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 a sum 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

Dividing 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 a rational equation

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

Multiplying complex numbers

Dividing 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

Determining the domain and range of a function as well as intervals where it's increasing decreasing, and/or constant

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 a function is not 1-1

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

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

Deriving the distance formula

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

Definition of a set

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

Determining the Cartesian product of two sets as well as the cardinality of a Cartesian product 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

Calculating the values of the six trigonometric functions for a given angle passing through a point (example #2)

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

Using a calculator to assist with problems involving trigonometric functions and their inverses (part 1)

Using a calculator to assist with problems involving trigonometric functions and their inverses (part 2)

Solving right triangles (example 1)

Solving right triangles (example 2)

Deriving the law of sines

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 two side lengths and the measure of the included angle are known

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

Calculating a weighted mean

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 z-scores

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

Determining z-scores associated with certain probabilities from a standard normal probability distribution

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

Solving problems involving the sampling distribution of the sample mean (using the Central Limit Theorem) (part 1)

Solving problems involving the sampling distribution of the sample mean (using the Central Limit Theorem) (part 2)

Solving problems involving the sampling distribution of the sample mean (using the Central Limit Theorem) (part 3)

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

Discussing p-values

Explaining how to use p-values to determine whether or not to reject the null hypothesis of a hypothesis test

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)

Investigating the procedure for a two-sample (dependent) hypothesis test on a population mean difference (part 1)

Investigating the procedure for a two-sample (dependent) hypothesis test on a population mean difference (part 2)

Investigating the procedure for a two-sample (dependent) hypothesis test on a population mean difference (part 3)

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)

Constructing a confidence interval (using independent samples) to estimate a difference in two population means

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