Video:  Factoring Polynomials By GCF, Grouping, Substitution, Sum and Difference of Squares (and Completing the Square)  (45:42 mins)

Video:  Exponents and Powers of Zero Patterns (6:55 mins)

Video:  Logarithms Review (1:20:05 mins)

Number and Quantity

Video:  Imaginary Numbers Explained (27:13 mins)

Video:  Adding Complex Numbers (1:11 mins)

Video:  Subtracting Complex Numbers (1:52 mins)

Video:  Multiplying Complex Numbers (5:31 mins)

Video:  Dividing Complex Numbers (4:57 mins)

Video:  Fundamental Theorem of Algebra (“Descarte’s Rule of Signs”) (5:33 mins)

Video:  Possible number of real roots (3:45 mins)

Video:  How To Find All Real and Imaginary Solutions or Zeros of Polynomial Functions (33:19 mins)

 

  • Extend the system of powers and roots to include rational exponents.

  • Create and recognize equivalent expressions involving radical and exponential forms of expressions.

  • Add, subtract, multiply and divide radical expressions.

  • Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.

  • Represent complex numbers.

  • Add, subtract, multiply and divide complex numbers.

  • Know and apply the Fundamental Theorem of Algebra

 

Seeing Structure in Expressions

Video:  Logarithms (7:01 mins)

Video:  Introduction to Logarithmic Properties – Part 1 (9:15 mins)

Video:  Introduction to Logarithmic Properties – Part 2 (10:04 mins)

Video:  Proof: log a + log b = log ab (7:08 mins)

Video:  Proof: a log b = log(b^a), log a – log b = log(a/b) (7:58 mins)

Video:  Fancier Logarithm Expressions (4:19 mins)

Video:  Graphing Logarithmic Functions (9:09 mins)

Video:  Solving Exponential Equations with Different Bases Using Logarithms (10:51 mins)

  • Develop the definition of logarithms based on properties of exponents.

  • Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic equations.

  • Use properties of logarithms to solve equations or find equivalent expressions.

  • Understand why logarithmic scales are used, and use them to solve problems.

 

Reasoning with Equations and Inequalities

Video:  Absolute value equations (10:40 mins)

Video:  Absolute value inequalities (13:12 mins)

Video:  Solving Absolute Value Equations and Inequalities – Number Line & Interval Notation (13:12 mins)

Video:  Special Types of Linear Systems (15:17 mins)

 

  • Create and solve equations and inequalities, including those that involve absolute value.

  • Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result.

  • Create and solve systems of equations that may include no-linear equations and inequalitities.

 

Arithmetic with Polynomials and Rational Expressions

Video: Adding and subtracting polynomials (1:43 mins)

Video:  More examples of addition and subtraction of polynomials (15:59 mins)

Video:  Multiplying binomials and polynomials (9:49 mins)

Video:  Factoring special products (10:08 mins)

Video:  More examples of factoring quadratics with a leading coefficient of 1 (16:29 mins)

Video:  Factoring trinomials with a non-1 leading coefficient by grouping (5:38 mins)

Video:  More examples of factoring by grouping (13:56 mins)

Video:  Polynomial Equations in Factored Form (9:28 mins)

Video:  Simplifying rational expressions introduction (15:22 mins)

Video:  Adding and subtracting rational expressions (8:14 mins)

Video:  Adding Rational Expressions Example 1 (3:46 mins)

Video:  Adding Rational Expressions Example 2 (6:39 mins)

Video:  Solving Rational Equations (12:56 mins)

Video:  Solving rational equations 1 (4:12 mins)

Video:  Solving rational equations 2 (4:07 mins)

Video:  Solving rational equations 3 (4:31 mins)

Video:  Extraneous solutions to rational equations (3:02 mins)

Video:  Extraneous solutions of radical equations (5:22 mins)

Video:  Applying rational equations 1 (Work and Rate Problems) (5:25 mins)

Video:  Applying rational equations 2 (Work and Rate Problems) (5:59 mins)

Video:  Applying rational equations 3 (Work and Rate Problems) (7:58 mins)

Video:  Rate Problem Involving Rational Equations (7:30 mins)

Video:  Another Take on the Rate Problem (3:34 mins)

Video:  Polynomial division (12:08 mins)

Video:  Dividing polynomials 1 (3:19 mins)

Video:  Dividing polynomials with remainders (6:22 mins)

Video:  Polynomial remainder theorem (6:42 mins)

Video:  Polynomial remainder theorem proof (5:41 mins)

Video:  Polynomial remainder theorem example (3:31 mins)

Video:  Polynomial remainder theorem to test factor (3:25 mins)

Video:  Synthetic division (5:20 mins)

Video:  Synthetic division example 2 (4:59 mins)

Video:  Constructing a polynomial that has a certain factor (3:38 mins)

Video:  Fundamental theorem of algebra (5:33 mins)

Video:  Finding zeros of polynomials (1 of 2) (9:08 mins)

Video:  Finding zeros of polynomials (2 of 2) (2:59 mins)

Video:  Finding zeros of polynomials (example 2) (6:44 mins)

  • Extend the knowledge of factoring to include factors with complex coefficients.

  • Understand the Remainder Theorem and use it to solve problems.

  • Find the least common multiple of two or more polynomials.

  • Add, subtract, multiply and divide rational expressions.

  • Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.

 

Interpreting Functions

Video:  Polynomial Functions Graphing – Multiplicity, End Behavior, Finding Zeros (28:53 mins)

Video:  How To Find All Real and Imaginary Solutions or Zeros of Polynomial Functions (33:19 mins)

Video:  Matching rational functions to their graphs (6:06 mins)

Video:  Asymptotes of rational functions (21:05 mins)

Video:  Another rational function graph example (8:19 mins)

Video:  A third example of graphing a rational function (11:30 mins)

Video:  Finding horizontal and vertical asymptotes (11:21 mins)

 

  • Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.

  • Translate between equivalent forms of functions

Building Functions

Video:  Introduction to function composition (6:14 mins)

Video:  Creating new function from composition (2:56 mins)

Video:  Evaluating composite functions (4:10 mins) 

Video:  Evaluating composite function using graphs (3:01 mins)

Video:  Evaluating composite functions using tables (4:09 mins)

Video:  Introduction to function inverses (9:05 mins)

Video:  Understanding inverse functions (6:18 mins)

Video:  Verifying function inverses example (6:40 mins)

Video:  Example of functions that are not inverses (4:11 mins)

 

  • Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).

  • Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.

  • Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections.

 

Modeling

Video: Modeling with function composition (4:14 mins)

Video: Modeling with combined functions (3:07 mins)

 

  • Create functions and use them to solve applications of quadratic and exponential function model problems.

 

Data and Statistical Analysis

Video:  Introduction to the normal distribution (26.23 mins)

Video:  Population standard deviation (8:04 mins)

Video:  Range, variance and standard deviation as measures of dispersion (12:33 mins)

Video:  Sampling distribution example problem (14:27 mins)

Video:  Comparing models to fit data (4:04 mins)

Video:  Inferring population mean from sample mean (10:02 mins)

Video:  Z-statistics vs. T-statistics (6:38 mins)

Video:  Margin of error 1 (15:01 mins)

Video:  Margin of error 2 (10:04 mins)

Video:  Probability explained (8:17 mins)

Video:  Free throwing probability (7:04 mins)

Video:  Three pointer vs free throwing probability (5:46 mins)

Video:  Coin flipping probability (9:19 mins)

Video:  Exactly three heads in five flips (6:51 mins)

Video:  Mega millions jackpot probability (5:29 mins)

Video:  Birthday probability problem (13:16 mins)

Video:  Test taking probability and independent events (4:43 mins)

Video:  Dependent probability introduction (6:37 mins)

Video:  Dependent probability example (9:00 mins)

Video:  Probability without equally likely events (8:57 mins)

Video:  Compound probability of independent events (5:59 mins)

Video:  Introduction to combinations  (6:17 mins)

Video:  Combination formula (11:16 mins)

Video:  Probability using combinations (9:09 mins)

 

  • Analyze how random sampling could be used to make inferences about population parameters.

  • Determine whether a specified model is consistent with a given data set.

  • Describe and explain the purposes, relationship to randomization and differences among sample surveys, experiments and observational studies.

  • Use data from a sample to estimate characteristics of the population and recognize the meaning of the margin of error in these estimates.

  • Describe and explain how the relative sizes of a sample and the population affect the margin of error of predictions.

  • Analyze decisions and strategies using probability concepts.

  • Evaluate reports based on data.

  • Know and use the characteristics of normally distributed data sets; predict what percentage of the data will be above or below a given value that is a multiple of standard deviations above or below the mean.

  • Fit a data set to a distribution using its mean and standard deviation to determine  whether the data is approximately normally distributed.

 

* Sources:  dese.mo.gov (Course Level Expectations (CLEs))