Math 125 Intermediate Algebra

Skill 
Notes 
Videos 
Practice 

Preparing for a Math Test 




Taking a Math Test 




ALGEBRAIC
EXPRESSIONS 



IA1 
Removing Nested Symbols of Grouping 


IA2 
Revisiting Rules of Integer Exponents 

IA3 
Using Scientific Notation 



IA4 
Multiplying “Long” Expressions Using Special Products for Binomials 

IA5 
Expanding Binomials (Pascal’s Triangle) 

IA6 
Performing Long Division on Polynomials with Rearranged and/or Missing Terms 


POLYNOMIAL
FACTORING 



IA7 
Factoring out the Greatest Common Factor 

IA8 
Factoring by Grouping I 


IA9 
Factoring Quadratic Trinomials 

IA10 
Recognizing Special Binomial Forms 



IA11 
Factoring the Difference of Squares 

IA12 
Factoring the Sum/Difference of Cubes 

IA13 
Factoring by Grouping II 



IA14 
Factoring Strategy 



IA15 
Factoring Using Combined Techniques 


IA16 
Factoring by Substitution 


RATIONAL
EXPRESSIONS 



IA17 
Simplifying Rational Expressions 


IA18 
Multiplying Rational Expressions 


IA19 
Dividing Rational Expressions 


IA20 
Adding/Subtracting Rational Expressions 


IA21 
Performing Combined Operations on Rational Expressions 


IA22 
Simplifying Complex Fractions Involving Rational Expressions 


IA23 
Simplifying “Rational” Expressions Involving Zero and/or Negative Exponents 



RADICAL
EXPRESSIONS (INDEX >=2) 



IA24 
Finding Cube Roots of Numbers 



IA25 
Simplifying Radical Expressions 


IA26 
Adding/Subtracting Radical Expressions 


IA27 
Multiplying Radical Expressions 


IA28 
Dividing Radical Expressions 


IA29 
Rationalizing the Denominator (Index 2) 


IA30 
Rationalizing the Denominator (Index >=3) 



RATIONAL
EXPONENTS 



IA31 
Writing Expressions Involving Rational Exponents in Radical Form 


IA32 
Writing Radical Expressions Using Rational Exponents 


IA33 
Evaluating Expressions Involving Rational Exponents 



IA34 
Simplifying Expressions Involving Rational Exponents Multiplying and Dividing Radicals with Different Indices Reducing the Index 




COMPLEX
NUMBERS 



IA35 
Introduction to Complex Numbers; Graph 


IA36 
Adding/Subtracting Complex Numbers 


IA37 
Multiplying Complex Numbers 


IA38 
Dividing Complex Numbers 


IA39 
Evaluating Powers of i 



SOLVING
EQUATIONS IN ONE VARIABLE 



IA40 
Solving Linear Equations Involving Nested Symbols of Grouping 


IA41 
Solving Linear Equations Involving Fractions 



IA42 
Solving Linear Equations Involving Decimals 



IA43 
Solving Absolute Value Equations 


IA44 
Solving Quadratic/Quadratic Form Equations 


IA44* Will fix this later 
Solving Equations in Quadratic Form 



IA45 
Solving Polynomial Equations 


IA46 
Solving Rational Equations 


IA47 
Solving Radical Equations 


IA48 
Solving Literal Equations 




SOLVING
LINEAR INEQUALITIES IN ONE VARIABLE 



IA49 
Writing Solution Sets, Graphs, Interval Notation 



IA50 
Solving Simple Linear Inequalities 


IA51 
Solving Compound Linear Inequalities 




SOLVING
NONLINEAR INEQUALITIES IN ONE VARIABLE 



IA52 
Solving Quadratic Inequalities 


IA53 
Solving Polynomial Inequalities 


IA54 
Solving Rational Inequalities 



IA55 
Solving Absolute Value Inequalities 



ANALYTIC GEOMETRY: LINES (REVIEW) 



IA56 
Graphing Lines 


IA57 
Identifying Parallel and Perpendicular Lines 



IA58 
Writing Equations of Lines 




ANALYTIC
GEOMETRY: CIRCLES 



IA59 
Finding the Distance Between Two Points 


IA60 
Finding the Midpoint of a Line Segment Connecting Two Points 



IA61 
Graphing Circles 


IA62 
Writing Equations of Circles 



ANALYTIC
GEOMETRY: PARABOLAS 



IA63 
Graphing Parabolas Given the Equation in Vertex Form 


IA64 
Finding the Vertex of a Parabola 



IA65 
Graphing Parabolas Given the General Equation 



IA66 
Graphing Sideways or Horizontal Parabolas 




ANALYTIC
GEOMETRY: ELLIPSES 



IA67 
Graphing Ellipses Given the Standard Equation 


IA68 
Graphing Ellipses Given the General Equation 




ANALYTIC
GEOMETRY: HYPERBOLAS 



IA69 
Graphing Hyperbolas Given the Standard Equation 


IA70 
Graphing Hyperbolas Given the General Equation 




ANALYTIC
GEOMETRY: IDENTIFYING CONIC SECTIONS 



IA71 
Classifying Conic Sections Given the Standard Equation 



IA72 
Classifying Conic Sections Given the General Equation 




SOLVING
SYSTEMS OF EQUATIONS: 2
X 2 LINEAR 



IA73 
Solving by Graphing 



IA74 
Solving by Substitution 


IA75 
Solving by Addition 


IA76 
Solving by Gaussian Elimination 



IA77 
Recognizing Inconsistent and Dependent Systems 




SOLVING
SYSTEMS OF EQUATIONS: 3
X 3 LINEAR 



IA78 
Solving by Addition 


IA79 
Solving a 3 x 3 System with Missing Variables 



IA80 
Solving by Gaussian Elimination/ GaussJordan Reduction 


IA81 
Solving by Pivoting 




SOLVING 2 X 2 NONLINEAR SYSTEMS 



IA82 
Solving a System of One Linear and One Quadratic Equation 


IA83 
Solving a Quadratic System 



IA84 
Solving Other Nonlinear Systems 




SETTING
UP AND SOLVING WORD PROBLEMS 



IA85 
Setting up Number Problems 



IA86 
Setting up Geometry Problems 



IA87 
Setting up Mixture Problems 



IA88 
Setting up Motion Problems 



IA89 
Setting up Work Problems 




FUNCTIONS 



IA90 
Identifying Functions and Relations 


IA91 
Finding the Domain and the Range 


IA92 
Understanding Function Notation 



IA93 
Finding the Domain Given the Equation 


IA94 
Sketching Graphs of Basic Functions 


IA95 
Sketching Graphs Involving Horizontal Translations 


IA96 
Sketching Graphs Involving Vertical Translations 



IA97 
Sketching Graphs Involving Stretching 



IA98 
Sketching Graphs Involving Shrinking 



IA99 
Sketching Graphs Involving Combined Transformations 



IA100 
Performing Operations on Functions 



IA101 
Solving Variation Problems 




INVERSE FUNCTIONS 



IA102 
Determining the Existence of the Inverse 


IA103 
Finding the Inverse of a Function 



IA104 
Graphing a Function and its Inverse 



IA105 
Finding the Domain and Range of a Function and its Inverse 




EXPONENTIAL AND LOGARITHMIC FUNCTIONS 



IA106 
Graphing the Basic Exponential Function 


IA107 
Finding the Domain and the Range of the Exponential Function Based on the Graph 



IA108 
Solving Exponential Equations; Bases Related 



IA109 
Graphing Transformations of the Basic Exponential Function 



IA110 
Evaluating Logarithms 



IA111 
Graphing the Logarithmic Function 



IA112 
Applying Properties of Logarithms 



IA113 
Expanding Logarithmic Expressions 



IA114 
Compressing Logarithmic Expressions 



IA115 
Solving Logarithmic Equations 



IA116 
Solving Compound Interest Problems 



IA117 
Solving Growth and Decay Problems 




SEQUENCES AND SERIES 



IA118 
Finding the Sum of the First n Terms of an Arithmetic Series 



IA119 
Finding the Sum of the First n Terms of a Geometric Series 

