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
• 35 Value Word Problems

Inequalities, absolute value, functions, & graphing

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

Linear equations in two variables

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

Systems of equations

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

Exponents & polynomials

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

Factoring

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

Rational expressions & equations

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

Radical expressions & equations

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

Quadratic equations

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

Imaginary & complex numbers

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

Quadratic functions

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

Introduction to geometry

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

Angle pairs & perpendicular lines

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

Parallel lines & polygons

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

Triangles & congruence

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

Quadrilaterals

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

Similarity

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

Right triangles

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

Circles

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

Area

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

Volume & surface area

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

Probability and counting

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

Coordinate geometry

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

Negative & rational exponents

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

Composite functions & inverses

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

Logarithms & exponential functions

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

Additional concepts

• 215 Systems of Inequalities
• 216 Systems of Three Equations
• 217 Sum and Difference of Two Cubes
• 218 Quadratic Word Problems
• 219 Polynomial Inequalities
• 220 Adding and Subtracting Polynomials
• 221 Polynomial Long Division
• 222 Synthetic Division