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 Math Fortress
 1 Season, 31 Episodes
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Algebra I (Beginning Algebra) Full Episode Guide

Conclude the course by examining more types of number sequences, discovering how rich and enjoyable the mathematics of pattern recognition can be. As in previous lessons, employ your reasoning skills and growing command of algebra to find order  and beauty  where once all was a confusion of numbers.

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.

Anytime you see a root symbol  for example, the symbol for a square root  then you're dealing with what mathematicians call a radical. Learn how to simplify radical expressions and perform operations on them, such as multiplication, division, addition, and subtraction, as well as combinations of these operations.

Examine the distinctive graphs formed by rational functions, which may form vertical or horizontal curves that aren't even connected on a graph. Learn to identify the intercepts and the vertical and horizontal asymptotes of these fascinating curves.

Continuing your exploration of rational expressions, try your hand at multiplying and dividing them. The key to solving these complicatedlooking equations is to proceed one step at a time. Close the lesson with a problem that brings together all you've learned about rational functions.

Most of the expressions you've studied in the course so far have been polynomials. Learn what characterizes a polynomial and how to recognize polynomials in both algebraic functions and in graphical form. Professor Sellers defines several terms, including the degree of an equation, the leading coefficient, and the domain.

Because it involves terms raised to the second power, the famous Pythagorean theorem, a2 + b2 = c2, is actually a quadratic equation. Discover how techniques you have previously learned for analyzing quadratic functions can be used for solving problems involving right triangles.

Quadratic functions often arise in realworld 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.

Drawing on your experience solving quadratic functions, analyze the parabolic shapes produced by such functions when represented on a graph. Use your algebraic skills to determine the parabola's vertex, its x and y intercepts, and whether it opens in an upward "cup" or downward in a "cap."

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.

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.

Begin to find solutions for quadratic equations, starting with the FOIL technique in reverse to find the binomial factors of a quadratic trinomial (a binomial expression consists of two terms, a trinomial of three). Professor Sellers explains the tricks of factoring such expressions, which is a process almost like solving a mystery.

Transition to a more complex type of algebraic expression, which incorporates squared terms and is therefore known as quadratic. Learn how to use the FOIL method (first, outer, inner, last) to multiply linear terms to get a quadratic expression.

Shift gears to consider linear inequalities, which are mathematical expressions featuring a less than sign or a greater than sign instead of an equal sign. Discover that these kinds of problems have some very interesting twists, and they come up frequently in business applications.

When two lines intersect, they form a system of linear equations. Discover two methods for finding a solution to such a system: by graphing and by substitution. Then try out a realworld example, involving a farmer who wants to plant different crops in different proportions.

Investigating more realworld applications of linear equations, derive the formula for converting degrees Celsius to Fahrenheit; determine the boiling point of water in Denver, Colorado; and calculate the speed of a rising balloon and the time for an elevator to descend to the ground floor.

Linear equations reflect the behavior of reallife phenomena. Practice evaluating tables of numbers to determine if they can be represented as linear equations. Conclude with an example about the yearly growth of a tree. Does it increase in size at a linear rate?

This video continues illustrating the 3 step problem solving plan for solving word problems. This video goes over 5 challenging examples illustrating how to translate word problems that contain three facts and three unknowns into equations.

This video introduces a 3 step problem solving plan for solving word problems. This video goes over 3 examples illustrating how to translate word problems into equations.

This video goes over 9 examples, covering the proper way to translate sentences into equations that require the use of formulas.

This video goes over 8 examples, covering the proper way to translate sentences usually containing the key word "is" into equations.

This video goes over a couple of examples modeling the proper way of translating phrases into variable expressions. Examples includes simple phrases, height between two individuals, and phrases that require the use of formulas.

This video shows you how to translate mathematical phrases written in words and translating them into variable expressions. Common phrases involving addition, subtraction, multiplication, and division are covered. In addition, the video introduces the use of formulas. Specifically, the area and perimeter of a rectangle, the distance traveled and cost formula.

This video goes over a couple of examples modeling the proper way to find the solution set of simple algebraic equations over a given domain. The video goes over equations that have one solution, many solutions and no solutions.

This video goes over the basic structure of open sentences and finding solutions (roots) of simple algebraic equations over a given domain.

This video goes over a couple of examples showing how to simplify and evaluate algebraic expressions with and without grouping symbols.

This video goes over the proper way to simplify numerical expressions using grouping symbols, nested grouping and expressions without grouping symbols.

This video goes over a couple of examples showing how to determine if a statement is true or false, how to simplify numerical expressions and how to evaluate variable expressions.

This video will teach you the fundamentals of algebra. You will learn about variables, variable expressions, numerical expressions, simplifying and evaluating algebraic expressions.