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Basic Mathematics

This is a remedial course that includes the essentials of mathematics. It is a very basic and preparatory course covering calucations to strengthen the student's knowledge and skills in preparation for more advance levels of mathematics.

Chapter 3 Word Problems and Equations

Chapter 4 International System of Units

Pre-Algebra

Whole Numbers

Unit 1.1 Place, Value, and Names of Numbers

Unit 1.2.pdf - Addition with Whole Numbers, and Perimeter

Unit 1.3.pdf Rounding Numbers and Estimating Answers

Unit 1.4.pdf Subtracting with Whole Numbers

Unit 1.5.pdf Multiplication with Whole Numbers

Unit 1.6.pdf Division with Whole Numbers

Unit 1.7.pdf Exponents, Order of Operations, and Averages

**Pre- Algebra Unit 1.1 Whole Numbers Quiz**

**Introduction to Algebra**

Unit 2.1 Positive and Negative Numbers

Unit 2.2 Addition with Negative Numbers

Unit 2.3 Subtraction with Negative Numbers

Unit 2.4 Multiplication with Negative Numbers

Unit 2.5 Division with Negative Numbers

Unit 2.6 Simplifying Algebraic Expressions

**Pre-Algebra Unit 2 Introduction to Algebra Quiz**

**Fractions and Mixed Numbers**

Unit 3.1 The Meaning and Properties of Fractions

Unit 3.2 Prime Numbers, Factors, and Reducing to Lowest Terms

Unit 3.3 Multiplication with Fractions, and the Area of a Triangle.

Unit 3.4 Division with Fractions

Unit 3.5 Addition and Subtraction with Fractions

Unit 3.6 Mixed- Number Notation

Unit 3.7 Multiplication and Division with Mixed Numbers

Unit 3.8 Addition and Subtraction with Mixed Numbers

**Pre-Algebra Unit 3 Fractions and Mixed Numbers Quiz**

**Solving Equations**

Unit 4.1 The Distributive Property and Algebraic Expressions

Unit 4.2 The Addition Property of Equality

Unit 4.3 The Multiplication of Equality

Unit 4.4 Linear Equations in One Varibale

Unit 4.7 Paired Data and Equations in Two Variables

Unit 4.8 The Rectangular Coordinate System

Unit 4.9 Graphing Straight Lines

**Pre- Algebra Unit 4 Solving Equations**

**Decimals**

Unit 5.1 Decimal Notation and Place Value

Unit 5.2 Addition and Subtraction with Decimals

Unit 5.3 Multiplication with Decimals; Circumference and Area of a Circle

Unit 5.4 Division with Decimals

Unit 5.5 Fraction with Decimals

Unit 5.6 Equations Containing Decimals

Unit 5.7 Square Roots and the Pythagorean Theorem

Unit 5.8 Simplifying Square Roots

Unit 5.9 Adding and Subtracting Roots

**Pre-Algebra Unit 5 Decimals Quiz**

**Ratio and Proportion**

Unit 6.2 Rates and Unit Pricing

Unit 6.4 Applications of Proportions

**Pre-Algebra Unit 6 Ratio and Proportion Quiz**

**Percent**

Unit 7.1 Percents, Decimal and Fractions

Unit 7.2 Basic Percent Problems

Unit 7.3 General Applications of Percent

Unit 7.4 Sales Tax and Commissions

Unit 7.5 Percent Increase or Decrease, and Discount

**Pre-Algebra Unit 7 Percent Quiz**

**Measurement**

Unit 8.1 Unit Analysis I: Length

Unit 8.2 Unit Analysis II: Volume

Unit 8.3 Unit Analysis III: Weight

Unit 8.4 Converting Between the Two Systems and Temperature

Unit 8.5 Operations with Time and Mixed Units

**Pre-Algebra Unit 8 Measurement Quiz**

**Exponents and Polynomials**

Unit 9.1 Multiplication Properties of Exponents

Unit 9.2 Adding and Subtracting Polynomials

Unit 9.3 Multiplying Polynomials: An Introduction

Unit 9.6 Multiplication and Division wtih Scientific Notation

**Pre-Algebra Unit 9 Exponents and Polynomials Quiz**

Algebra I

Chapter I Real Numbers And Variable Expressions

Unit 1-1 Introduction to Integers

Unit 1-2 Operations with Integers

Unit 1-4 Exponents and the Order of Operations Agreement

Unit 1-6 Translating Variable Expressions into Verbal Expressions

Chapter 2 Solving Equations and Inequalities

Unit 2-1 Introduction to Equations

Unit 2-3 Value Mixture and Uniform Motions Problem

Unit 2-5 Mark Up and Discount Problems

Unit 2-6 Applications: Problems Involving Percents

Unit 2-7 Inequalities in one Variable

Chapter 3 Linear Functions and Inequalities in two Variables

Unit 3-1 The Rectangular Coordinate System

Unit 3-2 Introduction to Functions

Unit 3-4 Slope of a Straight Line

Unit 3-5 Finding Equations of Lines

Unit 3-6 Parallel and Perpendicular Lines

Unit 3-7 Inequalities in Two Variables

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Unit__ 3 Quiz

Chapter 4 System of Equations

Unit 4-1 Solving Systems of Linear Equations by Graphing and by the Substitution Method

Unit 4-2 Solving the Systems of Linear Equations by the Addition Method

Unit 4-3 Solving System of Equations by Using Determinants and by Using Matrices

Unit 4-5 Solving Systems of Linear Inequalities

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Unit__ 4 Quiz

Chapter 5 Polynomials

Unit 5-1 Introduction to Polynomials

Unit 5-2 Multiplication of Monomials

Unit 5-3 Multiplication of Polynomials

Unit 5-4 Integer Exponents and Scientific Notation

Unit 5-5 Division of Polynomials

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Unit__ 5 Quiz

Chapter 6 Factoring

Unit 6-2 Factoring Polynomials of the Form x2+bx+c

Unit 6-3 Factoring Polynomials of the Form ax2+bx+c

Unit 6-5 Factor Polynomials Completely

__Unit__ 6 Quiz

Algebra II

Chapter 7 Rational Expressions

Unit 7-1 Introductions to Rational Functions

Unit 7-2 Operations on Rational Expressions

Unit 7-5 Proportions and Variation

Chapter 8 Rational Exponents

Unit 8-1 Rational Exponents and Radical Expressions

Unit 8-2 Operations and Radical Expressions

Unit 8-4 Solving Equations Containing Radical Expressions

Chapter 9 Quadratic Equations

Unit 9-1 Solving Quadratic Equations by Factoring or Taking Square Root

Unit 9-2 Solving Quadratic Equations Completing the Square and by Using Quadric Formula

Unit 9-3 Equations that are Reducible to Quadratic Equations

Unit 9-4 Applications of Quadratic Equations

Unit 9-5 Properties of Quadratic Functions

Unit 9-6 Applications of Quadratic Functions

Unit 9-7 Nonlinear Inequalities

Chapter 10 Functions and Relations

Unit 10-1 Translations of Graphs

Unit 10-2 Algebra of Functions

Unit 10-3 One-to-One and Inverse Functions

Chapter 11 Exponential Logarithmic

Unit 11-1 Exponential Functions

Unit 11-2 Introduction to Logarithms

Unit 11-3 Graphs of Logarithmic Functions

Unit 11-4 Exponential and Logarithmic Equations

Unit 11-5 Applications of Exponential and Logarithmic Functions

Chapter 12 Coric Sections

Unit 12-3 The Ellipse and the Hyperbola

Unit 12-4 Solving Nonlinear Systems of Equations

Unit 12-5 Quadratic Inequalities and Systems of Inequalities

Geometry

Unit 1.1 Sets Statements and Reasons.

Unit 1.2 Informal Geometry and Measurement

Unit 1.3 Definitions and Posulates

Unit 1.4 Angles and Their Relationships

Unit 1.5 Introduction to Geometric Proof

Unit 1.6 Relationships: Perpendicular Lines

Unit 1.7 The Formal Proof of a Theorem

Unit 2.1 The Parallel Postulate and Special Angles

Unit 2.3 Proving Lines Parallel

Unit 2.6 Symmetry and Transformation

Unit 3.2 Corresponding Parts of Congruent Triangle

Unit 3.4 Basic Constructions Justified

Unit 3.5 Inequalities in a Triangle

Unit 4.1 Properties of Parallelogram

Unit 4.2 The Parallelogram and Kite

Unit 4.3 The Rectangle, Square, and Rhombus

Unit 5.1 Ratios, Rates, and Proportions

Unit 5.3 Proving Triangles Similar

Unit 5.4 The Pythagorean Theorem

Unit 5.5 Special Right Triangles

Unit 5.6 Segments Divided Proportionally

Unit 6.1 Circles and Related Segments and Angles

Unit 6.2 More Angle Measures in the Circles

Unit 6.3 Line and Segment Relationships in the Circle

Unit 6.4 Some Constructions and Inequalities for the Circle

Unit 7.3 More About Regular Polygons

Unit 8.1 Aeas and Initial Postulates

Unit 8.2 Perimeter and Area of Polygons

Unit 8.4 Regular Polygons and Areas

Unit 8.5 More Area Relationships in a Circle

Unit 9.1 Prisms, Area, and Volume

Unit 9.2 Pyramids, Area, and Volume

Unit 9.4 Polyhedrons and Spheres

Unit 10.1 The Rectangular Coordinate System

Unit 10.2 Graphs of Linear Equations and Scope

Unit 10.3 Preparing to Do Analytic Proofs

Unit 10.6 The Three-Demensional Coordinate System

Unit 11.1 The Unit Sign Ratio and Applocatins

Unit 11.2 The Cosine Ratio and Applications

Unit 11.3 The Tangent Ratio and Other Ratios

Unit 11.4 Applications with Acute Triangles

Trigonometry

**
Chapter 1 **
The Six Trignonmetric Functions

Section 1.1 Angles, Degrees, and Special Triangles

Section 1.2 The
Rectangular Coordinate System

Section 1.3 Definition I: Trigonometric Functions

**
Chapter 2**
Right Triangle Trigonometry

Section 2.1 Definition II: Right Triangle Trigonometry

Section 2.2 Calculators and Trigonometric Functions of an Acute Angle

Section 2.3 Solving Right Triangles

Section 2.5 Vectors: A Geometric Approach

**
Chapter 3**
Radian Measurement **
**

Section 3.2 Radians and Degrees

Section 3.3 Definition III: Circular Functions

Section 3.4 Arc Length and Area of a Sector

**
Chapter 4 **
Graphing and Inverse Functions

Section 4.2 Amplitude, Reflection, and Period

Section 4.3 Vertical and Horizontal Translations

Section 4.4
The Other Trigonometric Functions

Section 4.5
Finding an Equation from Its Graph

Section 4.6
Graphing Combinations of Functions

Section 4.7
Inverse Trigonometric Functions

**
Chapter 5 **
Identities and Formulas

Section 5.2 Sum and Difference Formulas

**
Chapter 6 **
Equations

Section 6.1 Solving Trigonometric Equations

Section 6.2 More on Trigonometric Equations

Section 6.3 Trigonometric Equations Involving Multiple Angles

Section 6.4 Parametric Equations and Further Graphing

**
Chapter 7 **
Triangles

Section 7.2 The Law of Cosines

Section 7.3 The Ambiguous Case

Section
7.4 The Area of a Triangle

Section 7.5 Vectors: An Algebraic Approach

Section 7.6 Vectors: The Dot Product

**
Chapter 8**
Complex Numbers and Polar Coordinate

Section 8.2 Trigonometric Form for Complex Numbers

Section 8.3 Products and Quotients in Trigonometric Form

Section 8.4 Roots of a Complex Number

Section 8.6 Equations in Polar Coordinates and Their Graphs