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Lecture Notes and Sample Exams



PreAlgebra

Lecture Notes and Worksheets


About Mathematics
Division by Zero
The Order of Operations Agreement
Factors of a Number
New! Prime Factorization
New! The GCF and LCM
Evaluating Algebraic Expressions
Solutions of Equations

Operations on integers Quiz

Order of Operations on integers Quiz

Integers Fractions - Part 1 - the definition
      Reading, Practice, Answers,
Practice Quiz, and Quiz

Basic Percent Problems   -  
Quiz
Solving Two-Step Linear Equations
Fractions, Decimals, Percents - Conversions
Conversions between units of measurement
Standard labeling in triangles
Angles of a Triangle
Area
Decimals and Fractions


Beginning Algebra

Lecture Notes and Worksheets


New! Square Root of a Number
Evaluating Algebraic Expressions
Solutions of Equations and Inequalities
Graphs of Equations     Examples - Answers
Combining Like Terms
Equations with the Unknown on Both Sides
Simplifying Algebraic Expressions
Solving Linear Equations - Part 2
Angles In a Triangle:   Theory - Problem Solving -
Quiz
Solving Linear Inequalities
Linear Inequalities (practice)
Graphing Straight Lines
        Practice     Examples - Answers
Basic Percent Problems
Word Problems 1 (Linear)
Solving Linear Systems by Substitution
The Zero Product Rule
Factoring out the GCF
Factoring 1 (GCF, difference of squares theorem)
Factoring by Grouping (practice)
Factoring by the AC-method - Practice
Factoring the difference of cubes (Practice)
Factoring the sum of cubes (Practice)
Wordproblems 2 (Quadratic)
Rules of exponents (formulas only)
Exponents 1
Integer Exponents
Sample Exams


Sample Exam 1 - Answers
Sample Exam 2 - Answers
Sample Exam 2 - Version B - Answers
Exam 3 Review - Answers - Solutions
Exam 3 Review - Version B - Answers
Exam 4 Review - Answers - Solutions
Final Review 1
Final Review 2 - Answers
Final Review 3 - Answers - Solutions


Intermediate Algebra

Lecture Notes and Worksheets


New! Introduction to Combinatorics
New! Introduction to Number Theory
New! The nth Root of a Number
Factoring by completing the square   Part 1   Part 2   Part 3   Part 4
Review of Factoring 1 (GCF, difference of squares, completing the square)
Review of Factoring 2 (grouping, AC-method, sum and difference of cubes)
Review of Quadratic Wordproblems (Quadratic)
Solving Linear Systems by Elimination
Linear Word Problems
Mixture Problems
Motion Problems
The Pythagorean Theorem
Similar Triangles
Writing Equations of Straight Lines
New! Smallest Value of a Quadratic Expression
Graphing a Parabola - Part 1 - Practice
Graphing a Parabola - Part 2
Rational Expressions
Complex Fractions
Radical Expressions
Radical Equations
The Real Number System
The Quadratic Formula
The proof that square root of 2 is irrational
Rules of Exponents
Rational Exponents (practice)

Fun, Challenging Problems:
Algebraic Transformations


Sample Exams


Exam 1 Review
Exam 2 Review
Exam 3 Review - Solutions
Exam 3 Review - Version B
Final Review - Solutions
Final Review - Version B - Solutions
Final Review - Version C
College Algebra and Trigonometry

College Algebra


Review of Linear Equations -
Quiz
Factoring by Completing the Square - Parts 1, 2, 3 (Review)
Factoring by Completing the Square - Part 4 (Review)
Applications of Linear Equations
The Pythagorean Theorem
Division of Polynomials
Remainder Theorem
Nonlinear Systems
Arithmetic Sequences
Exercises in Symmetry
Functions - Definition
Graphical Solutions
Quadratic Inequalities
Rational Inequalites:
  The Coolest Method
  Two Other Methods
  One More Method
Domain of Functions (no logarithms)
Domain of Functions (with logarithms)
The Arithmetic, Geometric, and Harmonic Mean
Complex Numbers
Optimization
Equations with Parameters
Tangent Lines (completing the square)
Tangent Lines (quadratic formula)
Logarithms 1
Basic functions and their properties
Transformations on graphs
Rules of Logarithms (formulas only)
Logarithms 2
Basic Exponential and Logarithmic Equations
Exponential Equations
Geometric Sequences
The Fibonacci Sequence
Circles - Part 1
Circles - Part 2
Intersections
Inverse Functions
Inverse Functions (older version)
Limits at Infinity: Part 1, Part 2
Limits at infinity
Graphing Polynomials - 1
Graphing Factored Polynomials
Graphing the Reciprocal of a Function
Discontinuities of Rational Functions
Graphing Rational Functions
Factoring Polynomials
Equation of an ellipse
Induction
Summation
Trigonometry



The Pythagorean Theorem
Similar Triangles
Arcs and Sectors in a Circle
Right Triangle Trigonometry
Trig Function Values of Famous Angles
Simplifying Trigonomic Expressions
All Trigonometric Identities
Trigonometric Identities 1
Computing Trigonometric Expressions
Unit Circle Definitions
Symmetries of the Unit Circle
All Trigonometric Equations
Trigonometric Equations 1
Graphing Basic Trigonometric Functions (sinx, cosx, tanx)
Graphing All Six Trigonometric Functions
Trigonometric Identities 2
Trigonometric Equations 2
Proof of Sum Formulas
Trigonometric Identities 3
Trigonometric Identities 4
Trigonometric Equations 3
Trigonometric Equations 4
Trigonometric Equations 5
Law of Sines
Solving Triangles
Half-Angle Formulas
Product-Sum Identities
Graphing Inverse Trigonometric Functions
Graphing Trigonometric Functions (practice)
Inverse Trigonometric Expressions
Vectors 1 (Geometrically Defined)
Vectors 2 (Algebraically Defined)
Vectors 3 (Dot Product)
Vectors
Graphing in Polar Coordinates



Calculus and Analytic Geometry

Calculus 1



Preliminary

Guide to Review
Are you ready for calculus? - Answers
Complete Analysis of a Function - Part 1
Complete Analysis of a Function - Part 2
Complete Analysis of a Function - Part 3

Limits
Limits at infinity - Part 1
Limits at infinity - Part 2
Properties of limits at infinity
Two-sided limits
Properties of limits
Limits involving logarithms
Limits involving e
Trigonometric Limits


Instantaneous Velocity
Average Velocity - Part 1
Average Velocity - Part 2
Instantaneous Velocity


Differentiation
Differentiating by Finding Limits
Proving the Rules
Practice 1 (generalized polynomials)
Differentiating sinx and cosx (proofs)
Antiderivatives (practice)
Proving the Product Rule
Differentiating Logarithmic Functions
Practice 2 (after product rule, sinx, cosx, lnx)
Proving the quotient rule
Practice 3
Chain Rule (practice)
Practice 4 (after chain rule)
Practice 5 (after exponential functions)
Antiderivatives 2 (practice)
Differentiating Trigonometric Functions
Practice 6 (after inverse trig functions)
Implicit Differentiation

Applications of Derivative
Relative Extrema (polynomials only)
Tangent Lines (generalized polynomials only)
Optimization 2 (generalized polynomials)
Optimization 3 (after chain rule)
More Optimization (after chain rule)
Related Rates
Hyperbolic Functions
Complete analysis of a function
l'Hôpital's Rule

Integration
Riemann Sums
The Fundamental Theorem
Definite Integrals (practice)
Integration by substitution
Trigonometric Differentiation and Integration Formulas
Applications of the Integral - 1 (practice)
Applications of the Definite Integral - 2
Improper integrals
Integration by parts

Other
Leibniz notation
Graphing in Polar Coordinates
Graphing the antiderivative (Practice)
Proving the Mean Value Theorem
Calculus 2



Preliminary
Are you ready for calculus 2? - Some Solutions
Review of Differentiation (practice)
Exponential and Logarithmic Functions
Basic Differentiation and Integration Formulas
Review of Differentiation 2 (practice)

Techniques of Integration
Integration by substitution
Trigonometric Integrals 1
Integration by Parts
Trigonometric Substitutions
Hyperbolic Functions
Partial Fractions
Integrating Hyperbolic Functions
Numerical Integration
Improper Integrals

Applications of Integration
Applications of the Definite Integral - 1 (Areas)
Volumes 1 (Cross-sections)
Volumes 2 (disk method)
Volumes 3 (washer method)
Volumes 4 (shell method)
Arc Length
Work
Center of Mass

Sequences and Series
The Real Number System
Sequences - Part 1
Sequences - Part 2
Sequences - Part 3
Sequences - Part 4
Limits of Sequences
Fractions and decimals (review)
Geometric Series
Series 1 (definition, telescoping, geometric, integral test)
Series 2 (comparison test)
Series 3 (ratio test and root tests)
Series 4 (alternating test)
Power Series
Taylor Series

Other
Parametrization
Graphing in Polar Coordinates



Business Calculus

Limits at infinity - Part 1
Limits at infinity - Part 2
Two-sided limits
Rules of differentiation 1 (proofs)
Differentiation 1 (practice)
Relative Extrema
Optimization 2
Differentiation 2
More Optimization
Implicit Differentiation
Riemann Sums (practice)
Definite Integrals (practice)
Applications of the Definite Integral (practice)
Integration by substitution
Improper integrals
Integration by parts


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This page was last updated on July 2, 2017. Questions, comments: please e-mail to mhidegkuti@ccc.edu.