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