James A Sellers
Author
Series
Great Courses volume 33
Language
English
Description
Discover how to solve equations that contain radical expressions. A key step is isolating the radical term and then squaring both sides. As always, it's important to check the solution by plugging it into the equation to see if it makes sense. This is especially true with radical equations, which can sometimes yield extraneous, or invalid, solutions.
Author
Series
Algebra II volume 21
Language
English
Description
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.
Author
Series
Algebra II volume 7
Language
English
Description
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.
Author
Series
Algebra II volume 35
Language
English
Description
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?
Author
Series
Algebra II volume 33
Language
English
Description
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.
Author
Series
Great Courses volume 20
Language
English
Description
In some circumstances, quadratic expressions are given in a special form that allows them to be factored quickly. Focus on two such forms: perfect square trinomials and differences of two squares. Learning to recognize these cases makes factoring easy.
Author
Series
Great Courses volume 24
Language
English
Description
Quadratic functions often arise in real-world settings. Explore a number of problems, including calculating the maximum height of a rocket and determining how long an object dropped from a tree takes to reach the ground. Learn that in finding a solution, graphing can often help.
Author
Series
Algebra II volume 29
Language
English
Description
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.
Author
Series
Algebra II volume 4
Language
English
Description
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.
Author
Series
Great Courses volume 4
Language
English
Description
Advance to the next level of problem solving by using variables as the building blocks to create algebraic expressions, which are combinations of mathematical symbols that might include numbers, variables, and operation symbols. Also, learn some tricks for translating the language of problems (phrases in English) into the language of math (algebraic expressions).
Author
Series
Algebra II volume 26
Language
English
Description
Drawing on your experience with roots and radicals from the previous episode, 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.
Author
Series
Great Courses volume 34
Language
English
Description
In previous lessons, you moved from linear, quadratic, and rational functions to the graphs that display them. Now do the same with radical functions. For these, it's important to pay attention to the domain of the functions to ensure that negative values are not introduced beneath the root symbol.
Author
Series
Great Courses volume 22
Language
English
Description
After learning the definition of a function, investigate an additional approach to solving quadratic equations: completing the square. This technique is very useful when rewriting the equation of a quadratic function in such a way that the graph of the function is easily sketched.
Author
Series
Algebra II volume 19
Language
English
Description
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.
Author
Series
Algebra II volume 18
Language
English
Description
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.
Author
Series
Algebra II volume 1
Language
English
Description
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.
Author
Series
Algebra II volume 30
Language
English
Description
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.
Author
Series
Algebra II volume 10
Language
English
Description
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.
Author
Series
Algebra II volume 36
Language
English
Description
After a short introduction to probability, celebrate your completion of the series 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!
Author
Series
Algebra II volume 16
Language
English
Description
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.