Algebra II
Categories: Algebra, Mathematics
Course Content
Polynomial arithmetic

Intro to polynomials

Polynomials intro

The parts of polynomial expressions

Average rate of change of polynomials

Finding average rate of change of polynomials

Sign of average rate of change of polynomials

Adding and subtracting polynomials

Adding polynomials

Subtracting polynomials

Polynomial subtraction

Multiplying monomials by polynomials

Multiplying monomials

Multiplying monomials by polynomials: area model

Area model for multiplying polynomials with negative terms

Multiplying monomials by polynomials

Multiplying binomials by polynomials

Multiplying binomials by polynomials: area model

Multiplying binomials by polynomials

Special products of polynomials

Polynomial special products: difference of squares

Polynomial special products: perfect square
Complex numbers

The imaginary unit i

Intro to the imaginary numbers

Simplifying roots of negative numbers

Powers of the imaginary unit

i as the principal root of 1

Complex numbers introduction

Intro to complex numbers

Classifying complex numbers

The complex plane

Plotting numbers on the complex plane

Adding and subtracting complex numbers

Adding complex numbers

Subtracting complex numbers

Multiplying complex numbers

Multiplying complex numbers

Quadratic equations with complex solutions

Solving quadratic equations: complex roots

Factoring monomials

Introduction to factoring higher degree polynomials

Introduction to factoring higher degree monomials

Which monomial factorization is correct?

Worked example: finding the missing monomial factor

Worked example: finding missing monomial side in area model
Polynomial factorization

Greatest common factor

Greatest common factor of monomials

Taking common factors

Taking common factor from binomial

Taking common factor from trinomial

Taking common factor: area model

Factoring higher degree polynomials

Factoring higher degree polynomials

Factoring higherdegree polynomials: Common factor

Factoring using the difference of squares pattern

Factoring using structure

Identifying quadratic patterns

Factorization with substitution

Factoring using the perfect square pattern

Polynomial identities

Polynomial identities introduction

Analyzing polynomial identities

Describing numerical relationships with polynomial identities

Geometric series

Geometric series introduction

Finite geometric series formula

Worked examples: finite geometric series

Geometric series word problems: swing

Geometric series word problems: hike

Dividing polynomials by x

Intro to long division of polynomials

Dividing quadratics by linear expressions (no remainders)

Dividing quadratics by linear expressions with remainders

Dividing quadratics by linear expressions with remainders: missing xterm

Dividing polynomials by linear factors

Dividing polynomials by linear expressions

Dividing polynomials by linear expressions: missing term

Factoring using polynomial division

Factoring using polynomial division: missing term
Polynomial division

Polynomial Remainder Theorem

Intro to the Polynomial Remainder Theorem

Remainder theorem: finding remainder from equation

Remainder theorem examples

Remainder theorem: checking factors

Remainder theorem: finding coefficients

Proof of the Polynomial Remainder Theorem

Zeros of polynomials

Zeros of polynomials introduction

Zeros of polynomials: plotting zeros

Zeros of polynomials: matching equation to zeros

Zeros of polynomials: matching equation to graph

Zeros of polynomials (with factoring): grouping

Zeros of polynomials (with factoring): common factor

Positive and negative intervals of polynomials

Positive and negative intervals of polynomials

Multiplicity of zeros of polynomials

Zeros of polynomials (multiplicity)

End behavior of polynomials

Intro to end behavior of polynomials
Polynomial graphs

Intro to rational exponents

Rewriting roots as rational exponents

Exponential equation with rational answer

Rational exponents

Rewriting quotient of powers (rational exponents)

Rewriting mixed radical and exponential expressions

Properties of exponents (rational exponents)

Evaluating fractional exponents

Evaluating fractional exponents: negative unitfraction

Evaluating fractional exponents: fractional base

Evaluating quotient of fractional exponents

Evaluating mixed radicals and exponents

Evaluating exponents & radicals

Equivalent forms of exponential expressions

Rewriting exponential expressions as A⋅Bᵗ

Equivalent forms of exponential expressions
Rational exponents and radicals

Solving exponential equations using properties of exponents

Solving exponential equations using exponent properties

Solving exponential equations using exponent properties (advanced)

Interpreting the rate of change of exponential models

Interpreting change in exponential models

Interpreting time in exponential models

Constructing exponential models according to rate of change

Constructing exponential models

Constructing exponential models: half life

Constructing exponential models: percent change

Advanced interpretation of exponential models

Interpreting change in exponential models: with manipulation

Interpreting change in exponential models: changing units

Introduction to logarithms

Intro to logarithms

Evaluating logarithms (advanced)

Relationship between exponentials & logarithms

Relationship between exponentials & logarithms: graphs

Relationship between exponentials & logarithms: tables

The constant e and the natural logarithm

𝑒 and compound interest

𝑒 as a limit

Evaluating natural logarithm with calculator
Exponential models

Properties of logarithms

Intro to logarithm properties (1 of 2)

Intro to logarithm properties (2 of 2)

Using the logarithmic product rule

Using the logarithmic power rule

Using the properties of logarithms: multiple steps

Proof of the logarithm product rule

Proof of the logarithm quotient and power rules

Evaluating logarithms: change of base rule

Using the logarithm change of base rule

Proof of the logarithm change of base rule

The change of base formula for logarithms

Solving exponential equations using logarithms: base10

Solving exponential equations using logarithms: base2

Solving exponential equations with logarithms

Exponential model word problem: medication dissolve

Exponential model word problem: bacteria growth

Solving exponential models
Logarithms

Shifting functions

Shifting functions introduction

Shifting functions examples

Graphing shifted functions

Reflecting functions

Reflecting functions introduction

Reflecting functions: examples

Symmetry of functions

Function symmetry introduction

Even and odd functions: Graphs

Even and odd functions: Tables

Even and odd functions: Equations

Even and odd functions: Find the mistake

Scaling functions

Scaling functions introduction

Scaling functions vertically: examples

Scaling functions horizontally: examples

Identifying horizontal squash from graph

Putting it all together

Identifying function transformations

Graphs of square and cube root functions

Graphing square and cube root functions

Graphs of exponential functions

Transforming exponential graphs

Transforming exponential graphs (example 2

Graphing exponential functions
Transformations of functions

Graphs of logarithmic functions

Graphical relationship between 2ˣ and log₂(x)

Graphing logarithmic functions (example 1

Graphing logarithmic functions (example 2)

Rational equations

Rational equations intro

Equations with rational expressions

Equations with rational expressions (example 2)

Finding inverses of rational functions

Squareroot equations

Intro to squareroot equations & extraneous solutions

Squareroot equations intro

Solving squareroot equations: one solution

Solving squareroot equations: two solution

Solving squareroot equations: no solution

Extraneous solutions

Extraneous solutions

Equation that has a specific extraneous solution

Cuberoot equations

Solving cuberoot equations (Opens a modal)

Quadratic systems

Quadratic systems: a line and a parabola

Quadratic systems: a line and a circle

Quadratic system with no solutions

Solving equations by graphing

Solving equations by graphing

Solving equations by graphing: intro

Solving equations by graphing: graphing calculator

Solving equations by graphing: word problems

Unit circle introduction

Unit circle

The trig functions & right triangle trig ratios

Radians

Intro to radians

Radians & degrees

Degrees to radians

Radians to degrees

Radian angles & quadrants
Equations

Using the Pythagorean trig identity

The Pythagorean identity

Proof of the Pythagorean trig identity

Trig values of special angles (Opens a modal)

Trigonometric values of special angles

Graph of y=sin(x)

Intersection points of y=sin(x) and y=cos(x)

Graph of y=tan(x)

Graphs of sin(x), cos(x), and tan(x)

Features of sinusoidal functions

Amplitude, midline and period

Amplitude & period of sinusoidal functions from equation

Transforming sinusoidal graphs: vertical stretch & horizontal reflection

Transforming sinusoidal graphs: vertical & horizontal stretches

Transforming sinusoidal graphs

Sinusoidal function from graph

Graphing sinusoidal functions

Trig word problem: modeling daily temperature

Trig word problem: modeling annual temperature

Trig word problem: length of day (phase shift)

Sinusoidal models
Trigonometry

Modeling with function combination

Modeling with function combination

Interpreting features of functions

Periodicity of algebraic models

End behavior of algebraic models

Symmetry of algebraic models

Manipulating formulas

Manipulating formulas: perimeter

Manipulating formulas: area

Manipulating formulas: temperature

Modeling with equations and inequalities

Rational equation word problem

Quadratic inequality word problem

Exponential equation word problem

Cancelling common factors

Intro to rational expression simplification

Simplifying rational expressions: opposite common binomial factors

Simplifying rational expressions: grouping

Simplifying rational expressions: higher degree terms

Simplifying rational expressions: two variables

Simplifying rational expressions: common monomial factors

Simplifying rational expressions: common binomial factors

End behavior of rational functions

End behavior of rational functions

Discontinuities of rational functions

Discontinuities of rational functions

Analyzing vertical asymptotes of rational functions

Graphs of rational functions

Graphing rational functions according to asymptotes

Graphs of rational functions: yintercept

Graphs of rational functions: horizontal asymptote

Graphs of rational functions: vertical asymptotes

Graphs of rational functions: zeros

Graphs of rational functions (old example)

Graphing rational functions 1

Graphing rational functions 2

Graphing rational functions 3

Graphing rational functions 4

Modeling with rational functions

Analyzing structure word problem: pet store (2 of 2)

Rational equations word problem: combined rates

Rational equations word problem: combined rates (example 2)

Rational equations word problem: eliminating solutions

Reasoning about unknown variables

Reasoning about unknown variables: divisibility

Structure in rational expression

Analyzing structure word problem: pet store (1 of 2)

Multiplying and dividing rational expressions

Multiplying & dividing rational expressions: monomials

Multiplying rational expressions

Dividing rational expressions

Multiplying rational expressions: multiple variables

Dividing rational expressions: unknown expression
Modeling

Adding and subtracting rational expressions intro

Adding & subtracting rational expressions: like denominators

Intro to adding rational expressions with unlike denominators

Adding rational expression: unlike denominators

Subtracting rational expressions: unlike denominators

Adding and subtracting rational expressions (factored)

Subtracting rational expressions: factored denominators

Least common multiple of polynomials

Adding and subtracting rational expressions (not factored)

Subtracting rational expressions
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