EN

Algebra II GRADE-12

Duration

10 Months

Prerequisites

Student Must Have Completed Grade 11

Requirements

Graphing calculator or graphing software of student’s choice

Course Summary

Starting with a review of introductory algebra, you will learn polynomials, quadratic equations, exponential and logarithmic relations, probability, and statistics. Throughout the course, these mathematical concepts are applied to everyday occurrences to demonstrate how the world around us functions.

MAJOR TOPICS AND CONCEPTS

Review of Algebra

  • Introduction to Functions
  • Graphing Linear Equations and Inequalities
  • Writing the Equation of a Line
  • Comparing Functions

Rational, Complex, and Polynomials

  • Rational Exponents
  • Properties of Rational Exponents
  • Solving Radical Equations
  • Complex Numbers
  • Operations of Complex Numbers
  • Review of Polynomials
  • Polynomial Operations

Factoring and Quadratics

  • Greatest Common Factors and Special Products
  • Factoring by Grouping
  • Sum and Difference of Cubes
  • Graphing Quadratics
  • Completing the Square
  • Solving Quadratic Equations
  • Solving Quadratic Equations with Complex Solutions
  • Investigating Quadratics

Dividing and Solving Polynomials

  • Polynomial Long Division
  • Polynomial Synthetic Division
  • Theorems of Algebra
  • Rational Root Theorem and Descartes’ Rule of Signs
  • Solving Polynomial Equations
  • Graphing Polynomial Functions
  • Polynomial Identities and Proofs

Rational Expressions

  • Simplifying Rational Expressions
  • Multiplying and Dividing Rational Expressions
  • Adding and Subtracting Rational Expressions
  • Simplifying Complex Fractions
  • Discontinuities of Rational Expressions
  • Asymptotes of Rational Functions
  • Solving Rational Equations
  • Applications of Rational Equations

Systems of Equations and Inequalities

  • Solving Systems of Equations Algebraically
  • Solving Systems of Non-Linear Equations
  • Graphing Systems of Linear Equations
  • Graphing Systems of Non-Linear Equations

Exponential and Logarithmic Functions

  • Exponential Functions
  • Logarithmic Functions
  • Properties of Logarithms
  • Solving Exponential Equations with Unequal Bases
  • Graphing Exponential Functions
  • Graphing Logarithmic Functions
  • Exponential and Logarithmic Functions

Sequences and Series

  • Arithmetic Sequences
  • Arithmetic Series
  • Geometric Sequences
  • Geometric Series
  • Sigma Notation
  • Infinite, Convergent, and Divergent Series
  • Graphing Sequences and Series

Statistics

  • Events and Outcomes in a Sample Space
  • Independent Probability
  • Conditional Probability
  • Normal Distribution
  • Models of Populations
  • Using Surveys
  • Using Experiments

Trigonometry

  • Introduction to the Unit Circle
  • Unit Circle and the Coordinate Plane
  • Trigonometric Functions with Periodic Phenomena
  • Pythagoras, Trigonometry, and Quadrants
  • Functions of All Types
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