Math 113/114/115 Elementary Algebra

 Skill Notes Sample Problems Videos Pencast Lectures Practice Preparing for a Math Test Taking a Math Test PREALGEBRA REVIEW EA-1 Performing Operations on Integers Evaluate: EA-2 Performing Operations on Fractions Evaluate: EA-3 Performing Operations on Decimals Evaluate: EA-4 Knowing the Real Number System Given the set . Identify the natural numbers, the whole numbers, the integers, the rational numbers, and the irrational numbers. EXPONENT RULES EA-5 Applying the Product Rule Simplify: EA-6 Applying the Power Rule Simplify: EA-7 Applying the Distributivity of Exponentiation over Multiplication Simplify: EA-8 Removing Zero Exponents Simplify: EA-9 Removing Negative Exponents Simplify: EA-10 Applying the Quotient Rule Simplify: EA-11 Applying the Distributivity of Exponentiation over Division Simplify: EA-12 Applying Combined Rules Simplify: POLYNOMIALS EA-13 Identifying and Characterizing Polynomials Find the degree of and arrange the terms in descending order. EA-14 Adding and Subtracting Polynomials Subtract: EA-15 Multiplying Polynomials Multiply: EA-16 Multiplying Polynomials Using Special Products Multiply: Expand: EA-17 Dividing Polynomials Divide: EA-18 Performing Various Operations on Polynomials POLYNOMIAL FACTORING EA-19 Factoring out the Greatest Common Factor Factor: EA-20 Factoring by Grouping Factor: EA-21 Finding Two Numbers that Add to One Number and Multiply to Another (Sum-Product) EA-22 Factoring Quadratic Trinomials with Leading Coefficient of 1 Factor: EA-23 Factoring Quadratic Trinomials with Leading Coefficient Different from 1 Factor: EA-24 Factoring the Difference of Squares Factor: EA-25 Factoring the Sum/Difference of Cubes Factor: EA-26 Factoring Strategy EA-27 Factoring Using Combined Techniques Factor completely: RATIONAL EXPRESSIONS EA-28 Determining When a Rational Expression is Undefined Find the excluded values of EA-29 Simplifying Rational Expressions Simplify: EA-30 Simplifying Rational Expressions Involving Opposite Binomials Simplify: EA-31 Multiplying Rational Expressions Multiply: EA-32 Dividing Rational Expressions Divide: EA-33 Adding/Subtracting Rational Expressions with the Same Denominator Subtract: EA-34 Finding the LCM of Monomials Find the LCM: EA-35 Finding the LCM of Polynomials Find the LCM: EA-36 Adding/Subtracting Rational Expressions with Different  Denominators Subtract: EA-37 Performing Combined Operations on Rational Expressions Perform the operations: EA-38 Simplifying Complex Fractions Involving Rational Expressions Simplify: EA-39 Performing Various Operations on Rational Expressions RADICAL EXPRESSIONS (INDEX 2) EA-40 Finding Square Roots of Perfect Squares (Numbers) Evaluate: Simplify: EA-41 Simplifying Radical Expressions Simplify: EA-42 Adding/Subtracting Radical Expressions Add: EA-43 Multiplying Radical Expressions Multiply: EA-44 Dividing Radical Expressions Divide: EA-45 Rationalizing the Denominator (Single Radical) Rationalize the denominator: EA-46 Rationalizing the Denominator (Binomial Radical) Rationalize the denominator: EA-47 Performing Various Operations on Radical Expressions SOLVING LINEAR EQUATIONS EA-48 Solving Equations Involving Fractions Solve: EA-49 Solving Equations Involving Decimals Solve: EA-50 Solving Equations: Combined Techniques SOLVING NONLINEAR EQUATIONS EA-51 Solving Quadratic Equations by Factoring Solve: EA-52 Solving Quadratic Equations by the Square Root Law Solve: EA-53 Solving Quadratic Equations by Completing the Square Solve: EA-54 Remembering the Quadratic Formula (by listening to this out-of-tune song) EA-55 Solving Quadratic Equations by the Quadratic Formula Solve:  EA-56 Solving Polynomial Equations Solve: EA-57 Solving Rational Equations Solve:  EA-58 Solving Radical Equations Solve:  EA-59 Solving Various Types of Equations (Linear and Nonlinear) ANALYTIC GEOMETRY: LINES EA-60 Graphing Linear Equations in Two Variables Graph and discuss the intercepts and slope. EA-61 Finding the Slope of a Line Given the Graph EA-62 Finding the Slope of a Line Given the Coordinates of Two Points Find the slope of the line containing the points and . EA-63 Finding the Slope of a Line Given the Equation Find the slope of the line whose equation is given by . EA-64 Finding the Slope of Horizontal and Vertical Lines Find the slope of the line EA-65 Finding the Slope of a Line Parallel to a Given Line Find the slope of the line parallel to the line . EA-66 Finding the Slope of a Line Perpendicular to a Given Line Find the slope of the line perpendicular to the line . EA-67 Writing Equations of Horizontal and Vertical Lines Find the equation of the line parallel to the x-axis and containing the point . EA-68 Writing Equations of Lines Given Certain Properties Find the standard equation of the line through the point and perpendicular to the line . EA-69 Writing Equations of Lines Given the Graph SOLVING SYSTEMS OF TWO LINEAR EQUATIONS IN TWO VARIABLES EA-70 Solving by the Substitution Method Solve: EA-71 Solving by the Addition Method Solve: EA-72 Practicing Skills on Lines and 2 by 2 Systems WORD PROBLEMS: NUMBER EA-73 Setting up and Solving Number Problems Leading to Linear Equations The quantity three times the sum of a number and 2, decreased by the quantity twice the number increased by  4 is the same as the number less 9. EA-74 Setting up and Solving Number Problems Leading to Quadratic Equations The difference of the square of a number and the number is equal to 6. EA-75 Setting up and Solving Number Problems Leading to Polynomial Equations The sum of the cube of a number and the number is the same as the sum of nine times the square of the number and 9. EA-76 Setting up and Solving Number Problems Leading to Rational Equations Four times the reciprocal of a number less the reciprocal of the quantity 1 more than the number gives the ratio of 5 and the sum of the number and 1. EA-77 Setting up and Solving Number Problems Leading to Radical Equations A number less 1 is the same as the square root of the quantity 1 more than twice the number. EA-78 Setting up and Solving Number Problems Leading to Various Types of Equations EA-79 Setting up and Solving Number Problems Leading to a 2 by 2 System of Linear Equations The sum of two numbers is 8.  Twice the first number less three times the second number gives 1. EA-80 Setting up and Solving Number Problems Involving Consecutive Numbers The product of two consecutive positive odd integers is 143. EA-81 Setting up and Solving Number Problems Involving the Value of a Fraction The numerator of a fraction is 2 less than the denominator.  If 3 is added to the numerator and 1 is subtracted from the denominator, the value of the fraction becomes 3/2.  Find the original fraction. EA-82 Setting up and Solving Number Problems Involving the Value of a Two-Digit Number The sum of the digits of a two-digit number is 8.  If the digits are reversed, twice the new number is 17 more than the old number.  Find the original number. OTHER WORD PROBLEMS EA-83 Setting up and Solving Geometry Problems The length of a rectangle is 2 units more than twice the width.  Find the perimeter of the rectangle if the area is 24 square units. EA-84 Setting up and Solving Motion Problems Ana was walking to work at a certain rate.  After half an hour, she realized that she was running late so she jogged at a rate that was 1 mph faster than her walking rate and reached her place of work after 20 minutes.  How fast was she walking if the distance from her starting point to her ending point was 3 miles? EA-85 Setting up and Solving Work Problems Worker A needs 4 hours more than Worker B to finish a task.  Find how long it takes each worker to finish the task if together they can finish the task in 5 hours. EA-86 Setting up and Solving Mixture Problems A chemist wants to mix a 30% acid solution with a 75% acid solution to produce 10 liters of a 50% acid solution.  How many liters of each solution does the chemist need to mix? EA-87 Setting up and Solving “Mixture” Problems Two apples and four bananas cost \$2.45.  Three apples and two bananas cost \$3.40.  How much will an apple and five bananas cost? EA-88 Setting up and Solving Various Types of Word Problems GETTING READY FOR MATH 125 EA-89 Practicing all the Math 115 Skills