ALBEBRA 2

Algebra 2: 1st SEMESTER

Module 1: Equations and Inequalities

 1.1 Real Numbers 
Become familiar with the subsets of real numbers and review their properties  

1.2 Simplifying Algebraic Expressions and Equations 
Solve and simplify algebraic expressions and equations for a variable or number  

.3 Solving Linear Equations
Solve equations in one variable using one, two, or multiple steps  

1.4 Solving Linear Inequalities 
  Solve and graph any linear inequality in one variable  

1.5 Solving Absolute Value Equations and Inequalities 
Solve equations and inequalities that involved absolute value  

1.6 Interpreting Word Problems 
Learn how to write a word problem as a mathematical equation  

1.7 Problem-Solving Plan
Read and understand given problem situations Make a plan to solve the problem Solve the problem and check the results Compare alternative approaches to solving the problem Solve real-world problems using a plan  

Module 2: Linear Equations and Functions
 

2.1 Finding the Slope and Equation of a Line

Review how to find the slope and equation of a line

  2.2 Standard Form of a Line

Become familiar with the standard form of a line, as well as finding the equations of lines that are parallel or perpendicular to a given line 
  2.3 Graphing Lines
Graph the equation of a line in slope-intercept or standard form

  2.4 Relations and Functions
Determine what a relation, function, the domain, and range are for linear equations

  2.5 Graphing Linear Inequalities in Two Variables 
Graph a linear inequality in two variables on the Cartesian plane

  2.6 Graphing Absolute Value Functions
To understand and graph a basic absolute value function

  2.7 Analyzing Scatterplots
Plot and analyze scatterplots and find the equation of best fit

    Module 3: Systems of Linear Equations and Inequalities

  3.1 Solving Linear Systems by Graphing 
Review the concept of the solution to a linear system in the context of a graph

  3.2 Solving Linear Systems by Substitution 
Solve linear systems in two variables by using substitution to make an equation in one variable that can be solved

  3.3 Solving Linear Systems by Linear Combinations (Elimination)
Solve systems by combining the two equations (or multiples of the two equations) to eliminate a variable

  3.4 Graphing and Solving Linear Inequalities 
Identify solutions to and solve linear inequalities

  3.5 Solving Linear Systems in Three Variables 
Identify solutions to and solve linear systems in three variables

  Module 4: Matrices

  4.1 Operations on Matrices  
Understand the concept of a matrix and perform basic operations on a matrix including addition, subtraction and scalar multiplication

  4.2 Multiplying Matrices  
Multiply matrices together when possible
Identify cases where matrices can and cannot be multiplied
Perform matrix operations on the graphing calculator

  4.3 Determinants and Cramer’s Rule   
Determine the determinants of 2 × 2 and 3 × 3 matrices by hand and the determinants of larger square matrices using the graphing calculator
Solve systems of linear equations in two and three variables using Cramer’s Rule

    4.4 Identity and Inverse Matrices 
Find the inverse matrix of a non singular 2 × 2 matrix by hand and using the calculator
Inverses of larger square matrices will be found using the calculator
Use the inverses of 2 × 2 and 3 × 3 matrices to solve matrix equations

  4.5 Solving Linear Systems Using Inverse Matrices 
Solve systems of linear equations in two variables using inverse matrices

  Module 5: Quadratic Functions

  5.1 Solving Quadratics by Factoring 
Factor and solve any quadratic equation that is considered “factorable”

  5.2 Solving Quadratics by Using Square Roots 
Review simplifying square roots to solve quadratic equations by using square roots

  5.3 Complex Numbers 
Define and use complex and imaginary numbers
Solve quadratic equations with imaginary solutions

  5.4 Completing the Square 
Solve quadratic equations through completing the square

  5.5 The Quadratic Formula
Derive and use the Quadratic Formula to solve quadratic equations and determine how many solutions an equation has

  5.6 Analyzing the Graph of a Quadratic Function 
Graph and find the vertex and x−intercepts, and using all the forms of a quadratic equation

  Module 6: Polynomial Functions

  6.1 Properties of Exponents 

  Use the properties of exponents to simplify numeric and algebraic expressions

  6.2 Adding, Subtracting, and Multiplying Polynomials 
Add, subtract, and multiply polynomials 6.3 Factoring and Solving Polynomial Equations 
Solve and factor polynomials using several different methods

6.4 Dividing Polynomials 
Divide one polynomial by another using long or synthetic division

  6.5 Finding all Solutions of Polynomial Functions 
Find all the solutions to higher-degree polynomials using synthetic division, factoring, and the Quadratic Formula

  6.6 Analyzing the Graph of Polynomial Functions 
Learn about the parts of a polynomial function and how to graph them

  Module 7: Roots, Radicals, and Function Operations

  7.1 Using Rational Exponents and nth Roots
Introduce rational exponents and nth roots. Then, we will apply the properties of exponents to rational functions and nth roots

  7.2 Graphing Square Root and Cubed Root Functions 
Graph square root and cubed root functions by hand and using a graphing calculator

  7.3 Solving Radical Equations 
Solve radical equations

  7.4 Function Operations and the Inverse of a Function 
Manipulate functions by taking the inverse and composing them with other functions

 

Algebra 2: 2nd SEMESTER

  Module 1: Exponential and Logarithmic Functions

    1.1 Exponential Growth and Decay
Analyze and use exponential growth and decay functions

  1.2 Logarithmic Functions 
Learn about the inverse of an exponential function, the logarithm

  1.3 Properties of Logarithms 
Simplify expressions involving logarithms

  1.4 Solving Exponential and Logarithmic Equations 
Solve exponential and logarithmic equations

  Module 2: Trigonometric Functions and Identities

  2.1 Graphing Trigonometric Functions 
Graph, translate, and reflect the sine, cosine, and tangent functions

  2.2 Using Trigonometric Identities 
Use trigonometric identities to solve and prove trigonometric statements and problems

  2.3 Solving Trigonometric Equations
Learn how to solve equations with trigonometric functions

  2.4 Right Triangle Trigonometry 
Develop an understanding of trigonometric ratios
Use the trigonometric ratios sine, cosine and tangent along with their inverses to solve right triangles

  2.5 The Unit Circle 
Understand the concept of angles of rotation, co-terminal angles, and reference angles
Find the exact value trigonometric ratios for angles that are multiples of 30 and 45 degrees given in degrees and radians

  2.6 The Law of Sines 
Use the Law of Sines proportion to solve non right triangles and find the area of triangles

    2.7 The Law of Cosines 
Use the Law of Cosines equation to solve non right triangles and find the area of triangles using Heron’s Formula.

  Module 3: Introduction to Probability

  3.1 The Fundamental Counting Principle 
Use the Fundamental Counting Principle to determine the number of unique arrangements that can be made of multiple items

  3.2 Permutations and Combinations 
Use factorials to determine the numbers of permutations or combinations that can be made of multiple items

  3.3 The Binomial Theorem 
Identify the connection between the elements in Pascal’s Triangle and the expansion of Binomials
Use the Binomial Theorem to expand binomials

  3.4 Introduction to Probability 
Understand of the probability of a particular outcome of an event and to calculate this probability

  3.5 Venn Diagrams and Independence 
Use Venn diagrams and the related set notation to show the relationships between sets

  Module 4: Sequences and Series
  4.1 General Sequences 
Identify patterns in sequences of numbers, describe the pattern and determine additional terms in the sequence

  4.2 Arithmetic Sequences and Series 
Identify arithmetic sequences
Find the nth term rule for an arithmetic sequence
Find the sum of a finite arithmetic sequence

    4.3 Geometric Sequences and Series 
Identify geometric sequences
Find the nth term rule for a geometric sequence
Find the sum of a finite geometric sequence

  4.4 Infinite Series 
Evaluate partial sums of infinite series and determine the sum of convergent infinite geometric series

  Module 5: Conic Sections

  5.1 Parabolas 
Find the vertex, focus, directrix, and graph a parabola

  5.2 Circles 
Identify the parts of and graph a circle, whether or not centered on the origin

  5.3 Ellipses 
Discover the parts of and graph ellipses

  5.4 Hyperbolas 
Identify parts of and graph hyperbolas, whether or not centered on the origin

  5.5 General Conic Equations and Solving Non-Linear Systems 
Become familiar with the general conic equation
Classify conics
Solve systems of equations with conics, quadratics, and lines

  Module 6: Rational Functions

  6.1 Direct, Inverse, and Joint Variation 
Determine if a set of data is related directly, indirectly, or jointly

  6.2 Graphing Rational Functions 
Graph several different types of rational functions and identify the critical values

    6.3 Simplifying, Multiplying, and Dividing Rational Expressions
Simplify, multiply, and divide rational expressions

  6.4 Adding and Subtracting Rational Expressions and Complex Fractions
Add and subtract two or more rational expressions.

  6.5 Solving Rational Equations
Solve equations involving rational expressions