Algebra 2

Syllabus

The Basics

• The order of operations
• Evaluating expressions
• Simplifying algebraic expressions

Equations and Inequalities

• Solving multi-step equations
• Work word problems
• Distance-rate-time word problems
• Mixture word problems
• Solving absolute value equations
• Solving multi-step inequalities
• Solving compound inequalities
• Solving absolute value inequalities

Linear Relations and Functions

• Graphing linear equations
• Writing linear equations
• Graphing absolute value equations
• Graphing linear inequalities
• Systems of Equations and Inequalities
• Graphing systems of two linear inequalities
• Solving systems of two linear equations by graphing
• Solving systems of two linear equations by elimination
• Solving systems of two linear equations by substitution
• Systems of two equations word problems
• Points in three dimensions
• Planes
• Solving systems of three linear equations by elimination
• Solving systems of three linear equations by substitution

Matrices

• Basic matrix operations
• Matrix multiplication
• Determinants
• Matrix inverses
• Cramer’s Rule
• Matrix equations
• Geometric transformations with matrices

Quadratic Functions and Inequalities

• Graphing quadratic functions
• Solving quadratic equations by graphing
• Factoring quadratic trinomials
• Factoring special case trinomials
• Solving quadratic equations by taking square roots
• Solving quadratic equations by factoring
• Completing the square
• Solving quadratic equations by completing the square
• Solving quadratic equations using the Quadratic Formula
• The discriminant
• Graphing quadratic inequalities

Complex Numbers

• Adding / subtracting / multiplying / absolute value of complex numbers
• Graphing complex numbers
• Rationalizing imaginary denominators

Polynomial Functions

• Naming polynomials
• Adding / subtracting / multiplying polynomials
• The Binomial Theorem
• Dividing polynomials
• Factoring by grouping
• Factoring sum/difference of cubes
• Factoring quadratic form
• Synthetic division and synthetic substitution
• The Remainder Theorem and The Factor Theorem
• Imaginary Root Theorem and Irrational Root Theorem
• Polynomials, factors, and roots
• Writing polynomial functions
• The Rational Root Theorem
• Descartes’ Rule of Signs
• The Fundamental Theorem of Algebra
• Solving polynomial equations, all methods
• End behavior of polynomial functions
• Sketching the general shape of polynomial functions
• Graphing polynomial functions, including minima/maxima
• Solving polynomial functions by graphing

Radical Functions and Rational Exponents

• Simplifying radical expressions
• Operations with radical expressions
• Dividing radical expressions
• Relating rational exponents and radical expressions
• Evaluating rational exponent expressions
• The laws of exponents
• Solving radical equations
• Solving rational exponent equations
• Graphing radical functions
• Domain and range of radical functions

General Functions

• Evaluating functions
• Function operations
• Inverse functions

Conic Sections

• Properties of parabolas
• Writing equations of parabolas
• Properties of circles
• Writing equations of circles
• Properties of ellipses
• Writing equations of ellipses
• Properties of hyperbolas
• Writing equations of hyperbolas
• General conic sections
• Systems of quadratic relations

Rational Expressions

• Graphing simple rational expressions
• Graphing general rational expressions
• Simplifying rational expressions
• Multiplying / dividing rational expressions
• Adding / subtracting rational expressions
• Complex fractions
• Solving rational equations

Exponential and Logarithmic Functions

• Graphing exponential functions
• Solving exponential equations not requiring logarithms
• Rewriting logarithms
• Evaluating logarithms
• Logarithms and exponential functions as inverses
• Properties of logarithms
• Common logarithms
• Natural logarithms
• Solving exponential equations requiring logarithms
• Solving logarithmic equations
• Graphing logarithmic functions

Sequences and Series

• General sequences
• Arithmetic sequences
• Geometric sequences
• Arithmetic and geometric mean
• General series
• Arithmetic series
• Geometric series
• Infinite geometric series

Trigonometry

• Angles and angle measure
• Radians and degrees
• Coterminal angles
• Arc length and sector area
• Right triangle trig.
• Trig. functions of general angles
• The Law of Sines
• The Law of Cosines
• Heron’s Formula
• Graphing trig. functions
• Translations of trig. functions
• Angle sum and angle difference identities
• Half-angle and double-angle identities
• Trig. equations, neither factoring nor identities required