Preview Big Book of ACT Practice Tests 2017 (ACT course book) by Kaplan (2017)

Preview Big Book of ACT Practice Tests 2017 (ACT course book) by Kaplan (2017) Preview Big Book of ACT Practice Tests 2017 (ACT course book) by Kaplan (2017) Preview Big Book of ACT Practice Tests 2017 (ACT course book) by Kaplan (2017) Preview Big Book of ACT Practice Tests 2017 (ACT course book) by Kaplan (2017) Preview Big Book of ACT Practice Tests 2017 (ACT course book) by Kaplan (2017)

Official Partner for Live, Online Prep for Big Book of ® ACT Practice Tests 2017 Official Partner for Live, Online Prep for , for more information visit kaptest.com/onlinepreplive Big Book of ACT Practice Tests ® 2017 BRING THIS BOOK TO EVERY CLASS ACT® is a registered trademark of ACT, Inc., which neither sponsors nor endorses this product Let’s Get Started Thanks for choosing Kaplan for your ACT* Preparation Get ready to experience Kaplan ACT and score higher—guaranteed or your money back † Everything you need to score higher on the ACT You’ll review critical test concepts and learn methods to improve your test performance and optimize your study time ® Realistic Practice & In-depth Analysis Official Partner for Live, Online Prep for , for more information visit kaptest.com/onlinepreplive ACT Course Book Big Book of ACT Practice Tests Course Book Official Partner for Live, Online Prep for , for more information visit kaptest.com/onlinepreplive INTEGRATED WITH YOUR COURSE ® Test your skills with the most realistic practice and use insightful analytics and guidance to target your prep to gain the most points in the least amount of time ACT Practice Tests 2017 STEP Score-raising Strategies & Tactics Official Partner for Live, Online Prep for Big Book of Check the contents of your ACT Kit ACT Course Book ACT Course Book is a dynamic prep program that combines review, strategies, practice, and analysis to provide the most efficient path to a higher score You should have the following: Official Partner for Live, Online Prep for ® Big Book of ACT Practice Tests ® 2017 Want more on the ACT and other college entrance exams? Join the conversation online: kaptest.com/college facebook.com/KaplanACT BRING THIS BOOK TO EVERY CLASS twitter.com/KaplanSATACT Facebook ® is a registered trademark of Facebook, Inc Twitter® is a registered trademark of Twitter, Inc ACT® is a registered trademark of ACT, Inc., which neither sponsors nor endorses this product ACT® is a registered trademark of ACT, Inc., which neither sponsors nor endorses this product ACT® is a registered trademark of ACT, Inc., which neither sponsors nor endorses this product STEP Take your Diagnostic Test The Diagnostic Test establishes a baseline of your performance and fuels your custom study plan in your online resources • Classroom students: You will take your Diagnostic Test with your class, so bring your Big Book of Practice Tests to your first session • Tutoring students: Take your Diagnostic Test on your own before your first tutoring session Log into your online resources STEP Go to kaptest.com/myhome and log into your online center After you log in, you can: • Open the Getting Started tab and watch the ACT Course Orientation video • View your Diagnostic Test results Ready to score higher? 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Call 1-800-KAP-TEST or email us at customer.care@kaplan.com 10/13/16 7:03 AM 01_PSAT2014_CS_1.indd 40 4/3/14 1:59 PM ACT Course Book 2017 ACT_CB_FM.indd 10/10/16 8:09 pm Copyright ©2016 Kaplan, Inc All rights reserved No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without the written permission of the Publisher, except where permitted by law 10 ISBN-13: 978-1-5062-0719-3 ACT_CB_FM.indd 10/10/16 8:09 pm Table of Contents Introduction to the ACT�������������������������������������������������������������������������������������������������������������������������vi Keys to ACT Success�����������������������������������������������������������������������������������������������������������������������������xiii Course Overview���������������������������������������������������������������������������������������������������������������������������������xvii Welcome to Kaplan!������������������������������������������������������������������������������������������������������������������������ xvii Course Structure����������������������������������������������������������������������������������������������������������������������������� xvii ACT Course Materials������������������������������������������������������������������������������������������������������������������������xx Digital Resources�������������������������������������������������������������������������������������������������������������������������������xx How to Achieve Your Best Score����������������������������������������������������������������������������������������������������� xxi UNIT ONE: ENGLISH INTRODUCTION CHAPTER 1:  ACT English����������������������������������������������������������������������������������������������������������� UNIT TWO: CONVENTIONS OF STANDARD ENGLISH CHAPTER 2: The Kaplan Method for ACT English & Sentence Structure and Formation����������������������������������������������������������������������������������������������������� 13 CHAPTER 3:  Punctuation��������������������������������������������������������������������������������������������������������� 39 CHAPTER 4:  Usage������������������������������������������������������������������������������������������������������������������� 57 UNIT THREE: P  RODUCTION OF WRITING & KNOWLEDGE OF LANGUAGE CHAPTER 5:  Organization, Unity, and Cohesion�������������������������������������������������������������������� 83 CHAPTER 6:  Topic Development������������������������������������������������������������������������������������������� 101 CHAPTER 7:  Knowledge of Language����������������������������������������������������������������������������������� 123 ACT_CB_FM.indd 10/13/16 7:15 AM iv TABLE OF CONTENTS UNIT FOUR: MATH INTRODUCTION CHAPTER 8:  ACT Math����������������������������������������������������������������������������������������������������������� 145 UNIT FIVE: INTEGRATING ESSENTIAL SKILLS CHAPTER 9:  Essential Skills��������������������������������������������������������������������������������������������������� 157 UNIT SIX: HIGHER MATH CHAPTER 10:  Number and Quantity������������������������������������������������������������������������������������� 207 CHAPTER 11:  Algebra������������������������������������������������������������������������������������������������������������ 241 CHAPTER 12:  Functions��������������������������������������������������������������������������������������������������������� 283 CHAPTER 13:  Geometry�������������������������������������������������������������������������������������������������������� 329 CHAPTER 14:  Statistics and Probability������������������������������������������������������������������������������� 391 UNIT SEVEN: READING INTRODUCTION CHAPTER 15:  ACT Reading���������������������������������������������������������������������������������������������������� 431 UNIT EIGHT: ACT READING CHAPTER 16: The Kaplan Method for ACT Reading & Global and Inference Questions��������������������������������������������������������������������������������� 441 CHAPTER 17:  Detail and Vocab-in-Context Questions��������������������������������������������������������� 461 CHAPTER 18:  Function and Writer’s View Questions������������������������������������������������������������ 479 CHAPTER 19:  Paired Passages����������������������������������������������������������������������������������������������� 497 UNIT NINE: SCIENCE INTRODUCTION CHAPTER 20:  ACT Science����������������������������������������������������������������������������������������������������� 517 ACT_CB_FM.indd 10/14/16 10:32 AM TABLE OF CONTENTS v UNIT TEN: SCIENCE CHAPTER 21:  Data Representation��������������������������������������������������������������������������������������� 529 CHAPTER 22:  Research Summaries��������������������������������������������������������������������������������������� 563 CHAPTER 23:  Conflicting Viewpoints����������������������������������������������������������������������������������� 593 UNIT ELEVEN: ACT WRITING CHAPTER 24:  ACT Writing Introduction�������������������������������������������������������������������������������� 623 CHAPTER 25:  ACT Writing in Depth�������������������������������������������������������������������������������������� 631 UNIT TWELVE: REVIEW CHAPTER 26:  Putting It All Together������������������������������������������������������������������������������������ 653 ANSWERS & EXPLANATIONS 669 ACT_CB_FM.indd 10/20/16 2:27 PM Introduction to the ACT INTRODUCTION TO THE ACT The first step to achieving ACT success is to learn about the structure of the test and why it’s so important for your future The ACT, like any standardized test, is predictable The more comfortable you are with the test structure, the more confidently you will approach each question type, thus maximizing your score ACT STRUCTURE The ACT is hours and 55 minutes long, or hours and 35 minutes long if you choose to complete the optional Writing test It consists of a total of 215 scored multiple-choice questions and one optional essay Test Allotted Time (min.) Question Count English 45 75 Math 60 60 Reading 35 40 Science 35 40 Writing (optional) 40  1 Total 175 or 215 (w/Writing) 215 or 216 (w/Writing) ACT SCORING The ACT is scored differently from most tests that you take at school Your ACT score on a test section is not reported as the total number of questions you answered correctly, nor does it directly represent the percentage of questions you answered correctly Instead, the test makers add up all of your correct answers in a section to get what’s called your raw score They then use a conversion chart, or scale, that matches up a particular raw score with what’s called a scaled score The scaled score is the number that gets reported as your score for that ACT subject test For each version of the ACT administered, the test makers use a unique conversion chart that equates a particular raw score with a particular scaled score ACT scaled scores range from to 36 Nearly half of all test takers score within a much narrower range: 17–23 Tests and scores on different dates vary slightly, but the information below is based on a recent administration of the test and can be considered typical vi ACT_CB_FM.indd ACT Approximate Percentile Rank Scaled (or Composite) Score Percentage of Questions Correct 99% 33 90% 90% 28 75% 74% 24 63% 56% 21 53% 30% 17 43% I ntroduction to the ACT 10/10/16 8:09 pm I ntroduction to the  ACT Notice that to earn a score of 21 (the national average), you need to answer only about 53% of the questions correctly On most tests, getting just a bit more than half the questions right would not be a passing grade, let alone an average score Not so on the ACT A score of 21 puts you in the middle range of test takers Expert Tip Just a few questions right or wrong on the ACT can make a big difference Answering only five extra questions correctly on each subject test can move you from the bottom of the applicant pool into the middle or from the middle up to the top The score table includes two very strong scores: 28 and 33 Either score would impress almost any college admissions officer A 28 would put you in the top 10% of the students who take the exam, and a 33 would put you in the top 1% Even a 33 requires getting only about 90% of the questions right! So the best-scoring students will probably get at least a dozen questions wrong but will still get the scores they need to get into a highly competitive college If you earn a score of 24, you’ll be in about the 74th percentile That means that you did as well as or better than 74% of the test takers—in other words, you’re in the top quarter of people who took the ACT That’s a strong score, but notice that to earn this score, you need to get only about 63% of the questions correct On most tests, a score of 63% is probably a D or lower But on the ACT, it’s about a B+ HOW MANY ACT SCORES WILL YOU GET? The ACT scaled score we’ve talked about so far is technically called the Composite score—when people say “I got _ on the ACT,” this is what they’re talking about While the Composite score is really important, you’ll see a dozen or more scores and reporting categories when you get your ACT results: the Composite score, (or 5) subject scores, 18 reporting categories, and domain scores Though the subject scores can play a role in decisions or course placement at some schools, the reporting categories and domain scores usually aren’t as important as the Composite.  ACT_CB_FM.indd I ntroduction to the ACT vii 10/13/16 7:16 AM English Production Extra Practice Of Writing & Knowledge Of Language Thomas Paine is also credited with conceiving the name 10 “The United States of America.” Because Thomas Paine was 10 F NO CHANGE G tasked H helped J noted a writer, Thomas Jefferson and John Adams drew 11 heavily on his work when drafting the Declaration of 11 Which choice maintains the essay’s positive tone regarding Paine and best describes why Jefferson and Adams used his work? Independence Later in life, Paine wrote other, A an extremely talented writer, B the best writer in the colonies, C an adequate author, D an author of controversial content, highly controversial works 12 In 1797, Paine did his part to inspire what would become Social Security He 12 The writer is considering adding the following sentence: suggested a system of social insurance for the young and  He was even exiled from England and imprisoned in France for his writings the elderly in his last great work, Agrarian Justice Should the writer make this addition here? F Yes, because the passage focuses on Paine’s international relations G Yes, because it adds an interesting detail that contributes to the purpose of the paragraph H No, because it detracts from the emphasis on controversy J No, because it does not describe Paine’s writings Given Thomas Paine’s contributions to America, he deserves recognition as one of our more important 13 Founding Fathers 13 A NO CHANGE B very most important C mostly important D most important 140 Unit Three: Production of Writing & Knowledge of Language chapter07.indd 140 10/10/16 5:39 pm KnowledgeExtra of Language Practice Whether you think of him as a patriot who named remembered as a seminal figure in the development of a new, autonomous nation English a whole entire nation or a controversial activist who 14 lobbied for socialist ideas, he should at the very least be 14 F NO CHANGE G a whole nation itself H an entire nation J the entire, whole nation Question 15 asks about the passage as a whole 15 Suppose the writer’s primary purpose had been to advocate placing a greater emphasis on Thomas Paine’s contributions to American history Would this essay accomplish that purpose? A Yes, because it praises Paine’s influence B Yes, because it is a thorough treatise on American history C No, because it does not establish that Paine’s contributions were beneficial D No, because it focuses too much on the American Revolution Answers and Explanations are provided at the end of the book chapter07.indd 141 Chapter 7: Knowledge of Language 141 10/10/16 5:39 pm chapter07.indd 142 10/10/16 5:39 pm UNIT FOUR MATH INTRODUCTION BY THE END OF THIS UNIT, YOU WILL BE ABLE TO: Identify the format and timing for the ACT Math test Identify the three primary ACT Math question types Apply tips and strategies to the ACT Math test 143 Chapter08.indd 143 10/10/16 5:50 pm Chapter08.indd 144 10/10/16 5:50 pm CHAPTER ACT Math CHAPTER OBJECTIVES By the end of this chapter, you will be able to: Identify the categories into which ACT Math questions fall Use SmartPoints to determine the highest-yield Math categories INSIDE THE ACT MATH TEST The Math test is 60 minutes long and includes 60 questions That works out to minute per question, but you’ll wind up using more time on some questions and less on others The Format All of the Math questions have the same basic multiple-choice format, with a stand-alone question and five possible answers (unlike questions on the other subject tests, which have only four choices each) Occasionally, you may encounter a set of two or three questions that share a table, graph, or other relevant information The questions cover a wide range of math topics, from pre-algebra to coordinate geometry and even a little bit of trigonometry More emphasis is placed on earlier-level math skills (such as order of operations, working with variables, solving basic equations, and geometry) and less on higher-level math (such as sequences, logarithms, and matrices).  Chapter08.indd 145 Chapter 8: ACT Math 145 10/10/16 5:50 pm Math Introduction Test Day Directions and Format Here’s what the Math directions will look like: DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document Math Do not linger over problems that take too much time Solve as many as you can; then return to the others in the time you have left for this test You are permitted to use a calculator on this test You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator Note: Unless otherwise stated, all of the following should be assumed: Illustrative figures are NOT necessarily drawn to scale Geometric figures lie in a plane The word line indicates a straight line The word average indicates arithmetic mean When it comes to directions on the ACT, the golden rule is this: Don’t read anything on Test Day you already know! Familiarize yourself with everything now to save time later The Math directions don’t really tell you much anyway Of the four special notes at the end of the Math directions, #2, #3, and #4 almost go without saying Note #1 is pretty important, though— while this rule “bends” a little bit when you have to guess, it’s important to know that your eyes don’t tell you what you need to know about figures; you really have to the math What a figure looks like won’t reliably get you the right answer Question Types The types of questions you’ll see on the ACT can be divided into three main types—those that include a diagram (or for which you need to draw one), story problems, and concept questions Diagram Questions About one-third of the Math questions either give you a diagram or describe a situation that should be diagrammed For these questions, the diagrams are crucial—you don’t get any points for solving questions in your head, so draw everything out 146 Unit Four: Math Introduction Chapter08.indd 146 10/10/16 5:50 pm ACT Math Example The figure below contains five congruent triangles The longest side of each triangle is meters long What is the area of the whole figure in square meters? Math A 12.5  B 15 C 20 D 30 E Cannot be determined from the given information Getting to the Answer: The key to this question is to let the diagram tell you what you need to know: Each triangle represents one-quarter of the area of the square, and the sides of the square are meters (you can figure this out because the top side of the square is the hypotenuse of the triangle that makes the “roof”) Because the area of a square can be found by squaring its side length, the area of the square is 16 square meters Thus, each triangle has an area that is one-fourth as much, or 4 square meters Because the whole figure consists of five triangles, each with area 4, the total area is × = 20 square meters The answer is (C) Expert Tip In ACT Math questions, the choice “cannot be determined” is rare When it does appear, it’s rarely the right answer, and is almost always incorrect in a question that comes with a diagram or for which you can draw one Chapter08.indd 147 Chapter 8: ACT Math 147 10/10/16 5:50 pm Math Introduction Story Problems About another third of the Math questions are story problems, which are also referred to as modeling questions Here’s an example: Example Math Evan drove halfway home at 20 miles per hour, then sped up and drove the rest of the way at 30 miles per hour What was his average speed for the entire trip? F 20 miles per hour G 22 miles per hour H 24 miles per hour J 25 miles per hour K 28 miles per hour Getting to the Answer: A good way to comprehend—and resolve—a story problem like this is to think of a real situation like the one in the story Imagining an actual trip with miles and speeds may make the question more approachable For example, what if Evan had 60 miles to drive? (You should pick a distance that’s easily divisible by both rates.) He would go 30 miles at 30 mph, then 30 miles at 20 mph How long would it take? Consider each leg of the trip: 30 miles at 30 mph is hour, and 30 miles at 20 mph is 1.5 hours That’s a total of 60 miles in 2.5 hours; 60 divided by 2.5 gives an average speed of 24 mph The correct answer is (H) Expert Tip Don’t let variables or abstract stories confuse you When you see them, stay calm and make them simpler by putting real numbers in for the variables You’ll learn more about this Picking Numbers strategy a bit later Concept Questions Finally, about one-third of ACT Math questions directly ask you to demonstrate your knowledge of specific math concepts Example If angles A and B are supplementary, and the measure of angle A is 57°, what is the measure, in degrees, of angle B ? A     33 B     43 C     47 D 123 E 147 148 Unit Four: Math Introduction Chapter08.indd 148 10/10/16 5:50 pm ACT Math Getting to the Answer:  This question requires that you know the concept of supplementary angles: Two angles are supplementary when they form a straight line—in other words, when they add up to 180° Thus, question boils down to this: What number, added to 57, makes 180? The answer is (D), 123 Math These three types of Math questions, of course, will be discussed more fully in the Math chapters that follow Outside Knowledge The ACT Math test thoroughly covers rules from a variety of common Math topics, mostly from courses students typically complete by the end of the 11th grade The needed math “facts” are addressed in the strategic discussion throughout the math chapters in this book The Inside Scoop The ACT Math test is designed to measure problem solving and logical reasoning, along with basic computational skills Covered topics include: • Rates, percents, proportions, and unit conversion • Number properties • Number operations • Algebra • Functions • Graphing • Geometry and trigonometry • Statistics and probability Although Math questions aren’t ordered in terms of difficulty, questions drawn from elementary or middle school curricula tend to come earlier in the test, while those from high school curricula tend to come later But this doesn’t mean that the easy questions come first and the hardest ones come later We’ve found that high school subjects tend to be fresher in most students’ minds than things they were taught years ago, so you may actually find the later questions easier.  TIMING You have an average of minute to spend per question Ideally, you’ll be able to spend significantly less time on easy questions so you can buy more time for the hard questions Chapter08.indd 149 Chapter 8: ACT Math 149 10/10/16 5:50 pm Math Introduction Spend about 45 minutes on your first pass through the Math subject test Do the easier questions, guess on the questions you suspect aren’t going to come to you no matter what, and mark the tough ones that you’ll want to come back to Spend the last 15 minutes picking up those questions you skipped on the first pass Math We recommend you grid your answers at the end of every page or two Don’t wait until the end of the test or you may run out of time And make sure that you have an answer (even if it’s a blind guess) gridded for every question by the time the test is over Don’t worry if you have to guess on a lot of the Math questions You can miss a lot of questions on the Math test and still get a great score Remember that the average ACT test taker gets fewer than half of the Math questions right! When You’re Running Out of Time If at some point you realize you have more questions left than you have time for, be willing to skip around, looking for questions you understand right away Pick your points and concentrate on the questions you have the best chance of correctly answering Just be sure to grid an answer—even if it’s just a wild guess—for every question SCORING You will receive a Math subject score—from to 36—for the entire Math subject test This score will be averaged into your ACT Composite Score, equally weighted with your scores on the other three major subject tests You will also receive eight other scores based on specific knowledge and concepts These are called reporting categories and consist of: • Integrating Essential Skills • Preparing for Higher Mathematics, which also includes separate scores for Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability • Modeling QUICK TIPS Mind-Set • The end justifies the means Your goal is to get as many points as possible, not to demonstrate how great you are at any particular math area, or show all your work, or get all the “hard” questions—just to get points, plain and simple That means getting as many correct answers 150 Unit Four: Math Introduction Chapter08.indd 150 10/10/16 5:50 pm ACT Math as quickly as possible If the best way to get this done is to straightforward questions in a straightforward way, that’s fine But many questions can be solved faster by using Kaplan strategies, such as Backsolving and Picking Numbers, which will make you both faster and more accurate.  Math • Take time to save time It sounds paradoxical, but to go your fastest on the Math test, you sometimes have to slow down Don’t just dive in headlong, wildly crunching numbers or manipulating equations without first giving the question some thought Remember your priority is the whole section, not just one particular question • When in doubt, shake it up ACT Math questions are not always what they seem at first glance Sometimes all you need is a new perspective to break through the disguise Take a step back and look at the question another way Special Strategies: If You Get Stuck If after a few moments of thought you find you still can’t come up with a reasonable way of doing a question, try one of these techniques: • Restate When you get stuck, try looking at the question from a different angle Try rearranging the numbers, changing decimals to fractions, changing fractions to decimals, multiplying out numbers, factoring problems, redrawing a diagram, or doing anything that might help you to look at the information you’ve been given a bit differently • Remove the disguise Find out what the question is really asking—it might not be obvious at first glance • Find the objective and circle it This is especially helpful when you’re confused • Try eyeballing Even though the directions warn you that diagrams are “not necessarily” drawn to scale, eyeballing is a surprisingly effective guessing strategy You won’t be able to get specifics without doing the math, sometimes, but you will be able to rule some answers out or get a better idea of what you’re looking for SMARTPOINTS BREAKDOWN By studying the information released by the ACT,  Kaplan has been able to determine how often certain topics are likely to show up on the test and, therefore, how many points these topics are worth on Test Day If you master a given topic, you can expect to earn the corresponding number of SmartPoints on Test Day Here is a brief overview of what exactly to expect and how much of it you should be expecting Chapter08.indd 151 Chapter 8: ACT Math 151 10/10/16 5:50 pm Math Introduction Essential Skills—14 Points  Approximately 40–43% of the Math test will be Essential Skills questions These questions test your knowledge and skill level associated with concepts you likely learned in middle school Topics include but are not limited to: Math • Numbers and operations • Rates, percents, proportions, and unit conversion • Expressions and equations • Basic geometry • Basic statistics and probability Many of the concepts that you’ll see in Essential Skills questions will also be present in Higher Math questions—the questions in the latter group will just be more advanced and will require more steps to arrive at a final solution For example, an Essential Skills question may involve finding the mean of a list of numbers A related Higher Math question may involve calculating a mean from a bar graph or a frequency table—the underlying concept is the same, but getting to the final answer requires significantly more work and finesse Higher Math—22 Points Approximately 57–60% of the test will consist of Higher Math questions These questions capture the mathematics that you most likely learned more recently, or are learning right now, in high school This category is divided into the five subcategories described next Number and Quantity—3 Points Number and Quantity questions make up about 7–10% of the Math test These questions test your knowledge of the real and complex number systems You will need to understand, reason about, and use numerical quantities in various forms, including integer and rational exponents, and matrices and vectors. Number and Quantity questions require that you understand the behavior of numbers, particularly evens and odds and positives and negatives These questions are ripe for Picking Numbers, which will be discussed in the next chapter You’ll also need to use properties of divisibility, such as factors, multiples, and prime numbers Tested operations include all parts of the PEMDAS order of operations (parentheses, exponents, multiplication, division, addition, and subtraction) Rarer questions test basic knowledge of radical and imaginary numbers Algebra—5 Points Algebra questions make up about 12–15% of the Math test and extensively test your ability to solve for an unknown quantity given a wide range of information of varying complexity The simplest questions are pulled from elementary algebra and require you to solve for a single variable They 152 Chapter08.indd 152 Unit Four: Math Introduction 10/10/16 5:50 pm ACT Math build up to more advanced algebra, asking you to solve systems of equations, equations involving absolute value, inequalities, and quadratic equations These questions also test your ability to write the equation of a line given certain types of information The slope-intercept form of a line is the most important equation to remember here, and slope in general is paramount You may even see radical and rational expressions and equations sprinkled in among the more typical polynomial equations Math Functions—5 Points Functions questions make up about 12–15% of the Math test You’ll need to know how to interpret function notation and recognize the different ways in which functions can be represented You will also be tested on function operations, which include adding, subtracting, multiplying, dividing, and finding compositions Questions in this category will also involve using functions to solve problems about real-world scenarios and describing important features of graphs of functions The types of functions you may see include but are not limited to linear, polynomial, radical, rational, exponential, logarithmic, trigonometric, and piecewise functions Finally, the Functions category includes questions involving arithmetic and geometric sequences.  Geometry—5 Points Geometry includes coordinate geometry, plane geometry, and solid geometry Geometry questions make up about 12–15% of the Math test. These questions test your ability to graph equations and inequalities in the coordinate plane and to solve problems related to lines, angles, and figures Triangles—specifically right triangles—and circles are the two most commonly tested shapes, but you can expect to see questions on a variety of polygons, as well as complex 2-D and simple 3-D shapes The test will ask you to break down complex figures into recognizable shapes and use problem-solving skills to transfer information throughout a figure Fortunately, as on the rest of the ACT Math test, the number of rules to remember is limited The test will ask questions that require knowledge of the Midpoint and Distance formulas, and occasionally you will need to work with the graphs of simple shapes such as triangles and circles in the coordinate plane.  Statistics and Probability—4 Points Statistics and Probability questions make up about 8–12% of the Math test.  These questions test your ability to interpret and/or use data presented in a variety of forms Common questions include finding or using averages and describing or analyzing the center or spread of a set of data. You’ll also see questions involving counting techniques, such as combinations and permutations, as well as questions about Venn diagrams Finally, you’ll have to calculate simple and conditional probabilities that are based on a description of a scenario, data presented in a two-way table or other type of chart or graph, or a probability distribution function Chapter08.indd 153 Chapter 8: ACT Math 153 10/10/16 5:50 pm Math Introduction A Note About Modeling Math Together, Essential Skills and Higher Math questions make up 100% of the Math test However, there is a third category, Modeling, to be aware of, although it doesn’t have a SmartPoints value associated with it The test makers have indicated that more than 25% of the test will involve modeling, but don’t let this fact intimidate you Modeling just means using mathematical equations, graphs, diagrams, scatterplots, etc to represent real-world scenarios Word problems certainly fit within this category, but you’ll also see some concept questions that fit within the Modeling category Every modeling question will also be counted in the reporting categories described earlier 154 Unit Four: Math Introduction Chapter08.indd 154 10/10/16 5:50 pm ... 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