Algebra II

Algebra II

सीज़न 1
Make sense of Algebra II in the company of award-winning Professor James A. Sellers. Algebra II gives you all the tools you need to thrive in a core skill of mathematics. In 36 engaging half-hour episodes designed for learners of all ages, Professor Sellers walks you through hundreds of problems, showing every step in their solution and highlighting the most common missteps made by students.
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एपिसोड

  1. S1 E1 - An Introduction to Algebra II

    3 मार्च 2011
    32मिन
    टीवी-पीजी
    Professor Sellers explains the topics covered in the series, the importance of algebra, and how you can get the most out of these episodes. Then, launch into the fundamentals of algebra by reviewing the order of operations and trying your hand at several problems.
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  2. S1 E2 - Solving Linear Equations

    3 मार्च 2011
    31मिन
    टीवी-पीजी
    Explore linear equations, starting with one-step equations and then advancing to those requiring two or more steps to solve. Next, apply the distributive property to simplify certain problems, and then learn about the three categories of linear equations.
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  3. S1 E3 - Solving Equations Involving Absolute Values

    3 मार्च 2011
    31मिन
    टीवी-पीजी
    Taking your knowledge of linear equations a step further, look at examples involving absolute values, which can be thought of as a distance on a number line, always expressed as a positive value. Use your critical thinking skills to recognize absolute value problems that have limited or no solutions.
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  4. S1 E4 - Linear Equations and Functions

    3 मार्च 2011
    29मिन
    टीवी-पीजी
    Moving into the visual realm, learn how linear equations are represented as straight lines on graphs using either the slope-intercept or point-slope forms of the function. Next, investigate parallel and perpendicular lines and how to identify them by the value of their slopes.
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  5. S1 E5 - Graphing Essentials

    3 मार्च 2011
    29मिन
    टीवी-पीजी
    Reversing the procedure from the previous episode, start with an equation and draw the line that corresponds to it. Then test your knowledge by matching four linear equations to their graphs. Finally, learn how to rewrite an equation to move its graph up, down, left, or right, or by flipping it entirely.
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  6. S1 E6 - Functions - Introduction, Examples, Terminology

    3 मार्च 2011
    31मिन
    टीवी-पीजी
    Functions are crucially important not only for algebra, but for precalculus, calculus, and higher mathematics. Learn the definition of a function, the notation, and associated concepts such as domain and range. Then try out the vertical line test for determining whether a given curve is a graph of a function.
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  7. S1 E7 - Systems of 2 Linear Equations, Part 1

    3 मार्च 2011
    29मिन
    टीवी-पीजी
    Practice solving systems of two linear equations by graphing the corresponding lines and looking for the intersection point. Discover that there are three possible outcomes: no solution, infinitely many solutions, and exactly one solution.
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  8. S1 E8 - Systems of 2 Linear Equations, Part 2

    3 मार्च 2011
    30मिन
    टीवी-पीजी
    Explore two other techniques for solving systems of two linear equations. First, the method of substitution solves one of the equations and substitutes the result into the other. Second, the method of elimination adds or subtracts the equations to see if a variable can be eliminated.
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  9. S1 E9 - Systems of 3 Linear Equations

    3 मार्च 2011
    31मिन
    टीवी-पीजी
    As the number of variables increases, it becomes unwieldy to solve systems of linear equations by graphing. Learn that these problems are not as hard as they look and that systems of three linear equations often yield to the strategy of successively eliminating variables.
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  10. S1 E10 - Solving Systems of Linear Inequalities

    3 मार्च 2011
    29मिन
    टीवी-पीजी
    Make the leap into systems of linear inequalities, where the solution is a set of values on one side or another of a graphed line. An inequality is an assertion such as "less than" or "greater than," which encompasses a range of values.
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  11. S1 E11 - An Introduction to Quadratic Functions

    3 मार्च 2011
    32मिन
    टीवी-पीजी
    Begin your investigation of quadratic functions by visualizing what these functions look like when graphed. They always form a U-shaped curve called a parabola, whose location on the coordinate plane can be predicted based on the individual terms of the equation.
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  12. S1 E12 - Quadratic Equations - Factoring

    3 मार्च 2011
    32मिन
    टीवी-पीजी
    One of the most important skills related to quadratics is factoring. Review the basics of factoring, and learn to recognize a very useful special case known as the difference of two squares. Close by working on a word problem that translates into a quadratic equation.
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  13. S1 E13 - Quadratic Equations - Square Roots

    3 मार्च 2011
    31मिन
    टीवी-पीजी
    The square root approach to solving quadratic equations works not just for perfect squares, such as 3 × 3 = 9, but also for values that don't seem to involve squares at all. Probe the idea behind this technique, and also venture into the strange world of complex numbers.
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  14. S1 E14 - Completing the Square

    3 मार्च 2011
    30मिन
    टीवी-पीजी
    Turn a quadratic equation into an easily solvable form that includes a perfect square, a technique called completing the square. An important benefit of this approach is that the rewritten form gives the coordinates for the vertex of the parabola represented by the equation.
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  15. S1 E15 - Using the Quadratic Formula

    3 मार्च 2011
    30मिन
    टीवी-पीजी
    When other approaches fail, one tool can solve every quadratic equation: the quadratic formula. Practice this formula on a wide range of problems, learning how a special expression called the discriminant immediately tells how many real-number solutions the equation has.
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  16. S1 E16 - Solving Quadratic Inequalities

    3 मार्च 2011
    30मिन
    टीवी-पीजी
    Extending the exercises on inequalities from a previous episode, step into the realm of quadratic inequalities, where the boundary graph is not a straight line but a parabola. Use your skills analyzing quadratic expressions to sketch graphs quickly and solve systems of quadratic inequalities.
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  17. S1 E17 - Conic Sections - Parabolas and Hyperbolas

    3 मार्च 2011
    32मिन
    टीवी-पीजी
    Delve into the algebra of conic sections, which are the cross-sectional shapes produced by slicing a cone at different angles. In this episode, study parabolas and hyperbolas, which differ in how many variable terms are squared in each. Also learn how to sketch a hyperbola from its equation.
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  18. S1 E18 - Conic Sections - Circles and Ellipses

    3 मार्च 2011
    32मिन
    टीवी-पीजी
    Investigate the algebraic properties of the other two conic sections: ellipses and circles. Ellipses resemble stretched circles and are defined by their major and minor axes, whose ratio determines the ellipses' eccentricity. Circles are ellipses whose eccentricity = 1, with the major and minor axes equal.
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  19. S1 E19 - An Introduction to Polynomials

    3 मार्च 2011
    32मिन
    टीवी-पीजी
    Pause to examine the nature of polynomials: a class of algebraic expressions that you've been working with since the beginning of the series. Professor Sellers introduces several useful concepts, such as the standard form of polynomials and their degree, domain, range, and leading coefficients.
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  20. S1 E20 - Graphing Polynomial Functions

    3 मार्च 2011
    31मिन
    टीवी-पीजी
    Deepen your insight into polynomial functions by graphing them to see how they differ from non-polynomials. Then learn how the general shape of the graph can be predicted from the highest exponent of the polynomial, known as its degree. Finally, explore how other terms in the function also affect the graph.
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  21. S1 E21 - Combining Polynomials

    3 मार्च 2011
    34मिन
    टीवी-पीजी
    Switch from graphs to the algebraic side of polynomial functions, learning how to combine them in many different ways, including addition, subtraction, multiplication, and even long division, which is easier than it seems. Discover which of these operations produce new polynomials and which do not.
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  22. S1 E22 - Solving Special Polynomial Equations

    3 मार्च 2011
    32मिन
    टीवी-पीजी
    Learn how to solve polynomial equations where the degree is greater than two by turning them into expressions you already know how to handle. Your "toolbox" includes techniques called the difference of two squares, the difference of two cubes, and the sum of two cubes.
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  23. S1 E23 - Rational Roots of Polynomial Equations

    3 मार्च 2011
    32मिन
    टीवी-पीजी
    Going beyond the approaches you've learned so far, discover how to solve polynomial equations by applying two powerful tools for finding rational roots: the rational roots theorem and the factor theorem. Both will prove very useful in succeeding lessons.
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  24. S1 E24 - The Fundamental Theorem of Algebra

    3 मार्च 2011
    32मिन
    टीवी-पीजी
    Explore two additional tools for identifying the roots of polynomial equations: Descartes' rule of signs, which narrows down the number of possible positive and negative real roots; and the fundamental theorem of algebra, which gives the total of all roots for a given polynomial.
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  25. S1 E25 - Roots and Radical Expressions

    3 मार्च 2011
    32मिन
    टीवी-पीजी
    Shift gears away from polynomials to focus on expressions involving roots, including square roots, cube roots, and roots of higher degrees (all known as radical expressions). Practice multiplying, dividing, adding, and subtracting a wide variety of radical expressions.
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