Introduction 1

About This Book 1

Foolish Assumptions 2

Icons Used in This Book 2

Beyond the Book .2

Where to Go from Here .3

**Part 1: Getting Started With the Praxis Core 5**

**Chapter 1: Previewing the Praxis** **7**

Why Take the Praxis? .7

Breaking Down the Praxis .8

Knowing what topics are covered .8

Seeing what types of questions you’ll face .9

Understanding How the Test Is Scored 10

**Chapter 2: Getting Ready for Test Day** **13**

Registering for the Test 13

Using Your Time Wisely 14

Budgeting your study time leading up to test day 14

Budgeting your time while taking the test 15

When Test Day Has Arrived 16

Knowing what to bring and what to leave at home 17

Getting familiar with computer testing 17

If You Are Retaking the Test 18

**Chapter 3: Practicing the Praxis: Sampling Some Practice Questions** **19**

Going through the Pre-Assessment Questions 19

Looking at the Pre-Assessment Answers 28

Reading answers and explanations 28

Writing answers and explanations 31

Math answers and explanations 33

Assessing Your Results 35

Identifying categories where you struggled 36

Understanding where you went wrong specifically 36

**Part 2: Mastering Math Concepts 39**

**Chapter 4: Count on It: Number and Quantity** **41**

Working with Integers: Whole Numbers and Their Opposites 41

Doing basic operations with integers 42

Finding factors of whole numbers 43

Employing some helpful divisibility rules 44

Finding multiples of integers 45

Determining the greatest common factor and least common multiple 45

Exponents and square roots 46

Computing with Fractions and Mixed Numbers 47

Simplifying fractions 47

Converting between fractions and mixed numbers 48

Performing basic operations with fractions and mixed numbers 49

Working with Decimals and Percents 52

Converting between decimals and percents 52

Performing basic operations with decimals 53

Understanding the Number Line 54

Interpreting numeration and place values 54

Knowing the basics of order 55

Finding orders of magnitude 55

Finding numbers in sequences 56

Following Orders: The Order of Operations 56

Remembering “GEMDAS” 57

Using the order of operations within itself 57

Reasoning with Quantities 58

Using the two major systems of measurement 58

Converting units of measurement 59

Basic word problems 60

Practice Questions about Number and Quantity 61

Answers and Explanations 62

**Chapter 5: Introducing Letters: Algebra** **63**

Variables: When Letters Represent Numbers 63

Laying out the terms: Variable terms and expressions 64

Let’s get together: Combining like terms 64

Multiplying and dividing with terms and expressions 65

When variable values are given 67

Working with Equations 68

Solving for x and other variables 68

Undoing addition and subtraction 69

Undoing multiplication and division 70

Multistep equations 70

Proportions 71

Systems of equations 72

Solving for variables in terms of other variables 74

Solving Inequalities 74

Following two more rules when solving inequalities 75

Graphing inequalities 76

Describing solution steps 76

Factoring in Algebra 77

Factoring terms out of bigger terms 77

Using reverse FOIL 78

Decoding Algebra Word Problems 79

Translating English into mathematical language 79

Algebraic word problems 80

Thinking Outside the Algebra Box 81

Recognizing relational patterns 81

Algebraic reasoning 81

Practice Questions about Algebra 83

Answers and Explanations 84

**Chapter 6: Grasping Geometry Concepts 87**

Understanding the Building Blocks of Geometry 87

Getting to the point 88

Defining lines and parts of lines 88

Moving along planes in space 88

Getting the right angles on angles 89

Recognizing congruence 90

Understanding Angle Measures and Relationships 90

Distinguishing degrees of angle measure and naming angles 90

Working with angle relationships 91

Knowing Common Shapes and Their Basic Properties 93

Defining polygons in general 93

Analyzing triangles: Three-sided polygons 93

Identifying facts about quadrilaterals 95

Working with other types of polygons 96

Knowing the basic facts about circles 96

Working with Shapes that Are Alike 97

Forming conclusions about congruent shapes 97

Working with similar shapes 98

Figuring out Geometric Formulas 99

Finding the perimeter 99

Circling the circumference 100

Getting into the area 101

Finding the right volume 102

Combining Shapes 103

Coming together: Shapes that have joined without an invasion 103

Preparing for invasion: When one shape invades another 104

Knowing the Ways of the XY Coordinate Plane 105

Naming coordinate pairs 105

Identifying linear equations and their graphs 106

Using the distance and midpoint formulas 107

Finding meaning in intersecting graphs 107

Transforming coordinate plane figures 108

Touching on Right Triangles 110

Knowing what Pythagoras discovered 111

Working with special right triangles 111

Practice Questions about Geometry 113

Answers and Explanations 114

**Chapter 7: Pinning Down Data Interpretation and Representation, Statistics, and Probability** 115

Representing Data 115

Tables 116

Bar graphs and line graphs 117

Pie charts 118

Stem-and-leaf plots 119

Box-and-whisker plots 121

Venn diagrams 123

Scrambling around scatter plots 124

Loitering around line plots 124

Analyzing Data 125

Combing through comparisons 125

Homing in on the range 125

Measuring arithmetic mean, median, or mode 126

Variably affecting data 127

Measuring the spread of data 128

Scrutinizing samples for data analysis 129

Interpreting linear models 129

Calculating Probability 130

Determining the likelihood of an event 130

Using complements 130

Pointing Out Scientific Notation Facts 131

Practice Questions about Probability and Statistics 132

Answers and Explanations 134

**Chapter 8: Test-Taking Strategies for Core Math** **135**

Using Helpful Shortcuts 135

Solving equations versus determining what must be solved 136

Using estimation and approximation 137

Using the calculator 137

Identifying calculations you can make in your head 137

The art of guessing as a last resort 138

Working backward 139

Narrowing Down Answer Choices 139

How to eliminate obviously wrong answer choices 139

Avoiding the most common wrong answers 141

Tackling the Constructed Response 142

Tips for preparing responses and answering questions 142

Some proper ways of representing answers 143

Understanding the importance of avoiding careless errors 143

**Part 3: Refining Your Reading Comprehension Skills 145**

**Chapter 9: Reading Comprehension: Finding Meaning and Identifying Purpose** **147**

Previewing the Praxis Reading Test 147

Knowing what the test contains 148

Applying a general strategy 148

Mastering Short-Passage Questions 149

Ferreting out the main idea 149

Discerning the author’s tone and intent 151

Putting vocabulary in context 152

Looking at Long-Passage Questions 153

Purpose and paraphrase 153

Arguments and support 154

Getting the hang of “If” questions 154

Sample questions for long passages 156

Visual- and Quantitative-Information Questions 158

Rethinking charts and graphs 159

Getting graphs 159

Practice Reading-Comprehension Questions 162

Answers and Explanations 165

**Chapter 10: Test-Taking Strategies for Core Reading** **169**

Figuring Out Which to Read First: The Passage or the Question 169

Examining Strategies for the Various Passages 171

Approaching long and short passages 171

Approaching the paired passages 172

Approaching Questions about Charts and Graphs 173

Eliminating Wrong Answers 174

Tips for Slow Readers 174

**Part 4: Fine-Tuning Your Writing Skills** **177**

**Chapter 11: Acing the Essay** **179**

Perusing the Types of Prompts: “Picking a Side” versus “Exploring an Idea” 179

Writing persuasively 180

Sticking to the facts 180

Creating a Solid Essay 180

Making an outline: Essential or overrated? 181

Looking at the sections of your essay 181

Don’t box yourself in: Theses aren’t set in stone 182

Citing the sources 182

Checking out some additional writing pointers 182

Turning a Good Essay into a Great One 183

Adding interesting anecdotes 183

Painting a picture with words 183

Anticipating objections against your position 184

Understanding How the Essay Is Scored 184

Checking Out Some Practice Prompts 185

Prompts for argumentative essays 185

Prompts for informative/explanatory essays 185

Reviewing a Sample Essay 187

Evaluating Your Essay 188

**Chapter 12: Giving Grammar a Glance 191**

Getting a Grip on the Parts of Speech 191

Finding nouns as subjects and objects 192

Putting verbs to work 192

Using adjectives to describe people, places, and things 195

Calling on adverbs to describe actions and conditions 196

Getting the lowdown on pronouns 197

Considering conjunctions 201

Perusing prepositions 201

Making Sense of Sentence Structure 203

Independent clauses versus everything else 203

The sentence skeleton: Identifying the main subject and verb 204

Run-ons and comma splices 205

Pondering Punctuation 206

Commas 206

Semicolons 208

Apostrophes 209

Misplaced Modifiers 209

Redundancy and Double Negatives 210

Homophones: “They’re in there with their bear” 211

Which one has the apostrophe? 211

Spelled and used differently, but sound the same 212

Capitalization: What You Need to Know 213

Practice Questions about Grammar 214

Answers and Explanations 217

**Chapter 13: Test-Taking Strategies for Core Writing** **221**

Knowing the Types of Selected-Response Writing Questions 221

Type 1: Answering usage questions 222

Type 2: Showing your research skills 223

Type 3: Making sentence corrections 224

Type 4: Regarding revision-in-context questions 225

Identifying and Correcting Errors in Selected-Response Items 226

Eliminating the obviously wrong choices 226

Don’t be afraid to say it’s right the way it is 226

The art of guessing as a last resort 227

A word of advice about “trusting your ear” 227

Mastering the Essay 227

Outlining your thoughts and managing your time 228

Arm yourself with versatile examples 228

Practicing ahead of time 229

**Part 5: Tackling Praxis Core Practice Tests 231**

**Chapter 14: Practice Exam 1** **233**

Answer Sheet for Practice Exam 1 235

Part 1: Reading 237

Part 2: Writing 253

Argumentative Essay 260

Source-Based Essay 261

Part 3: Mathematics 263

**Chapter 15: Practice Exam 1: Answers and Explanations** **273**

Part 1: Reading 273

Part 2: Writing 289

Argumentative Essay 299

Source-Based Essay 301

Part 3: Mathematics 302

Answer Key 322

**Chapter 16: Practice Exam 2** **325**

Answer Sheet for Practice Exam 2 327

Part 1: Reading 329

Part 2: Writing 343

Argumentative Essay 350

Source-Based Essay 351

Part 3: Mathematics 352

**Chapter 17: Practice Exam 2: Answers and Explanations** **363**

Part 1: Reading 363

Part 2: Writing 380

Argumentative Essay 390

Source-Based Essay 391

Part 3: Mathematics 392

Answer Key 405

**Part 6: The Part of Tens** **407**

**Chapter 18: Ten Common Math Errors to Avoid** **409**

Misusing Negative Signs 409

Confusing Perimeter and Area 410

Incorrectly Combining Like Terms 410

Messing Up When Moving Decimals 410

Not Solving for the Actual Variable 410

Misrepresenting “Less Than” in Word Problems 411

Mixing Up Supplementary and Complementary Angles 411

Finding the Wrong Median 411

Fearing Fractions 411

Forgetting about Fractions in Formulas 412

**Chapter 19: Ten Mistakes to Avoid on the Praxis Reading and Writing Exams** **413**

Avoiding Mistakes Common to the Writing and Reading Tests 413

Don’t look for patterns in the answers 413

Don’t change answers merely for the sake of changing them 414

Sidestepping Mistakes on the Writing Test 415

Don’t equate different with wrong 415

Don’t assume something must be correct just because it sounds fancier or more complex 415

Don’t turn the essay into a thesaurus explosion 416

Don’t paint yourself into a corner with a rigid thesis 416

Evading Mistakes on the Reading Test 416

Don’t rule out the “too obvious” 417

Don’t word-match 417

Don’t ignore your outside knowledge 417

Don’t try to answer more than the question asks you to 418

Index 419