












Lecture 13 - Growing by a Percentage



Growing a quantity by a percentage.












Lecture 14 - Another Percent Word Problem



Finding the full price when you know the discount price.












Lecture 15 - More Percent Problems



Slightly harder percent problems.












Lecture 16 - Systems of Equations



Systems of equations.












Lecture 17 - Ratios



What a ratio is. Simple ratio problems.












Lecture 18 - Ratio Problem with Basic Algebra



A slightly more involved ratio problem with algebra.












Lecture 19 - Ratio Problem: Advanced



More advance ratio problem with algebra.












Lecture 20 - Alternate Solution to Ratio Problem



An alternate solution to the advanced ratio problem in the last video.












Lecture 21 - Introduction to Ratios



Basic ratio problems.












Lecture 22 - Advanced Ratio Problems



More advanced ratio problems.












Lecture 23 - Age Word Problems Part 1



Age word problems.












Lecture 24 - Age Word Problems Part 2



Second set of age word problems.












Lecture 25 - Age Word Problems Part 3



Part 3 of the presentation on age word problems.












Lecture 26 - Level 1 Multiplying Expressions



(Ax+By)(Ax+By).












Lecture 27 - Solving a Quadratic by Factoring



Factoring quadratics.












Lecture 28 - i and Imaginary Numbers



Introduction to i. Raising i to arbitrary exponents.












Lecture 29 - Complex Numbers Part 1



Introduction to complex numbers. Adding, subtracting and multiplying complex numbers.












Lecture 30 - Complex Numbers Part 2



Dividing complex numbers. Complex conjugates.












Lecture 31 - Introduction to the Quadratic Equation



Introduction to using the quadratic equation to solve 2nd degree polynomials.












Lecture 32 - Quadratic Equation Part 2



2 more examples of solving equations using the quadratic equation.












Lecture 33 - Completing the Square



Solving a quadratic by completing the square.












Lecture 34 - Quadratic Formula



Deriving the quadratic formula by completing the square.












Lecture 35 - Quadratic Inequalities



Solving quadratic inequalities using factoring.












Lecture 36 - Functions Part 1



An introduction to functions.












Lecture 37 - Functions Part 2



More examples of solving function problems.












Lecture 38 - Functions Part 3



Even more examples of function exercises. Introduction of a graph as definition of a function.












Lecture 39 - Functions Part 4



An example of a functions problem submitted by a youtube viewer.












Lecture 40 - Domain of a Function



Figuring out the domain of a function.












Lecture 41 - Proof: log a + log b = log ab



Proof of the logarithm property: log a + log b = log ab.












Lecture 42 - Proof: A(log B) = log (B^A), log A - log B = log (A/B)



Proofs of the logarithm properties: A(log B) = log (B^A) and log A - log B = log (A/B).












Lecture 43 - Proof: log_a (B) = (log_x (B))/(log_x (A))



Proof of the logarithm property.












Lecture 44 - Algebraic Long Division



Dividing one polynomial into another.












Lecture 45 - Introduction to Conic Sections



What are conic sections and why are they called "conic sections"?












Lecture 46 - Conic Sections: Circles



Introduction to the Circle.












Lecture 47 - Conic Sections: Ellipses



Introduction to the ellipse.












Lecture 48 - Conic Sections: Hyperbolas Part 1



Introduction to the hyperbola.












Lecture 49 - Conic Sections: Hyperbolas Part 2



Continuation of the intro to hyperbolas.












Lecture 50 - Conic Sections: Hyperbolas Part 3



Part 3 of the intro to hyperbolas.












Lecture 51 - Identifying Conics Part 1



Part 1 of identifying and graphic conic sections.












Lecture 52 - Identifying Conics Part 2



Part 2 of identifying and graphing conic sections.












Lecture 53 - Identifying Conics Part 3



Let's identify (and graph) a couple of more conics!












Lecture 54 - Foci of an Ellipse



Calculating the foci (or focuses) of an Ellipse.












Lecture 55 - Foci of a Hyperbola



Introduction to the foci (focuses) of a hyperbola.












Lecture 56 - Hyperbola Foci



Proof of the hyperbola foci formula.












Lecture 57 - Partial Fraction Expansion Part 1



Introduction to partial fraction expansion.












Lecture 58 - Partial Fraction Expansion Part 2



A more complex problem.












Lecture 59 - Partial Fraction Expansion Part 3



Dealing with repeated factors.












Lecture 60 - Parabola Focus and Directrix Part 1



Parabola as the locus of all points equidistant from a point and a line.












Lecture 61 - Parabola Focus and Directrix Part 2



Finding the focus and directrix of a parabola.












Lecture 62 - Two Passing Bicycles Word Problem



Algebra word problem involving two bicycles passing each other.












Lecture 63 - Passed Bike Word Problem



Fun algebra word problem involving a train passing a bike.












Lecture 64 - Passing Trains



Trains passing at different rates.












Lecture 65 - Overtaking Word Problem



3 people overtaking each other at different rates.












Lecture 66 - Early Train Word Problem



Fun word problem that is almost a brain teaser.












Lecture 67 - Officer on Horseback



Not quite a brain teaser but fun nonetheless!












Lecture 68 - Rational Inequalities Part 1



Two ways to solve a rational inequality (or an inequality involving a fractional expression).












Lecture 69 - Rational Inequalities Part 2



Slightly harder rational inequality problem.












Lecture 70 - Interesting Polynomial



Finding the coefficients of a third degree polynomial given 2 roots and the y-intercept.












Lecture 71 - Geometric Series Sum to Figure Out Mortgage Payments



Figuring out the formula for fixed mortgage payments using the sum of a geometric series.












Lecture 72 - Function Inverses Part 1



Function Inverse Example 1.












Lecture 73 - Function Inverses Part 2



Function Inverse Example 2.












Lecture 74 - Function Inverses Part 3



Function Inverse Example 3.





Source: http://academicearth.org/courses/algebra

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