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It guides you step by step through what you should be working on at every moment to best improve your score. It customizes to your strengths and weaknesses , and then gives you focused practice so you learn the patterns on the ACT. Furthermore, it motivates you to study so that you put in enough time. There's a 4-point guarantee, too— meaning that if you don't improve your score by 4 points or more , you get all of your money back!

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He's committed to providing the highest quality resources to help you succeed. Allen graduated from Harvard University summa cum laude and earned two perfect scores on the SAT in , and in and a perfect score on the ACT. You can also find Allen on his personal website, Shortform , or the Shortform blog. How to Get a Perfect , by a Perfect Scorer. Score on SAT Math. Score on SAT Reading. Score on SAT Writing. What ACT target score should you be aiming for? How to Get a Perfect 4. How to Write an Amazing College Essay. A Comprehensive Guide. Choose Your Test.

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By contrast, most other ACT book guides just list a few books without much rationale about what makes them worth buying. Other guides tend to assume all students are the same. Other sites, such as about. Other writers don't always have the expertise needed to differentiate between ACT prep books and thus recommend books as an afterthought and you can probably tell.

Books for Low Scorers and Low Motivation: If you want to study for only a handful of hours and improve your ACT score by just a little bit, these are the best books to use. That said, we don't recommend putting such little time into your prep! Critical ACT Prep Books These must-have books are what I believe everyone should have, regardless of your current score or what you need to improve. Pros It has the best set of ACT practice tests you can get anywhere, period.

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The book's five full-length practice tests offer a sufficient amount of practice for most students. Since each test takes at least four hours to complete and review, that's already 20 hours of material! Includes additional practice questions. Answers for each question are available in the book.

Answer explanations in the book are not particularly helpful for self-learning. B is correct for these reasons. Five tests isn't enough for ambitious students. You'll need to supplement your prep with other free practice tests or the official online ACT program , which is good only for the extra test it offers. You're really only buying it for the tests, and ACT, Inc. Here are a couple of examples of what you'll learn: The ACT is designed to be a predictable, standardized test. It needs to test basic concepts so that it can be administered nationwide to all students, but it also needs to be difficult, so it distorts the questions in weird ways.

Every answer must be unambiguously correct, or else students would complain that their incorrect answers are correct. This means that your strategy should be to rule out all incorrect answer choices, which is especially important on ACT Reading. Pros It offers a very lucid take on the ACT. The ideas in it will change your view on the ACT and hopefully motivate you to work harder, knowing that any student can excel on the test.

It contains practical strategies that are more helpful than those in most other ACT books; you don't simply learn to rely on tricks. It offers a few alternatives for strategies, and then suggests that you try them out to see which one works best for you. It offers a solid set of answer explanations for the hardest questions in the Official Guide see previous book. The author breaks down the best way to approach each question in a straightforward way. Cons This book requires a ton of self-discipline and insight to use effectively.

For some students, following a set of straight guidelines could be less confusing. Question explanations are based on the old third edition of the Red Book. If you don't have that book, large parts of this book will be either difficult to use. Most question explanations cover the hardest questions in the Red Book.

The fundamental content is lacking. This book is more about teaching an approach to prepping for the ACT. Its English and Science sections are not as strong as its Reading and Math sections are. These books all follow my prep philosophy: Divide ACT content into skills, and get focused training on those skills.

Use realistic, high-quality questions to prep effectively for the ACT. Cover only what you need to know—not advanced material that's not on the ACT. Pros This book articulates grammar rules clearly and accurately. It covers only what you need to know for the ACT and cuts out extraneous material.

Practice questions use a realistic ACT-passage format. They're also all grouped by topic so you can get repeated practice with the same skill. Testing a single grammar skill in this format can be misleading practice for the real test.

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Pros Its lessons teaching math concepts are clear and helpful. They stay focused on math you need to know for the ACT and don't dive into any irrelevant topics. The book divides math into more manageable sub-topics.

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For example, algebra is divided into solving equations, FOILing, word problems, etc. This division into smaller skills lets you concentrate on and attack specific points in your prep. It contains higher-level strategies on how to prep effectively. Cons Answer explanations are lacking. They show you why an answer is correct but don't teach you how to recognize the problem and solve it.

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Though high quality, questions could be more creative. The ACT has a host of questions that are unique and unusual, and having this variety is important to mastering the test. The book doesn't distinguish by difficulty level. On the ACT, the hardest questions are much more challenging than the easiest questions.

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Trying to understand these can be a waste of time when you should instead build your fundamental skills. Pros It offers a great breakdown of the Reading section on a skill-by-skill level. You'll get some of the most helpful strategies for every Reading question type. The book has lots of realistic, high-quality passages and questions. It contains useful strategies on skimming and how to approach Reading passages.

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  • Quick arithmetic a self teaching guide.

The writing style is dry and clinical, like an academic textbook. I personally prefer this—cut out the fluff—but it can be quite dense for the average student. Its lack of creative page layouts and tendency to use a lot of text on large pages can get tiresome. Pros The book contains a complete breakdown of every type of passage and question type you'll see on ACT Science. Could you recommend any references for this topic?

I am using your text to learn analysis and I enjoy it very much. But I am puzzled by exercise 2. I found a solution from internet as follow. Rephrase lemma 2.

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Proof: P 0 is true vacuously. Suppose P n is true. Is this proof correct? Tao, I find that in definition 9. I set myself as an exercise to prove that and are the same for both of these two cases. And I think it should true, isn't it? Generally, what's the principle or advantages to use one of them instead of another?