Algebra II
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Episodes
- S1 E1 - An Introduction to Algebra II
March 3, 201132minProfessor 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. #Science & MathematicsFree trial of The Great Courses Signature Collection or buy - S1 E2 - Solving Linear Equations
March 3, 201131minExplore 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.Free trial of The Great Courses Signature Collection or buy - S1 E3 - Solving Equations Involving Absolute Values
March 3, 201131minTaking 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.Free trial of The Great Courses Signature Collection or buy - S1 E4 - Linear Equations and Functions
March 3, 201129minMoving 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.Free trial of The Great Courses Signature Collection or buy - S1 E5 - Graphing Essentials
March 3, 201129minReversing 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.Free trial of The Great Courses Signature Collection or buy - S1 E6 - Functions - Introduction, Examples, Terminology
March 3, 201131minFunctions 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.Free trial of The Great Courses Signature Collection or buy - S1 E7 - Systems of 2 Linear Equations, Part 1
March 3, 201129minPractice 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.Free trial of The Great Courses Signature Collection or buy - S1 E8 - Systems of 2 Linear Equations, Part 2
March 3, 201130minExplore 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.Free trial of The Great Courses Signature Collection or buy - S1 E9 - Systems of 3 Linear Equations
March 3, 201131minAs 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.Free trial of The Great Courses Signature Collection or buy - S1 E10 - Solving Systems of Linear Inequalities
March 3, 201129minMake 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.Free trial of The Great Courses Signature Collection or buy - S1 E11 - An Introduction to Quadratic Functions
March 3, 201132minBegin 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.Free trial of The Great Courses Signature Collection or buy - S1 E12 - Quadratic Equations - Factoring
March 3, 201132minOne 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.Free trial of The Great Courses Signature Collection or buy - S1 E13 - Quadratic Equations - Square Roots
March 3, 201131minThe 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.Free trial of The Great Courses Signature Collection or buy - S1 E14 - Completing the Square
March 3, 201130minTurn 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.Free trial of The Great Courses Signature Collection or buy - S1 E15 - Using the Quadratic Formula
March 3, 201130minWhen 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.Free trial of The Great Courses Signature Collection or buy - S1 E16 - Solving Quadratic Inequalities
March 3, 201130minExtending 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.Free trial of The Great Courses Signature Collection or buy - S1 E17 - Conic Sections - Parabolas and Hyperbolas
March 3, 201132minDelve 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.Free trial of The Great Courses Signature Collection or buy - S1 E18 - Conic Sections - Circles and Ellipses
March 3, 201132minInvestigate 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.Free trial of The Great Courses Signature Collection or buy - S1 E19 - An Introduction to Polynomials
March 3, 201132minPause 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.Free trial of The Great Courses Signature Collection or buy - S1 E20 - Graphing Polynomial Functions
March 3, 201131minDeepen 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.Free trial of The Great Courses Signature Collection or buy - S1 E21 - Combining Polynomials
March 3, 201134minSwitch 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.Free trial of The Great Courses Signature Collection or buy - S1 E22 - Solving Special Polynomial Equations
March 3, 201132minLearn 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.Free trial of The Great Courses Signature Collection or buy - S1 E23 - Rational Roots of Polynomial Equations
March 3, 201132minGoing 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.Free trial of The Great Courses Signature Collection or buy - S1 E24 - The Fundamental Theorem of Algebra
March 3, 201132minExplore 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.Free trial of The Great Courses Signature Collection or buy - S1 E25 - Roots and Radical Expressions
March 3, 201132minShift 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.Free trial of The Great Courses Signature Collection or buy
Extras
Bonus
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.
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.
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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