PRAXIS CORE
TABLE OF CONTENTS
Introduction to the PRAXIS ...................................................................................................... 1 What is the PRAXIS? .................................................................................................................... 1 Question Types ............................................................................................................................ 2 General Test-Taking Advice ......................................................................................................... 3 The Praxis Reading Test ........................................................................................................... 6 Introduction................................................................................................................................. 6 Type One: The Main Idea ............................................................................................................ 8 Type Two: Details ...................................................................................................................... 12 Type Three: Vocabulary............................................................................................................. 15 Type Four: Organization ............................................................................................................ 22 Type Five: Inferences................................................................................................................. 28 Type Six: Evidence ..................................................................................................................... 31 Type Seven: Assumptions.......................................................................................................... 33 Type Eight: Fact or Opinion ....................................................................................................... 35 Type Nine: Attitude ................................................................................................................... 37 Type Ten: Extensions ................................................................................................................. 41 Type Eleven: Conclusions .......................................................................................................... 42 Type Twelve: Application .......................................................................................................... 44 Key Take-Aways ......................................................................................................................... 46 Quiz............................................................................................................................................ 48 The Praxis Writing Test .......................................................................................................... 53 Introduction............................................................................................................................... 53 Usage and Sentence Correction ................................................................................................ 54 Revision in Context .................................................................................................................... 62
Research Skills ........................................................................................................................... 63 The Essays.................................................................................................................................. 69 Key Take-Aways ......................................................................................................................... 78 Quiz............................................................................................................................................ 80 The Praxis Mathematics Test ................................................................................................. 84 Introduction............................................................................................................................... 84 Numbers .................................................................................................................................... 87 Functions and Algebra ............................................................................................................. 106 Geometry................................................................................................................................. 125 Statistics and Probability ......................................................................................................... 137 Key Take-Aways ....................................................................................................................... 142 Quiz.......................................................................................................................................... 144 Practice Test ........................................................................................................................ 152 Reading .................................................................................................................................... 152 Writing ..................................................................................................................................... 165 Math ........................................................................................................................................ 175
INTRODUCTION TO THE PRAXIS Welcome to this guide to the PRAXIS Core tests. In this introductory chapter, we will cover three topics: the nature of the PRAXIS exams, the question types you will see on the PRAXIS, and general test-taking advice. Let’s begin by considering what the PRAXIS exams are.
WHAT IS THE PRAXIS? Depending on which state you live in, different PRAXIS tests are required at different points along the path to teacher certification. You will want to check your state’s requirements before you begin studying for any PRAXIS tests so that you can be sure that you are preparing for the right test at the right time. There are three families of PRAXIS tests. These are called the PRAXIS Core, PRAXIS Subject Assessments, and PRAXIS Content Knowledge for Teaching Assessments. This guide will prepare you for the first family, the PRAXIS Core. The PRAXIS Core test will evaluate your knowledge in skills in mathematics, writing, and reading. In some states, the PRAXIS Core is taken before the student enters a teacher preparation program. In some states, PRAXIS Core is taken later, as part of the process to become certified to teach. The PRAXIS test must be taken on a computer. You do not need to be a technical genius to take the test, but you should be able to type reasonably well and to interact with a software program. If you are concerned that slow typing will interfere with your ability to do your best on this test, there are many websites that will guide you through the process of becoming a better typist. When you take the test, there will be a brief tutorial period before the test. Use this time to be sure that you understand how the computer, the software, and the test itself should function. The PRAXIS exam must be taken in English. There are technically three PRAXIS Core tests— reading, writing, and mathematics. You can take all three on one day, or you can spread them out over three different test sessions. If you choose to take all three tests on the same day, the 1
tests will take you about five hours to complete. If you take the tests on three different days, each test will take about two hours. If your schedule permits, you might find it less stressful to take the tests at separate times. Most people are not at their best after five straight hours of test-taking. Also, if you separate the tests, you can focus your study on one section, and then take that test before studying for the other sections. You can register for the PRAXIS at the website e-t-s-dot-org. You will get your official score about two weeks after you take the test. Each state has different PRAXIS scores required to pass the test.
QUESTION TYPES In this section, we will cover the types of questions that you will see on the PRAXIS test. There are three types of questions that you will see: One. The PRAXIS calls some questions “constructed response” questions. This means that you will type in your own answer to the question. There will be two essay questions on the PRAXIS test, and we will review them in this guide in the chapter on the writing test. Two. The PRAXIS will have what it calls “selected response” questions. These include traditional multiple-choice questions, which will be most of the questions. But in some cases, the question may ask you to select all of the answers which are correct. Or, it might ask you to click on a sentence or on part of a graphic. Another question type asks you to “drag and drop” something from one part of the screen to another part. A final question type involves a drop-down menu from which you will select the correct answer by clicking on it. Three. The PRAXIS also has what it calls “numeric entry” questions. For this question type, you will enter a number. Because there are several different types of questions, be sure that you read the directions carefully so that you are clear about exactly what the question is asking for. There will always
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be directions for each type of question on the PRAXIS. Also, the E-T-S website has a demonstration of the types of test questions if you would like to become more familiar with them.
GENERAL TEST-TAKING ADVICE Soon, we’ll review the reading, writing, and mathematics content that you’ll need to know in order to do your best on the PRAXIS. But first, we will cover some general test-taking advice. First. You need to develop a study plan. Decide when you will take the PRAXIS tests. Then, develop a plan to prepare for each of the tests. Write it down, check it frequently, and stick to it. Second. Do not try to cram for the test. Studies show that this is not effective. Instead, spread out your study sessions over as long of a time period as possible. It is much better to study for a small amount each day than to study for hours and hours the day before the test. Third. Do not study the night before the test. Instead, do something relaxing and go to bed early. Fourth. Eat a good breakfast on the day of the test. Research has shown that this improves test performance. Don’t overeat, but be sure to consume some fat, protein, and water. Fifth. Plan to arrive at the test center early. Be sure that you know how to get to the testing center. This will allow you some time to get settled, as well as a time buffer in case something goes wrong. You should plan on arriving about a half hour before the test is scheduled to begin. Sixth. Dress in layers on test day. You can never know if the testing center will be hot or cold, and either one can distract you from the test. Seventh. Be sure to bring your admission ticket and a photo ID to the test center. You do not need to bring pens or pencils—the testing center will provide these for you. Do not bring any
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electronics to the testing center, including a calculator. Testing center workers are likely to ask you to remove jewelry, scarves, headbands, and other similar items, so it is best to just leave these at home. You may not bring scratch paper, but you will be provided some. Eighth. Be prepared to be examined at the testing center to be sure that you haven’t brought any notes or other prohibited items. You may be asked, for example, to take off your eyeglasses and allow the testing center worker to examine them. Ninth. Stay calm during the test. If you find yourself getting stressed out or panicky, close your eyes and take a few slow, deep breaths. Tenth. You should answer every question on the PRAXIS, even if you do not know the answer. Some tests give you a penalty for wrong answers, but the PRAXIS is not one of those tests. This means that it is to your advantage to answer all of the questions, even if you are just randomly guessing. If you are about to run out of time, pick one letter and answer all of the remaining questions using that one letter. This will maximize your chances of earning the highest possible score on the PRAXIS. Eleventh. Be careful to read all of the directions carefully. If you overlook the word “not,” “except,” “least,” or “always” in the question, you are likely to choose the wrong answer. If you didn’t realize that you were supposed to mark more than one correct answer, you are likely to lose points on that question. Twelfth. Use the process of elimination. Here is how that works: if you are having a hard time with a question, change your perspective from asking yourself, “What is the correct answer?” to asking yourself, “Which answers are wrong?” Here is an example of how that might work. Question: How far is it from New York to Los Angeles? A. twenty-seven miles B. two hundred miles C. three thousand miles D. twenty thousand miles 4
You may not know the actual distance from New York to Los Angeles, but you probably had no difficulty answering that question correctly because the wrong answers are so obviously wrong. You were able to eliminate the incorrect options, and the only option left was the correct answer. Now, the PRAXIS probably won’t have any questions where the answers are so obviously wrong—and it won’t have any geography questions, either—but this question is a good illustration of the process of elimination. So, remember, if you get stuck, use the process of elimination to ask yourself which answers are wrong. Then choose from the remaining answer options. This concludes this introductory chapter to the PRAXIS. Next, we will prepare for the reading test.
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THE PRAXIS READING TEST INTRODUCTION This section of the guide will prepare you to do your best on the PRAXIS reading test. This test will have fifty-six questions, and you will have eighty-five minutes to answer the questions. The questions in this section will be selected-response questions, and they will be answered based on reading passages that will be provided to you. There will be four types of passages. First, paired passages. You will be given two passages, each about two hundred words. Second, one longer passage, which will be about two hundred words. Third, one shorter passage, of about one hundred words. Fourth, brief statements. The number of questions following each passage can vary. The passages may also include visual information, such as charts, tables, diagrams, maps, political cartoons, or drawings. There will usually be numbers running down the side of the passage. These are not normally part of the original passage but were added by the test makers so that they can ask you questions such as, “How does the author defend the tax increase proposal in lines seven through ten?” If a question mentions line numbers, be absolutely sure that you consider them. You may have a situation where the passage included four arguments for a tax increase, but if the question asks about the reason in lines seven through ten, and you answer according to what is found in lines eleven through fourteen, you will get the wrong answer. This is a test of your reading comprehension, specifically your ability to comprehend, analyze, and evaluate written materials. An important point for you to understand is that all of the questions can be answered based on the material in the passage. For example, if there is a passage about the discovery of water on Mars, you are not expected to know anything about this topic. All of the questions will be answerable based on the passage itself. In fact, if you recently watched a news broadcast about water on Mars, you need to do your best to separate
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in your mind what you already know from what you read in the passage. The reason for this is that you will sometimes see questions such as, “What evidence does the author provide in the second paragraph for the presence of water on Mars?” You may be familiar with other evidence from the news broadcast. In fact, the evidence from the broadcast may be included in one of the answer options. But if that evidence is not found in the second paragraph, then that answer is wrong. The key is that you need to focus on the information in the passage—not on what you might know about the topic from other sources. There is another issue that you need to be aware of: just because an answer choice repeats words or phrases from the passage does not mean that it is the correct answer. For example, a passage might include the phrase “extensive extracurricular activities,” and an answer choice might include that same phrase, but it could still be the wrong answer. If the author had written that extensive extracurricular activities are stressful for young children, but the question was asking about ways to promote healthy living, then the answer about the extracurricular activities would be wrong. Similarly, it is possible that the correct answer will not repeat any words from the passage. For example, you might read a passage about the benefits of long vacations, followed by a question about what idea the author would support. The correct answer could by extended holidays. “Extended holidays” means about the same thing as “long vacations,” despite the fact that the wording is different. So remember: it isn’t enough for an answer choice to repeat words or phrases that are found in the passage; this doesn’t automatically make it the correct answer choice, and it doesn’t automatically make an answer the wrong choice just because it doesn’t repeat the words that were in the passage. You should know that it is possible for an answer option to be the wrong choice even when the information in that answer choice is factually accurate. Imagine that you had read a passage about President Kennedy’s plan for astronauts to go to the moon, followed by a question that asked, “What evidence does the passage use to explain why President Kennedy thought a moon voyage was important?” followed by these answer choices: A. the United States was in a Cold War with the Soviet Union B. President Kennedy was assassinated in the early 1960s 7
C. President Kennedy’s wife was popular with the press D. President Kennedy’s older brother had died during World War Two All four of those answer choices are factually accurate statements. But only one of them can be the correct answer choice. The question was asking specifically about why a manned trip to the moon was important, and only option A answers the question. So remember: an answer choice can be factually accurate and contain true information without being the correct answer to the question. This may be different from tests that you have taken in the past, so do not be confused when you see multiple answer choices with information that is factually correct. Remember to focus on what the question is asking you. The PRAXIS Reading test questions are divided into twelve skill areas. We will now look at each of those twelve areas.
TYPE ONE: THE MAIN IDEA You have probably been learning about the main idea since you were in elementary school. Of course, when this concept is tested on the PRAXIS, its presentation will be a little more sophisticated than what a young student learns. For one thing, you may find questions about the main idea that use other language, such as: Which of the following is the best summary of this passage? Which of the following would be the best title for this passage? What is the core concept in this passage? What is the theme of this passage? What is the author’s primary purpose in this passage? All of these questions are asking you to reflect on the main idea of the passage. If you are struggling to figure out what the main idea is, it can be helpful to first think about the topic. You should be able to state the topic in just a few words, such as “The Gilded Age” or “scorpions.” Once you have identified the topic, ask yourself, “What is the author saying about
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the topic?” And your answer might be something such as, “The Gilded Age was brought about by rapid technological change” or “scientists recently discovered three new types of scorpions.” Now you have the main idea: once you have identified what the author is saying about the topic, you have the main idea. When test takers have difficulty with main idea questions, it is often because they had a hard time distinguishing the main idea from the details. We will talk more about details in a moment, but for now, remember that a passage would still be fundamentally the same if you deleted any particular detail, but it would not be the same if you deleted the main idea. You can use this knowledge to distinguish between a main idea and a detail by asking yourself, “Would the passage be completely different if this were missing?” If the answer to that question is “no,” then it is a detail. If the answer to that question is “yes,” then it could be the main idea. Details are included in a passage in order to support the main idea, but they are not the point of the passage. One other technique that you can use to be sure that you have correctly identified the main idea is to quickly skim the passage and be sure that what you think is the main idea applies to the entire passage. If there are several sentences that aren’t relevant, then you probably have not correctly identified the main idea. Remember: the main idea has to describe the entire passage and not just parts of it. Let’s look at a sample reading passage followed by a main idea question: In recent decades, there has, rightly, been an increased emphasis on the needs of urban schools. Unfortunately, this emphasis has been accompanied by a near-complete neglect of the situation of rural schools. Perhaps part of the problem is that policymakers are unaware that a full one-third of school districts are located in rural areas. But whatever the cause, the unique challenges faced by rural schools are left largely unaddressed, and so critical issues such as teacher retention, technology development, and a lack of diversity contribute to poor performance in many of these struggling systems.
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Question: What is the author’s primary purpose in this passage? A. to criticize the emphasis on urban education B. to condemn policymakers for living in urban areas C. to remind the reader of the number of rural school districts D. to emphasize the need to address challenges in rural schools The correct answer to this question is option D. Overall, the passage is concerned with the fact that rural schools do not receive enough attention, given their unique problems. Option A is not correct, although it requires very close reading to determine that. Notice that the passage does not actually criticize the attention given to urban education, but rather the author criticizes the lack of attention given to rural schools without saying that attention to urban schools is a problem. Options B and C are incorrect: notice that they contain some ideas and words from the passage but go beyond what the passage states. The passage doesn’t condemn policymakers for living in urban areas; it just points out that they might not be aware of the number of students who live in rural areas. The passage doesn’t say anything about where the policymakers live or should live. Similarly, the passage includes a reference to the number of students who are in rural districts, but that statistic isn’t the point of the passage. Instead, it is a detail used to support the main point of the passage. Let’s try another sample passage followed by a main idea question. Parenting can be described on a continuum from authoritarian to permissive. Authoritarian parenting can best be summarized as expecting the child to be instantly obedient. At the opposite end of the spectrum are permissive parents, who do not set consistent limits for their children. Both ends of the spectrum result in children who are less well adjusted: children of authoritarian parents tend not to learn the reasons why rules exist and therefore have trouble once their parents are no longer managing their affairs, while children of permissive parents struggle with a lack of security and connection. The happy medium is to be found when parents set reasonable limits and enforce them by explaining to their children why the rules are important.
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Question: Which of the following would be the best title for this passage? A. Why Permissive Parenting Is Problematic B. Negative Outcomes from Authoritarian Parenting C. Neither Authoritarian or Permissive: The Case for Parenting in the Middle D. Parenting in the Twenty-First Century Option A is not the correct answer to this question. You will notice that it does reflect information that was presented in the passage, but the problems with permissive parenting concern only part of the passage and not the entire passage, so this would not be the best title because it would ignore several important ideas in the passage. Similarly, option B is not correct because it also contains a description of part—but not all—of the passage. Option C is the best answer because it incorporates the key concepts found in the entire passage. The problem with option D is that it is too vague: it does not do nearly as good of a job as option C does in describing what the passage is actually about.
TYPE TWO: DETAILS Details are also known as supporting ideas. Remember that authors do not include information at random but rather selectively choose details in order to provide evidence for the main idea. A supporting idea might be a fact, a statistic, or a logical argument. When you are asked questions about details, the question might be worded in one of the following ways: Which fact is mentioned in the first passage but not in the second passage? Based on the passage, which of the following is true about decorative fans? The passage lists all of the following as habits of expert swimmers except for which one? The author claims that one of the results of increased screen time for toddlers is what? According to the passage, what is the result of increased sodium intake? As you can see from these sample questions, correctly answering detail questions will require you to read the passage closely.
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Sometimes, when test takers realize that they will face detail questions, they decide to read the passage so slowly and thoroughly that they are, in effect, attempting to memorize the passage. But this is a very poor strategy. Remember that you can always go back to the passage to answer the detail questions. So attempting to memorize every detail in the passage when you read it is not a good use of your time, which is limited. Not only are you unlikely to be able to memorize all of the details, but you will end up spending too much time on reading, and you may run out of time to answer all of the questions. A better strategy is to read the passage at a middle pace—don’t skim it, but don’t try to memorize it. Just try to get a general feel for what is in the passage. Then, when you encounter a detail question, you will have an idea of where in the passage the detail can be found, and you can look at the passage again to refresh your memory. So remember: just because there are detail questions on the PRAXIS doesn’t not mean that you should try to memorize all of the details as you read the passage. You can always return to the passage later to check on the details. Just like with the main idea questions, it isn’t enough for an answer choice to use words that are in the passage. You need to be sure that the answer choice is a correct answer to the question. Let’s try a sample passage followed by a detail question. If you think that democracy began in ancient Greece and then enjoyed a complete slumber until the American Revolution, you are missing several interesting slices of world history. For example, the emperor of the Habsburg Empire was elected by a group of seven electors, chosen from various dukes, kings, and church leaders. This is not exactly direct democracy, but it serves as an example of the variety of types of governments that have been instituted at various points in time. Question: Which of the following people would have been least likely to vote to choose the next leader of the Habsburg Empire? A. a farmer B. a duke
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C. an archbishop D. a king The correct answer is Option A. The passage states that the electors were chosen from, “various dukes, kings, and church leaders,” so Options B, C, and D are reasonable choices for who might have had a vote, but a farmer, Option A, is not a reasonable choice. As you can see from this example, it would not be a good use of your time to try to memorize who the electors were and how many electors there were. That would take too long. Rather, you can return to the passage to look up the information that you need once you realize that there is going to be a question about who the electors were. Let’s try another sample passage followed by a detail question. While they tend to get combined into the category of computer languages, there are significant differences between mark-up languages and programming languages. Mark-up languages include HTML and CSS, which are used to design webpages. While these languages are powerful, they do not include the key components of programming languages, such as recursion and iteration. On the other hand, programming languages, such as Python, permit the programmer to use complicated routines of recursion and iteration to accomplish a variety of goals. Question: Which of the following would, according to the passage, NOT be true of HTML? A. It can be used to design a webpage. B. It can incorporate recursion. C. It is a computer language. D. It is easy to learn. The passage states that HTML can be used to design a webpage, so option A is incorrect. This is one of those instances where it is crucial to notice the word “NOT” in the question. According to the passage, HTML does not support recursion, so option B is the correct answer. The first sentence of the passage groups HTML as a computer language, so option C is not correct. And the passage does not say anything about whether HTML is or is not easy to learn, so option D is 14
not correct. You may have an opinion as to whether HTML is or is not easy to learn but remember that you need to stick with what is presented in the passage and not rely on what you know from other sources, so you need to eliminate option D from consideration. You may or may not be familiar with computer programming. If you are not, you might have gotten a little bit nervous to see a passage about programming and an answer choice that mentions recursion—a concept that you might have never heard of. But notice that you should be able to figure out the correct answer to this question without knowing what recursion is. All you need to do is to observe what the passage says about which languages do or do not support recursion—you don’t need to be able to define the word to answer the question correctly. It is important that you do not lose confidence when you see a passage or a question that contains concepts that you are not familiar with. This is to be expected. Remember, this is not a test of subject matter but rather a reading test. You will be able to answer the questions correctly using your reading skills even if you are not familiar with the subject matter. So do not worry if the topic or the details of the passage are new to you. Stay calm and focus on the question.
TYPE THREE: VOCABULARY You will probably see some questions on the PRAXIS that ask you about the meaning of a word. The most important thing to know about these questions is that they will always ask you about the meaning of a word in the context in which it is used, not about the meaning of that word in general. The reason that this difference is important is that many words have more than one meaning, and you need to focus on how the word is used in the passage, not on how it might be used in other contexts. Think about this sentence: “He vacationed at the cape.” In that sentence, a cape is a place along the coastline. It has nothing to do with the piece of clothing that is also called a cape. Some test takers are tempted to save time by answering the vocabulary questions without checking how the word is used in the passage. Do not be tempted to do this. Be sure to check how the word is used in the passage.
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When you are asked about the meaning of words, it will probably be with a question similar to these: Which word could be used to replace the word “elevate” in the passage? The phrase “curry favor” means to do what? What does the author use the phrase “collateral damage” to refer to? For all of these questions, you are being asked to show that you understand how a word or phrase is used in the passage. Once you have selected an answer choice, you should re-read the sentence in the passage, substituting your answer choice, to be sure that it makes sense. This is a good way to check your work. Do not panic if you do not know the meaning of the word. Let’s look at an example that shows how you may still be able to answer the question correctly, even if you are not sure of the meaning of the word. Imagine that one of the sentences in the passage read, “Because he was in a hurry, he blah-blah-blah the other drivers on the freeway.” Here, we are using “blah-blahblah” in place of a word that you don’t know. Then a question asked, “Which of the following words is the best substitute for the word “blah-blah-blah” in the passage?” followed by these answer choices: A. yielded to B. assisted C. passed D. evaluated We might not know what the word “blah-blah-blah” means, but we can use the other words in the sentence as clues about what would be a good replacement for it. Notice that the sentence involves a man who is in a hurry. Does it make sense that someone in a hurry would yield? No, it does not, so option A is unlikely to be correct. Would being in hurry lead you to assist other drivers? Probably not, so option B is not correct. Would being in a hurry lead you to pass other drivers? Yes, so option C sounds pretty good, but we should check option D. Would being in a hurry lead you to evaluate other drivers? This is unlikely, so we should settle on option C.
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Notice that we were able to select the best answer to this question even without knowing what the word “blah-blah-blah” means. This can be a powerful strategy to use on the vocabulary questions if you are unsure of the meaning of the word that the question is focused on. You may be asked questions that ask you to distinguish between the literal and figurative uses of language. Words and phrases can be used literally or figuratively. A figurative meaning is anything other than the actual, physical, literal meaning of a word or phrase. Think about these examples: One. “He won’t stop talking. He’s driving me up a wall.” Two. “He is playing with a blue toy car. He’s driving it up a wall.” In the first sentence, no one is literally driving you up a wall—that’s an expression that means that something is annoying. So, this is an example of figurative language. In the second sentence, a toy car is literally, actually being driven up a wall, so this is literal language. It isn’t figurative. Some vocabulary questions may ask you to distinguish between literal and figurative meanings of words. Think about this sentence that you might find in a reading passage: She thought that her lack of promotion after seven years as a vice president was due to the glass ceiling. Now consider this question: The phrase “glass ceiling” most probably refers to what? A. an expensive office complex B. a policy limiting women C. environmental design choices D. a commitment to solar energy In the context of the sample sentence, the glass ceiling refers to the fact that the woman believes that she was denied opportunities to advance because she was a woman. The phrase is not meant to be taken literally, which means that options A, C, and D are not correct; option B is correct. 17
Let’s try another short reading passage and vocabulary question. He devoured the works of Augustine, driven by his passion for the ancient world’s wisdom. Question: Which word is the best substitute for “devoured” in the passage? A. considered lackadaisically B. skimmed petulantly C. read voraciously D. ignored tiredly This question is testing your ability to recognize a figurative meaning of the word “devoured.” Clearly, the person in the sentence is not eating books. Instead, you can use clues in the sentence, especially if you are unsure of the meaning of the word “devoured.” We know that the person in the sentence is interested in the topic of the books. So we are looking for an answer choice that implies this. Option C is the best answer, because it suggests that the person in the sentence is positive and enthusiastic about what he is reading. On the other hand, options A, B, and D all imply something negative about the relationship between the reader and the books, but that isn’t what the reading passage suggests. This is why C is the best answer. If you struggle with vocabulary questions, there are steps that you can take to improve your vocabulary. One is to study Greek and Latin roots. Many of the more sophisticated English words contain parts of words that come from Greek and Latin, so studying these roots is an effective way to improve your vocabulary. Use the three charts of Greek and Latin roots in Figures 1, 2, and 3 to study.
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