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 





EA1 
Performing Operations on Integers 

Evaluate: 



EA2 
Performing Operations on Fractions 

Evaluate: 



EA3 
Performing Operations on Decimals 

Evaluate: 



EA4 
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 





EA5 
Applying the Product Rule 
Simplify: 

EA6 
Applying the Power Rule 
Simplify: 


EA7 
Applying the Distributivity of Exponentiation over Multiplication 
Simplify: 


EA8 
Removing Zero Exponents 
Simplify: 


EA9 
Removing Negative Exponents 
Simplify: 


EA10 
Applying the Quotient Rule 
Simplify: 


EA11 
Applying the Distributivity of Exponentiation over Division 
Simplify: 


EA12 
Applying Combined Rules 
Simplify: 



POLYNOMIALS 





EA13 
Identifying and Characterizing Polynomials 

Find the degree of and arrange the terms in descending order. 


EA14 
Adding and Subtracting Polynomials 

Subtract: 

EA15 
Multiplying Polynomials 

Multiply: 

EA16 
Multiplying Polynomials Using Special Products 

Multiply: Expand: 


EA17 
Dividing Polynomials 

Divide: 

EA18 
Performing Various Operations on Polynomials 






POLYNOMIAL
FACTORING 





EA19 
Factoring out the Greatest Common Factor 
Factor: 

EA20 
Factoring by Grouping 
Factor: 



EA21 
Finding Two Numbers that Add to One Number and Multiply to Another (SumProduct) 




EA22 
Factoring Quadratic Trinomials with Leading Coefficient of 1 
Factor: 

EA23 
Factoring Quadratic Trinomials with Leading Coefficient Different from 1 
Factor: 

EA24 
Factoring the Difference of Squares 
Factor: 

EA25 
Factoring the Sum/Difference of Cubes 
Factor: 


EA26 
Factoring Strategy 





EA27 
Factoring Using Combined Techniques 
Factor completely: 




RATIONAL
EXPRESSIONS 





EA28 
Determining When a Rational Expression is Undefined 

Find the excluded values of 



EA29 
Simplifying Rational Expressions 

Simplify: 

EA30 
Simplifying Rational Expressions Involving Opposite Binomials 

Simplify: 



EA31 
Multiplying Rational Expressions 

Multiply: 

EA32 
Dividing Rational Expressions 

Divide: 


EA33 
Adding/Subtracting Rational Expressions with the Same Denominator 

Subtract: 


EA34 
Finding the LCM of Monomials 

Find the LCM: 



EA35 
Finding the LCM of Polynomials 

Find the LCM: 


EA36 
Adding/Subtracting Rational Expressions with Different Denominators 

Subtract: 

EA37 
Performing Combined Operations on Rational Expressions 

Perform the operations: 


EA38 
Simplifying Complex Fractions Involving Rational Expressions 

Simplify: 

EA39 
Performing Various Operations on Rational Expressions 






RADICAL
EXPRESSIONS (INDEX 2) 





EA40 
Finding Square Roots of Perfect Squares (Numbers) 

Evaluate: Simplify: 



EA41 
Simplifying Radical Expressions 
Simplify: 


EA42 
Adding/Subtracting Radical Expressions 
Add: 

EA43 
Multiplying Radical Expressions 
Multiply: 


EA44 
Dividing Radical Expressions 
Divide: 


EA45 
Rationalizing the Denominator (Single Radical) 
Rationalize the denominator: 


EA46 
Rationalizing the Denominator (Binomial Radical) 
Rationalize the denominator: 

EA47 
Performing Various Operations on Radical Expressions 






SOLVING
LINEAR EQUATIONS 





EA48 
Solving Equations Involving Fractions 

Solve: 


EA49 
Solving Equations Involving Decimals 

Solve: 


EA50 
Solving Equations: Combined Techniques 






SOLVING
NONLINEAR EQUATIONS 





EA51 
Solving Quadratic Equations by Factoring 

Solve: 

EA52 
Solving Quadratic Equations by the Square Root Law 

Solve: 

EA53 
Solving Quadratic Equations by Completing the Square 

Solve: 

EA54 
Remembering the Quadratic Formula (by listening to this outoftune song) 





EA55 
Solving Quadratic Equations by the Quadratic Formula 

Solve: 

EA56 
Solving Polynomial Equations 

Solve: 


EA57 
Solving Rational Equations 

Solve: 

EA58 
Solving Radical Equations 

Solve: 

EA59 
Solving Various Types of Equations (Linear and Nonlinear) 






ANALYTIC
GEOMETRY: LINES 





EA60 
Graphing Linear Equations in Two Variables 

Graph and discuss the intercepts and slope. 


EA61 
Finding the Slope of a Line Given the Graph 



EA62 
Finding the Slope of a Line Given the Coordinates of Two Points 

Find the slope of the line containing the points and . 



EA63 
Finding the Slope of a Line Given the Equation 

Find the
slope of the line whose equation is given by . 



EA64 
Finding the Slope of Horizontal and Vertical Lines 

Find the slope of the line 



EA65 
Finding the Slope of a Line Parallel to a Given Line 

Find the slope of the line parallel to the line . 


EA66 
Finding the Slope of a Line Perpendicular to a Given Line 

Find the slope of the line perpendicular to the line. 



EA67 
Writing Equations of Horizontal and Vertical Lines 

Find the equation of the line parallel to the xaxis and
containing the point . 


EA68 
Writing Equations of Lines Given Certain Properties 

Find the standard equation of the line through the point and perpendicular to the line . 

EA69 
Writing Equations of Lines Given the Graph 






SOLVING SYSTEMS OF TWO LINEAR EQUATIONS IN TWO VARIABLES 





EA70 
Solving by the Substitution Method 

Solve: 

EA71 
Solving by the Addition Method 

Solve: 

EA72 
Practicing Skills on Lines and 2 by 2 Systems 






WORD
PROBLEMS: NUMBER 





EA73 
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.



EA74 
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. 

EA75 
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. 



EA76 
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. 


EA77 
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. 



EA78 
Setting up and Solving Number Problems Leading to Various Types of Equations 





EA79 
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. 



EA80 
Setting up and Solving Number Problems Involving Consecutive Numbers 

The product of two consecutive positive odd integers is 143. 



EA81 
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. 



EA82 
Setting up and Solving Number Problems Involving the Value of a TwoDigit Number 

The sum of the digits of a twodigit 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 





EA83 
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. 


EA84 
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? 


EA85 
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. 


EA86 
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? 


EA87 
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? 



EA88 
Setting up and Solving Various Types of Word Problems 





GETTING
READY FOR MATH 125 





EA89 
Practicing all the Math 115 Skills 



