Catalog Search Results
Author
Series
Algebra II ; 17
Language
English
Description
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.
Author
Series
Algebra II ; 31
Language
English
Description
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.
Author
Series
Algebra II ; 6
Language
English
Description
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.
Author
Series
Algebra II ; 32
Language
English
Description
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.
Author
Series
Algebra II ; 20
Language
English
Description
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.
Author
Series
Algebra II ; 9
Language
English
Description
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.
Author
Series
Algebra II ; 27
Language
English
Description
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.
Author
Series
Algebra II ; 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 ; 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 ; 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 ; 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
Algebra II ; 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 ; 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
Algebra II ; 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
Algebra II ; 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 ; 25
Language
English
Description
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.
Author
Series
Algebra II ; 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 ; 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.
Author
Series
Algebra II ; 13
Language
English
Description
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.
Author
Series
Algebra II ; 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?
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