## 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

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

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

7.4 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

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