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

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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