Objectives

The learners will...

• Plot ordered pairs in a Cartesian coordinate system.

• Graph equations by plotting points.

• Graph equations with a graphing utility.

• Find x-intercepts and y-intercepts.

• Use the distance formula.

• Use the midpoint formula.

Part 1 of an Introduction to the Cartesian Plane. 

https://www.youtube.com/watch?v=O9HXGy5N5ik

Part 2 of an Introduction to the Cartesian Plane. 

https://www.youtube.com/watch?v=PicahjzN5-M

Introduction to Graphing Equations Through the Simplest Method - Plotting Points 

https://www.youtube.com/watch?v=kYdZlyJ8S80

Introduction to Graphing Equations by Plotting Intercepts. 

https://www.youtube.com/watch?v=Wgpq0zO6z3o

The Distance Formula. 

https://www.youtube.com/watch?v=TiAEH1qPTQU

Finding the Midpoint of a Segment. 

https://www.youtube.com/watch?v=1Hf_bWSQsuc

Objectives

The learners will...

• Solve equations in one variable algebraically.

• Solve a rational equation.

• Find a linear equation.

• Given the equations of two lines, determine whether their graphs are parallel or perpendicular.

• Write the equation of a line parallel or perpendicular to a given line.

Solving multi-step equations. 

https://www.youtube.com/watch?v=ufTjNFRJJRc

Solving rational equations. 

https://www.youtube.com/watch?v=MMORnvhR4wA

Determining linear equations in slope-intercept form. 

https://www.youtube.com/watch?v=2mmOa4YrFbs

Determining an equation through the use of point-slope form. 

https://www.youtube.com/watch?v=ndRpJxdmZJI

Determine the equation of a horizontal or vertical line given the graph. 

https://www.youtube.com/watch?v=kdPWd_c3UXY

Determining equations of parallel and perpendicular lines. 

https://www.youtube.com/watch?v=QpzN4XeHrHE

Objectives

The learners will...

• Set up a linear equation to solve a real-world application.

• Use a formula to solve a real-world application.

Problem-solving using linear equations - Dimensions of a bookcase. 

https://www.youtube.com/watch?v=yW2AJed4JcQ

Problem-solving using linear equations - Cost of a rental car 

https://www.youtube.com/watch?v=H8KR3w2nXqs

Problem-solving using linear equations - Modeling cricket chirps. 

https://www.youtube.com/watch?v=uhkXKZ55xdI

Solving a formula for a specific variable. 

https://www.youtube.com/watch?v=BUVJlJXfuFo

Objectives

The learners will...

• Add and subtract complex numbers.

• Multiply and divide complex numbers.

• Simplify powers of i

Adding and subtracting complex numbers. 

https://www.youtube.com/watch?v=eyy_SR1JfyQ

Multiplying complex numbers. 

https://www.youtube.com/watch?v=Fmr3o2zkwLM

Multiplying complex conjugates. 

https://www.youtube.com/watch?v=VbOzEkvMb_A

Dividing complex numbers. 

https://www.youtube.com/watch?v=XBJjbJAwM1c

Powers of i. 

https://www.youtube.com/watch?v=sfP6SmEYHRw

Objectives

The learners will...

•    Solve quadratic equations by factoring.
•    Solve quadratic equations by the square root property.
•    Solve quadratic equations by completing the square.
•    Solve quadratic equations by using the quadratic formula.

Solving a quadratic equation by factoring (GCF) 

https://www.youtube.com/watch?v=gIwMkTAclw8

Solving a quadratic equation - factoring by grouping 

https://www.youtube.com/watch?v=uUdgJexMjOA

Solving a quadratic equation - difference of squares 

https://www.youtube.com/watch?v=PNFMcIhG-CM

Solving a quadratic equation - factoring 

https://www.youtube.com/watch?v=YuLxs61LNF4

https://www.youtube.com/watch?v=kDj_qdKW-ls

Forming perfect square trinomials 

https://www.youtube.com/watch?v=9MZ1m4mOqVc

Forming perfect square trinomials - example 

https://www.youtube.com/watch?v=NwXyVcU5cg8

Completing the square 

https://www.youtube.com/watch?v=3LB4fUyyCL8

Completing the square - real rational solutions 

https://www.youtube.com/watch?v=PsbYUySRjFo

Completing the square - real irrational solutions 

https://www.youtube.com/watch?v=IjCjbtrPWHM

Completing the square - complex solutions 

https://www.youtube.com/watch?v=Nc09Ttq-_UI

Using the quadratic formula - Two real rational solutions 

https://www.youtube.com/watch?v=xtwO-n8lRPw

Using the quadratic formula - One repeated rational solution 

https://www.youtube.com/watch?v=OXwwzWcxFgE

Using the quadratic formula - Two real irrational solutions 

https://www.youtube.com/watch?v=Nwx4ZO9Hopk

Using the quadratic formula - complex solutions 

https://www.youtube.com/watch?v=11EwTcRMPn8

Objectives

The learners will...

• Solve equations involving rational exponents.

• Solve equations using factoring.

• Solve radical equations.

• Solve absolute value equations.

• Solve other types of equations.

Solve an equation with a rational exponent - one solution 

https://www.youtube.com/watch?v=p4hJvjLczFk

Solve an equation with a rational exponent - two solutions 

https://www.youtube.com/watch?v=l7-eXSCvNvM

Solve an equation with a rational exponent using reciprocal exponents 

https://www.youtube.com/watch?v=xs-D0MixxLM

Solve a radical equation - one square root 

https://www.youtube.com/watch?v=qkZHKK77grM

Solve a radical equation - two square roots 

https://www.youtube.com/watch?v=vFdkSCKzQnw

Solve a radical equation - cube roots and fourth roots 

https://www.youtube.com/watch?v=jRGpLRVfmnk

Solving a radical equation - application 

https://www.youtube.com/watch?v=PEUNMdux5fU

Solving absolute value equations 

https://www.youtube.com/watch?v=MJRrJX0VvGI

Sometimes absolute value equations have no solutions! 

https://www.youtube.com/watch?v=T-z5cQ58I_g

Solving a higher-order equation in quadratic form. 

https://www.youtube.com/watch?v=5FHTggnUAtU

Objectives

The learners will...

• Use interval notation.

• Use properties of inequalities.

• Solve inequalities in one variable algebraically.

• Solve absolute value inequalities.

Solving Linear Inequalities in One Variable 

https://www.youtube.com/watch?v=iklg78Nmc5M

Compound Inequalities 

https://www.youtube.com/watch?v=U20Dp4lPVoo

Compound Inequalities - 2 

https://www.youtube.com/watch?v=o5clgmyYCZE

Absolute value inequalities 

https://www.youtube.com/watch?v=qmCQ92IpmMw

Absolute Value Inequalities - 2 

https://www.youtube.com/watch?v=qmCQ92IpmMw

Objectives

The learners will...

• Determine whether a relation represents a function.

• Find the value of a function.

• Determine whether a function is one-to-one.

• Use the vertical line test to identify functions.

• Graph the functions listed in the library of functions.

Introduction to Functions 

https://www.youtube.com/watch?v=vO5qqfsWzhc

Determining a Function Value from a Graph 

https://www.youtube.com/watch?v=HRCD79-uXKo

Determining Function Inputs from a Graph 

https://www.youtube.com/watch?v=zmBAeLri6aE

The Vertical Line Test 

https://www.youtube.com/watch?v=gO5WN9g1fJo

Determining if a Relation is a One-to-One Function (Table) 

https://www.youtube.com/watch?v=gO5WN9g1fJo

Determining if a Relation is a One-to-One Function (Graph) 

https://www.youtube.com/watch?v=tbSGdcSN8RE

Graphing and Recognition of Nine Basic Functions 

https://www.youtube.com/watch?v=IP70kcTtWkI

Objectives

The learners will...

• Find the domain of a function defined by an equation.

• Graph piecewise-defined functions.

Finding the Domain and Range of a Function 

https://www.youtube.com/watch?v=FtJRstFMdhA

Interval and Set Notation 

https://www.youtube.com/watch?v=wmX1PI-Rs-8

Interpreting and Graphing Piecewise Functions 

https://www.youtube.com/watch?v=rn_Z3yCRCt0

Determining Functional Values for a Piecewise Defined Function 

https://www.youtube.com/watch?v=E2F2-gP-2qU

Writing a Piecewise Function from a Graph 

https://www.youtube.com/watch?v=AQaKh_1poBI

Objectives

The learners will...

• Combine functions using algebraic operations.

• Create a new function by composition of functions.

• Evaluate composite functions.

• Find the domain of a composite function.

• Decompose a composite function into its component functions.

Introduction to Composite Functions 

https://www.youtube.com/watch?v=qxBmISCJSME

Evaluating Compositions of Functions Defined as a Table 

https://www.youtube.com/watch?v=Blvv-Dnfubo

Evaluating Compositions of Functions Defined on a Graph 

https://www.youtube.com/watch?v=b-i7N0hE-Ys

Function Decomposition 

https://www.youtube.com/watch?v=gFSSk8jaAwA

Domains of Composite Functions 

https://www.youtube.com/watch?v=aV7HtrEj2hA

Objectives

The learners will...

• Graph an absolute value function.

• Solve an absolute value equation.

Objectives

The learners will...

• Verify inverse functions.

• Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one.

• Find or evaluate the inverse of a function.

• Use the graph of a one-to-one function to graph its inverse function on the same axes.

Objectives

The learners will...

• Represent a linear function.

• Determine whether a linear function is increasing, decreasing, or constant.

• Interpret slope as a rate of change.

• Write and interpret an equation for a linear function.

• Graph linear functions.

• Determine whether lines are parallel or perpendicular.

• Write the equation of a line parallel or perpendicular to a given line.

Objectives

The learners will...

• Build linear models from verbal descriptions.

• Model a set of data with a linear function.

This video gives good examples of how to represent a problem with a linear equation. 

https://www.youtube.com/watch?v=BR7MJpvUL0Q

Linear regression has a lot of applications and is used widely in all fields of investigation.  This video gives some of those examples.  It then gets into more complex examples, like multiple regression and logistic regression, which we do not cover. 

https://www.youtube.com/watch?v=FLJ0yYetywE

How do we do this in desmos?  This is how... 

https://www.youtube.com/watch?v=V_vfAPlqj2o

This video shows the same thing, and also extends it to non-linear regression: 

https://www.youtube.com/watch?v=VfC8uQGm5W8

Objectives

The learners will...

• Recognize characteristics of graphs of polynomial functions

• Use factoring to find zeros of polynomial functions

• Identify zeros and their multiplicities

• Determine end behavior

• Understand the relationship between degree and turning points

• Graph polynomial functions

• Use the Intermediate Value Theorem

Finding the intercepts on the polynomial function. 

https://www.youtube.com/watch?v=2ebWSFDGgjM

Finding the equation of a polynomial from its graph. 

https://www.youtube.com/watch?v=Ly8mygYGwLo

Finding the equation of a polynomial from the roots and their multiplicities. 

https://www.youtube.com/watch?v=DN8i7sZHUqg

Objectives

The learners will...

• Use long division to divide polynomials

• Use synthetic division to divide polynomials

Polynomial long division. 

https://www.youtube.com/watch?v=brpNxPAkv1c

https://www.youtube.com/watch?v=gvBn-UcQL1k

Polynomial synthetic division. 

https://www.youtube.com/watch?v=5dBAdzl2Mns

Objectives

The learners will...

• Find zeros of a polynomial function

• Use the Linear Factorization to find polynomials with given zeros

• Solve real-world applications of polynomial equations

Find a polynomial given its zeros. 

https://www.youtube.com/watch?v=353wpqLB1V8

Find the zeros of a polynomial function. 

https://www.youtube.com/watch?v=LeZdCSCIb3Q

Find the zeros of a polynomial function with complex zeros. 

https://www.youtube.com/watch?v=uc7sg106MGI