GACE Middle Grades Math Test Prep Course

Exponents, variables, and properties

• 1 Exponents
• 2 Variables
• 3 Field Properties

Integers and evaluating expressions

• 4 Graphing and Writing Integers
• 5 Comparing Integers
• 6 Adding and Subtracting Integers
• 7 Multiplying and Dividing Integers
• 8 Integer Word Problems
• 9 Order of Operations
• 10 Evaluation
• 11 Absolute Value

Understanding fractions

• 12 Divisibility Rules
• 13 Factors and Primes
• 14 Prime Factorization
• 15 Multiples and Least Common Multiple
• 16 Greatest Common Factor
• 17 Introduction to Fractions
• 18 Equivalent Fractions (Part I)
• 19 Reducing Fractions to Lowest Terms
• 20 Equivalent Fractions (Part II)
• 21 Improper Fractions and Mixed Numbers
• 22 Comparing Proper Fractions
• 23 Comparing Mixed Numbers and Improper Fractions
• 24 Adding and Subtracting Fractions
• 25 Multiplying and Dividing Fractions
• 26 Adding Mixed Numbers
• 27 Subtracting Mixed Numbers
• 28 Multiplying Mixed Numbers
• 29 Dividing Mixed Numbers

Decimals

• 30 Understanding Decimals
• 31 Converting Decimals to Fractions
• 32 Converting Fractions to Decimals
• 33 Comparing Decimals
• 34 Rounding Decimals
• 35 Estimating Sums and Differences of Decimals
• 36 Adding and Subtracting Decimals Word Problems
• 37 Multiplying and Dividing Decimals Word Problems
• 38 Powers of 10
• 39 Converting from Scientific to Standard Notation
• 40 Converting from Standard to Scientific Notation
• 41 Terminating and Repeating Decimals
• 42 Determining if a Number is Rational or Irrational

Simplifying expressions and solving equations

• 43 Combining Like Terms
• 44 Distributive Property
• 45 Distributive Property and Combining Like Terms
• 46 One-Step Equations
• 47 Two-Step Equations
• 48 Equations with Fractions
• 49 Equations Involving Distributive
• 50 Equations with Variable on Both Sides
• 51 Equations with Variable on Both Sides and Distributive
• 52 Literal Equations

Ratio, proportion, and percent

• 53 Introduction to Ratios
• 54 Equal Ratios
• 55 Unit Rate
• 56 Introduction to Proportion
• 57 Solving Proportions
• 58 Understanding Percents
• 59 Fractions and Percents
• 60 Decimals and Percents
• 61 Percent Word Problems
• 62 Percent Increase or Decrease
• 63 Discount
• 64 Sales Tax
• 65 Interest

Word problems

• 66 Translating English to Algebra
• 67 Number Word Problems
• 68 Value Word Problems
• 69 Mixture Word Problems
• 70 Motion Word Problems

Inequalities and absolute value

• 71 Solving and Graphing Inequalities
• 72 Combined Inequalities
• 73 Advanced Inequalities
• 74 Absolute Value Equations
• 75 Absolute Value Inequalities

Graphing and transformations

• 76 The Coordinate Grid
• 77 Transformations
• 78 Reflections
• 79 Translations
• 80 Rotations
• 81 Dilations
• 82 Symmetry

Functions and graphing

• 83 Domain and Range
• 84 Definition of a Function
• 85 Function and Arrow Notation
• 86 Graphing within a Given Domain
• 87 Graphing Lines
• 88 The Intercept Method
• 89 Graphing Inequalities in Two Variables

Linear equations and functions

• 90 Recognizing Patterns
• 91 Patterns and Table Building
• 92 Word Problems and Table Building
• 93 Slope of a Line
• 94 Slope Formula
• 95 Slope-Intercept Form
• 96 Converting to Slope-Intercept Form and Graphing
• 97 Interpreting Graphs
• 98 Linear Parent Graph and Transformations
• 99 Writing Equations of Lines
• 100 Writing Equations of Lines Using Tables
• 101 Writing Equations of Lines in Standard Form
• 102 Writing Equations of Lines Using the Point-Slope Formula
• 103 Writing Equations of Lines Given Two Points
• 104 Writing Equations of Parallel and Perpendicular Lines

Systems of linear equations and inequalities

• 105 Solving Systems by Graphing
• 106 Solving Systems by Addition
• 107 Solving Systems by Substitution
• 108 Number and Value Word Problems
• 109 Systems of Inequalities

Exponents and polynomials

• 110 The Product Rule
• 111 The Power Rule
• 112 The Quotient Rule
• 113 Numerical Bases and Exponents of Zero
• 114 Multiplying Polynomials
• 115 F.O.I.L.
• 116 Advanced Multiplying Polynomials
• 117 Adding and Subtracting Polynomials
• 118 Polynomial Long Division

Factoring and polynomial equations

• 119 Greatest Common Factor
• 120 Factoring out the Greatest Common Factor
• 121 Factoring Trinomials with Positive Constants
• 122 Factoring Trinomials with Negative Constants
• 123 Difference of Two Squares
• 124 Factoring Trinomials with Lead Coefficients and Positive Constants
• 125 Factoring Trinomials with Lead Coefficients and Negative Constants
• 126 Factoring Completely
• 127 Factoring by Grouping
• 128 Beginning Polynomial Equations
• 129 Intermediate Polynomial Equations
• 130 Quadratic Word Problems
• 131 Polynomial Inequalities

Rational expressions and equations

• 132 Simplifying Rational Expressions
• 133 Multiplying and Dividing Rational Expressions
• 134 Adding Rational Expressions
• 135 Subtracting Rational Expressions
• 136 Rational Equations
• 137 Advanced Rational Equations

Radical expresions and equations

• 138 Simplifying Radicals
• 139 Multiplying Radicals
• 140 Dividing Radicals
• 141 Adding Radicals and FOILing with Radicals
• 142 Dividing Radicals Using Conjugates
• 143 Radical Equations

Quadratic equations

• 144 Taking the Square Root of Both Sides
• 145 Completing The Square
• 146 Quadratic Formula

Imaginary and complex numbers

• 147 Imaginary Numbers
• 148 Advanced Imaginary Numbers
• 149 Complex Numbers

Quadratic functions and graphing

• 150 Understanding y - k = a(x - h)² Form
• 151 Graphing Quadratic Equations in y - k = a(x - h)² Form
• 152 Writing Quadratic Equations in y - k = a(x - h)² Form
• 153 Graphing Quadratic Functions

Negative and rational exponents

• 154 Negative Exponents
• 155 Numerical Bases with Negative Exponents
• 156 Multiplying and Dividing with Negative Exponents
• 157 Rational Exponents
• 158 Numerical Bases with Rational Exponents
• 159 Writing Radicals in Exponential Form
• 160 Solving Equations with Rational Exponents

Introduction to geometry

• 161 Points, Lines, Planes, and Space
• 162 Segments, Rays, and Length
• 163 Segment Addition Postulate and Midpoint
• 164 Angles and Measure
• 165 Angle Addition Postulate and Angle Bisector

Angle pairs and perpendicular lines

• 166 Complementary and Supplementary Angles
• 167 Vertical Angles
• 168 Problems Involving Perpendicular Lines
• 169 Theorems Involving Perpendicular Lines

Parallel lines and polygons

• 170 Parallel Lines Vocabulary
• 171 Given Lines are Parallel
• 172 Triangle Vocabulary and Triangle Sum Theorem
• 173 Triangle Word Problems and Exterior Angle Theorem
• 174 Polygon Vocabulary
• 175 Sum of Interior and Exterior Angles of a Polygon
• 176 Regular Polygons

Triangles and congruence

• 177 Congruent Figures
• 178 Proving Triangles are Congruent by SSS, SAS, and ASA
• 179 Isosceles Triangle Theorems
• 180 Proving Triangles are Congruent by AAS and HL
• 181 Medians, Altitudes, and Perpendicular Bisectors

Quadrilaterals

• 182 Properties of Parallelograms
• 183 More Parallel Line Theorems
• 184 Rectangles, Rhombuses, and Squares
• 185 Trapezoids

Similarity

• 186 Proportion
• 187 Properties of Similar Polygons
• 188 Angle-Angle Similarity Postulate
• 189 Similarity Word Problems

Right triangles

• 190 Pythagorean Theorem
• 191 Pythagorean Theorem Word Problems
• 192 30-60-90 and 45-45-90 Degree Triangles
• 193 Sine, Cosine, and Tangent
• 194 Sine, Cosine, and Tangent with a Calculator

Circles

• 195 Circle Vocabulary
• 196 Tangents
• 197 Arcs and Central Angles
• 198 Arcs and Chords
• 199 Inscribed Angles
• 200 Angles Formed by Chords, Secants, and Tangents
• 201 Circle Segment Lengths

Measurement and area

• 202 Customary Unit Conversions
• 203 Metric Unit Conversions
• 204 Units of Measurement
• 205 Perimeter
• 206 Area of Squares and Rectangles
• 207 Area of Triangles
• 208 Area of Parallelograms and Trapezoids
• 209 Area and Circumference of Circles
• 210 Changing Dimensions
• 211 Perimeter and Circumference Word Problems
• 212 Area Word Problems

Volume and surface area

• 213 Classifying 3-Dimensional Figures
• 214 Nets
• 215 Surface Area
• 216 Volume of Prisms and Pyramids
• 217 Volume of Cylinders, Spheres, and Cones
• 218 Surface Area and Volume Word Problems

Coordinate geometry

• 219 Distance Formula
• 220 Midpoint Formula
• 221 Equation of a Circle

Data and statistics

• 222 Bar Graphs
• 223 Line Graphs
• 224 Circle Graphs
• 225 Stem-and-Leaf Plots and Frequency Charts
• 226 Histograms
• 227 Scatterplots and Trends
• 228 Misleading Graphs
• 229 Range, Median, and Mode
• 230 Box-and-Whisker Plots
• 231 Mean
• 232 Central Tendency Word Problems
• 233 Simple Probability
• 234 Experimental Probability
• 235 Probability of Independent Events
• 236 Probability of Dependent Events
• 237 Tree Diagrams and the Counting Principle
• 238 Permutations
• 239 Combinations