Algebra II
Categories: Algebra, Mathematics
Course Content
Polynomial arithmetic
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Intro to polynomials
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Polynomials intro
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The parts of polynomial expressions
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Average rate of change of polynomials
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Finding average rate of change of polynomials
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Sign of average rate of change of polynomials
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Adding and subtracting polynomials
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Adding polynomials
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Subtracting polynomials
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Polynomial subtraction
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Multiplying monomials by polynomials
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Multiplying monomials
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Multiplying monomials by polynomials: area model
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Area model for multiplying polynomials with negative terms
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Multiplying monomials by polynomials
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Multiplying binomials by polynomials
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Multiplying binomials by polynomials: area model
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Multiplying binomials by polynomials
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Special products of polynomials
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Polynomial special products: difference of squares
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Polynomial special products: perfect square
Complex numbers
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The imaginary unit i
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Intro to the imaginary numbers
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Simplifying roots of negative numbers
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Powers of the imaginary unit
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i as the principal root of -1
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Complex numbers introduction
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Intro to complex numbers
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Classifying complex numbers
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The complex plane
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Plotting numbers on the complex plane
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Adding and subtracting complex numbers
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Adding complex numbers
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Subtracting complex numbers
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Multiplying complex numbers
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Multiplying complex numbers
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Quadratic equations with complex solutions
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Solving quadratic equations: complex roots
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Factoring monomials
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Introduction to factoring higher degree polynomials
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Introduction to factoring higher degree monomials
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Which monomial factorization is correct?
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Worked example: finding the missing monomial factor
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Worked example: finding missing monomial side in area model
Polynomial factorization
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Greatest common factor
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Greatest common factor of monomials
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Taking common factors
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Taking common factor from binomial
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Taking common factor from trinomial
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Taking common factor: area model
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Factoring higher degree polynomials
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Factoring higher degree polynomials
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Factoring higher-degree polynomials: Common factor
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Factoring using the difference of squares pattern
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Factoring using structure
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Identifying quadratic patterns
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Factorization with substitution
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Factoring using the perfect square pattern
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Polynomial identities
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Polynomial identities introduction
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Analyzing polynomial identities
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Describing numerical relationships with polynomial identities
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Geometric series
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Geometric series introduction
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Finite geometric series formula
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Worked examples: finite geometric series
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Geometric series word problems: swing
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Geometric series word problems: hike
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Dividing polynomials by x
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Intro to long division of polynomials
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Dividing quadratics by linear expressions (no remainders)
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Dividing quadratics by linear expressions with remainders
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Dividing quadratics by linear expressions with remainders: missing x-term
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Dividing polynomials by linear factors
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Dividing polynomials by linear expressions
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Dividing polynomials by linear expressions: missing term
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Factoring using polynomial division
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Factoring using polynomial division: missing term
Polynomial division
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Polynomial Remainder Theorem
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Intro to the Polynomial Remainder Theorem
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Remainder theorem: finding remainder from equation
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Remainder theorem examples
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Remainder theorem: checking factors
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Remainder theorem: finding coefficients
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Proof of the Polynomial Remainder Theorem
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Zeros of polynomials
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Zeros of polynomials introduction
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Zeros of polynomials: plotting zeros
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Zeros of polynomials: matching equation to zeros
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Zeros of polynomials: matching equation to graph
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Zeros of polynomials (with factoring): grouping
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Zeros of polynomials (with factoring): common factor
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Positive and negative intervals of polynomials
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Positive and negative intervals of polynomials
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Multiplicity of zeros of polynomials
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Zeros of polynomials (multiplicity)
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End behavior of polynomials
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Intro to end behavior of polynomials
Polynomial graphs
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Intro to rational exponents
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Rewriting roots as rational exponents
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Exponential equation with rational answer
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Rational exponents
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Rewriting quotient of powers (rational exponents)
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Rewriting mixed radical and exponential expressions
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Properties of exponents (rational exponents)
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Evaluating fractional exponents
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Evaluating fractional exponents: negative unit-fraction
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Evaluating fractional exponents: fractional base
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Evaluating quotient of fractional exponents
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Evaluating mixed radicals and exponents
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Evaluating exponents & radicals
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Equivalent forms of exponential expressions
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Rewriting exponential expressions as A⋅Bᵗ
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Equivalent forms of exponential expressions
Rational exponents and radicals
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Solving exponential equations using properties of exponents
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Solving exponential equations using exponent properties
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Solving exponential equations using exponent properties (advanced)
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Interpreting the rate of change of exponential models
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Interpreting change in exponential models
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Interpreting time in exponential models
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Constructing exponential models according to rate of change
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Constructing exponential models
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Constructing exponential models: half life
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Constructing exponential models: percent change
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Advanced interpretation of exponential models
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Interpreting change in exponential models: with manipulation
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Interpreting change in exponential models: changing units
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Introduction to logarithms
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Intro to logarithms
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Evaluating logarithms (advanced)
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Relationship between exponentials & logarithms
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Relationship between exponentials & logarithms: graphs
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Relationship between exponentials & logarithms: tables
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The constant e and the natural logarithm
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𝑒 and compound interest
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𝑒 as a limit
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Evaluating natural logarithm with calculator
Exponential models
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Properties of logarithms
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Intro to logarithm properties (1 of 2)
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Intro to logarithm properties (2 of 2)
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Using the logarithmic product rule
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Using the logarithmic power rule
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Using the properties of logarithms: multiple steps
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Proof of the logarithm product rule
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Proof of the logarithm quotient and power rules
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Evaluating logarithms: change of base rule
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Using the logarithm change of base rule
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Proof of the logarithm change of base rule
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The change of base formula for logarithms
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Solving exponential equations using logarithms: base-10
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Solving exponential equations using logarithms: base-2
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Solving exponential equations with logarithms
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Exponential model word problem: medication dissolve
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Exponential model word problem: bacteria growth
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Solving exponential models
Logarithms
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Shifting functions
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Shifting functions introduction
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Shifting functions examples
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Graphing shifted functions
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Reflecting functions
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Reflecting functions introduction
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Reflecting functions: examples
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Symmetry of functions
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Function symmetry introduction
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Even and odd functions: Graphs
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Even and odd functions: Tables
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Even and odd functions: Equations
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Even and odd functions: Find the mistake
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Scaling functions
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Scaling functions introduction
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Scaling functions vertically: examples
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Scaling functions horizontally: examples
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Identifying horizontal squash from graph
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Putting it all together
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Identifying function transformations
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Graphs of square and cube root functions
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Graphing square and cube root functions
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Graphs of exponential functions
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Transforming exponential graphs
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Transforming exponential graphs (example 2
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Graphing exponential functions
Transformations of functions
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Graphs of logarithmic functions
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Graphical relationship between 2ˣ and log₂(x)
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Graphing logarithmic functions (example 1
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Graphing logarithmic functions (example 2)
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Rational equations
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Rational equations intro
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Equations with rational expressions
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Equations with rational expressions (example 2)
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Finding inverses of rational functions
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Square-root equations
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Intro to square-root equations & extraneous solutions
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Square-root equations intro
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Solving square-root equations: one solution
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Solving square-root equations: two solution
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Solving square-root equations: no solution
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Extraneous solutions
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Extraneous solutions
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Equation that has a specific extraneous solution
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Cube-root equations
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Solving cube-root equations (Opens a modal)
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Quadratic systems
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Quadratic systems: a line and a parabola
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Quadratic systems: a line and a circle
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Quadratic system with no solutions
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Solving equations by graphing
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Solving equations by graphing
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Solving equations by graphing: intro
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Solving equations by graphing: graphing calculator
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Solving equations by graphing: word problems
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Unit circle introduction
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Unit circle
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The trig functions & right triangle trig ratios
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Radians
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Intro to radians
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Radians & degrees
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Degrees to radians
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Radians to degrees
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Radian angles & quadrants
Equations
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Using the Pythagorean trig identity
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The Pythagorean identity
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Proof of the Pythagorean trig identity
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Trig values of special angles (Opens a modal)
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Trigonometric values of special angles
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Graph of y=sin(x)
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Intersection points of y=sin(x) and y=cos(x)
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Graph of y=tan(x)
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Graphs of sin(x), cos(x), and tan(x)
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Features of sinusoidal functions
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Amplitude, midline and period
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Amplitude & period of sinusoidal functions from equation
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Transforming sinusoidal graphs: vertical stretch & horizontal reflection
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Transforming sinusoidal graphs: vertical & horizontal stretches
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Transforming sinusoidal graphs
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Sinusoidal function from graph
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Graphing sinusoidal functions
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Trig word problem: modeling daily temperature
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Trig word problem: modeling annual temperature
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Trig word problem: length of day (phase shift)
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Sinusoidal models
Trigonometry
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Modeling with function combination
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Modeling with function combination
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Interpreting features of functions
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Periodicity of algebraic models
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End behavior of algebraic models
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Symmetry of algebraic models
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Manipulating formulas
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Manipulating formulas: perimeter
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Manipulating formulas: area
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Manipulating formulas: temperature
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Modeling with equations and inequalities
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Rational equation word problem
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Quadratic inequality word problem
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Exponential equation word problem
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Cancelling common factors
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Intro to rational expression simplification
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Simplifying rational expressions: opposite common binomial factors
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Simplifying rational expressions: grouping
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Simplifying rational expressions: higher degree terms
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Simplifying rational expressions: two variables
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Simplifying rational expressions: common monomial factors
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Simplifying rational expressions: common binomial factors
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End behavior of rational functions
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End behavior of rational functions
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Discontinuities of rational functions
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Discontinuities of rational functions
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Analyzing vertical asymptotes of rational functions
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Graphs of rational functions
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Graphing rational functions according to asymptotes
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Graphs of rational functions: y-intercept
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Graphs of rational functions: horizontal asymptote
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Graphs of rational functions: vertical asymptotes
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Graphs of rational functions: zeros
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Graphs of rational functions (old example)
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Graphing rational functions 1
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Graphing rational functions 2
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Graphing rational functions 3
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Graphing rational functions 4
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Modeling with rational functions
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Analyzing structure word problem: pet store (2 of 2)
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Rational equations word problem: combined rates
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Rational equations word problem: combined rates (example 2)
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Rational equations word problem: eliminating solutions
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Reasoning about unknown variables
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Reasoning about unknown variables: divisibility
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Structure in rational expression
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Analyzing structure word problem: pet store (1 of 2)
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Multiplying and dividing rational expressions
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Multiplying & dividing rational expressions: monomials
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Multiplying rational expressions
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Dividing rational expressions
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Multiplying rational expressions: multiple variables
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Dividing rational expressions: unknown expression
Modeling
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Adding and subtracting rational expressions intro
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Adding & subtracting rational expressions: like denominators
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Intro to adding rational expressions with unlike denominators
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Adding rational expression: unlike denominators
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Subtracting rational expressions: unlike denominators
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Adding and subtracting rational expressions (factored)
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Subtracting rational expressions: factored denominators
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Least common multiple of polynomials
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Adding and subtracting rational expressions (not factored)
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Subtracting rational expressions
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