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Lecture Notes and Sample Exams

PreAlgebra

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
Quiz
The Set of All Integers
Division by Zero
Order of Operations on Integers
More Practice
Fractions
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

Quiz
Solving TwoStep 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
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 TwoStep Equations
Multiplying Algebraic Expressions over Z
Equations with the Unknown on Both Sides
More
Solving Linear Equations  Part 2
Solving Linear Equations  Part 3
Weighted Average
Angles In a Triangle:
Theory 
Problem Solving

Quiz
Intervals
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 ACmethod 
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 TwoStep 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, ACmethod, 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


Calculus and Analytic Geometry

Business Calculus
Limits at infinity  Part 1
Limits at infinity  Part 2
Twosided 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 email to mhidegkuti@ccc.edu.
