ACT GAME THEORY

ACT GAME THEORYt h e b e g i n n e r ’ s g u i d e t o

5T h e B e g i n n e r ’ s g u i d e T o A C T g A m e T h e o r y

Table of ContentsACT Basics .....................................................................................................................................................................7

What is the ACT? ......................................................................................................................................................7

What is the ACT really? ............................................................................................................................................7

How to think about the ACT strategically ................................................................................................7

Why does the ACT matter?......................................................................................................................................7

Why is the ACT an opportunity? .............................................................................................................................8

What is the best way to get ready for the ACT? ....................................................................................................8

When should I start getting ready for the ACT? ....................................................................................................8

How many times should I take the ACT? ..............................................................................................................10

A closer look at the ACT ....................................................................................................................................10

1. Predictable exam sections .................................................................................................................................10

2. Predictable section formats ...............................................................................................................................11

3. Predictable question types ................................................................................................................................12

How to score the ACT ..........................................................................................................................................13

Calculating your raw score (multiple-choice sections only) ................................................................................13

Calculating your scaled score ................................................................................................................................14

Scoring the ACT Essay ...........................................................................................................................................15

What does it mean to “beat” the ACT? .....................................................................................................16

Beating the ACT with “Game Theory” .......................................................................................................17

What is ACT Game Theory? ..................................................................................................................................17

Strategy 1. Have a system. .....................................................................................................................................17

Strategy 2. Organize the content ..........................................................................................................................18

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7T h e B e g i n n e r ’ s g u i d e T o A C T g A m e T h e o r y6

Strategy 3. Manage your time effectively .............................................................................................................18

Strategy 4. Use your pencil ....................................................................................................................................19

Strategy 5. Get passionate about the ACT ..........................................................................................................20

ACT Game Theory Applied: Section-by-Section ..................................................................................22

1. ACT English (45 minutes, 75 questions) ............................................................................................................22

2. ACT Math (60 Questions, 60 Minutes) ..............................................................................................................24

3. Reading (40 questions, 35 minutes) ..................................................................................................................27

4. Science Reasoning ..............................................................................................................................................28

5. The Essay (30 minutes) .......................................................................................................................................29

What is the ACT? According to the official ACT website, the ACT exam “measures the knowledge, understanding, and skills that

you have acquired throughout high school.” The best preparation for the test, according to the test makers, is “a

sound, comprehensive, high school education.”

What is the ACT really?The ACT may be a proxy for many things, but the only thing the exam really measures is how good you are at

taking the test itself.

Every time the ACT is administered, it uses the same format, the same questions, and the same traps to test the

exact same small set of concepts that the test makers think are important. Thus the most useful way to think of the

ACT is not as a test of broad knowledge but as a narrowly defined game with simple and predictable rules.

Our experience is that students who do well on the ACT do so not because they are better at “reasoning” or have

more “aptitude” than their peers, but because they understand the concepts that the exams cover, are familiar

with each of the question-types used to test them, and possess specific strategies that make those questions easy

to answer correctly.

R E v O l u T i O n i n s i G H T

Doing well on the ACT isn’t about being smart. It’s about knowing how to take the test!

Why does the ACT matter? If the only thing the ACT really tests is how good you are at taking the ACT, why is it such a big deal?

The answer is simple: because colleges say it is!

ACT Basics

How to think about the ACT strategically


Admissions officers at almost every college in the United States use applicants’ test scores as one of the primary

criteria in making their admissions decisions. In fact, at most schools, ACT or SAT scores are the single

strongest predictor of admissions success next to high school grades. Many schools even use them to decide

how much merit-based financial aid students receive.

If you find it disturbing that colleges place more weight on a single test than things like extracurricular leadership,

community service, or personal qualities, you’re not alone. But since it is such a critical factor, our goal at

Revolution Prep is to ensure that your ACT scores will drive your success and not hold you back. You can trust our

curriculum team who have repeatedly beat the tests to know exactly what it takes to make your scores and asset.


The ACT should be important to you for one reason and one reason alone: because, next to high school

grades, it is the most important criterion used in college admissions decisions.

Why is the ACT an opportunity?At Revolution Prep, we view the ACT as an opportunity to gain a strategic advantage in the college admissions

process. Why? Because the ACT is the part of your college application that can be improved most

dramatically in the least amount of time.

Think about it: Your high school grades may count for half of your college admissions outcome, but they are the

result of over 4,000 hours that you’ll spend in school by the time you apply to college. The ACT, on the other

hand, is worth almost as much as your grades, yet it is a 3-hour test that most students spend less than 20 hours

preparing for.

To gain an advantage in the college admissions process by raising your GPA you would need to put hundreds of

hours of extra work into your classes. To gain an advantage on the ACT, all you have to do is be better prepared

than the person sitting next to you on test day (since the ACT is a curved test). Given that the average student

does 20 hours of (usually misguided) prep, that’s not a very high bar to surpass!


The ACT is an opportunity to get maximum “bang for your buck.” 34 hours of test prep (the number of

hours in a Revolution Prep Hybrid Course) will do more toward improving your college admissions chances

than 340 hours of extra time spent on your schoolwork!

What is the best way to get ready for the ACT?Rule #1: Don’t reinvent the wheel. Your first step in beating the ACT should be to learn from those who have

already done it—that is, from real students who used real strategies to raise their scores.

At Revolution Prep, this is what we’ll help you do. All Revolution Prep instructors are graduates from top

universities who scored in the 99th percentile on the ACT. The Revolution Prep curriculum, meanwhile, leverages

the insights of some of the top test-takers in the world to break the ACT down into a simple and beatable game.

Combine superior instructors with an unmatched curriculum and multiple full-length practice tests and you have a

recipe for ACT success.


Raising your ACT scores doesn’t require you to reinvent the wheel. At Revolution Prep, we focus on

leveraging the first-hand insights of elite test-takers to help high school students raise their scores

When should I start getting ready for the ACT?The three most common times to prep are the summer before your junior year, the spring of your junior year, and

the summer before your senior year.

Getting a foundation early ensures that you don’t have to cram during the notoriously busy ∑ and stressful - junior

and senior years.

8


How many times should I take the ACT?You can take the ACT as many times as you want. Because you can choose which scores you want to send to

colleges, admissions officers will only see your best scores. However, the most effective test-takers prepare for the

exam fully each time they take it. Taking the test without being fully prepared or with the expectation that you will

take it again is both a waste of time and money.

The ACT is the most predictable test you will ever take. Every time it is given, it will have the same parts, the same

sections and the same question types.

1. Predictable exam sectionsThe ACT is divided into five parts ranging in length from 30 to 60 minutes: English, Mathematics, Reading,

Science Reasoning and the Essay. The English, Reading and Science sections are further divided into multiple

subsections, which we’ll soon discuss. Now, let’s take a closer look at what each part of the exam covers and what

the format of each section will look like.

English (45 minutes)

The ACT English section has questions that can be placed into one of two major groups—usage/mechanics and

rhetorical skills. The questions in the usage/mechanics category will test your understanding of the conventions

of standard written English, such as punctuation, grammar and sentence structure. Meanwhile, the questions in

the rhetorical skills category will test your ability to use strategy, organization and style to effectively convey the

ideas in a particular passage. The questions on the English section are, in general, much shorter than questions

you’ll see on other parts of the ACT.

Mathematics (60 minutes)

The ACT Math section is the only section, apart from the essay, that cannot be broken down into passages

or smaller subsections. The ACT Math section will test very basic math concepts in both straightforward and

sometimes tricky ways. You will need to know the basics of Pre-Algebra, Algebra and Geometry. There are only a

few questions on concepts from Advanced Algebra and Trigonometry.

A closer look at the ACT

Reading (35 minutes)

The ACT reading section consists of four different passages, with each passage followed by a series of ten

questions. The four passages are always consistent in their genres. According to the ACT test-makers, the

questions on the Reading section “will ask you to use referring and reasoning skills to determine main ideas;

locate and interpret significant details; understand sequences of events; make comparisons; comprehend cause-

effect relationships” and more. What does this mean for you? In plain English, you’re going to need a systematic

set of strategies that will allow you to quickly find answers as you move through each passage.

Science Reasoning (35 minutes)

The ACT Science Reasoning contains seven sets, or subsections, of scientific information followed by five to seven

questions after each set. Each of the information sets will fall into one of three types: data representation, research

summaries or conflicting viewpoints. The key thing to remember about the Science Reasoning section is that it has

nothing to do with how much actual science you know. In fact, all the answers are going to be right there in front of

you! This part of the ACT is simply meant to see if you can “reason” well enough to sort through often-confusing

data and come up with the correct answer.

Essay (30 minutes)

The ACT Writing Test is optional and can be taken after the completion of the four multiple-choice sections of the

exams. The Writing Test is a single, thirty-minute essay that will test your ability to write logically and persuasively

while employing the standard conventions of written English to your utmost ability. While thirty minutes may

seem like too short of a time period to write and develop a whole essay, the test-graders take this time-crunch

into account while grading. Students who take the ACT Writing Test will receive, in addition to their normal ACT

score, a Combined Writing/English score out of 36 and a Writing score out of 12.

2. Predictable section formatsThe sections of the ACT will always contain the same formats:

> English = 5 short passages. Each passage will always be accompanied by 15 questions, and the questions will

usually deal with a short, underlined portion of a sentence in the passage.

> Math = 60 non-related questions. For a general rule of thumb, the Math section tends to start with easier

questions and works its way to harder ones.

T h e B e g i n n e r ’ s g u i d e T o A C T g A m e T h e o r y

> Reading = 4 passages, each with 10 questions. There will always be one prose fiction passage, one social

science passage, one humanities passage and one natural science passage, and the passages will always come in

that order.

> Science = 7 sections, each accompanied by 5-7 questions. There will always be three data representation

passages, three research summary passages and one conflicting viewpoints passage. Data representation

passages are five questions long (15 questions total), research summaries are six questions long (18 questions

total) and the conflicting viewpoints passage is seven questions long (15 + 18 + 7 = 40).

> Essay = The essay always comes at the end of the four multiple-choice sections, and it is always thirty minutes

long.

Below is a section-by-section breakdown of a typical ACT:

Section Type Length

1 English 45 minutes

2 Math 60 minutes

3 Reading 35 minutes

4 Science Reasoning 35 minutes

5 Essay 30 minutes

Total 3 hours and 25 minutes


The easiest way to think of the ACT is as four mini-tests followed by a short essay.

3. Predictable question typesThe four sections on the ACT always use the same types of questions. Here is a brief summary:

English (75 total questions)

1. Economy (verbosity, redundancy and irrelevancy)

2. Sentence construction

3. Grammar and punctuation

4. Rhetorical skills

Math (60 total questions)

1. Pre-Algebra/Elementary Algebra

2. Intermediate Algebra/Coordinate Geometry

3. Plane Geometry/Trigonometry

Reading (40 total questions)

1. Passage Details

2. Identifying Main Ideas

3. Cause-Effect Relationships

4. Meaning of Words/Phrases

5. Sequence of Events

Science Reasoning (40 total questions)

1. Graph/Chart Interpretation

2. Experiment Setup

3. Passage-Based Details


The ACT has the same question types every time. If you prepare for these questions beforehand, you will

succeed on test day!

Calculating your raw score (multiple-choice sections only)The first thing you need to know to understand the scoring of the ACT is the difference between your raw score

and your scaled score. Every question that you answer correctly on the ACT earns you one raw point. Every

question that you answer incorrectly earns you zero points. Every question that you leave blank also earns you

zero points. How does this information help you? If you don’t know an answer, guess! Unlike the SAT, guessing

incorrectly is worth the same as leaving a question blank. This means that for every single question on the

test (215 in all!), you should have either your answer or your best guess filled in on the score sheet. Here is the

breakdown of raw score one last time:

How to score the ACT

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T h e B e g i n n e r ’ s g u i d e T o A C T g A m e T h e o r y

> Correct answer = +1 raw point

> Incorrect answer = 0 raw points

> Omitted answer = 0 raw points

When your actual ACT is scored, all of your correct answers are added up using this formula to yield your raw

score for each section of the test. The total number of raw points possible for each part of the test is just the

number of questions on that test:

> English = 75 questions = 75 raw points possible

> Math = 60 questions = 60 raw points possible

> Reading = 40 questions = 40 raw points possible

> Science = 40 questions = 40 raw points possible

Calculating your scaled scoreOnce you have calculated your raw score on each section of the ACT, you’re ready to figure out your scaled score,

which is the score out of 36 points that colleges will be looking at. To calculate your scaled ACT score, the test-

makers use a magical ∑ or not so magical ∑ table to translate your raw score on each section of the exam into a

scaled score out of 36. It is important to note that this table will vary slightly from test to test. Although the test-

makers try to keep the level of difficulty for, say, the October test the same as the level of difficulty for the April

test, there will always be a little bit of variance. Take a look at the table:

English Math Reading Science

Raw Scaled Raw Scaled Raw Scaled Raw Scaled

70-75 32-36 55-60 32-36 35-40 32-36 35-40 31-36

60-69 26-32 45-54 27-31 25-34 25-31 25-34 23-30

50-59 22-26 35-44 23-26 15-24 17-24 15-24 18-22

40-49 18-21 25-34 18-22 5-14 9-16 5-14 10-17

30-39 15-18 15-24 15-17 0-4 0-8 0-5 0-9

20-29 9-18 5-14 9-14

0-19 0-9 0-4 0-8

The actual table that the test-makers use is obviously more detailed, but the summary above should give you a

good sense of how the translation process works. Based on the analysis above, you can now understand what a

“composite” score on the ACT is. Your “composite” will be simply the average of the four scaled scores that you

receive on each multiple-choice section.

For example, let’s say you got 50 questions right on English, 40 on Math, 20 on Reading and 20 on Science. Using

a slightly more detailed version of the table, you would have received a scaled score of 22 on English, 25 on Math,

21 on Reading and 20 on Science. Thus, your composite would be (22 + 25 + 21+ 20) / 4 = 22.


The ACT is scored by converting your “raw score” for each part of the test to a “scaled score” out of 36. At

the end, your four scaled scores are averaged to produce a final “composite” score also out of 36.

Scoring the ACT Essay As we mentioned before, the Essay section on the ACT is optional but recommended by most colleges. Because

the Essay is obviously not a multiple-choice test, the ACT employs a slightly different scoring method in order to

score your essay.

How does this work? Each essay is read by two different graders. These graders have been specifically trained

to read and score the essays of ACT test-takers nationwide. Each of the readers gives the essay a score on a 1-6

scale, with 1 being the lowest possible score and 6 being the highest possible score. The two scores, which are

usually the same or only one point different, are then summed up to give your essay a score on a 2-12 scale. For

example, if the first reader gave your essay a 4 and the second reader also gave your essay a 4, you would have an

essay score of 8.

For the last important item on your score sheet, the ACT goes on to give you a “Combined English/Writing”

score. This score is on a 1-36 scale as well, and it is determined by the scaled score of 1-12 that you received on

your essay and by the scaled score of 1-36 that you got on the English multiple-choice section. An abbreviated

version of the table that the test-makers use to offer this score is seen below:

English section

Score (1-36)

Writing Test Subscore (2-12)2 4 6 8 10 12

0-8 1-6 3-8 5-10 7-12 9-14 11-159-16 7-12 9-14 11-15 13-17 15-20 16-21

17-24 13-17 15-19 16-21 18-22 21-25 22-2624-31 18-23 20-24 22-26 23-28 26-31 27-3232-36 24-26 25-28 27-30 29-32 32-34 33-36

1514



Your performance on the ACT Essay does not in any way affect your composite score on the 1-36 scale. But,

do not ignore the ACT Essay! It is intended to offer colleges a sample of your writing skills, and they can even

request to see a copy of it should they so choose.

Beating the ACT means different things to different people. Maybe beating the ACT for you means getting a

perfect score. Or maybe you’ll feel like you beat the ACT if you can just make it through with a score that is above

average.

Regardless of what your absolute score goals are, we recommend that your relative score goals—that is, your

score improvement goals—be to raise your score by 4 points per section of the test (i.e., English, Math,

Reading, Science). In working with over 200,000 students during the last nine years, we’ve found that with the right

preparation, 4 points per ACT section is a very reachable goal.

How hard is it to raise your score 4 points on a section of the test? Not as hard as you think. Consider the ACT

Science Reasoning Test, which contains 40 multiple-choice questions. A score of 21 (the national average) on

the ACT Science section corresponds to about 22 questions answered correctly. That’s just about half of the

questions correct. A score of 25, meanwhile, corresponds to about 28 questions answered correctly, or 6 more

correct answers than a 21.

The ACT Science Reasoning section includes seven passages. This means that you can think of a 4-point

improvement as the benefit that comes from answering just one more question correctly on six of the seven

passages!

In practice, most Revolution Prep students have a goal to improve their Science scores by more than 4 points.

This shouldn’t be much of a surprise now that you know how little it actually takes to get there. In the next section

we’re going to show you the secret to doing it: ACT Game Theory.

What does it mean to “beat” the ACT?


Improving your ACT score by four points on each part of the test is easier than you think. An improvement

of four points on the Science section, for example, corresponds to just six or seven more questions correct.

What is ACT Game Theory?ACT Game Theory is a revolutionary approach to test-taking developed by perfect scorers at Harvard University.

ACT Game Theory is unique because it replaces the typical framing of the ACT as an “aptitude test” with the

belief that in most important respects, the ACT is a game.

Like any game, the ACT has consistent rules that always apply. Like any game, it involves the use of a limited

number of skills over and over. And, of course, like any game, if you learn those skills and practice them enough,

the ACT can be beaten.

Below are the five strategies that comprise the core of the Game Theory approach to beating the ACT. These

strategies are woven throughout every Revolution Prep course and tutoring program and represent the shared

insights of some of the best ACT test-takers in the world.

Strategy 1. Have a system.The most important thing that all top ACT scorers have in common is that they approach each section of the

exam the same way every time they take the test. In other words, they have a system.

Revolution Prep courses teach the systems that have worked for top test-takers on each section of the ACT, but

you shouldn’t feel bound to our systems alone. As you practice, try to figure out what mix of strategies works best

for you. Decide which strategies will form the core of your system and which ones will play smaller roles, which

strategies you have a tendency to forget and which provide you with the most bang for your buck.

How will you know when you have a system for a given section of the exam? When you can explain it. Very simply,

if someone were to ask you, “How do you handle the passages on the Reading section of the ACT?” you should

Beating the ACT with “Game Theory”


be able to give them an answer—and an exact one. The more deliberate your strategy, the more effective it

will tend to be.


Great test-takers approach the ACT systematically. For each part of the test, you should have a concrete

system for moving through the sections. The more deliberate your system, the higher (and more consistent)

your scores will be.

Strategy 2. Organize the content If there were only one or two concepts covered on the ACT, this wouldn’t be an issue. But the ACT has four

distinct sections (English, Math, Reading and Science) and numerous content areas within each. With this much

information being tested, you need a foolproof organization system to be successful.

Enter information hierarchies. The idea of an information hierarchy is to take a large amount of information and

then successively organize it along greater and greater levels of detail. The reason that information hierarchies are

so useful is that they allow our minds to compartmentalize the information being remembered. Each level in the

hierarchy is an additional layer of detail. By remembering the levels and then remembering what belongs in each

level, you can avoid the difficulty of trying to recall too much information at once.

Revolution Prep courses break the ACT down into an information hierarchy with three layers: Exam Parts, Core

Content Areas, and Concepts.


By organizing the questions on the ACT into a content taxonomy, you will enable yourself to recognize what an

ACT question is testing the moment you see it and recall the similar questions you’ve solved correctly in the past.

Strategy 3. Manage your time effectivelyTime is your most precious resource on the ACT. Every time you take the test, you will have the same amount of

time. One way to think about raising your score is as increasing your points/time ratio. In layman’s terms: Use your

time effectively!

Watch your clock

To manage your time effectively, it is essential that you always know how much time you have left on the section

you’re working on. We recommend using a digital stop watch to time every section you take on the ACT. Focus

on keeping your timing on each section to the following:

> On the English section, try to spend about 9 minutes per passage.

> On the Math section, try to average about 1 minute per question.

> On the Reading section, try to spend about 8-9 minutes per passage.

> On the Science section, try to spend about 5 minutes per passage.

Spend your time on the questions you know you can get right

It’s a simple fact that some questions on each section will be easier than others. It’s also a fact that you do not get

any more points for answering a difficult question than for answering an easy one.

The conclusion is obvious: Don’t waste time working on difficult questions at the expense of easy ones! If the five

minutes you spend on Question 11 could have been used to answer 12, 13, and 14, you shouldn’t be doing 11 unless

you know you’ll have time to get to 12, 13 and 14. Similarly, if you know that the last ten questions in each Math

section are very difficult, you shouldn’t be racing through the first fifty questions (and likely making silly mistakes

along the way) just so that you can waste time on one or two questions that you might get wrong anyway.


Easy and hard questions are worth the same number of points on the ACT. It is better to slow down and

make sure you get easy and medium questions right than spend your time on hard questions that you

aren’t as likely to answer correctly anyway.

Strategy 4. Use your pencilOne of the things we emphasize over and over at Revolution Prep is the importance of making things explicit

when you are taking a standardized test – have a system, pay attention, focus, etc.

One of the best tricks we know for forcing yourself to be explicit is to use your pencil to guide your thoughts.

Here are some of the things you should use your pencil for:


> Reading questions: Use your pencil to circle key words and make sure that you are understanding the

Revolution Insights that the question is getting at. After you read a question, always ask yourself, “What is this

question really asking?” You should be able to answer this in your own words.

> Zeroing in on important parts of answers: As you read an answer, underline or circle the parts that seem

important. Often, individual phrases or even single words can be the difference between a wrong answer and a

right answer.

> Crossing out answers: Use your pencil to cross out answers as you determine that they are incorrect. This

will have two benefits. First, it will help you keep momentum as you move through the answer choices. More

importantly, crossing out answers will keep you focused on the answers you are still considering instead of the

ones you’ve already eliminated, which saves you time.

> Marking your answer book: One of the most important things that high scorers on the ACT do is skip

questions they are struggling with and come back to them later. If you don’t use a marking system in your

answer booklet when you do this, you will forget what questions to come back to. We recommend a three-mark

system. If you skip a question and do not answer at it at all, put a circle around the number on your answer

sheet so that you know that it is blank. If you answered a question but are unsure whether it is correct, put

a small question mark to the left of the number. If you answered it and are VERY unsure, put two question

marks. This three-mark system will allow you to prioritize your time once you come to the end of a section and

want to return to the questions that gave you trouble. Some students have the misconception that any mark on

their answer sheet will lead to the answer sheet being incorrectly read. This is not the case! You just need to

be careful that the marks you are putting on the sheet aren’t made in the answer bubbles.


Using your pencil to read questions, cross out answers, and mark your answer book will help you to stay

focused, eliminate silly mistakes, and manage your time more efficiently.

Strategy 5. Get passionate about the ACTHow many people do you know who are good at something they don’t like? Probably not many. Your friends who

are good at sports probably enjoy them. Your friends who are good at math like math. Most people assume that

this is because people like things they are good at. More often, the chain of causality actually runs in the other

direction. People get good at things because they like them.

The ACT is no different than any other skill in this respect. If your attitude every time you sit down to do some

practice is “Why do I have to do this? I hate the ACT,” you will not improve. The human brain has a remarkable

screening mechanism: it learns what it finds interesting and filters out everything else.

Here are a few tips for how to actually get excited about the ACT:

> Ban negative thinking. Most students’ internal monologues about the ACT are litanies of negativity: “This

sucks.” “I hate the ACT.” “This is so boring.” “I’m never going to get better so how can I at least get it done

with.” You get the idea. These kinds of internal monologues are the road to ACT failure. From now on, when

you catch yourself thinking negatively about the ACT, stop yourself. Put a ban on negative thinking.

> Pretend the ACT really is a game. Everyone has become addicted to a video game at some point. Tetris,

Pong, Pac Man, Mario Cart, Halo, Snood, whatever. Think of the ACT the same way you thought of that stupid

game on your computer that you couldn’t stop playing. Every time you sit down to practice or study, get

pumped up about improving your skills, getting to the next level, beating your “old record.”

> Get into the zone. You have probably heard great athletes talk about the “zone,” a state of heightened mental

and physical awareness where they are entirely focused on the task at hand. Whenever you sit down to study

for the ACT, focus on getting yourself into the zone. Close your door, clear your desk, turn your cell phone off,

and shut down your computer. Try to be 100% focused on what you are doing and nothing else. Place yourself

in the very situation that you will encounter on test-day. In sports, this piece of advice is comparable to a coach

telling his team to treat every practice like it’s a game. You will be amazed at how much more you get done ∑

and how much your score improves as a result!


Getting passionate about the ACT is where it all starts. If you can psych yourself up to beat the test, the rest

will fall into place. As the old saying goes, “Where there is a will, there is a way.”


1. ACT English (45 minutes, 75 questions)Question Types

1. Economy Questions

2. Sentence Construction Questions

3. Grammar and Punctuation Questions

4. Rhetorical Skills Questions

Game Theory Tips

> Trust your ear.

> Remember that good English is concise, clear, and active.

> Don’t be afraid to read questions or answers twice.

Economy Question Example

When I look at that picture of my family by the Christmas tree, it is almost as if that I can picture myself again

opening presents and sipping hot cocoa on that fun Christmas morning.

(A) NO CHANGE (B) I can picture myself (C) I can picture myself and imagine that I am again

(D) it is like that I can again picture myself

Answer: Keep in mind the overall goal of picking the answer that is grammatically correct and succeeds in

shortening the sentence. Our first step tells us that the sentence just doesn’t sound right at all, which is a

good use of our instincts. Because of that, we can eliminate (A). By using our other strategy of looking for

the shortest answer, we can immediately see that (C) and (D) are definitely longer than (B). Try replacing the

underlined portion with (B). Does the sentence sound better? Is it grammatically correct? The answer to

both questions is yes, and it is important to note that the overall idea of the sentence remains unchanged.

Therefore, (B) is the correct answer.

ACT Game Theory Applied: Section-by-Section

Sentence Construction Example

The hurricane ruined the central part of the town, flooding the roads, destroying store windows and telephone

poles were knocked over.

(A) NO CHANGE (B) telephone lines knocking over (C) knocking over telephone poles

(D) knocked over telephone poles

Answer: The first two items in this list are gerund phrases, but the last one is in the past tense. To preserve

parallel structure, we need to change the phrase “telephone poles were knocked over” to “knocking over

telephone poles.” Thus the correct answer is (C).


Grammar and Punctuation Example

The number of seats available last Thursday prove how popular the sport has become in just a few years time.

(A) NO CHANGE (B) are proving (C) is proving (D) proved

Answer: The subject of the sentence is “number,” a singular noun. Therefore, we need a singular verb.

We also need a singular verb that is in the past tense, for the seats were for an event that took place “last

Thursday.” The only past-tense, singular verb is “proved,” so (D) is the correct answer.

Rhetorical Skills Example

Roberta claims that Isabel Allende’s books were once more celebrated and respected than any other Spanish-

language author.

(A) NO CHANGE (B) than any other author who wrote in the Spanish language

(C) than any other Spanish language author’s (D) than any Spanish-language author

Answer: The sentence contains a faulty comparison between Isabel Allende’s books and “other Spanish-

language author.” The logical comparison would be between Allende’s books and the books of other Spanish-

language authors. Thus, (C) is correct.

2. ACT Math (60 Questions, 60 Minutes)Core Content Areas Covered

> Arithmetic

> Algebra

> Geometry

> Advanced Algebra

Game Theory Tips

> Focus on the easier questions; don’t be afraid to skip tough questions.

> Read carefully - 40 percent of all math questions the average test-taker gets wrong are “silly mistakes,” not

knowledge errors.

> Don’t use algebra if you don’t have to (plug in!).

Examples

1. The fi gure above is a right triangle. What is the value of ?

(A) 50 (B) 51 (C) 72 (D) 98 (E) 100

Solution: The key thing on this question is to notice fi rst that the fi gure is a right triangle and second, that the

hypotenuse has length 10. Right away, you should remember your 6-8-10 Triangle (a simple multiple of the

3-4-5 Triangle). If you look at the other two sides, you’ll notice that if x is 1, you’ll get your 6-8-10 relationship.

Thus the answer is (A). If you didn’t notice that you had a 6-8-10 Triangle, you’d have to solve this question by

walking through the entire Pythagorean Theorem.

Concept: Special Right Triangles

2. In the fi gure above, the two circles are tangent at point B and 6AC = . If the circumference of the circle

with center C is twice the circumference of the circle with center A, what is the length of BC ?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 6

Solution: Start with your defi nition of circumference: 2πr. If the circumference of the circle with center C is twice

as large as the circumference of the circle with center A, then we can write the relationship as 2πrc = 2 * (2π)ra. If

we cancel the 2π on both sides, we are left with rc = 2ra. If AC = 6, then it’s not hard to see that this means that

AB = 2 and BC = 4 will satisfy our relationship between the radii of the two circles. Thus our answer is (D).

Concept: Circles

10

Note: Figure not drawn to scale.

A B C

24


3. If x is divisible by 3 and y is divisible by 5, which of the following must be divisible by 15?

I. xy

II. 3x + 5y

III. 5x + 3y

(A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III

Solution: This is a perfect example of a question where you shouldn’t use Algebra if you don’t have to. All you

have to do is substitute. First, pick numbers that satisfy the conditions in the question. For x, we could pick 6

(divisible by 3) and for y we can pick 10 (divisible by 5). Now we just test our numbers in each of the answer

choices. For (I), 6 x 10 = 60. That works: 60 is divisible by 15. How about (II)? (3 x 6) + (5 x 10) = 68. This is not

divisible by 15. And III: (5 x 6) + (3 x 10) = 60. That works. So your answer is (D), (I) and (III) only.

Concepts: Number Properties, Substitution

4. If , then which of the following must be true?

I.

II.

III.

(A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III

Solution: This question begs for substitution, but be careful! In this case, they are asking which of the

statements is always true. Whenever this happens, you have to consider the numbers that tend to be

exceptions: 0, 1, negatives, and fractions between 0 and 1. In this case, since we are told that n is not zero, we

check fractions, negative numbers, and 1. (I) isn’t true for 1, and (II) isn’t true for negative numbers. Only (III)

passes the test for all of these numbers. Thus the answer is (C).

Concepts: Number Properties, Substitution

5. If n = 31 , what is the value of

€

1n

+1

n −1 ?

(A)

€

56

(B) 1 (C)

€

32

(D) 2 (E) 3

Solution: This question is a classic example of the ACT’s testing of specifi c concepts in very well defi ned ways.

In this case, you’re just being tested on your ability to substitute a number for a variable and then divide

fractions. As long as you remember that dividing by a fraction is the same as multiplying by its reciprocal,

you’ll be all set.

€

113

+1

13

−1= 3+

1−23

= 3−32

=32

Concepts: Substitution, Dividing Fractions

3. Reading (40 questions, 35 minutes) Game Theory Tips

> Focus on the questions, not the passage.

> Read actively (use your pencil).

> Don’t be afraid to read a question more than once.

> Remember that sometimes fi nding wrong answers is easier than fi nding right answers!

Examples

Question 10 is based on the following passage.

In between school days, we gathered hazelnuts, fi shed, had long deer-hunting

weekends, went to powwows, beaded on looms, and made quilts. I did not question

the necessity or value of our school education, but somehow I grew up knowing it

wasn’t the only education I would need. I’m thankful for those experiences of my

Anishinaabe heritage, because now I know by heart not only the national anthem, but

the ancient song of the loon. I recognize not only the alphabet and the parts of an

English sentence, but the intricate language of a beaver’s teeth and tail.

10. The author’s overall tone in this passage is best described as one of

(A) jubilation (B) frustration (C) curiosity (D) appreciation

Solution: The key word in this question is “tone.” You might think that trying to judge the tone of a

passage is subjective, but rest-assured: every answer on the ACT can be supported by evidence! If

you read actively and underlined key words, you probably noticed that the author is “thankful for [the]

experiences of [his] Anishinaabe heritage.” Sounds like the tone of this passage is (D) appreciation. You

should always be able to point to specifi c evidence in the passage that supports your answer choice!


4. Science Reasoning (40 questions, 35 minutes)Game Theory Tips

> Go straight to the questions!

> Remember, the graphs and tables tell you what you need to know.

> Beware of overcomplicating things.

Example

The fi nal stage of ecological succession is characterized by the presence of the climax community, the oak-

hickory forest. Figure 3 depicts the gradual change from pine to hardwoods.

According to the information in Figure 3, a 150-year-old climax community would contain oak and hickory

trees with a density of approximately:

(A) 3,000 trees per unit area.

(B) 5,000 trees per unit area.

(C) 15,000 trees per unit area.

(D) 20,000 trees per unit area.

Solution: You don’t need to understand any science in order to answer this question correctly – you just need

to look at Figure 3! The age of the climax community is measured along the x-access of this graph. The density

of oak and hickory trees is represented by the dotted line. When you check the density of oak and hickory

trees when x=150 years, you’ll see that it equals approximately 15,000. The correct answer is (C).

5. The Essay (30 minutes) Game Theory Tips

> The essay will always be about a topic that is general and that “anyone” can write about.

> Make sure you know exactly what the prompt is asking you to address before you begin writing.

> Your essay should be a single argument. Don’t try to do too much!

> Structure and organization are as important as content.

Example Prompt

Educators debate extending high school to fi ve years because of increasing demands on students from

employers and colleges to participate in extracurricular activities and community service in addition to having

high grades. Some educators support extending high school to fi ve years because they think students need more

time to achieve all that is expected of them. Other educators do not support extending high school to fi ve years

because they think students would lose interest in school and attendance would drop in the fi fth year. In your

opinion, should high school be extended to fi ve years?

In your essay, take a position on this question. You may write about either one of the two points of view given,

or you may present a different point of view on this question. Use specifi c reasons and examples to support your

position.

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ACT GAME THEORY

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