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Power Pack - Math Test Prep Course

This course is designed for anyone looking to learn or review the essentials of high school mathematics.  Specifically, the course covers all the main topics studied in high school algebra, geometry and algebra 2. This program is not a formal course, so there are no tests included. The Power Pack is a perfect math review for those studying for a wide variety of exams to include, but not limited to:

• SAT
• ACT
• GED
• ASVAB
• CLEP
• COMPASS
• ACCUPLACER
• GMAT
• GRE
• PRAXIS

NOTE: this program is not a formal course and does not include test materials or portal access.

Chapter 1: Introduction to Algebra Terms and Concepts

This chapter introduces students to basic terms and concepts used in algebra. Time is taken to ensure the student understands basic number operations, variables and their applications. Additionally, the student gains a fundamental sense of equations, inequalities and their solutions.

Sections:

• Number Operations

• Variables

• Order of Operations

• Translating Verbal and Algebraic Phrases

• Equations/Inequalities/Solutions

Chapter 2: Real Numbers and Variable Expressions

This chapter focuses on getting the student to master working with the Real Numbers. Students learn the rules of integers and practice through many examples. Also, students will learn to apply the Distributive Property and simplify variable expressions by combining like terms.

Sections:

• Real Numbers/Simplifying Variable Expressions

• Real Number System

• Adding Real Numbers

• Subtracting Real Numbers

• Multiplying and Dividing Real Numbers

• Distributive Property

• Simplifying by Combining Like Terms

Chapter 3: Fractions and Decimals

This chapter reviews how to work with fractions. Although it is assumed students posses these skills, time is taken to ensure the student has mastered the procedures to perform operations involving fractions.

Sections:

• Introduction to Fractions and Decimals

• Least Common Multiple/Denominator

• Multiplying and Dividing Fractions

• Adding and Subtracting Fractions

Chapter 4: Solving Equations

The chapter breaks down the steps to solve multi-step linear equations. Students will build up their skills as they progress from one and two-step equations to more advance equations. Core concepts involved will be reviewed to include the Distributive Property and combining like terms.

Sections:

• One Step Equations

• Solving Two Step Equations

• Solving Multi-Step Equations

• Formulas and Literal Equations

Chapter 5: Graphing Linear Equations

This very important chapter walks the student step-by-step to master how to graph linear equations. Concepts involving the coordinate plane, slope and methods to graph lines are thoroughly reviewed and introduced. Upon completion of the chapter students will gain the necessary knowledge and skills needed to learn more advance topics involving linear equations.

Sections:

• Graphing Lines with One Variable

• Graphing Lines with Two Variables

• The Slope of a Line

• Slope Intercept Method

• XY Intercept Method

Chapter 6: Writing the Equations of Lines

This chapter builds on the student’s prior knowledge and skill of linear equations. Various methods to find and write the equation of a line are introduced and practiced. The chapter focuses on the proper way to set-up and use formulas to write linear equations. Additional related topics are explored to include linear models, linear regression and word problems.

Sections:

• Using Slope-Intercept Form

• Using Point-Slope intercept

• Given the Slope and a Point

• Given Two Points

• Standard Form of Linear Equations

• Best Fitting Line

• Linear Models/Word Problems

Chapter 7: Inequalities

In this chapter students will apply their equation solving skills to solve linear inequalities. Basic concepts and terms are introduced first, along with how to graph inequalities.

Sections:

• Linear Inequalities

• Compound Inequalities

• Graphing Linear Inequalities in Two Variables

Chapter 8: Systems

Understanding systems and the methods to solve them are vital in algebra. This chapter introduces/reviews techniques to solve linear systems. Students will also explore special systems, word problems and systems of linear inequalities. Lastly, the topic of Linear Programming will be introduced. This powerful way to use systems in business and industry will connect the chapter's concepts to "real world" applications.

Sections:

• Solving Systems by Graphing

• Solving Systems Substitution Method

• Solving Systems by Elimination/Linear Combination

• Solving Linear System Word Problems

• Special Linear Systems

• Solving Systems of Linear Inequalities

• Linear Programming

Chapter 9: Absolute Value

Absolute value problems can be challenging for some students to grasp. Time is taken to teach students core concepts and build understanding. Students will learn how to graph absolute value functions and apply the steps to solve absolute value equations/inequalities.

Sections:

• Introduction to Absolute Value

• Graphing Absolute Value Equations

• Solving Absolute Value Equations

• Absolute Value Inequalities

Chapter 10: Powers and Exponents

This chapter covers the rules of powers and exponents a student needs to learn in algebra. Also, important applications of these rules are covered to include scientific notation, compound interest and exponential growth and decay.

Sections:

• Product and Power Rules of Exponents

• Negative and Zero Exponents Rules

• Division Rules of Exponents

• Scientific Notation

• Compound Interest

• Exponential Growth and Decay

• Rational Roots

Chapter 11: Polynomials and Factoring

The first part of the chapter covers the parts of a polynomial, related terminology and how to perform polynomial operations. A special focus is placed on avoiding common mistakes. The second part of the chapter focuses on the extremely important skill of factoring polynomials. Students will first understand how to factor out a polynomial GCF and build on this to learn many techniques to factor polynomials.

Sections:

• Introduction to Polynomials

• Adding and Subtracting Polynomials

• Multiplying Polynomials

• Multiplying Polynomials Special Cases

• Sum and Difference of Two Cubes

• Factoring Greatest Common Factor

• Factoring Quadratic Trinomials

• Special Factoring Rules

Chapter 12: Quadratic Equations and Complex Numbers

Understanding the properties and methods to solve quadratic equations is essential for the student to advance in algebra. This chapter explains each concept in a very specific and focused manner. After students have been introduced to quadratic equations they build up their knowledge by learning various techniques to solve them. Additionally, they will learn the connection between solutions and graphs of quadratic functions. Methods and procedures are applied to graph quadratic inequalities and solve word problems. Lastly, the chapter covers complex and imaginary numbers. Students are introduced to complex number operations, graphs and the role complex and imaginary numbers have as solutions to equations.

Sections:

• Introduction to Quadratic Equations

• Solving Quadratic Equations by Square Roots

• Graphing Quadratic Equations

• The Quadratic Formula

• Solving Quadratic Equations by Factoring

• The Discriminant – Types of Roots

• Completing The Square

• Quadratic Equation Word Problems

• Graphing Quadratic Inequalities

• Complex and Imaginary Numbers

Chapter 13: Functions and Relations

Functions and relations transcend all through mathematics. This chapter explains core concepts at the Algebra 1/2 level and prepares the student for more advance study of the topic. Time is taken to explain the difference between a function and relation and introduce the student to the language of functions to include the domain, range and linear/nonlinear functions. Students will also learn function operations, composite functions and graphing.

Sections:

• Introduction to Functions and Relations

• Function Operations

• Inverse Functions

• Graphing Functions

• Linear and Nonlinear Functions

• Special Functions

• Composite Functions

Chapter 14: Rational Expressions/Equations

The first part of the chapter takes the student through fundamental rational expressions to include ratios, rates, proportions, percent and variation. Special emphasis is placed on learning different methods to solve rational expression problems. The section on simplifying rational algebraic expressions starts by reviewing basic examples using numbers before introducing variable examples.

The second part of the chapter builds from the student’s knowledge of polynomials and covers operations with rational expressions. Instruction will focus on learning to multiply, divide, find the LCD and solve rational expressions. Additionally, a section is dedicated to the procedure/ methods to graph rational functions; new terms like vertical and horizontal asymptotes will be explained.

Sections:

• Ratios and Proportions

• Percent

• Direct and Inverse Variation

• Simplifying Rational Expressions

• Multiplying and Dividing Rational Expressions

• Finding the LCD of Rational Expressions

• Solving Rational Equations

• Adding and Subtracting Rational Expressions

• Operations and Equations with Rational Exponents

• Graphing Rational Functions (vertical and horizontal asymptotes)

Chapter 15: Radical Expressions/Equations

This chapter introduces the concept of radical expressions/equations at the Algebra 1 level. Students will first learn the properties of square roots and associated operations to include solving basic radical equations. Next the chapter looks at the application of radicals and how they help solve many problems in algebra. Specifically, the chapter will focus on the Pythagorean Theorem and the Distance and Mid-Point formula.

Sections:

• Simplifying Radicals

• Operations with Radicals

• Solving Radical Equations

• The Distance and Mid-Point Formula

• The Pythagorean Theorem

Chapter 16: Matrices and Determinants

This chapter introduces the core concepts of matrices and determinants to students. Time is taken to teach terminology and common applications of matrices. Students will learn how to perform various matrix operations to include matrix addition, subtraction, multiplication and scalar multiplication. Additionally, students will learn the steps to find determinants and inverse of a matrix. The chapter also focuses on how matrices can be used to solve linear systems by using an inverse matrix or Cramer’s Rule.

Sections:

• Introduction to Matrices

• Matrix Operations

• Matrix Multiplication

• Determinants

• Identity and Inverse Matrices

• Solving Systems using Inverse Matrices

• Solving Systems using Cramer’s Rule

Chapter 17: Logarithmic and Exponential Functions

For most students this chapter will be their first introduction to logarithms. As such the chapter focuses on teaching the basic core concepts of a logarithm and its relationship to an exponential function. Students will learn how to covert between a logarithm/exponential equation.

Additionally, the chapter defines the properties of logarithms and how to condense and expand logarithmic expressions. The Natural Base e and Natural logarithms are explored with explanations of how to use the “log and ln” functions on a scientific calculator. Finally, the chapter covers the methods and procedure to solve exponential and logarithmic equations.

Sections:

• Exponential Growth and Decay Functions

• Introduction to Logarithms

• Properties of Logarithms

• The Natural Base e

• Natural Logarithms

• Solving Logarithmic Equations

• Solving Exponential Equations

Chapter 18: Polynomial Functions

This chapter goes into the various methods and techniques to solve a polynomial of any degree. Students will specifically learn how to apply key concepts, skills (polynomial long and synthetic division) and theorems (Rational Root and Fundamental Theorem of Algebra) to find the roots of polynomial functions.

Sections:

• Graphing Polynomials

• Polynomial Division (long and synthetic division)

• Remainder and Factor Theorem

• Rational Root Theorem (Rational-Zero Test)

• Solving Polynomial Equations by Factoring

• Solving n-degree Polynomials

Chapter 19: Foundations for Geometry

This chapter will introduce students to the key terms and concepts in geometry. Students will learn how to write the notation for various geometric expressions like angles, lines, rays, planes, points and segments. Lastly, the concept of theorems and postulates are introduced and their importance explained.

Sections:

• Welcome to geometry

• Points, lines and planes

• Line segments, rays

• Angles

• Theorems and postulates

Chapter 20: Reasoning and Proof

In this chapter students will study the role of logic and proof in geometry. Students will learn how to identify the hypothesis and conclusion in conditional statements and write the converse. In addition, students will learn more about the properties of lines and angles. Lastly, students will learn the structure of a geometric proof and study the steps to write an entire proof on their own.

Sections:

• Conditional statements and converses

• Algebra properties

• Deductive and inductive reasoning

• More on angles and lines

• How to plan and write a proof

Chapter 21: Perpendicular/Parallel Lines, Polygons

In this chapter students will study the relationships of perpendicular and parallel lines. Several important properties will be covered essential to solve common problems in geometry. A critical section in this chapter is dedicated to theorems that state when two or more lines are parallel. Students are also introduced to polygons and their types.

Sections:

• Parallel lines and transversals

• Properties of parallel and perpendicular lines

• Proving lines parallel

• Introduction to polygons

Chapter 22: Congruent Triangles

Congruency is a core concept in geometry. Students will learn the concept of congruency by studying the properties of congruent triangles. After an introduction to congruent figures students will focus on learning to prove triangles are congruent using the SSS, SAS, ASA, AAS and HL Theorems.

Sections:

• Congruent figures

• Proving congruent triangles: Side-Side-Side and Side-Angle-Side Theorem

• Proving congruent triangles: Angle-Side-Angle and Angle-Angle-Side Theorem

• Proving congruent triangles: Hypotenuse-Leg Theorem

Chapter 23: Properties of Triangles

In this chapter students will learn the various properties of triangles. Several definitions and theorems will be introduced about the medians, altitudes and bisectors of triangles. In addition the chapter has an important section on the inequalities found in triangles between sides and angles.

Sections:

• Medians, altitudes and bisectors

• Bisector theorems

• Triangle inequalities

Chapter 24: Quadrilaterals

In this chapter students will learn the various properties and type of quadrilaterals. The first two sections focus on the properties of parallelograms to include proving a quadrilateral is a parallelogram. Next, additional sections look in-depth at trapezoids, special quadrilaterals to include the rhombus and theorems involving midpoints in quadrilaterals and triangles.

Sections:

• Parallelograms

• Proving quadrilaterals are parallelograms

• Trapezoids

• Special quadrilaterals

• Quadrilaterals, triangles and midpoints

Chapter 25: Similarity

Similarity is a core geometric relationship. To solve most similar polygon problems students need to have the algebra skills to solve ratios and proportions, hence this is the first section in the chapter. The remaining sections focus on similar polygons problem solving and the properties and theorems of similar triangles.

Sections:

• Ratios and proportions

• Similar polygons

• Similar triangles

Chapter 26: Transformations

In this chapter students will learn to apply transformations to images. Sections in the chapter focus on the transformations of reflections, rotations, dilations, translations and glide reflections. An emphasis is placed on developing the skills to construct the graphs of transformations found in common geometry problems.

Sections:

• Reflections

• Rotations and dilations

• Translations and glide reflections

Chapter 27: Right Triangle Trigonometry

In this chapter students will learn a wide array of concepts about right triangles. Sections in the chapter look at similar right triangles, the Pythagorean Theorem and special right triangles. For most students the section on trigonometry will be their first introduction to the topic. The chapter ends on a section that applies right triangle trigonometry to solving word problems.

Sections:

• Similar right triangles

• The Pythagorean Theorem

• Special right triangles

• Trigonometric ratios

• Right triangle word problems

Chapter 28:  Circles

In this chapter students will learn the important properties and relationships found in circles. First, students will learn the parts of a circle and understand the properties of a tangent line. Additional sections will explore key theorems about arcs, chords and inscribed circles. Lastly, the chapter looks at other angle and segment relationships found in circles.

Sections:

• Introduction to circles and tangents

• Arcs and chords

• Inscribed circles

• Other angle relationships in circles

• Segment lengths and circles

Chapter 29: Area and Volume

In this chapter students will learn how to find the area, surface area and volume of various geometric figures. Sections will explain the formulas to find area, surface area and volume of figures to include cubes, circles, cylinders, prisms, pyramids and others shapes. An entire section explains how to find the area of regular polygons. Lastly, students will learn how to find the area of sectors and arc lengths found in circles.

Sections:

• Area of basic figures

• Surface area of basic figures

• Volume of basic figures

• Area of regular polygons

• Area of circles/sectors and arc length