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Algebra II

Make sense of Algebra II with this clear course that walks you through hundreds of problems, showing every step in their solutions and highlighting common missteps.
Algebra II is rated 4.4 out of 5 by 56.
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Rated 5 out of 5 by from great review This course has enabled me to understand and help my teenage grandson with advanced algebra
Date published: 2021-09-05
Rated 3 out of 5 by from too rudimentary I am not sure who are the intended audience of this course. The content is too basic. Not many explanations on why. The teaching style reminds me of elementary school math classroom.
Date published: 2021-03-24
Rated 5 out of 5 by from Thoroughly enjoyable and illuminating! I just retired and want to learn calculus for the first time. Therefore, I watched Professor Sellers' two Algebra courses, and have just finished Algebra II. As with his Algebra I course, his teaching is entirely clear and helpful. He anticipates a degree of math anxiety that viewers may have, and addresses it very well. His course builds in a nice step-wise fashion. I feel much more confident about proceeding to pre-calculus and then calculus for having taken these wonderful two courses from Professor Sellers.
Date published: 2021-03-01
Rated 5 out of 5 by from Very clear Dr Sellers is very clear and concise in what he teaches. I was always afraid of anything to do with numbers, especially Mathematics but his style of teaching made this comprehensible and easy to follow, even what I feel are complex topics.
Date published: 2021-02-10
Rated 5 out of 5 by from A great review It's been a while since I first studied algebra and this was a great review to prepare me for Pre-Calculus and beyond. Thank you for this course.
Date published: 2021-02-06
Rated 5 out of 5 by from Four and a half. The three courses taught by the same teacher in this series, Pre Algebra? Algebra, and Algebra II are generally excellent from the viewpoint of someone only using the most rudimentary math for many years. My only criticism would echo some of the other reviews that in some cases the teacher tends to spend half the lesson belaboring two plus two, then swiftly takes the student through several complicated transformations that you would rather have explained more thoroughly. Possibly a relic of the classroom where you can ask questions. Learning styles differ though, and generally the teacher is very helpful and communicates clearly and enthusiastically about his subject. For some reason there are lots of comments by other math teachers who seem to want to show off their knowledge. My recommendation is for other math students only.
Date published: 2021-01-27
Rated 5 out of 5 by from Excellent course. During the shutdown, I enrolled in college 25 years after graduating high school to complete my degree and I needed to pass College Algebra. In the online class version of community colleges, there's no instruction, no lectures, just an online homework program and suggestions to go to Kahn Academy videos. I never would have passed my College Algebra class without the Algebra I and Algebra II Great Course course. I love these lectures. I've watched both courses at least twice and referred to some a few more times than that when needed to remember information. Thank you, Professor Sellers! I never would have passed College Algebra without this course.
Date published: 2020-10-23
Rated 5 out of 5 by from Very systematic and clear I completed both Algebra I and Algebra II and enjoyed the lectures very much. James teaches very clearly and systematically, making it easy to grasp all concepts. The pace was a bit slow for my taste, but not too bad. Also, it is next to impossible to fix one pace that suits all.
Date published: 2020-10-14
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Overview

Make sense of Algebra II in the company of master educator and 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 lectures, Professor Sellers walks you through hundreds of problems, showing every step in their solution and highlighting the most common missteps made by students. Designed for learners of all ages, this course will prove that algebra can be an exciting intellectual adventure and not nearly as difficult as many students fear.

About

James A. Sellers
James A. Sellers

If you are shaky on basic math facts, algebra will be harder for you than it needs to be. Spend every day reviewing flashcards of math facts, and you will be surprised at how much better at math you are!

INSTITUTION

The Pennsylvania State University
Dr. James A. Sellers is Professor of Mathematics and Director of Undergraduate Mathematics at The Pennsylvania State University. He earned his B.S. in Mathematics from The University of Texas at San Antonio and his Ph.D. in Mathematics from Penn State. In the past few years, Professor Sellers has received the Teresa Cohen Mathematics Service Award from the Penn State Department of Mathematics and the Mathematical Association of America Allegheny Mountain Section Mentoring Award. More than 60 of Professor Sellers's research articles on partitions and related topics have been published in a wide variety of peer-reviewed journals. In 2008, he was a visiting scholar at the Isaac Newton Institute at the University of Cambridge. Professor Sellers has enjoyed many interactions at the high school and middle school levels. He has served as an instructor of middle-school students in the TexPREP program in San Antonio, Texas. He has also worked with Saxon Publishers on revisions to a number of its high-school textbooks. As a home educator and father of five, he has spoken to various home education organizations about mathematics curricula and teaching issues.

By This Professor

Algebra I
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Algebra II
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Mastering the Fundamentals of Mathematics
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Algebra II

Trailer

An Introduction to Algebra II

01: An Introduction to Algebra II

Professor Sellers explains the topics covered in the course, the importance of algebra, and how you can get the most out of these lessons. You then launch into the fundamentals of algebra by reviewing the order of operations and trying your hand at several problems.

32 min
Solving Linear Equations

02: Solving Linear Equations

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.

31 min
Solving Equations Involving Absolute Values

03: Solving Equations Involving Absolute Values

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.

31 min
Linear Equations and Functions

04: Linear Equations and Functions

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.

29 min
Graphing Essentials

05: Graphing Essentials

Reversing the procedure from the previous lesson, 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 flip it entirely.

29 min
Functions-Introduction, Examples, Terminology

06: Functions-Introduction, Examples, Terminology

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.

31 min
Systems of 2 Linear Equations, Part 1

07: Systems of 2 Linear Equations, Part 1

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.

29 min
Systems of 2 Linear Equations, Part 2

08: Systems of 2 Linear Equations, Part 2

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.

30 min
Systems of 3 Linear Equations

09: Systems of 3 Linear Equations

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.

31 min
Solving Systems of Linear Inequalities

10: Solving Systems of Linear Inequalities

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.

29 min
An Introduction to Quadratic Functions

11: An Introduction to Quadratic Functions

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.

32 min
Quadratic Equations-Factoring

12: Quadratic Equations-Factoring

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.

32 min
Quadratic Equations-Square Roots

13: Quadratic Equations-Square Roots

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.

31 min
Completing the Square

14: Completing the Square

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.

30 min
Using the Quadratic Formula

15: Using the Quadratic Formula

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....

30 min
Solving Quadratic Inequalities

16: Solving Quadratic Inequalities

Extending the exercises on inequalities from lecture 10, 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.

30 min
Conic Sections-Parabolas and Hyperbolas

17: Conic Sections-Parabolas and Hyperbolas

Delve into the algebra of conic sections, which are the cross-sectional shapes produced by slicing a cone at different angles. In this lesson, 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.

32 min
Conic Sections-Circles and Ellipses

18: Conic Sections-Circles and Ellipses

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 ellipse's eccentricity. Circles are ellipses whose eccentricity = 1, with the major and minor axes equal.

32 min
An Introduction to Polynomials

19: An Introduction to Polynomials

Pause to examine the nature of polynomials-a class of algebraic expressions that you've been working with since the beginning of the course. Professor Sellers introduces several useful concepts, such as the standard form of polynomials and their degree, domain, range, and leading coefficients.

32 min
Graphing Polynomial Functions

20: Graphing Polynomial Functions

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.

31 min
Combining Polynomials

21: Combining Polynomials

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.

34 min
Solving Special Polynomial Equations

22: Solving Special Polynomial Equations

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.

32 min
Rational Roots of Polynomial Equations

23: Rational Roots of Polynomial Equations

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.

32 min
The Fundamental Theorem of Algebra

24: The Fundamental Theorem of Algebra

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.

32 min
Roots and Radical Expressions

25: Roots and Radical Expressions

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.

32 min
Solving Equations Involving Radicals

26: Solving Equations Involving Radicals

Drawing on your experience with roots and radicals from the previous lesson, try your hand at solving equations with these expressions. Begin by learning how to manipulate rational, or fractional, exponents. Then practice with simple equations, while being on the lookout for extraneous, or "imposter," solutions.

31 min
Graphing Power, Radical, and Root Functions

27: Graphing Power, Radical, and Root Functions

Using graph paper, experiment with curves formed by simple radical functions. First, determine the domain of the function, which tells you the general location of the graph on the coordinate plane. Then, investigate how different terms in the function alter the graph in predictable ways.

32 min
An Introduction to Rational Functions

28: An Introduction to Rational Functions

Shift your focus to graphs of rational functions-functions that are the ratio of two polynomials. These graphs are more complicated than those from the previous lesson, but their general characteristics can be quickly determined by calculating the domain, the x- and y-intercepts, and the vertical and horizontal asymptotes....

31 min
The Algebra of Rational Functions

29: The Algebra of Rational Functions

Combine rational functions using addition, subtraction, multiplication, division, and composition. The trick is to start each problem by putting the expressions in factored form, which makes the calculations go more smoothly. Leaving the answer in factored form also allows other operations, such as graphing, to be easily performed.

31 min
Partial Fractions

30: Partial Fractions

Now that you know how to add rational expressions, try the opposite procedure of splitting a more complicated rational expression into its component parts. Called partial fraction decomposition, this approach is a topic in introductory calculus and is used for solving a wide range of more advanced math problems.

30 min
An Introduction to Exponential Functions

31: An Introduction to Exponential Functions

Exponential functions are important in real-world applications involving growth and decay rates, such as compound interest and depreciation. Experiment with simple exponential functions, exploring such concepts as the base, growth factor, and decay factor, and how different values for these terms affect the graph of the function.

30 min
An Introduction to Logarithmic Functions

32: An Introduction to Logarithmic Functions

Plot a logarithmic function on the coordinate plane to see how it is the mirror image of a corresponding exponential function. Just like a mirror image, logarithms can be disorienting at first; but by studying their properties you will discover how they make certain calculations much simpler.

32 min
Uses of Exponential and Logarithmic Functions

33: Uses of Exponential and Logarithmic Functions

Delve deeper into exponential and logarithmic functions with the goal of solving a typical financial investment problem using the "Pert" formula. To prepare, study the change of base formula for logarithms and the special function of the base called e....

30 min
The Binomial Theorem

34: The Binomial Theorem

Pascal's triangle is a famous triangular array of numbers that corresponds to the coefficients of binomials of different powers. In a lesson connecting a branch of mathematics called combinatorics with algebra, investigate the formula for each value in Pascal's triangle, the factorial function, and the binomial theorem.

31 min
Permutations and Combinations

35: Permutations and Combinations

Continue your study of the link between combinatorics and algebra by using the factorial function to solve problems in permutations and combinations. For example, what are all the permutations of the letters a, b, c? And how many combinations of four books are possible when you have six to choose from?...

32 min
Elementary Probability

36: Elementary Probability

After a short introduction to probability, celebrate your completion of the course with a deck of cards. Can you use the principles of probability, permutations, and combinations to calculate the probability of being dealt different hands? As with the rest of algebra, once you know the rules, it's simplicity itself!

34 min