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Gruber's Complete ACT Guide 2010

THE MOST TRUSTED AND EFFECTIVE ADVICE IN TEST PREP

“Dr. Gary Gruber has developed a method that will raise students’ test scores by sharpening their thinking skills.”—Boston Globe

“By learning Dr. Gruber’s strategies, a student can increase his orher IQ to do well on any exam.”—Teen Magazine

“His methods make the questions seem amazingly simple to solve.”—Library Journal

“With the aid of your books, my scores improved so dramatically that I am now anticipating acceptance into schools that I was reluctant to even apply to.”—Lauren F., New Jersey

NO GIMMICKS, NO TRICKS, JUST EASY STRATEGIES THAT WILL ACTUALLY RAISE YOUR SCORE.
—Includes 3 full-length practice tests
—Inside info on how ACT questions are created
—Strategies that will save you study time by pointing you directly to the answer

“GRUBER CAN RING THE BELL ON ANY NUMBER OF STANDARDIZED EXAMS.”
—Eric Zorn, Chicago Tribune

GET THE SKILLS THAT UNLOCK THE ANSWERS
With the explanation to a question, you can answer that one question. With the Gruber strategies, you can answer thousands of questions! These strategies show you how to think about problems instead of trying to solve each one individually, and they can be used consistently on every ACT test.

USE THE MOST TRUSTED METHODS
More schools use Dr. Gruber’s books for test-prep courses than any other test-prep books.
PBS chose Dr. Gruber to train teachers nationally to improve the nation’s test scores.
National learning centers, state agencies, and state education departments have contracted with Dr. Gruber to improve test scores and critical thinking ability.

EVERYTHING YOU NEED TO STUDY TO GET THE TOP SCORE
Exclusive 4-Hour Cram Plan
ACT-Specific Math and Grammar Review
Advice on Tackling the Optional Writing Section
Essential Strategies for English, Math, Reading, and Science
And Everything Else You Need

* ACT® is a registered trademark of ACT, Inc. ACT, Inc., is not associated with and does not endorse this book.

Table of Contents

Table of Contents

Important Note about This Book and Its Author
The Author Has Something Important to Tell You about How to Raise Your ACT Score
PART 1
INTRODUCTION
I. Important Facts about the ACT
II. What Are Critical Thinking Skills?
III. A 4-Hour Study Program for the ACT
IV. Longer-Range Study Program and Helpful Steps for Using This Book

PART 2
The Shortest ACT Test—20 Questions to Approximate Your ACT Score
English Test
Mathematics Test
Reading Test
Science Test
Answers
Explanatory Answers

PART 3
THE 101 MOST IMPORTANT MATH QUESTIONS YOU NEED TO KNOW HOW TO SOLVE           
101 Math Questions Test
101 Math Questions: Answers, Diagnosis, Solutions, Generalizations, Rules
101 Math Questions: Answers
Basic Skills Math Diagnosis
Solutions, Generalizations, Rules

PART 4
Strategy SECTION
5 General Strategies
28 Easy-to-Learn Strategies
19 Math Strategies
Reading Strategies
Summary
9 Reading Comprehension Strategies
Hot Prefixes and Roots

PART 5
THE ACT SCIENCE TEST—INTRODUCTION, EXAMPLES, AND STRATEGIES

PART 6
MINI-MATH REFRESHER
Algebra and Arithmetic  
Geometry

PART 7
COMPLETE ACT MATH REFRESHER
Session 1: Fractions, Decimals, Percentages, etc.
Fractions, Decimals, Percentages
Deviations
Ratios and Proportions
Variations
Comparison of Fractions
Practice Test 1
Answer Key for Practice Test 1
Answers and Solutions for Practice Test 1
Session 2: Rate Problems
Word Problem Setup
Distance and Time
Work
Mixture
Cost
Practice Test 2
Answer Key for Practice Test 2
Answers and Solutions for Practice Test 2
Session 3: Area, Perimeter, and Volume Problems
Area, Perimeter, and Volume
Practice Test 3
Answer Key for Practice Test 3
Answers and Solutions for Practice Test 3
Session 4: Algebra Problems
Algebraic Properties
Algebraic Expressions
Equations
Algebra of Graphs
Inequalities
Exponents and Roots
Practice Test 4
Answer Key for Practice Test 4
Answers and Solutions for Practice Test 4
Session 5: Geometry Problems
Basic Definitions
Triangles
Properties of Triangles
Four-Sided Figures
Many-Sided Figures
Circles
Formulas
Practice Test 5
Answer Key for Practice Test 5
Answers and Solutions for Practice Test 5
Session 6: Miscellaneous Problems
Averages, Medians, and Modes
Series
Properties of Integers
Approximations
Combinations
Probability
The Absolute Value Sign
Functions
Logarithms
Imaginary Numbers
Practice Test 6
Answer Key for Practice Test 6
Answers and Solutions for Practice Test 6
Session 7: Tables, Charts, and Graphs
Charts and Graphs
Tables and Charts
Graphs
Bar Graphs
Circle Graphs
Line Graphs
Practice Test 7 and Solutions
Session 8: Modern Math
Sets
Relations
Solution Sets
Axioms
Closed Sets
Mathematical Symbols
Practice Test 8 and Solutions
Session 9: Trigonometry
Diagnostic Test on Trigonometry
Answers to Diagnostic Test
Instructional Material on Trigonometry—17 Trig Identities to Know
Practice Test 9 and Solutions

PART 8
A BRIEF REVIEW OF ENGLISH GRAMMAR

PART 9
ACT GRAMMAR AND USAGE REFRESHER
Sentence Sense
The Parts of Speech
Phrases
Clauses
Sentence Logic
Sentence Coherence
Word Effectiveness

PART 10
THE ACT Writing Test
The ACT Writing Section
The Essay on the ACT Writing Test
6-Point Holistic Scoring Rubric for the ACT Writing Test
Important Tips on How to Write the Best Essay

PART 11
3 ACT PRACTICE TESTS
5 Important Reasons for Taking These Practice Tests
9 Tips for Taking the Practice Tests

ACT Practice Test 1
Answer Sheet for Practice Test 1
How Did You Do on This Test?
Answer Keys for Practice Test 1
Table for Converting Raw Scores to Scaled Scores
Norms Tables
6-Point Holistic Scoring Rubric for the ACT Writing Test
Calculating Your Combined English/Writing Score
Explanatory Answers for Practice Test 1
What You Must Do Now to Raise Your ACT Score

ACT Practice Test 2
Answer Sheet for Practice Test 2
How Did You Do on This Test?
Answer Keys for Practice Test 2
Table for Converting Raw Scores to Scaled Scores
Norms Tables
6-Point Holistic Scoring Rubric for the ACT Writing Test
Calculating Your Combined English/Writing Score
Explanatory Answers for Practice Test 2
What You Must Do Now to Raise Your ACT Score

ACT Practice Test 3
Answer Sheet for Practice Test 3
How Did You Do on This Test?
Answer Keys for Practice Test 3
Table for Converting Raw Scores to Scaled Scores
Norms Tables
6-Point Holistic Scoring Rubric for the ACT Writing Test
Calculating Your Combined English/Writing Score
Explanatory Answers for Practice Test 3
What You Must Do Now to Raise Your ACT Score

Excerpt

Excerpt

Excerpt from Part One

What Is on the ACT?
The ACT is divided into four parts with an optional Written Essay as a fifth part:

1. The ACT English Test
75 questions–45 minutes that tests standard written English—punctuation, grammar and usage, and sentence structure—and tests rhetorical skills (strategy, organization, and style). Spelling, vocabulary, and rote memory of rules of grammar are not tested. The test consists of five essays, or passages, each accompanied by a sequence of multiple-choice questions. Three scores are reported: a total test score of 75 questions, a sub-score in Usage/Mechanics based on all 40 questions, and a sub-score in Rhetorical Skills based on 35 questions. If you spend 1½ minutes skimming through each passage, you will have about 30 seconds to answer each question.

2. The ACT Math Test
60 questions–60 minutes that tests mathematical skills taken in courses up to grade 12. Four scores are reported: a total test score based on 60 questions, a sub-score in Pre-Algebra/Elementary Algebra based on 24 questions, a sub-score in Intermediate Algebra/Coordinate Geometry based on 18 questions, and a sub-score in Plane Geometry/Trigonometry based on 18 questions.

3. The ACT Reading Test 40 questions–35 minutes that tests your reading comprehension skills. Four passages with 10 questions each. One passage in prose Fiction, one in Humanities, one in Social Studies, and one in Natural Science. All information will be found in each passage. For example, you don’t need any outside knowledge or course knowledge in Natural Science to answer the questions in that area. There will be a sub-score based on 20 questions in the Social Studies/Natural Science passages and a sub-score based on 20 questions in the prose Fiction/Humanities passages. If you spend 2–3 minutes reading through each passage, you will have about 35 seconds to answer each question.

4. The ACT Science Test
40 questions–35 minutes that measures the interpretation, analysis, evaluation, reasoning, and problem-solving skills required in the natural sciences. The tests includes seven sets of scientific data and information each followed by a set of mutliple-choice questions. Although all data and information is based on the natural sciences, you will not need any knowledge of the particular subject or course area to answer the questions. Note that you are not permitted to use a calculator on the Science Test. If you spend about 2 minutes reading each passage, then you will have about 30 seconds to answer each question. You may want to spend less time in first reading the passage or looking at the data and refer back to the information when looking at the questions.
5. ACT Writing T est (Optional) 30 minutes. This is the last part of the ACT Test and will not affect your other scores or your composite score. Rather, you will receive two additional scores; a combined English/Writing score on a scale of 1 through 36 and a Writing sub-score on a scale of 2 through 12. The image of your essay will be given to your high school and the colleges to which the ACT Test scores are reported. The test consists of one writing prompt that will define an issue and describe two points of view based on that issue. You are asked to write a response to a question about your position on the issue described in the writing prompt. You may also present a different point of view on the issue.

How Will the Test Be Scored?

Each Test (English, Math, Reading and Science) will have a scaled score from 1–36. A composite score will be the total scaled score from all 4 tests, divided by 4. There will also be subscores as described before.

How Long Will the Test Be?

The total time of the 4 multiple-choice tests will be 2 hours and 55 minutes. There will be a 10-minute break between tests 2 and 3. If you are taking the Writing test, you will have a 5-minute break after test 4.

What Verbal/Grammar Background Must I Have?
The reading and vocabulary level is at the 10th to 12th grade level, but strategies presented in this book will help you even if you are at a lower grade level.

What Math Background Must I Have?

The math part will test first and second year algebra (Algebra I and II), geometry, and trigonometry. However, if you use common sense, rely on just a handful of geometrical formulas, and learn the strategies and thinking skills presented in this book, you don’t need to take a full course in geometry or memorize all the theorems. Many of the strategies in this book will help you quickly solve the problems on the test.

What Science Background Must I Have?
You don’t really need to have any science background such as knowledge of biology, chemistry, or physics. You merely need to think about how to interpret and analyze data and material presented in these areas.

Is Guessing Advisable?

There is no penalty for wrong answers, so you should always guess if you can’t answer he question.

Can I Use a Calculator on the Math Portion of the Test?

Students can continue to use a 4-function, scientific, or graphing calculator. Note, though, that it is possible to solve every question without the use of a calculator. Calculators not permitted include: Texas Instruments TI-89 or TI-92, TI-NspireCAS; Hewlett Packard HP 48GII and all model numbers that begin with HP 40G, HP 49G, or HP 50G; Casio Algebra fx 2.0, ClssPad 300, and all model numbers that begin with CFX-9970G; handheld tablet or laptop computers including PDA’s; electronic writing pads or pen-input devices. Note: The Sharp EL 9600 is permitted.

Should I Take an Administered Actual ACT for Practice?

Yes, but only if you will learn from your mistakes by seeing what strategies you should have used on your exam. Taking the ACT merely for its own sake is a waste of time and may in fact reinforce bad methods and habits. To find out the dates of an administered ACT that lets you later retrieve the test, a copy of your answers and scoring instructions, check www.actstudent.org.

Should I Use Scrap Paper to Write on and to Do Calculations?

Always use your test booklet (not your answer sheet) to draw or write on. Many of my strategies expect you to label diagrams, draw and extend lines, circle important words and sentences, etc., so feel free to write anything in your booklet. The booklets aren’t graded; only the answer sheets are. See General Strategy 4, page 53.

Should I Be Familiar with the Directions to the Various Items on the ACT before Taking the ACT?

Make sure that you are completely familiar with the directions to each of the item types (English, Reading, Math, Science, and Writing). See General Strategy 2, page 52.

The Test Is Given in One Booklet. Can a Student Skip between Sections?

No, you cannot skip between the sections. You have to work on one section until the time is called. If you get caught skipping sections or going back to an earlier section, then you risk being asked to leave the exam.

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