Lecture Notes and Sample Exams


Lecture Notes and Worksheets

About Mathematics
The Words And and Or
The Order of Operations Agreement
Factors of a Number
Perimeter and Area of Rectangles
Perimeter and Area of Right Triangles
Perimeter and Area of General Triangles
Division with Remainder
Prime Factorization
Divisibility Tests
The GCF and LCM
Evaluating Algebraic Expressions
Solutions of Equations
The Set of All Integers

Division by Zero
Order of Operations on Integers
More Practice
    Part 1 - the definition
  Practice Quiz and Quiz
    Part 2 - Equivalent Fractions
    Part 3 - Improper Fractions and Mixed Numbers
    Part 4 - Adding and Subtracting Fractions
    Part 5 - Multiplying and Dividing Fractions
Basic Percent Problems   -  
Solving Two-Step Linear Equations
Fractions, Decimals, Percents - Conversions
Conversions between units of measurement
Standard labeling in triangles
Angles of a Triangle
Decimals and Fractions

Beginning Algebra

Lecture Notes and Worksheets

The Set of All Natural Numbers
Introduction to Set Theory
The Set of All Integers
Order of Operations on Integers
Set Operations
Square Root of an Integer
Algebraic Expressions and Statements
Graphs of Equations     Examples - Answers
Combining Like Terms
Simplifying Algebraic Expressions over Z
One- and Two-Step Equations
Multiplying Algebraic Expressions over Z
Equations with the Unknown on Both Sides
Solving Linear Equations - Part 2
Solving Linear Equations - Part 3
Weighted Average
Angles In a Triangle:   Theory - Problem Solving -
Solving Linear Inequalities
Linear Inequalities (practice)
Graphing Straight Lines
        Practice     Examples - Answers
Basic Percent Problems
Word Problems 1 (Linear)
Solving Linear Systems by Elimination
Solving Linear Systems by Substitution
Slope of a Line
More on Linear Systems
The Zero Product Rule
Factoring out the GCF
Factoring via the difference of squares theorem
Factoring by Trial and Error
Factoring by Grouping
Factoring by the AC-method - Practice
Rational Expressions
The Pythagorean Theorem
Factoring the Sum and Difference of Cubes
Factoring the difference of cubes (Practice)
Factoring the sum of cubes (Practice)
The Pythagorean Theorem
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

Introduction to Intermediate Algebra
Introduction to Sets
Set Operations
More on Sets
Introduction to Combinatorics
Introduction to Number Theory
The nth Root of a Number
Simplifying Algebraic Expressions over Z (no FOIL)
One- and Two-Step Equations
Simplifying Algebraic Expressions (with FOIL)
More Linear Equations
Factoring by completing the square   Part 1   Part 2   Part 3   Part 4
Review of Factoring (GCF, difference of squares theorem)
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
Compound Inequalities
Smallest Value of a Quadratic Expression
Graphing a Parabola - Part 1 - Practice
Graphing a Parabola - Part 2
Rational Expressions
Complex Fractions
Radical Expressions - Part 1
Radical Expressions - Part 2
Radical Expressions (1 and 2)
Radical Equations
Absolute Value Equations
Rational Expressions - Part 1
Rational Expressions - Part 2
Rational Equations
New! Systems of Equations in Three Variables
The Real Number System
The Quadratic Formula
The proof that square root of 2 is irrational
Rules of Exponents
Rational Exponents
Work Word Problems

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 -
Review of Systems of Equations
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 and Geometric Means
The Arithmetic, Geometric, and Harmonic Means
Complex Numbers
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
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

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
Law of Cosines
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)
Graphing in Polar Coordinates

Calculus and Analytic Geometry

Calculus 1


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 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

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 (Polynomials)
Optimization 3 (Generalized Polynomials)
Optimization 4 (After Chain Rule)
More Optimization (after chain rule)
Related Rates
Hyperbolic Functions
Complete analysis of a function
l'Hôpital's Rule

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

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

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
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

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 May 13, 2019. Questions, comments: please e-mail to mhidegkuti@ccc.edu.