Continue your study of math fundamentals by exploring various procedures for converting between percents, decimals, and fractions. Professor Sellers notes that it helps to see these procedures as ways of presenting the same information in different forms.

Running Time

31 mins

Year

2009

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*36* episodes in this series

Episode 1 An Introduction to the Course

Professor Sellers introduces the general topics and themes for the course, describing his approach and recommending a strategy for making the best use of the lessons and supplementary workbook. Warm…

Episode 2 Order of Operations

The order in which you do simple operations of arithmetic can make a big difference. Learn how to solve problems that combine adding, subtracting, multiplying, and dividing, as well as…

Episode 3 Percents, Decimals, and Fractions

Continue your study of math fundamentals by exploring various procedures for converting between percents, decimals, and fractions. Professor Sellers notes that it helps to see these procedures as ways of…

Episode 4 Variables and Algebraic Expressions

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,…

Episode 5 Operations and Expressions

Discover that by following basic rules on how to treat coefficients and exponents, you can reduce very complicated algebraic expressions to much simpler ones. You start by using the commutative…

Episode 6 Principles of Graphing in 2 Dimensions

Using graph paper and pencil, begin your exploration of the coordinate plane, also known as the Cartesian plane. Learn how to plot points in the four quadrants of the plane,…

Episode 7 Solving Linear Equations, Part 1

In this lesson, work through simple one- and two-step linear equations, learning how to isolate the variable by different operations. Professor Sellers also presents a word problem involving a two-step…

Episode 8 Solving Linear Equations, Part 2

Investigating more complicated examples of linear equations, learn that linear equations fall into three categories. First, the equation might have exactly one solution. Second, it might have no solutions at…

Episode 9 Slope of a Line

Explore the concept of slope, which for a given straight line is its rate of change, defined as the rise over run. Learn the formula for calculating slope with coordinates…

Episode 10 Graphing Linear Equations, Part 1

Use what you've learned about slope to graph linear equations in the slope-intercept form, y = mx + b, where m is the slope, and b is the y intercept.…

Episode 11 Graphing Linear Equations, Part 2

A more versatile approach to writing the equation of a line is the point-slope form, in which only two points are required, and neither needs to intercept the y axis.…

Episode 12 Parallel and Perpendicular Lines

Apply what you've discovered about equations of lines to two very special types of lines: parallel and perpendicular. Learn how to tell if lines are parallel or perpendicular from their…

Episode 13 Solving Word Problems with Linear Equations

Linear equations reflect the behavior of real-life phenomena. Practice evaluating tables of numbers to determine if they can be represented as linear equations. Conclude with an example about the yearly…

Episode 14 Linear Equations for Real-World Data

Investigating more real-world 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…

Episode 15 Systems of Linear Equations, Part 1

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…

Episode 16 Systems of Linear Equations, Part 2

Expand your tools for solving systems of linear equations by exploring the method of solving by elimination. This technique allows you to eliminate one variable by performing addition, subtraction, or…

Episode 17 Linear Inequalities

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…

Episode 18 An Introduction to Quadratic Polynomials

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)…

Episode 19 Factoring Trinomials

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,…

Episode 20 Quadratic Equations - Factoring

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…

Episode 21 Quadratic Equations - The Quadratic Formula

For those cases that defy simple factoring, the quadratic formula provides a powerful technique for solving quadratic equations. Discover that this formidable-looking expression is not as difficult as it appears…

Episode 22 Quadratic Equations - Completing the Square

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…

Episode 23 Representations of Quadratic Functions

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…

Episode 24 Quadratic Equations in the Real World

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…

Episode 25 The Pythagorean Theorem

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…

Episode 26 Polynomials of Higher Degree

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…

Episode 27 Operations and Polynomials

Much of what you've learned about linear and quadratic expressions applies to adding, subtracting, multiplying, and dividing polynomials. Discover how the FOIL operation can be extended to multiplying large polynomials,…

Episode 28 Rational Expressions, Part 1

When one polynomial is divided by another, the result is called a rational function because it is the ratio of two polynomials. These functions play an important role in algebra.…

Episode 29 Rational Expressions, Part 2

Continuing your exploration of rational expressions, try your hand at multiplying and dividing them. The key to solving these complicated-looking equations is to proceed one step at a time. Close…

Episode 30 Graphing Rational Functions, Part 1

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…

Episode 31 Graphing Rational Functions, Part 2

Sketch the graphs of several rational functions by first calculating the vertical and horizontal asymptotes, the x and y intercepts, and then plotting several points in the function. In the…

Episode 32 Radical Expressions

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…

Episode 33 Solving Radical Equations

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…

Episode 34 Graphing Radical Functions

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…

Episode 35 Sequences and Pattern Recognition, Part 1

Pattern recognition is an important and fascinating mathematical skill. Investigate two types of number patterns: geometric sequences and arithmetic sequences. Learn how to analyze such patterns and work out a…

Episode 36 Sequences and Pattern Recognition, Part 2

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…

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