Algebra II | 1 Big School (By Blue Brain)

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 higher-degree 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 x-term
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 unit-fraction
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: base-10
Solving exponential equations using logarithms: base-2
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
Square-root equations
Intro to square-root equations & extraneous solutions
Square-root equations intro
Solving square-root equations: one solution
Solving square-root equations: two solution
Solving square-root equations: no solution
Extraneous solutions
Extraneous solutions
Equation that has a specific extraneous solution
Cube-root equations
Solving cube-root 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: y-intercept
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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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 higher-degree 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 x-term

Dividing polynomials by linear factors

Dividing polynomials by linear expressions

Dividing polynomials by linear expressions: missing term