GACE Middle Grades Math Test Prep Course

Whole numbers and properties

• 1 Place Value
• 2 Comparing Numbers
• 3 Rounding Numbers
• 4 Estimating Sums and Differences
• 5 Exponents
• 6 Estimating Products and Quotients
• 7 Variables
• 8 Field Properties

Integers and evaluating expressions

• 9 Graphing and Writing Integers
• 10 Comparing Integers
• 11 Adding and Subtracting Integers
• 12 Multiplying and Dividing Integers
• 13 Integer Word Problems
• 14 Order of Operations
• 15 Evaluation
• 16 Absolute Value

Understanding fractions

• 17 Divisibility Rules
• 18 Factors and Primes
• 19 Prime Factorization
• 20 Multiples and Least Common Multiple
• 21 Greatest Common Factor
• 22 Introduction to Fractions
• 23 Equivalent Fractions (Part I)
• 24 Reducing Fractions to Lowest Terms
• 25 Equivalent Fractions (Part II)
• 26 Improper Fractions and Mixed Numbers
• 27 Comparing Proper Fractions
• 28 Comparing Fractions Word Problems
• 29 Adding and Subtracting Like Fractions
• 30 Adding and Subtracting Unlike Fractions
• 31 Adding Mixed Numbers
• 32 Subtracting Mixed Numbers
• 33 Multiplying Fractions
• 34 Multiplying Mixed Numbers
• 35 Dividing Fractions
• 36 Dividing Mixed Numbers
• 37 Adding and Subtracting Fractions
• 38 Multiplying and Dividing Fractions

Decimals

• 39 Understanding Decimals
• 40 Converting Decimals to Fractions
• 41 Converting Fractions to Decimals
• 42 Comparing Decimals
• 43 Rounding Decimals
• 44 Estimating Sums and Differences of Decimals
• 45 Adding Decimals
• 46 Subtracting Decimals
• 47 Adding and Subtracting Decimals Word Problems
• 48 Multiplying Decimals by Whole Numbers
• 49 Multiplying Decimals by Decimals
• 50 Dividing Decimals by Whole Numbers
• 51 Dividing Decimals by Decimals
• 52 Multiplying and Dividing Decimals Word Problems
• 53 Powers of 10
• 54 Converting from Scientific to Standard Notation
• 55 Converting from Standard to Scientific Notation
• 56 Terminating and Repeating Decimals
• 57 Determining if a Number is Rational or Irrational

Simplifying expressions & solving equations

• 58 Combining Like Terms
• 59 Distributive Property
• 60 Distributive Property and Combining Like Terms
• 61 One-Step Equations
• 62 Two-Step Equations
• 63 Equations with Fractions
• 64 Equations Involving Distributive
• 65 Equations with Variable on Both Sides
• 66 Equations with Variable on Both Sides and Distributive
• 67 Literal Equations

Ratio, proportion, & percent

• 68 Introduction to Ratios
• 69 Equal Ratios
• 70 Unit Rate
• 71 Introduction to Proportion
• 72 Solving Proportions
• 73 Proportion Word Problems
• 74 Understanding Percents
• 75 Fractions and Percents
• 76 Decimals and Percents
• 77 Percent Word Problems
• 78 Percent Increase or Decrease
• 79 Discount
• 80 Sales Tax
• 81 Interest

Word problems

• 82 Translating English to Algebra
• 83 Number Word Problems
• 84 Geometry Word Problems
• 85 Value Word Problems
• 86 Interest Word Problems
• 87 Mixture Word Problems
• 88 Motion Word Problems

Inequalities and absolute value

• 89 Introduction to Inequalities
• 90 Solving and Graphing Inequalities
• 91 Combined Inequalities
• 92 Advanced Inequalities
• 93 Absolute Value Equations
• 94 Absolute Value Inequalities

Graphing and transformations

• 95 The Coordinate Grid
• 96 Transformations
• 97 Reflections
• 98 Translations
• 99 Rotations
• 100 Dilations
• 101 Symmetry

Functions and graphing

• 102 Domain and Range
• 103 Definition of a Function
• 104 Domain and Range
• 105 Function and Arrow Notation
• 106 Graphing within a Given Domain
• 107 Graphing Lines
• 108 The Intercept Method
• 109 Graphing Inequalities in Two Variables

Linear equations and functions

• 110 Recognizing Patterns
• 111 Finding the nth Term in a Pattern
• 112 Patterns and Table Building
• 113 Word Problems and Table Building
• 114 Slope as a Rate of Change
• 115 Slope of a Line
• 116 Slope Formula
• 117 Slope-Intercept Form
• 118 Converting to Slope-Intercept Form and Graphing
• 119 Interpreting Graphs
• 120 Linear Parent Graph and Transformations
• 121 Writing Equations of Lines
• 122 Writing Equations of Lines Using Tables
• 123 Direct Variation
• 124 Writing Equations of Lines in Standard Form
• 125 Writing Equations of Lines Using the Point-Slope Formula
• 126 Writing Equations of Lines Given Two Points
• 127 Writing Equations of Parallel and Perpendicular Lines

Systems of linear equations

• 128 Solving Systems by Graphing
• 129 Solving Systems by Addition
• 130 Solving Systems by Substitution
• 131 Number and Value Word Problems

Exponents and polynomials

• 132 The Product Rule
• 133 The Power Rule
• 134 The Quotient Rule
• 135 Numerical Bases and Exponents of Zero
• 136 Multiplying Polynomials
• 137 F.O.I.L.
• 138 Advanced Multiplying Polynomials

Factoring

• 139 Greatest Common Factor
• 140 Factoring out the Greatest Common Factor
• 141 Factoring Trinomials with Positive Constants
• 142 Factoring Trinomials with Negative Constants
• 143 Difference of Two Squares
• 144 Factoring Trinomials with Lead Coefficients and Positive Constants
• 145 Factoring Trinomials with Lead Coefficients and Negative Constants
• 146 Factoring Completely
• 147 Factoring by Grouping
• 148 Advanced Factoring Completely
• 149 Beginning Polynomial Equations
• 150 Intermediate Polynomial Equations

Rational expressions and equations

• 151 Simplifying Rational Expressions
• 152 Multiplying and Dividing Rational Expressions
• 153 Adding Rational Expressions
• 154 Subtracting Rational Expressions
• 155 Complex Fractions
• 156 Rational Equations
• 157 Advanced Rational Equations
• 158 Inverse Variation

Radical expresions and equations

• 159 Square Roots
• 160 Simplifying Radicals
• 161 Multiplying Radicals
• 162 Dividing Radicals
• 163 Adding Radicals and FOILing with Radicals
• 164 Dividing Radicals Using Conjugates
• 165 Radical Equations
• 166 Advanced Radical Equations

Quadratic equations

• 167 Graphs of Quadratic Functions and Beginning Transformations
• 168 Graphs of Quadratic Functions and Advanced Transformations
• 169 Taking the Square Root of Both Sides
• 170 Completing The Square
• 171 Advanced Completing The Square
• 172 Quadratic Formula

Imaginary and complex numbers

• 173 Imaginary Numbers
• 174 Advanced Imaginary Numbers
• 175 Complex Numbers

Quadratic functions and graphing

• 176 Understanding y - k = a(x - h)² Form
• 177 Graphing Quadratic Equations in y - k = a(x - h)² Form
• 178 Writing Quadratic Equations in y - k = a(x - h)² Form
• 179 Graphing Quadratic Functions

Introduction to geometry

• 180 Points, Lines, Planes, and Space
• 181 Segments, Rays, and Length
• 182 Segment Addition Postulate and Midpoint
• 183 Angles and Measure
• 184 Angle Addition Postulate and Angle Bisector
• 185 Inductive vs. Deductive Reasoning
• 186 Conditional Statements
• 187 Properties
• 188 Algebra Proofs with Properties
• 189 Geometry Proofs with Midpoints and Angle Bisectors

Angle pairs and perpendicular lines

• 190 Complementary and Supplementary Angles
• 191 Advanced Complementary and Supplementary Angles
• 192 Vertical Angles
• 193 Problems Involving Perpendicular Lines
• 194 Theorems Involving Perpendicular Lines

Parallel lines and polygons

• 195 Parallel Lines Vocabulary
• 196 Given Lines are Parallel
• 197 Proving Lines are Parallel
• 198 Triangle Vocabulary and Triangle Sum Theorem
• 199 Triangle Word Problems and Exterior Angle Theorem
• 200 Polygon Vocabulary
• 201 Sum of Interior and Exterior Angles of a Polygon
• 202 Regular Polygons

Triangles and congruence

• 203 Congruent Figures
• 204 Proving Triangles are Congruent by SSS, SAS, and ASA
• 205 Isosceles Triangle Theorems
• 206 Proving Triangles are Congruent by AAS and HL
• 207 Medians, Altitudes, and Perpendicular Bisectors

Quadrilaterals

• 208 Properties of Parallelograms
• 209 Proving a Quadrilateral is a Parallelogram
• 210 More Parallel Line Theorems
• 211 Rectangles, Rhombuses, and Squares
• 212 Trapezoids

Similarity

• 213 Proportion
• 214 Properties of Similar Polygons
• 215 Angle-Angle Similarity Postulate
• 216 Similarity Word Problems
• 217 SSS and SAS Similarity Theorems
• 218 Triangle Proportionality and Triangle Angle-Bisector Theorems

Right triangles

• 219 Pythagorean Theorem
• 220 Pythagorean Theorem Word Problems
• 221 Converse of the Pythagorean Theorem
• 222 30-60-90 and 45-45-90 Degree Triangles
• 223 Sine, Cosine, and Tangent
• 224 Sine, Cosine, and Tangent with a Calculator
• 225 Trigonometry Word Problems

Circles

• 226 Circle Vocabulary
• 227 Tangents
• 228 Arcs and Central Angles
• 229 Arcs and Chords
• 230 Inscribed Angles
• 231 Angles Formed by Chords, Secants, and Tangents
• 232 Circle Segment Lengths

Measurement and area

• 233 Customary Unit Conversions
• 234 Metric Unit Conversions
• 235 Units of Measurement
• 236 Area of Rectangles and Squares
• 237 Advanced Area of Rectangles and Squares
• 238 Area of Parallelograms
• 239 Area of Triangles
• 240 Area of Rhombuses
• 241 Area of Trapezoids
• 242 Area of Regular Polygons
• 243 Area and Circumference of Circles
• 244 Changing Dimensions

Volume and surface area

• 245 Classifying 3-Dimensional Figures
• 246 Nets
• 247 Area and Volume of Prisms
• 248 Advanced Area and Volume of Prisms
• 249 Area and Volume of Pyramids
• 250 Advanced Area and Volume of Pyramids
• 251 Area and Volume of Cylinders and Cones
• 252 Area and Volume of Spheres

Data and statistics

• 253 Bar Graphs
• 254 Line Graphs
• 255 Circle Graphs
• 256 Stem-and-Leaf Plots and Frequency Charts
• 257 Histograms
• 258 Scatterplots and Trends
• 259 Misleading Graphs
• 260 Range, Median, and Mode
• 261 Box-and-Whisker Plots
• 262 Mean
• 263 Central Tendency Word Problems
• 264 Simple Probability
• 265 Experimental Probability
• 266 Probability of Independent Events
• 267 Probability of Dependent Events
• 268 Tree Diagrams and the Counting Principle
• 269 Permutations
• 270 Combinations

Coordinate geometry

• 271 Distance Formula
• 272 Midpoint Formula
• 273 Equation of a Circle

Negative & rational exponents

• 274 Negative Exponents
• 275 Numerical Bases with Negative Exponents
• 276 Multiplying and Dividing with Negative Exponents
• 277 Multiplying and Dividing with Scientific Notation
• 278 Rational Exponents
• 279 Numerical Bases with Rational Exponents
• 280 Writing Radicals in Exponential Form
• 281 Solving Equations with Rational Exponents
• 282 Radical Exponents

Composite functions & inverses

• 283 Composite Functions: f(g(x)) and g(f(x))
• 284 Inverse Relations
• 285 Inverse Functions

Logarithms & exponential functions

• 286 Evaluating Logarithms and Logarithmic vs. Exponential Form
• 287 Solving Logarithmic Equations
• 288 Logarithm Rules and Properties
• 289 Evaluating Logarithms by Condensing or Expanding
• 290 Solving Advanced Logarithmic Equations
• 291 Logarithm Calculator Problems
• 292 Exponential Equations and Change of Base Formula
• 293 Exponential Growth and Decay
• 294 Half Life and Doubling Time Formulas
• 295 Natural Logarithms
• 296 Solving Natural Logarithm Equations with ln and e

Additional concepts

• 297 Systems of Inequalities
• 298 Polynomial Inequalities
• 299 Adding and Subtracting Polynomials
• 300 Polynomial Long Division