Video Library
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The following list is the entire collection of videos found on this website: To search for a particular topic, type Ctrl+f (which opens up a search box for this specific page) and type in keywords.
Factoring
Factoring out the greatest common factor (GCF) of an expression
Factoring an expression using the "grouping" method
Factoring trinomials with leading coefficients of 1
Illustration of the ac-method of factoring
Factoring a perfect-square trinomial
Factoring a difference of squares
Factoring a difference of cubes
Factoring an expression involving multiple factoring techniques
Rational expressions and equations
Evaluating a rational expression
Simplifying a rational expression
Finding the domain of a rational expression
Issues encountered with cancelling common factors
Multiplying rational expressions
Expressing numerical fractions in terms of their least common denominator
Expressing rational expressions in terms of their LCD
Adding and subtracting rational expressions
Simplifying a complex rational expression (method 1)
Simplifying a complex rational expression (method 2)
Discussing differences between rational expressions versus rational equations
Solving quadratic equations
Solving a quadratic equation by factoring
Discussing the square root property
Discussing perfect square trinomials
Discussing the concept of completing the square (part 1)
Discussing the concept of completing the square (part 2)
Applying the procedure of completing the square to solving quadratic equations
Solving a quadratic equation by completing the square
Solving a quadratic equation by completing the square (example 2)
Solving a quadratic equation by completing the square (example 3)
Solving a quadratic equation by completing the square (example 4)
Deriving the quadratic formula
Solving a quadratic equation using the quadratic formula
Solving a quadratic equation in nonstandard form using the quadratic formula
Solving a quadratic equation via the quadratic formula
Knowing when common factors can be cancelled
Solving an equation having quadratic form (part 1)
Solving an equation having quadratic form (part 2)
Variation
Discussing the concept of direct variation
Discussing the concept of inverse variation
Discussing the concept of joint variation
Illustrating the use of merging multiple variation models into one scenario
Linear equations and inequalities involving absolute value
Discussing the concept of linear equations involving absolute value (part 1)
Discussing the concept of linear equations involving absolute value (part 2)
Solving a linear equation with two terms involving absolute value
Discussing linear inequalities involving absolute value (part 1)
Discussing linear inequalities involving absolute value (part 2)
Solving linear inequalities involving absolute value
Compound linear inequalities
Discussing the concepts of intersection and union (of sets)
Discussing a compound linear inequality involving the word "and"
Discussing a compound linear inequality involving the word "or"
Discussing patterns when determining solution sets for compound linear inequalities
Solving a compound linear inequality
Solving a compound linear inequality (example 2)
Graphing linear inequalities in two variables
Graphing a linear inequality (method #1)
Graphing a linear inequality (method #2)
Solving non-linear inequalities
Solving a quartic inequality (part 1)
Solving a quartic inequality (part 2)
Solving a rational inequality (part 1)
Solving a rational inequality (part 2)
Fundamentals of radicals
Discussing nth roots of real numbers (part 1)
Discussing nth roots of real numbers (part 2)
Discussing nth roots of real numbers (part 3)
Simplifying basic radical expressions
Discussing functions with radicals (part 1)
Graphing a function containing a radical
Expressing radicals using exponent notation (part 1)
Expressing radicals using exponent notation (part 2)
Converting between radical notation and exponent notation
Simplifying an expression involving rules for working with exponents
Adding and/or subtracting radical expressions
Adding and subtracting radical expressions requiring the simplification of the radicals
Multiplying radicals involving the same index (assume all variables represent nonnegative quantities!!)
Multiplying radical expressions involving different indices (assume all variables represent nonnegative quantities!!)
Multiplying radical expressions involving previously learned "patterns"
Rationalizing denominators with one term (part 1)
Rationalizing denominators with one term (part 2)
Rationalizing denominators with two terms (part 1)
Rationalizing denominators with two terms (part 2)
Solving radical equations involving one radical expression
Solving radical equations involving two radical expressions
Fundamentals of complex numbers
Discussing the structure of the complex number system
Discussing the pattern with the powers of i
Simplifying square roots involving negative radicands
Adding and subtracting complex numbers
Fundamentals of functions
Determining the domain and range of a relation
Determine the domain and range of a relation from its graph
Understanding the concept of a function and how to evaluate a function
Evaluating a function for specified domain values
Understanding how to determine the domain of a function
Understanding how to determine the domain of a function (example 2)
Understanding how to determine the domain of a function (example 3)
Finding the domain of a function algebraically
Graphing a function by plotting points
Determining intercepts of the graphs of functions
Determining intercepts of the graphs of functions (example 2)
Graphing a piecewise-defined function
Sketching a graph of a piecewise-defined function
Discussing the vertical line test
Applying the vertical line test to a graph
Discussing when an equation represents a function
Sketching a graph of the reciprocal function
Graphing the greatest integer function
Determining the domain and range of a function given its graph
Graphically determining local maximums and local minimums of a function
Calculating the average rate of change of a function on a specified numeric interval
Determining the average rate of change of a function on an interval
Horizontal and vertical shifts of graphs of functions (part 1)
Horizontal and vertical shifts of graphs of functions (part 2)
Reflections of graphs about the axes
Discussing dilations of the graphs of functions
Using transformations to graph a function
Using transformations to graph a function (example 2)
Using transformations (involving reflections) to graph a function
Adding and subtracting functions
Multiplying and dividing functions
Arithmetic of functions (part 1)
Arithmetic of functions (part 2)
Discussing the concept of the composition of two functions
Finding the domain of a composition of functions (part 1)
Finding the domain of a composition of functions (part 2)
Finding the domain of a composition of two functions
Finding the domain of a composition of two functions (another example)
Understanding 1-1 functions and the horizontal line test
Applying the horizontal line test to the graph of a function
Showing that a function is 1-1
Discussing the concept of the inverse of a function
Discussing why only 1-1 functions have inverses
Discussing methods for finding the inverse of a function
Finding the inverse of a function
Explaining how to obtain the graph of the inverse of a function
Graphing the inverse of a function
Graphing quadratic functions
Discussing the vertex form of a quadratic function
Graphing quadratic functions in vertex form
Converting a quadratic function from standard form to vertex form
Deriving the vertex formula (part 1)
Deriving the vertex formula (part 2)
Using the vertex formula to convert a quadratic function (written in standard form) to vertex form
Exponential and logarithmic functions
Discussing the concept of an exponential function
Basic properties of the graph of an exponential function
Using transformations to graph an exponential function
Finding an exponential function given its graph
Discussing the concept of a logarithm (part 1)
Discussing the concept of a logarithm (part 2)
Determining the graph of a logarithmic function with base a
Converting between exponential form and logarithmic form
Evaluating logarithms (example 2)
Determining the domain of a logarithmic function
Finding a logarithmic function given its graph
Using transformations to graph a logarithmic function
Using the change of base rule to evaluate a logarithm
Explaining the change of base formula
Discussing the laws of logarithms (part 1)
Discussing the laws of logarithms (part 2)
Discussing the laws of logarithms (part 3)
Expanding a logarithmic expression
Expressing a logarithmic expression as a single logarithm
Solving an exponential equation
Solving an exponential equation (example 2)
Solving an exponential equation involving multiple bases
Solving an exponential equation involving two bases (example 2)
Solving a logarithmic equation
Discussing a population growth model
Applying an exponential growth model to a population growth scenario
Applying an exponential growth model to a population growth scenario (example 2)
Discussing an exponential model for radioactive decay
Solving a problem involving an exponential decay model
Applying an exponential decay model to a radioactive decay situation
Discussing Newton's Law of Cooling
An application involving Newton's Law of Cooling
Polynomial and rational functions
Discussing the "end behavior" of the graph of a polynomial function
Graphing a polynomial function in factored form
Graphing a polynomial function in factored form (example 2)
Performing synthetic division of polynomials
Performing synthetic division of polynomials (example 2)
Dividing polynomials using synthetic division
Illustration of the connection between synthetic division and the Remainder Theorem
Determining a polynomial function given its zeros
Determining a polynomial given specified real zeros
Determining all rational zeros of a polynomial
Determining the zeros of a polynomial
Graphing a polynomial function (part 1)
Graphing a polynomial function (part 2)
Determining all zeros (including complex zeros) of a polynomial
Determining a polynomial with complex zeros
Finding a polynomial having complex zeros (another example)
Determining a polynomial having specified complex zeros
Discussing the concept of graphing a rational function
Discussing intercepts of a graph of a rational function
Discussing vertical asymptotes of a graph of a rational function
Discussing horizontal asymptotes of a graph of a rational function
Constructing a graph of a rational function
Graphing a rational function (part 1)
Graphing a rational function (part 2)
Graphing a rational function in factored form
Graphing a rational function in factored form (example 2)
Circles
Calculating the distance between two points
Deriving the standard form of a circle
Sketching graphs of circles in standard form
Writing the equation of a circle (given in expanded form) in standard form
Determining the equation of a circle in standard form
Parabolas
Determining the equation of vertical parabola
Determining the equation of a parabola given its vertex and focus
Determining the equation of a shifted parabola
Finding the focus of a shifted parabola whose equation is in expanded form
Graphing a parabola in expanded form
Graphing a shifted horizontal parabola
Graphing a shifted horizontal parabola (example 2)
Sketching a graph of a vertical parabola
Graphing a vertical parabola whose vertex is at the origin
Ellipses
Determining the equation of a vertical ellipse
Finding the equation of a shifted horizontal ellipse
Finding the equation of an ellipse given its vertices and foci
Graphing an ellipse centered at the origin
Sketching a graph of a vertical ellipse
Graphing a shifted vertical ellipse
Hyperbolas
Finding an equation of a hyperbola given its vertices and foci
Finding the equation of a hyperbola
Finding the equation of a shifted vertical hyperbola
Graphing a horizontal hyperbola
Sketching a graph of a shifted vertical hyperbola
Fundamentals of sets
Determining whether a number is an element of a set
Determining the cardinality of a set
Determining whether two sets are equal
Determining the complement of a set
Determining whether a set is a subset of another set
Discussing the number of subsets that can be formed from a set having n elements
Determining the intersection and union of two sets
Determining the difference of two sets
An illustration of DeMorgan's Laws
Constructing a Venn diagram given cardinalities of various sets
Determining the cardinality of a set involving two sets, their intersection, and their union
Determining whether two sets are equivalent
Determining the cardinality of the set of negative even integers
Fundamentals of trigonometry
Discussing basic geometric figures
Discussing angle measurement and different types of angles
Converting between decimal degrees and degrees, minutes, seconds (DMS)
Adding and subtracting angle measurements written in DMS
Explaining the distance formula
Defining the six basic trigonometric functions of an angle in standard position
Calculating the values of the six trigonometric functions for a given angle passing through a point
Discussing the concept of trigonometric reciprocal identities
Using reciprocal identities to calculate values of trigonometric functions
Discussing the concept of the quotient identities
Calculating values of trigonometric functions for a given angle using identities
Calculating the values of the trigonometric functions given specified information about an angle
Discussing the signs of the trigonometric functions in the different quadrants
Defining the six trigonometric ratios for right triangles
Discussing the cofunction identities
Discussing the side lengths for a 30-60-90 triangle
Discussing the side lengths for a 45-45-90 triangle
Determining the reference angle associated with a given angle
Using reference angles to determine the values of trigonometric functions for a given angle measure
Solving right triangles (example 1)
Solving right triangles (example 2)
Solving an oblique triangle using the law of sines
Deriving the law of cosines (part 1)
Deriving the law of cosines (part 2)
Solving an oblique triangle using the law of cosines
Discussing alternative methods for calculating the area of a triangle (part 1)
Discussing alternative methods for calculating the area of a triangle (part 2)
Calculating the area of a triangle when all three side lengths are known
Descriptive statistics (graphical displays)
Constructing a relative frequency distribution
Constructing a relative frequency histogram
Constructing a histogram using the Statdisk software
Constructing a frequency distribution for a set of data
Constructing a frequency polygon for a set of data (Please ignore the momentary bird "squawk" towards the end. :) )
Constructing a stem-and-leaf plot for a set of data
Constructing a box plot for a set of data using Winstats software (free)
Descriptive statistics (numerical measures)
Determining measures of center for a set of data
Calculating a sample mean, median, mode, and midrange
Discussing the symmetry and skewness of a set of data
Measures of Variation for a set of data (part 1)
Measures of Variation for a set of data (part 2)
Measures of Variation for a set of data (part 3)
Discussing the Empiricial Rule
Discussing Chebyshev's Theorem
Discussing the concept of percentiles
How to determine if a data value is unusually high or unusually low
Determining usual and unusual values for a given set of data
Calculating and interpreting a z-score for a specified data value
Counting principles
Illustrating the fundamental counting principle
Discussing the concept of n-factorial
Arranging n objects without replacement where certain objects are identical
Discussing permutations of n objects taken r at a time
Counting problem involving permutations
Discussing combinations of n objects taken r at a time
Discussing the concept of the complements principle of counting
Discussing the concept of the additive principle of counting
Illustrating the complements principle of counting
Illustrating the additive principle of counting
Fundamentals of probability
Discussing the concept of a probability
Calculating the probability of an event involving combinations
Calculating a probability involving flips of a coin
Discussion of odds versus probabilities
Discussing the complement rule for calculating probabilities
Calculating probabilities using the addition rule
Discussing the concept of conditional probability
Discussing conditional probability
Discussing the multiplication rule
Discussing independent events versus mutually exclusive events
Discrete probability distributions
Discussing the concepts of a random variable and a probability distribution
Discussing the concept of a discrete probability distribution
Discussing the concept of the mean of a discrete random variable
Discussing the expected value of a discrete random variable
Calculating the expected number of heads in three flips of a coin
Determining the expected amount of net winnings for a game of chance
Determining the expected amount of profit on a stock
Discussing the concept of the standard deviation of a discrete random variable
Discussing the concept of the binomial probability distribution
Calculating probabilities using the binomial probability distribution
Calculating a probability involving a binomial distribution
Discussing the mean and standard deviation of a binomial random variable
Continuous probability distributions
Discussing the concept of a continuous uniform probabiltiy distribution
Calculating probabilities using a standard normal probability distribution
Calculating a probability involving a standard normal random variable
Calculating a probability involving a nonstandard normal random variable
Determining x-values given a probability from a normal probability distribution
Central limit theorem
Discussing the Central Limit Theorem
Confidence intervals (one sample)
Discussing the concept of estimating the population proportion p (part 1)
Discussing the concept of estimating the population proportion p (part 2)
Discussing the concept of estimating the population proportion p (part 3)
Calculating a confidence interval to estimate a population proportion
Sample size determinations (one sample)
Sample size considerations when estimating the population proportion p
Determining the minimum sample size needed to estimate a population proportion
Discussing the concept of estimating the population mean (part 1)
Discussing the concept of estimating the population mean (part 2)
Discussing a t distribution with "df" degrees of freedom (and the corresponding table)
Estimating the mean of a population with a confidence interval
Estimating the mean of a population with a confidence interval using a t-distribution
Determining the minimum sample size needed to estimate a population mean
Determining the sample size needed to estimate a population mean
Hypothesis tests (one sample)
Discussing the structure for a hypothesis test
Discussing null and alternative hypotheses for hypothesis tests
Discussing test statistics (part 1)
Discussing test statistics (part 2)
Explaining type 1 errors and type 2 errors
Discussing rejection regions for a 1-sample hypothesis test on p
Writing the conclusion of a hypothesis test
Discussing a 1-sample hypothesis test on the population proportion p
Conducting a one-tailed hypothesis test on a population proportion (part 1)
Conducting a one-tailed hypothesis test on a population proportion (part 2)
Discussing the structure of a one-sample hypothesis test on a population mean
Conducting a one-tailed hypothesis test on a population mean
conducting a one-sample hypothesis test on a population mean
Confidence intervals and hypothesis tests (two samples)
Estimating a population mean difference for two (dependent) samples with a confidence interval
Conducting a one-tailed t-test given two dependent samples
Discussing a two (independent) sample hypothesis test to estimate the true mean difference (part 1)
Discussing a two (independent) sample hypothesis test to estimate the true mean difference (part 2)
Discussing a two (independent) sample hypothesis test to estimate the true mean difference (part 3)
Conducting a one-tailed t-test for two independent samples
Fundamentals of linear correlation and regression
Creating a scatterplot of data using free Winstats software
Discussing the estimated linear correlation coefficient (part 1)
Discussing the estimated linear correlation coefficient (part 2)
Discussing the estimated linear correlation coefficient (part 3)
Calculating the Pearson linear correlation coefficient for a bivariate set of data
Discussing the estimated linear regression line (part 1)
Discussing the estimated linear regression line (part 2)
Discussing the estimated linear regression line (part 3)
Discussing the estimated linear regression line (part 4)
Determining the estimated least-squares regression line