Algebra

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

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   Lecture 1 - Simple Equations

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

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   Lecture 2 - Equations Part 2

   Slightly more complicated equations.

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   Lecture 3 - Equations Part 3

   Equations with the variable on both sides.

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   Lecture 4 - Linear Equations

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

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   Lecture 5 - Graphing Lines Part 1

   Graphing linear equations.

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   Lecture 6 - Slope and Y-intercept Intuition

   Getting a feel for slope and y-intercept.

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   Lecture 7 - Slope Part 1

   Figuring out the slope of a line.

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   Lecture 8 - Slope Part 2

   Second part of determining the slope of a line.

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   Lecture 9 - Slope Part 3

   Part 3 of slope.

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    Lecture 10 - Averages

    Introduction to averages and algebra problems involving averages.

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    Lecture 11 - Integer Sums

    Adding sums of consecutive integers.

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    Lecture 12 - Taking Percentages

    Taking a percentage of a number.

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    Lecture 13 - Growing by a Percentage

    Growing a quantity by a percentage.

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    Lecture 14 - Another Percent Word Problem

    Finding the full price when you know the discount price.

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    Lecture 15 - More Percent Problems

    Slightly harder percent problems.

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    Lecture 16 - Systems of Equations

    Systems of equations.

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    Lecture 17 - Ratio Problem with Basic Algebra

    A slightly more involved ratio problem with algebra.

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    Lecture 18 - Ratio Problem: Advanced

    More advance ratio problem with algebra.

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    Lecture 19 - Alternate Solution to Ratio Problem

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

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    Lecture 20 - Introduction to Ratios

    Basic ratio problems.

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    Lecture 21 - Advanced Ratio Problems

    More advanced ratio problems.

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    Lecture 22 - Age Word Problems Part 1

    Age word problems.

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    Lecture 23 - Age Word Problems Part 2

    Second set of age word problems.

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    Lecture 24 - Age Word Problems Part 3

    Part 3 of the presentation on age word problems.

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    Lecture 25 - Level 1 Multiplying Expressions

    (Ax+By)(Ax+By).

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    Lecture 26 - Solving a Quadratic by Factoring

    Factoring quadratics.

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    Lecture 27 - i and Imaginary Numbers

    Introduction to i. Raising i to arbitrary exponents.

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    Lecture 28 - Complex Numbers Part 1

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

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    Lecture 29 - Complex Numbers Part 2

    Dividing complex numbers. Complex conjugates.

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    Lecture 30 - Introduction to the Quadratic Equation

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

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    Lecture 31 - Quadratic Equation Part 2

    2 more examples of solving equations using the quadratic equation.

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    Lecture 32 - Completing the Square

    Solving a quadratic by completing the square.

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    Lecture 33 - Quadratic Formula

    Deriving the quadratic formula by completing the square.

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    Lecture 34 - Quadratic Inequalities

    Solving quadratic inequalities using factoring.

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    Lecture 35 - Functions Part 1

    An introduction to functions.

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    Lecture 36 - Functions Part 2

    More examples of solving function problems.

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    Lecture 37 - Functions Part 3

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

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    Lecture 38 - Functions Part 4

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

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    Lecture 39 - Domain of a Function

    Figuring out the domain of a function.

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    Lecture 40 - Proof: log a + log b = log ab

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

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    Lecture 41 - 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).

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    Lecture 42 - Proof: log_a (B) = (log_x (B))/(log_x (A))

    Proof of the logarithm property.

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    Lecture 43 - Algebraic Long Division

    Dividing one polynomial into another.

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    Lecture 44 - Introduction to Conic Sections

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

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    Lecture 45 - Conic Sections: Circles

    Introduction to the Circle.

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    Lecture 46 - Conic Sections: Ellipses

    Introduction to the ellipse.

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    Lecture 47 - Conic Sections: Hyperbolas Part 1

    Introduction to the hyperbola.

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    Lecture 48 - Conic Sections: Hyperbolas Part 2

    Continuation of the intro to hyperbolas.

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    Lecture 49 - Conic Sections: Hyperbolas Part 3

    Part 3 of the intro to hyperbolas.

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    Lecture 50 - Identifying Conics Part 1

    Part 1 of identifying and graphic conic sections.

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    Lecture 51 - Identifying Conics Part 2

    Part 2 of identifying and graphing conic sections.

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    Lecture 52 - Identifying Conics Part 3

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

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    Lecture 53 - Foci of an Ellipse

    Calculating the foci (or focuses) of an Ellipse.

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    Lecture 54 - Foci of a Hyperbola

    Introduction to the foci (focuses) of a hyperbola.

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    Lecture 55 - Hyperbola Foci

    Proof of the hyperbola foci formula.

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    Lecture 56 - Partial Fraction Expansion Part 1

    Introduction to partial fraction expansion.

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    Lecture 57 - Partial Fraction Expansion Part 2

    A more complex problem.

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    Lecture 58 - Partial Fraction Expansion Part 3

    Dealing with repeated factors.

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    Lecture 59 - Parabola Focus and Directrix Part 1

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

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    Lecture 60 - Parabola Focus and Directrix Part 2

    Finding the focus and directrix of a parabola.

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    Lecture 61 - Two Passing Bicycles Word Problem

    Algebra word problem involving two bicycles passing each other.

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    Lecture 62 - Passed Bike Word Problem

    Fun algebra word problem involving a train passing a bike.

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    Lecture 63 - Passing Trains

    Trains passing at different rates.

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    Lecture 64 - Overtaking Word Problem

    3 people overtaking each other at different rates.

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    Lecture 65 - Early Train Word Problem

    Fun word problem that is almost a brain teaser.

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    Lecture 66 - Officer on Horseback

    Not quite a brain teaser but fun nonetheless!

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    Lecture 67 - Rational Inequalities Part 1

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

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    Lecture 68 - Rational Inequalities Part 2

    Slightly harder rational inequality problem.

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    Lecture 69 - Interesting Polynomial

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

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    Lecture 70 - Geometric Series Sum to Figure Out Mortgage Payments

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