ACCUPLACER College-Level Math Test Prep Course

Evaluating expressions

• 1 Exponents
• 2 Variables
• 3 Field Properties
• 4 Graphing and Writing Integers
• 5 Comparing Integers
• 6 Opposites and Absolute Value
• 7 Adding and Subtracting Integers
• 8 Multiplying and Dividing Integers
• 9 Order of Operations
• 10 Evaluation
• 11 Adding and Subtracting Fractions
• 12 Multiplying and Dividing Fractions
• 13 Absolute Value

Decimals & scientific notation

• 14 Powers of 10
• 15 Converting from Scientific to Standard Notation
• 16 Converting from Standard to Scientific Notation
• 17 Terminating and Repeating Decimals
• 18 Determining if a Number is Rational or Irrational

Solving linear equations in one variable

• 19 Combining Like Terms
• 20 Distributive Property
• 21 Distributive Property and Combining Like Terms
• 22 One-Step Equations
• 23 Two-Step Equations
• 24 Equations with Fractions
• 25 Equations Involving Distributive
• 26 Equations with Variable on Both Sides
• 27 Equations with Variable on Both Sides and Fractions
• 28 Equations with Variable on Both Sides and Distributive
• 29 Literal Equations
• 30 Advanced Literal Equations

Word problems

• 31 Translating English to Algebra
• 32 Writing and Solving Multi-Step Equations
• 33 Number Word Problems
• 34 Geometry Word Problems

Inequalities, absolute value, functions, & graphing

• 35 Solving and Graphing Inequalities
• 36 Combined Inequalities
• 37 Advanced Inequalities
• 38 Absolute Value Equations
• 39 Absolute Value Inequalities
• 40 The Coordinate System
• 41 Domain and Range
• 42 Definition of a Function
• 43 Function and Arrow Notation
• 44 Graphing within a Given Domain
• 45 Graphing Lines
• 46 The Intercept Method
• 47 Graphing Inequalities in Two Variables

Linear equations in two variables

• 48 Slope of a Line
• 49 Using Slope to Graph a Line
• 50 Slope Formula
• 51 Slope-Intercept Form
• 52 Converting to Slope-Intercept Form and Graphing
• 53 Writing Equations of Lines Using Tables
• 54 Writing Equations of Lines in Standard Form
• 55 Writing Equations of Lines Using the Point-Slope Formula
• 56 Writing Equations of Lines Given Two Points
• 57 Writing Equations of Parallel and Perpendicular Lines
• 58 Direct Variation
• 59 Applications of Direct Variation and Linear Functions

Systems of equations

• 60 Solving Systems by Graphing
• 61 Solving Systems by Addition
• 62 Solving Systems by Substitution
• 63 Systems of Equations with Fractions and Method of Choice
• 64 Number and Value Word Problems

Exponents & polynomials

• 65 The Product Rule
• 66 The Power Rule
• 67 The Quotient Rule
• 68 Numerical Bases and Exponents of Zero
• 69 Combining Exponent Rules
• 70 Multiplying Polynomials
• 71 F.O.I.L.
• 72 Advanced Multiplying Polynomials

Factoring

• 73 Greatest Common Factor
• 74 Factoring out the Greatest Common Factor
• 75 Factoring Trinomials with Positive Constants
• 76 Factoring Trinomials with Negative Constants
• 77 Difference of Two Squares
• 78 Factoring Trinomials with Lead Coefficients and Positive Constants
• 79 Factoring Trinomials with Lead Coefficients and Negative Constants
• 80 Factoring by Grouping
• 81 Advanced Factoring by Grouping
• 82 Factoring Completely
• 83 Advanced Factoring Completely
• 84 Beginning Polynomial Equations
• 85 Intermediate Polynomial Equations

Rational expressions & equations

• 86 Simplifying Rational Expressions
• 87 Multiplying and Dividing Rational Expressions
• 88 Adding Rational Expressions
• 89 Subtracting Rational Expressions
• 90 Complex Fractions
• 91 Rational Equations
• 92 Advanced Rational Equations
• 93 Inverse Variation

Radical expressions & equations

• 94 Simplifying Radicals
• 95 Multiplying Radicals
• 96 Dividing Radicals
• 97 Adding Radicals and FOILing with Radicals
• 98 Dividing Radicals Using Conjugates
• 99 Radical Equations
• 100 Advanced Radical Equations

Quadratic equations

• 101 Taking the Square Root of Both Sides
• 102 Completing The Square
• 103 Advanced Completing The Square
• 104 Quadratic Formula

Imaginary & complex numbers

• 105 Imaginary Numbers
• 106 Advanced Imaginary Numbers
• 107 Complex Numbers
• 108 Advanced Complex Numbers

Quadratic functions

• 109 Understanding y - k = a(x - h)² Form
• 110 Graphing Quadratic Equations in y - k = a(x - h)² Form
• 111 Writing Quadratic Equations in y - k = a(x - h)² Form
• 112 Graphing Quadratic Functions
• 113 Sum and Product of Roots Formula
• 114 Writing Quadratic Functions

Introduction to geometry

• 115 Points, Lines, Planes, and Space
• 116 Segments, Rays, and Length
• 117 Segment Addition Postulate and Midpoint
• 118 Angles and Measure
• 119 Angle Addition Postulate and Angle Bisector
• 120 Inductive vs. Deductive Reasoning
• 121 Conditional Statements
• 122 Properties
• 123 Algebra Proofs with Properties
• 124 Geometry Proofs with Midpoints and Angle Bisectors

Angle pairs & perpendicular lines

• 125 Complementary and Supplementary Angles
• 126 Vertical Angles
• 127 Problems Involving Perpendicular Lines
• 128 Theorems Involving Perpendicular Lines

Parallel lines & polygons

• 129 Parallel Lines Vocabulary
• 130 Given Lines are Parallel
• 131 Triangle Vocabulary and Triangle Sum Theorem
• 132 Advanced Triangle Sum Theorem
• 133 Triangle Word Problems and Exterior Angle Theorem
• 134 Polygon Vocabulary
• 135 Sum of Interior and Exterior Angles of a Polygon
• 136 Regular Polygons

Triangles & congruence

• 137 Congruent Figures
• 138 Proving Triangles are Congruent by SSS, SAS, and ASA
• 139 Isosceles Triangle Theorems
• 140 Proving Triangles are Congruent by AAS and HL
• 141 Medians, Altitudes, and Perpendicular Bisectors

Quadrilaterals

• 142 Properties of Parallelograms
• 143 Proving a Quadrilateral is a Parallelogram
• 144 More Parallel Line Theorems
• 145 Rectangles, Rhombuses, and Squares
• 146 Trapezoids

Similarity

• 147 Ratio
• 148 Proportion
• 149 Properties of Similar Polygons
• 150 Angle-Angle Similarity Postulate
• 151 Similarity Word Problems
• 152 SSS and SAS Similarity Theorems
• 153 Triangle Proportionality and Triangle Angle-Bisector Theorems

Right triangles

• 154 Pythagorean Theorem
• 155 Pythagorean Theorem Word Problems
• 156 Converse of the Pythagorean Theorem
• 157 30-60-90 and 45-45-90 Degree Triangles
• 158 Sine, Cosine, and Tangent
• 159 Sine, Cosine, and Tangent with a Calculator
• 160 Trigonometry Word Problems

Circles

• 161 Circle Vocabulary
• 162 Tangents
• 163 Arcs and Central Angles
• 164 Arcs and Chords
• 165 Inscribed Angles
• 166 Angles Formed by Chords, Secants, and Tangents
• 167 Circle Segment Lengths

Area

• 168 Area of Rectangles and Squares
• 169 Advanced Area of Rectangles and Squares
• 170 Area of Parallelograms
• 171 Area of Triangles
• 172 Area of Rhombuses
• 173 Area of Trapezoids
• 174 Area of Regular Polygons
• 175 Area and Circumference of Circles

Volume & surface area

• 176 Area and Volume of Prisms
• 177 Advanced Area and Volume of Prisms
• 178 Area and Volume of Pyramids
• 179 Advanced Area and Volume of Pyramids
• 180 Area and Volume of Cylinders and Cones
• 181 Area and Volume of Spheres

Probability and counting

• 182 Simple Probability
• 183 Probability of Independent Events
• 184 Probability of Dependent Events
• 185 Tree Diagrams and the Counting Principle
• 186 Permutations
• 187 Combinations

Coordinate geometry

• 188 Distance Formula
• 189 Midpoint Formula
• 190 Equation of a Circle

Negative & rational exponents

• 191 Negative Exponents
• 192 Numerical Bases with Negative Exponents
• 193 Multiplying and Dividing with Negative Exponents
• 194 Multiplying and Dividing with Scientific Notation
• 195 Rational Exponents
• 196 Numerical Bases with Rational Exponents
• 197 Writing Radicals in Exponential Form
• 198 Solving Equations with Rational Exponents
• 199 Radical Exponents

Composite functions & inverses

• 200 Composite Functions: f(g(x)) and g(f(x))
• 201 Inverse Relations
• 202 Inverse Functions

Logarithms & exponential functions

• 203 Evaluating Logarithms and Logarithmic vs. Exponential Form
• 204 Solving Logarithmic Equations
• 205 Logarithm Rules and Properties
• 206 Evaluating Logarithms by Condensing or Expanding
• 207 Solving Advanced Logarithmic Equations
• 208 Logarithm Calculator Problems
• 209 Exponential Equations and Change of Base Formula
• 210 Exponential Growth and Decay
• 211 Half Life and Doubling Time Formulas
• 212 Natural Logarithms
• 213 Solving Natural Logarithm Equations with ln and e