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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
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
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
Discussing the concept of the binomial probability distribution
Calculating probabilities using the binomial probability distribution
Discussing the concepts of a random variable and a probability distribution
Discussing the expected value of a discrete random variable
Determining the expected amount of net winnings for a game of chance
Determining the expected amount of profit on a stock
Fundamentals of statistics
Constructing a frequency distribution for a set of data
Constructing a relative frequency distribution
Constructing a relative frequency histogram
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
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 Chebyshev's Theorem
Discussing the concept of percentiles
Constructing a box plot for a set of data using Winstats software (free)
Discussing the Empiricial Rule
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
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)
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)
Fundamentals of trigonometry
Discussing basic geometric figures
Discussing angle measurement and different types of angles
Converting between decimal degrees and degrees, minutes, seconds (DMS) (TYPO: During last problem, when converting minutes to degrees, I should divided 22.01055' by 60.)
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