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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 1 Fractions

 Chapter 2 Decimals

Chapter 3 Word Problems and Equations

Chapter 4 International System of Units

 Chapter 5 Percents

Chapters 1-5 Quiz

 

 Chapter 6 Commissions

 Chapter 7 Discounts

Chapter 8 Markup

Quiz Chapters 6-8

 

Pre-Algebra

Pre-Algebra Syllabus

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

Unit 1.8.pdf Area and Volume

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 4.5 Applications

Unit 4.6 Evaluating Formulas

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 6.1 Ratios

Unit 6.2 Rates and Unit Pricing

Unit 6.3 Proportions

Unit 6.4 Applications of Proportions

Unit 6.5 Similar Figures

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

Unit 7.6 Interest

Unit 7.7 Pie Charts

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 9.4 Negative Exponents

Unit 9.5 Scientific Notation

Unit 9.6 Multiplication and Division wtih Scientific Notation

Pre-Algebra Unit 9 Exponents and Polynomials Quiz

 

Algebra I

 

Algebra I Syllabus

Chapter I Real Numbers And Variable Expressions

Unit 1-1 Introduction to Integers

Unit 1-2 Operations with Integers

Unit 1-3 Rational Numbers

Unit 1-4 Exponents and the Order of Operations Agreement

Unit 1-5 Variable Expressions

Unit 1-6 Translating Variable Expressions into Verbal Expressions

Unit 1 Quiz

 

Chapter 2 Solving Equations and Inequalities

Unit 2-1 Introduction to Equations

Unit 2-2 General Equations

Unit 2-3 Value Mixture and Uniform Motions Problem

Unit 2-4 Geometry Problems

Unit 2-5 Mark Up and Discount Problems

Unit 2-6 Applications: Problems Involving Percents

Unit 2-7 Inequalities in one Variable

Unit 2 Quiz

 

Chapter 3 Linear Functions and Inequalities in two Variables

Unit 3-1 The Rectangular Coordinate System

Unit 3-2 Introduction to Functions

Unit 3-3 Linear 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

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 4-4 Application Problems

Unit 4-5 Solving Systems of Linear Inequalities

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

Unit 5 Quiz

 

Chapter 6 Factoring

Unit 6-1 Common Factors

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

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

Unit 6-4 Special Factoring

Unit 6-5 Factor Polynomials Completely

Unit 6-6 Solving Equations

Unit 6 Quiz

 

Algebra II

Algebra II Syllabus

Chapter 7 Rational Expressions

Unit 7-1 Introductions to Rational Functions

Unit 7-2 Operations on Rational Expressions

Unit 7-3 Complex Fractions

Unit 7-4 Rational Equations

Unit 7-5 Proportions and Variation

Unit 7-6 Literal Equations

Unit 7 Quiz

 

Chapter 8 Rational Exponents

Unit 8-1 Rational Exponents and Radical Expressions

Unit 8-2 Operations and Radical Expressions

Unit 8-3 Radical Functions

Unit 8-4 Solving Equations Containing Radical Expressions

Unit 8-5 Complex Numbers

 Unit 8 Quiz

 

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

Unit 9 Quiz

 

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

Unit 10 Quiz

 

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

Unit 11 Quiz

 

Chapter 12 Coric Sections

Unit 12-1 The Parabola

Unit 12-2 The Circle

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

Unit 12 Quiz

 

Geometry

Geometry Syllabus

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 I Quiz

 

Unit 2.1 The Parallel Postulate and Special Angles

Unit 2.2 Indirect Proof

Unit 2.3 Proving Lines Parallel

Unit 2.4 Angles and Triangles

Unit 2.5 Convex Polygons

Unit 2.6 Symmetry and Transformation

Unit 2 Quiz

 

Unit 3.1 Congruent Triangles

Unit 3.2 Corresponding Parts of Congruent Triangle

Unit 3.3 Isosceles Triangles

Unit 3.4 Basic Constructions Justified

Unit 3.5 Inequalities in a Triangle

Unit 3 Quiz

 

Unit 4.1 Properties of Parallelogram

 Unit 4.2 The Parallelogram and Kite

Unit 4.3 The Rectangle, Square, and Rhombus

Unit 4.4 Trapezoid

Unit 4 Quiz

 

Unit 5.1 Ratios, Rates, and Proportions

Unit 5.2 Similar Polygons

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 5 Quiz

 

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 6 Quiz

 

Unit 7.1 Locus of Points

Unit 7.2 Concurrence of Lines

Unit 7.3 More About Regular Polygons

Unit 7 Quiz

 

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 8 Quiz

 

Unit 9.1 Prisms, Area, and Volume

Unit 9.2 Pyramids, Area, and Volume

Unit 9.3 Cylinders and Cones

Unit 9.4 Polyhedrons and Spheres

Unit 9 Quiz

 

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 10.4 Analytic Proofs

Unit 10.5 Equations of Lines

Unit 10.6 The Three-Demensional Coordinate System

Unit 10 Quiz

 

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

Unit 11 Quiz

 

Trigonometry

Trigonometry Syllabus

 

Chapter 1 The Six Trignonmetric Functions

Section 1.1 Angles, Degrees, and Special Triangles

Quiz

Section 1.2 The Rectangular Coordinate System

Quiz

Section 1.3 Definition I: Trigonometric Functions

Quiz

 Section 1.4 Introduction to Identities

Quiz

 Section 1.5 More on Identities

 Quiz

Chapter 2 Right Triangle Trigonometry

Section 2.1 Definition II: Right Triangle Trigonometry

Quiz

Section 2.2 Calculators and Trigonometric Functions of an Acute Angle

Quiz

Section 2.3 Solving Right Triangles

Quiz

Section 2.4 Applications

Quiz

Section 2.5 Vectors: A Geometric Approach

Quiz

Chapter 3 Radian Measurement

Section 3.1 Reference Angle

Quiz

Section 3.2 Radians and Degrees

Quiz

Section 3.3 Definition III: Circular Functions

Quiz

Section 3.4 Arc Length and Area of a Sector

Quiz

Section 3.5 Velocities

Quiz

 

Chapter 4 Graphing and Inverse Functions

Section 4.1 Basic Graphs

Quiz

Section 4.2 Amplitude, Reflection, and Period

Quiz

Section 4.3 Vertical and Horizontal Translations

Quiz

Section 4.4 The Other Trigonometric Functions

Quiz

Section 4.5 Finding an Equation from Its Graph

Quiz

Section 4.6 Graphing Combinations of Functions

Quiz

Section 4.7 Inverse Trigonometric Functions

Quiz

 

Chapter 5 Identities and Formulas

 Section 5.1 Providing Identities

Quiz

Section 5.2 Sum and Difference Formulas

Quiz

 Section 5.3 Double-Angle Formulas

Quiz

 Section 5.4 Half-Angle Formulas

Quiz

 Section 5.5 Additional Identities

Quiz

  

Chapter 6 Equations

Section 6.1 Solving Trigonometric Equations

Quiz

Section 6.2 More on Trigonometric Equations

Quiz

Section 6.3 Trigonometric Equations Involving Multiple Angles

Quiz

Section 6.4 Parametric Equations and Further Graphing

Quiz 

Chapter 7 Triangles

Section 7.1 The Law of  Sines

Quiz

Section 7.2 The Law of Cosines

Quiz

Section 7.3 The Ambiguous Case

Quiz

Section 7.4 The Area of a Triangle

Quiz

Section 7.5 Vectors: An Algebraic Approach

Quiz

Section 7.6 Vectors: The Dot Product

Quiz

  

Chapter 8 Complex Numbers and Polar Coordinate

Section 8.1 Complex Numbers 

Quiz

Section 8.2 Trigonometric Form for Complex Numbers 

Quiz

Section 8.3 Products and Quotients in Trigonometric Form 

Quiz

Section 8.4 Roots of a Complex Number 

Quiz

Section 8.5 Polar Coordinates 

Quiz

Section 8.6 Equations in Polar Coordinates and Their Graphs

Quiz