act math practice questions (with answer explanations)

after you’ve worked through each question, click on the link for the video answer and explanation! you can also do them in a row and check your answers later, as a mini-practice test in math.

we’ve included buttons for you to click to save your answers as you work through these problems, but keep in mind that these are just for your use. they don’t submit or save your answers, so you may want to take notes as you go. and now, without further ado, here’s are 15 act sample math questions to test your knowledge and sharpen your test-taking skills!

act algebra sample questions

difficulty: medium

1. if \(\frac{x}{3}+\frac{x}{4}+15=\text{x}\), then \(\text{x}= \)

click here for the answer and video explanation for problem 1!

difficulty: medium

2. given that f(x) = 3x – 5 and g(x) = x^3 – x, what is f(g(2))?

click here for the answer and video explanation for problem 2!

difficulty: medium

3. a, b, and c are consecutive odd integers such that a<b<c.

if a + b + c = 81, then a + c =

click here for the answer and video explanation for problem 3!

difficulty: medium

4. five lemonades and two cookies cost $1.50. two lemonades and five cookies cost $2.70. how much does one cookie and one lemonade cost?

click here for the answer and video explanation for problem 4!

difficulty: medium

5. if x > x², which of the following must be true about x?

click here for the answer and video explanation for problem 5!

act geometry sample questions

difficulty: medium

6.
in trapezoid abcd, bc = ef = 6, af = de = 3, and

ab = cd = 5. if the area of a trapezoid is given by

\(\text{a}=(\frac{{\text{b}_1}+{\text{b}_2}}{2})\text{h}\)

then which of the following is the area of trapezoid abcd?

click here for the answer and video explanation for problem 6!

difficulty: hard

7. in the diagram below, chord df is parallel to the diameter ac. the length of df is 20 cm and the length of ac is 28 cm. what is the distance, in centimeters, from b, the center of the circle, to e, the midpoint of df?

click here for the answer and video explanation for problem 7!

difficulty: easy

8. tony plans to put a rectangular perimeter of fencing around his backyard pool. the area to be sectioned off for the pool area measures 22 feet by 30 feet. one long side of the pool area is along the house, so he only needs to fence off 3 sides. how many feet of fencing will he need?

click here for the answer and video explanation for problem 8!

difficulty: hard

9. circle b below has a radius of 4 and arc ac has a central degree measure of 145°. what is the approximate length of arc ac?

click here for the answer and video explanation for problem 9!

difficulty: very hard

10. △abc and △def are both equilateral. given de is 50% greater than ab, by what percentage is the area of △def greater than the area of △abc?

click here for the answer and video explanation for problem 10!

act trigonometry sample questions

difficulty: very hard

11. whenever cos(θ) = 0, and π ≤ θ ≤ 2π, the value of sin(θ) =

click here for the answer and video explanation for problem 11!

difficulty: hard

12.

which of the following is the value of

(sin(30°) – cos(30°))2 ?

click here for the answer and video explanation for problem 12!

difficulty: hard

13. which of the following angles has the same terminal side as 1,105°?

click here for the answer and video explanation for problem 13!

difficulty: hard

14. the tree below casts a shadow that is 24 feet long, and the angle of elevation from the tip of the shadow to the top of the tree has a cosine of \(\frac{4}{5}\). what is the height of the tree?

click here for the answer and video explanation for problem 14!

difficulty: medium

15. which of the following is the value of 240° in radians?

click here for the answer and video explanation for problem 15!

more resources for act math

want more act math practice questions and resources? impressive! so what are your next steps? check out these posts to get a better understanding of all the question types you’ll see on the act math test, from categories of questions to basic formulas to geometric figures and systems of equations. these resources will help your act math prep by letting you get a better sense of all the different kinds of act math questions you’ll see on the actual test! take a look.

• 7 free 2022世界杯入门名单s
• hard act math problems
• guide to act trig
• guide to common act math topics
• act math formulas to learn

the post act math practice questions and solutions appeared first on magoosh blog | high school.

• both options enable you to apply for college prior to regular admission deadlines and get an admission decision before regular applicants.
• if you apply early decision, you are bound to attending one school.
• you can apply to multiple colleges as an early action applicant (check the fine print of each school for their unique policies).
• both application types are usually due november 1st and you will hear about your admission status by mid-december.
• early action is not better than early decision and vice versa. each has its benefits and drawbacks.
• some admissions experts suggest that applying early increases your admission chances.

comparing early action vs. early decision

okay, now that you’ve got a general sense of the two ways to apply early to college, let’s look a little closer at the main differences between them.

think about the actual name of each option for a moment.

“early action” simply suggests that you’re taking action steps toward applying for college earlier.

“early decision,” on the other hand, has the word “decision” right in the name. it means that your mind is made up. you’ve decided that if you get into this school, you’re going no matter what—it’s your first-choice school. and that’s why early decision applications are binding. when you apply early decision to a school you are making a promise that you will attend if accepted.

binding vs. non-binding

a really important thing to know about early decision applications is that they aren’t legally binding. this means that you can’t be taken to court if you apply early decision, are accepted, and then want to back out. but—they are binding within the college system. so if you change your mind and decide to attend another college where you did not apply early decision, you could face having your admission revoked.

on the other hand, early action applications are non-binding. you’ll find out if you got in earlier, but you can still weigh your options. you’ll typically have until the regular commitment date (may 1st) to make a choice.

what to consider when choosing early action vs. early decision

when you’re deciding whether you want to apply early action vs. early decision, here’s the biggest factor:

how badly do you want to attend a particular college? do you have a true dream school? do just know, beyond a shadow of a doubt, that this is the school for you? if so, applying early decision is the way to go.

but before you take that plunge and commit, it may be worthwhile to spend some time really reflecting on the factors that make this school your #1 choice.

factors to consider

for instance, you may be dead set on a particular school on account of:

• a particular program of study — is it the only place this program is offered? is it the best of the best? are there specific faculty members you’d love to take classes with?
• geographic location — is it very important to you where you go to college when it comes to the city or state? what draws you to this particular place? why will living there be integral to your college experience?
• financial aid — some schools guarantee a certain amount of financial aid to admitted students, which may be a significant factor in your decision.
• extracurricular activities — is there a sports team you’ve been scouted for? a club that you’d absolutely love to be part of? a greek community that you feel drawn to?
• internships or other experiential opportunities — is there a school-to-career pipeline of some sort that is offered at this school? are you guaranteed some type of intern/externship, mentorship, or research opportunity you can’t get anywhere else?
• values — is there something about the school’s culture and values that appeals to you? for instance, is it affiliated with a particular religion or committed to building a diverse student population?
• other personal reasons — you may be set on a specific school because of family legacy or the school’s history or prestige.

if you don’t feel “all-in” on a college because of any combination of the above reasons, but you’d still like to apply early, then early action is likely the better route for you. also, if you’re a competitive applicant (great grades, class ranking, test scores, etc.), then early action or early decision may be a good choice for you.

still unsure? check out our quiz on whether you should accept early decision!

pros

of course, there are pros and cons to early action vs. early decision. on the upside, you’ll be better able to make your college plans earlier, which can be less stressful and more cost-effective. on the downside, you’ll have to assemble your application materials quickly, which could be stressful if you’re not prepared.

let’s look at some key points of early action vs. early decision.

early action:

• you will know your admission status early and have more time to make plans regarding housing, financial aid, jobs, classes, and so on.
• you can apply to multiple schools early action and therefore you will have options when it comes to choosing a school. this includes having time to weigh out financial aid package offers from each school.

early decision:

• if you get in, you can celebrate super early that you got into your dream school!
• by making this type of preemptive commitment, you may be more likely to be accepted (more on this shortly)

cons

early action:

• you may have more applications if you’re applying early action, which can add a lot of pressure on top of an already busy schedule during your senior year.
• if you get in more than one school, you may feel overwhelmed by indecision (although this isn’t an entirely bad problem to have!). conversely, if you don’t get into any of your early action schools, you will only have a short window to apply regular decision elsewhere.

early decision:

• you only get one early decision application, so if you start to waver on your decision, the entire college application process can get delayed.
• there may be less financial aid options available and you won’t have the opportunity to weigh out other options.

how do i decide which schools to apply to?

okay so once you have an idea of which early application route you’ll be taking, how do you decide schools to apply to?

1. look into which schools offer early action and/or early decision options; not all of them do.
   1. some of the most common early action schools include northeastern, university of michigan, mit, and georgetown.
   2. some of the most common early decision schools include nyu, rice university, and columbia university.
2. check the admissions page or call the admissions office of each school you’re interested in to double-check their early application policies and deadlines.

you can read more about how to choose the right college here!

does early action or early decision increase chances of acceptance?

when it comes to the odds of getting into a college or university by applying early decision, the truth is that your chances depend on the school. ask an admissions department directly about their acceptance rates and if early decision candidates are given any sort of priority, or take a look at their most recent class profile. also, consider that:

• because applying early decision is binding, less students apply, which may increase your chances of getting in.
• what appears to be higher acceptance rates could be due to stronger and more competitive candidates applying early decision.

in short, it certainly can’t hurt, so if you feel strongly about a particular fit, we say go for it! (on that note, check out these 3 tips for applying early decision).

other types of early action and early decision

to make matters a bit more complex, there are also a couple of lesser-known types of early action and early decision applications.

early decision 2

early decision 2 (often just abbreviated as ed2) is an option some schools offer that is virtually identical to early decision (1) but has a different due date. so while most early decision deadlines are november 1st, early decision 2 is later, often january 1st or 15th (with notifications arriving in february). both types of early decision applications are binding with one school, but ed2 allows you a bit more time to get your application together. it’s unclear if you stand a better chance of admission with early decision vs. early decision 2. but with either type of application, you’ll be demonstrating your seriousness about your interest in a particular school.

restrictive early action

restrictive early action (also known as single-choice early action or restrictive ea), on the other hand, is a type of early action application that is sort of like a hybrid of early decision and early action. it’s non-binding (like early action), but you can only choose one school to apply to (like early decision). a select number of elite colleges including princeton, yale, harvard, and stanford offer restrictive early action.

the gist is that you will want to look into the specific application types and deadlines for each school that you’re interested in and then go from there.

early action vs. early decision: a final word

overall, the decision to apply early action vs. early decision to college hinges largely on how prepared you are to apply as well as how clear you are on where you want to go and what you want to study. there’s no wrong choice, and whateverway you apply early will show your seriousness and commitment to attending college, which is always a good look to admissions boards. if you want more help deciding which route is best for you, we encourage you to chat with your school counselor.

and what about if you apply early decision but don’t get in? you may feel bummed but the good news is that you’re still able to apply to plenty of other schools by the regular deadline.

happy applying and good luck!

the post early action vs. early decision: understanding the difference appeared first on magoosh blog | high school.

*list prices given at time of publication and subject to change. click on the book cover found in each review to see the current price on amazon.

best sat books of 2021-2022: reviews

not all sat prep books are created equal: some you’ll want to use in their entirety (though only a few), others you’ll want to use only parts of, and others you’ll want to steer clear of. this is particularly true now that prices are falling and kindle versions are available—in some ways, that’s awesome, but it can also encourage students to buy a ton of books without seriously evaluating their quality.

to help you maximize your study time (and save your hard-earned cash) i’ve reviewed the options for the best sat books on the market and graded them from most to least helpful. keep in mind that some publishers do a good job on some things (like practice tests or a specific section of the sat) and a sub-par job on other things. this doesn’t necessarily mean that you shouldn’t buy the book, but it might mean that you won’t use the book in its entirety.

magoosh’s complete, free sat study guide

i want to start by pointing out that magoosh has a great, free sat study guide! we’ve spent years and years reviewing all of the sat study guides out there. we knew that our experts could cut through all of the unnecessary stuff and give you the best info out there…so that’s what we did! even better? it doesn’t cost you a cent. we even have a free sat practice test you can take after studying!

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sat prep black book: the most effective sat strategies ever published

how the current edition compares to the previous one
this book hasn’t been updated for a while (the most recent version was published in 2017), so steer clear of the first edition: it’s written for a previous edition of the test and won’t help you prepare for the current sat!

things to love

• this book provides in-depth explanations (and we mean really in-depth explanations) of the four official sat practice tests from the college board. the college board’s practice is great—but if you’re struggling to understand why you got questions wrong even after reading their explanations, this is a great place to turn.
• it’s also a great place to get your strategy set for test day. not only does mike barrett give you multiple workable methods to approach questions, but he also goes through possible issues and solutions to every type of everything: passages, questions, answers, even test-taking vocabulary.
• the book even covers what non-native english speakers should focus on (albeit in a slightly perfunctory way).

things to consider
is this the be-all and end-all of sat prep? well, no.

• in the first place, we definitely have some pedagogical (teaching) differences. barrett encourages you not to think about the average time you spend per question, and while we don’t think you should obsess over this, you should definitely be aware of it.
• he also doesn’t encourage taking notes while you read or taking a diagnostic test. those strategies can be helpful for many test-takers.
• in addition, barrett vastly underplays the importance of the sat essay, noting that a lot of test-takers won’t need to take it. while that may be true of some test-takers, more and more schools are requiring the sat essay—particularly the most competitive schools that students aiming for a 1600 are probably targeting.
• finally, you won’t find any practice questions here. barrett has his own arguments for why you should only use college board resources. we definitely disagree with that; for students aiming for top scores, a much deeper pool of questions is important (as long as they’re up to snuff)!

takeaway
at the end of the day, this is a pretty great addition to your sat library, particularly for those students just starting their test prep journey.

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kallis’ sat pattern strategy

how the current edition compares to the previous one
the 2018 kallis book and the previous 2016 edition are similar in many respects, but there have been a few distinct changes. most of these changes are good. the sat reading and sat math practice questions have been updated to better reflect the content of the real sat, with more recently written passages and a more even mix of math topics, respectively. there are a few changes that seem like downgrades though, with less tutorial support for certain topics in sat writing & language and sat math.

things to love

• the content review for each section is thorough, clear, engaging, and most importantly, helpful. of course, many publishers do content review fairly well.
• where most books flounder is in writing the practice tests, but kallis is relatively strong on that front. kallis isn’t perfect—it’s exceedingly difficult to write questions that mimic the real test—but they do a respectable job. and in the newest edition, the quality is more respectable than ever. the sat math practice is much improved–there no more long strings of problems that just focus on one topic, and kallis has added more complex word problems that resemble the college board ones more closely. the sat reading practice also now includes more passages that were written in the last 20 years, compared to the 2016 volume’s disproportionate use of late 1800s/early 1900s readings.
• the amount of practice content is great too: 6 full practice tests!

things to consider

• the writing questions tend to be more difficult than those on the actual test and don’t quite have the feel of those questions.
• the reading passages are sometimes spot-on. other times, they are too stylistic and more reminiscent of the old sat. there’s also slightly more of a focus on trap answers than on the actual test.
• the book does a great job in presenting the content you need to know for the new test. however, it doesn’t do the greatest job of discussing strategies. for instance, it shows you the tedious and not necessarily intuitive way of setting up complex equations rather than the tried-and-true way of plugging in values. likewise, the writing section recommends always reading the question first instead of reading the passage first, or at least a paragraph at a time. i advocate for a nuanced approach, one that takes into account both tactics.
• even with the addition of some more sat-like word problems, most of the word problems in the math section still tend to contain far fewer words than those on the actual exam. the contexts used in the examples are often a little too relatable. gone is the more esoteric fare of the actual test—bacteria in a petri dish, strength of a satellite signal, etc.
• frustratingly, support and advice for certain key writing & language and math topics that were in the 2016 version of kallis’ sat pattern strategy have been removed from the 2018 book. there is noticeably less support and advice for stats and functions, and advice on certain writing features such as passive voice or reporting verbs have been removed altogether.

takeaway
an all-around excellent prep book for the sat, one that is great for the motivated self-studier, especially one who aims to score in the top 20%. i intend to use it to tutor, which is a lofty compliment, given that i say this about very few prep books outside of the official materials.

(quick update: i ended up using this book for my class, and it turns out that quite a few of the writing questions have debatable answer choices or at least wrong answers that aren’t quite wrong enough. for that reason, i’ve lowered the grade from an a- to a b+.)

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ivy global: ultimate sat guide and sat 6 practice tests

ivy global is a lesser-known publisher that produces high-quality practice materials. they have two main books, the ultimate sat guide and sat 6 practice tests, and offer two free practice tests on their website (available to anyone whether you bought a book or not). the ultimate sat guide offers a thorough concept review for each section and three full practice tests. the 6 practice tests book gives a quick run-down of the sections and question types and offers 6 practice tests. each practice test is different from the others from ivy global, so you don’t have to worry about paying for the same material twice. the ultimate sat guide is a more refined version of ivy global’s new sat guide 2.0 but the test material is nearly the same. the only difference is some of the concept reviews and errors from the previous edition were fixed and improved slightly.

things to love

• in both books, the text and layout design are clear and understated. they don’t go for the whimsical or frenetic styles that other test prep books have, which can definitely be a plus if you want something a little more no-nonsense
• in the main book, the new sat guide, the introduction to the sat and test-taking strategies sections are clear and well-formatted.
• the section-specific explanations cover the necessary material and use lots of examples. not enough to teach you a concept if you’ve never seen it before, but definitely enough to help you refresh your memory and fill in any gaps.
• their practice tests are strong. the questions match the difficulty of the real thing, and there’s a good range of difficulty in each section.

things to consider

• the one small weakness is that there are no answer explanations in the back of the book, just the correct answer choices. answer explanations are available online, which isn’t too big of a deal, but it does add an extra step.
• this book might have jumped into the a range if it had more extensive review of strategies and made it clear how they are most advantageous for different topics and situations. similar to the kallis book, this is a great resource, but probably shouldn’t be your only test prep resource.

takeaway
great general-purpose practice source that deserves more attention!

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princeton review: sat premium prep, 2022 (formerly cracking the sat, 2020)

how the current edition compares to the previous one
the 2022 sat premium prep is the new evolution of the cracking the sat series. although it is presented as an update, the 2022 edition matches the 2020 edition aside from a few minor edits. previous reviewers have noted that the 2020 edition is also a near reprint of older editions from 2018/2019 so you may want to consider buying any version since they’re essentially the same over the last 3 years. the benefit of the premium version is that it gives you eight practice tests (four in the book and four online) whereas the conventional version gives you five practice tests (four in the book and one online). the rest of the content is the same.

things to love

• hey, want to learn a lot about sat math? this book has almost 300 pages of material to review, strategies to learn, and practice sets to, well, practice. if you want a total math review with lots of practice, this is a great place to start.
• the verbal sections are really strong in how they introduce the test format, then walk you through progressively more difficult (and sat-like) examples.
• unlike a lot of other books, the verbal here is pretty solid as well. in particular, the princeton review seems to actually understand the college board’s incorporation of graphs into the verbal section on the new sat—a nuanced concept that few publishers get right.
• also, the practice tests here are different than those included in the princeton review’s 10 practice tests for the sat, so if you’ve bought both books, you’ll really get your money’s worth.

things to consider

• what’s that you say? seems overwhelming? it is, a little.
• if you’re looking for practice on reading or writing and language, the book does offer good advice and practice sets—just not very much advice and not many practice sets (think 50-75 pages).
• yes, students do struggle with sat math, but there’s no need to push it on them to the exclusion of the other sections. after all, you need to look at that composite score, too!
• meanwhile, other parts are unnecessarily confusing, mainly because they use a ton of acronyms (including the unfortunate “pood”).

takeaway
a great place to overhaul your math scores if you have a lot of time before the exam. also worth looking into for the use of graphs in the verbal sections.

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pwn the sat: math guide

how the current edition compares to the previous one
the most recent edition of this book is from 2016, when the sat changed—so definitely don’t get earlier editions! they won’t prep you for the current test.

things to love

• many test prep books make the mistake of being dry—really dry. and that’s a problem when your subject matter is already dry to begin with. mike mcclenathan steers clear of any such aridity, injecting a “hey-we’re-in-this-together” voice as he takes you through all the important parts of the sat.
• you never feel like he’s writing this book to meet some deadline. it’s clearly a labor of love. his affection for the material and the test comes across in nearly every page. but it isn’t that he just wants to geek out on the material—he genuinely seems to care that students improve their score.
• luckily, the book gives us a clean breakdown of every question type in the official guide. that way, you can practice a concept on real sat questions and have a rough idea of how difficult they are (the difficulty of these questions depends on where the question shows up in the section—easier questions are at the beginning; harder questions at the end).
• overall, a strong book for the self-studier who needs an accessible refresher of the math tested on the sat.

things to consider

• this book alone isn’t enough to improve your score—though it is a good start. you’ll want to make sure to complement it with the official guide (as the author encourages). even then, i recommend a book like barron’s 1600 math book so you can get lots of extra practice questions.
• the questions in the pwn book, while okay, don’t quite impart the flavor of the current test. it seems that some of them are still steeped in the old-sat-style of asking questions.
• another issue is there is no indication of whether a question in a practice set is ‘easy,’ ‘medium,’ or ‘difficult.’ this is problematic because, often, the section that introduces the topic uses clear, easy-to-follow examples. then there’s a jump in difficulty in the problem sets, often because what you learned at the beginning of the chapter isn’t enough to answer the harder questions. for students who are just starting out, they might get easily frustrated and think, as they are wont to do, that they aren’t good at math. the problem sets would have been improved had they included easier questions and broken up the questions into discrete difficulty levels.

takeaway
on its own, this book isn’t enough to prepare you for test day. in combination with a few other resources, though (namely, the official guide), it’s a great resource for students aiming for top math scores.

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500+ practice questions for the new sat

how the current edition compares to the previous one
this book hasn’t been updated since 2015, but it does focus on the “new” (i.e. 2016-onwards) sat. so don’t get earlier editions, but this one is geared towards the current test.

things to love

• the princeton review has created questions that, while perfectly legitimate, aren’t quite as complex and nuanced as those found on the actual test. and you know what? that’s not necessarily a bad thing—if you are just starting off.
• unlike kaplan’s books, for instance, which—at least for verbal—are much easier than the real test in an inaccurate way, the princeton review mostly stays true to the underlying subtleties of the questions and answer choices. it just doesn’t have the hard-level questions that make up 15-20% of the actual test.

things to consider

• you’ll have to pick up another book to help you with strategies and to review the fundamentals.
• you’ll need a book that also has practice tests, since this book is made up of just one drill after another.

takeaway
as a companion guide to a book of strategies and fundamentals, this book is a great place to start.

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10 practice tests for the sat, 2022 edition

note: the practice tests in this book are not the same ones that appear in the princeton review’s cracking the sat (reviewed above). all commentary here applies to the 10 practice tests book alone.

how the current edition compares to the previous one
there are no changes from the 2020 edition (which had four new practice tests added and some older passages updated) to the 2022 edition. tests 1-6 are the exact same six tests seen in the 2017 book. the two new passages were written in 2008 and 2014, while the older essay prompt readings were from the early-to-mid 20th century.

things to love

• the verbal sections here are pretty strong, and there are also great medium- and low-level math items. the science passages in the reading section are outstanding, and so is the princeton review’s use of graphic stimuli in these sections. these types of problems are going to be a new kind of challenge for many students on test day, and here we have difficult, test-like problems! woohoo!
• answer explanations are also pretty good. the explanations of wrong answers are brief or even missing, but the clear explanations of why the right choice is right make this a relatively small issue.
• the upgrades from the previous edition are nice. 10 practice questions are literally greater than 6! and the two modernized essay prompts a minor but nice improvement.

things to consider

• the math here verges on the easy side, but not so much so that it’s unfaithful to the test. it’s just missing those tough problems that you’ll need to answer correctly for a 700+ sectional score. if you’re looking to get your score up in the top percentiles, you’ll want to supplement the tests with practice problems from books like the college board’s official guide.

takeaway
a good book for most students. if you’re hoping to score in the stratosphere (90th percentile or above), you might begin here, depending on where you are now, and move on to more challenging materials as you master these problems.

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barron’s sat, 31st edition

how the current edition compares to the previous one
the 2021 edition has been updated with few new changes compared to the 2020 edition. the most major change is the removal of all guides related to the sat essay that has been recently removed from the test. the second update that might prove more meaningful is the addition of an index at the end of the book. the index allows you to go straight to the page for nearly every concept on the test which is helpful if you’re looking for targeted practice. aside from the essay removal and index addition, the book is nearly identical to the previous edition.

things to love

• the math is great! the strategies are solid and helpful, the concepts are broken down well, and it hits that goldilocks sweet spot of around 200 pages—enough to help you enormously without being overwhelming.
• answer explanations are great on the practice sets (though less so on the practice tests…see below).
• there’s a flashcard app! this is exciting.
• the index makes it easier to find the content you want to review.

things to consider

• how long do you think it would take you to memorize 74 pages of word definitions in teensy-tiny type? is there enough time before test day? if not, and you’re looking for verbal help, you’d better look elsewhere. other than those 74 pages, there are only about 60 pages of reading test help here, and ditto for writing and language. furthermore, writing and language is full of lists that made even my eyes glaze over. how helpful is a list of conjugated irregular verbs when you’re studying for the sat? well…sorry, i just fell asleep there for a moment. those lists are not helpful at all.
• practice test answer explanations are really weak (“a is the right answer because xyz. b is not the right answer because it is not xyz”).
• yes, there’s a flashcard app…but is your time going to be best spent studying the 3,000 words the book claims are on that app? definitely not.

takeaway
this is great for math practice and really, really not student-friendly for the verbal.

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the official sat study guide 2020

how the current edition compares to the previous one
there are a few small, inconsequential changes to the math support in the official sat study guide (2020), compared to the previous 2018 version. a few example problems have been changed, with one algebra equation replaced by another, a geometry question replaced with a different geometry question on a similar topic, and so on. again, very minor changes, likely due to feedback or analysis that the college board received regarding the prior version of the book. the truly big change here is the eight practice tests: two of the practice exams are brand new, while the other 6 also appeared in the 2018 sat og.

things to love

• the questions in this book are mt. sinai level. the sat gods part the skies and give us a taste of what to expect when the test debuts in a couple of months. all the nuances, all the traps, all the idiosyncrasies are there for us to behold, and the more you understand them, the better prepared you’ll be come test day

things to consider

• the practice questions in this book are available for free online, and, since the questions are by far the best thing about this book, you might rightly start to wonder whether you need to actually purchase this book. what follows might indeed make you think you don’t need the book at all.
• the explanations are really weak. how weak? well….hi, i’m going to play pretend today. i’m going to pretend i’m the person or people who wrote the explanations for the questions.choice (a) is the best answer because the information in the passage best supports (a). lines 11-13, <insert quote here> show this.(b), (c), and (d) do not specifically answer the question.to be fair, the explanation of the right answer is often more thorough. as for why the wrong answer is wrong, forget about it. that is about as specific as it gets. in the end, you are likely to find these explanations laconic to the point of infuriation. this is problematic, since understanding your mistakes is one of the best ways to improve.as a result, i’ve put together video explanations to the official sat study guide questions. you can check them out for free in our magoosh sat youtube channel.
• the strategy tutorials leave a lot to be desired. admittedly, i like the way the book breaks down the test so and covers all its components and aspects. however, there is so much terminology that i imagine students getting bogged down thinking they have to know what nonrestrictive and parenthetical elements are, or that these needlessly complicated terms are known as “conventions of punctuation.”as indicated in my example above, the strategy support for sat writing & language is particularly frustrating. what we don’t get is a solid explanation of grammar concepts and how they relate to the test. nor do we get strategies on how to approach these questions. in fact, i feel like the first few hundred pages are more for people like me—people who want to understand how the test is constructed—and less for students, who need help understanding how to solve the actual questions.

takeaway
in sum, you don’t need to buy this book. for review, you are much better off going with any of the major publishers on the market. for practice questions, there is no better source than the college board, but the fact that they have made this content available for free online makes this book unnecessary, if not unhelpful. now let’s hope the clouds don’t part and the college board strikes me down with lightning. (my alternative grade for this book? ‘r’ for redundant.)

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using the best sat books in your studies

there you have it, the best sat books to use in your prep. for more information on how to put the best sat books to use in a complete study plan, check out our study schedules for the sat!

questions, comments, concerns? leave me a comment, and let’s get this discussion on the best sat books started!

the post best sat books 2021-2022 | book reviews appeared first on magoosh blog | high school.

let’s start out with a quick overview of the books and their quality before getting into greater detail with in-depth reviews below.

*list prices given at time of publication and subject to change

best act prep books of 2021: book reviews

below you’ll find even more information on the best act prep books we recommend for students as well as links to all of our act book reviews.

disclaimer: every book has pros or cons; make sure you pay close attention to what is important to you in a prep book!

act prep by magoosh

everything you need to know about the act, straight from magoosh’s experts.

it feels a bit awkward to promote our own book here, but the truth is that we made it because we realized that there wasn’t a great book out there that was up-to-date and comprehensive. our experts poured all of their knowledge about the act into this book and have made it available in act prep by magoosh.

there’s a ton of really important stuff in here, including 300+ practice questions, lessons in all act areas, great advice on how to approach each and every section of the exam, an in-depth study schedule…and a full-length practice test to help you gauge your progress! basically, everything you need to start your act prep is right here. (so, knowing all that, how could i not promote it?!)

the official act prep guide, 2021-2022

the tests in the official act prep guide are real former act tests. and there is no better way to hone your act skills than using actual questions crafted by the writers of the test.

the main differences between the 2020 and 2021 versions is the addition of a diagnostic exam at the end of chapter three. other than that the other 5 tests are almost identical to the 5 exams in the 2020 edition. the only other difference is that the 2021 version comes with access to 400 flash cards online.

check out our full official act prep guide review. (if you’re looking for reviews of earlier editions, you can find them here!)

act prep black book, 2nd edition

this is a bare-bones publishing job, but its information is pretty awesome. in addition to providing general strategy advice, the act prep black book walks students through many of the questions in the act “red book” (the real act prep guide) and explains how to strategically answer them.

yes, the red book gives you answer explanations, but the black book gives you strategic advice on how to answer them: which questions should be back-solved using the answer choices, for example, or how to use the english section answer choices to find the right answer without needing to understand the grammar. it’s a pretty great resource for learning how to get inside the heads of the test-makers.

check out our full review of the previous edition act prep black book.

barron’s act, 4th edition (2019)

as kristin mentioned in her review of the first edition of barron’s act, this book is one of the more useful unofficial act guides on the market. but was barron’s able to maintain this quality and build on it in barron’s act, 4th edition? to some extent, the answer is yes.

quality of the practice questions

as in previous editions, barron’s does a good job of capturing the basic format and “flavor” of real act practice materials. but once more, most of the practice questions are easier than the real test. the act writing prompts are top-notice, and there are multiple score sample essays for each question. the act english questions are a little too easy on average and largely unchanged from past editions. act reading questions are mostly the same and a little bit too easy. act math has too few data interpretation questions, though there are questions with figures which will give you some practice. finally, act science in this edition, two of the three science sections have six passages and the third has seven. this ratio of six passages and 40 questions is a better reflection of the current act. in fact, on the new act, you will pretty much always see six passages instead of seven.

answer explanations, strategies and skills

the start of the book gives a thorough account of what the act is and what it contains. the sections of strategy advice for act english, math, reading, and science are near-identical to the material in the previous version, all of which was excellent. still, this lack of change makes the new barron’s act book a not-so-appealing option if you already have the last edition. the act writing portion of the book is fully updated. this completely new content is really amazing, and it includes some extra practice questions and sample responses, with scorer commentary. the answer explanations are well-written and complete, just as they were in the last book.

grade

practice material: b+

answer explanations, strategies, and skills: b+

ivy global act guide, edition 1.2

ivy global is a less well-known name for test prep, but they continue to produce high-quality practice materials that are worth your attention. while they’re more commonly known in the realm of sat prep, they came out with an act guide in 2019 that is very good. they also released an updated act guide in 2020 but it is nearly the same as the 2019 version with only a few minor edits.

ivy global’s style is minimal and no-nonsense. it is a real breath of fresh air after other test prep books with a more cluttered and energetic style or format they offer a clear and concise introduction to the test and test taking strategies that are easy to understand. their section-specific review is great. not exactly enough to teach you a topic you’ve never seen before, but definitely enough to help you refresh or fill in any gaps. thankfully, they use lots of act-style questions and examples to help teach the concepts, rather than just rushing through a review.

the book offers three practice tests, and these are a good representation of the topics and difficulty on the real test. there are also free practice tests available to anyone on the ivy global site. it’s important to note that full answer explanations are available on the site only, which isn’t a huge deal, but does add an extra step. they offer a test only book with four full practice tests but the first three tests are the same tests from their act guide book.

grade

practice material: a-

manhattan 5 lb. book of act practice problems

the manhattan 5 lb. book of act practice problems may be the best unofficial act practice book, and it’s a great companion to the official act guide and official act website. still, this book does have some weaknesses alongside its many strengths.

quality of the practice questions

manhattan’s act math questions are excellent. they are 100% consistent with ones you’ll see on the real sat, and follow the same format and difficulty. the act reading and english are definitely act-like, but the sections as a whole are a little easier than the real thing. that’s because the real act will test you on more than one skill on each question, such as knowledge of vocabulary and literary devices. manhattan has a little too many one-skill prompts, which makes the sections easier on average. act science is also a little easier than it should be.

there are two other small issues. first, manhattan uses “except questions,” where you need to identify the one idea that is not in the passage. this is common in act reading but not in act science. second, there are some pre-algebra math operations that wouldn’t occur outside of act math. you’ll still get good practice, but just keep in mind that it’s not as accurate to the test as the other sections.

answer explanations, strategies and skill

each answer explanation really acts as a mini-lesson on academic content, and this allows you to walk away with knowledge that’s applicable to other similar act questions. as an added bonus, questions in this book are organized by subject. that way, you can focus your practice on the question types you find most challenging.

there is a potential shortcoming, though. unlike the current official act guide, manhattan’s explanations don’t directly address incorrect answers. you aren’t really given any insight into how incorrect answers are designed to trick you.

grade

practice material: a+ for math, b- for english and reading, c for science

answer explanations, strategies and skills: b

barron’s act 36, 4th edition

barron’s offers a smaller, more targeted book called act 36. the 4th edition is similar to previous editions, so i would direct anyone interested to kristin’s review of act 36, 2nd edition.

barron’s 36 has always been unusually short by test prep standards. this book is designed as a short introductory course for the act. key ideas and small sets of practice questions are much more clearly marked than before. certain content has been slightly re-ordered so that the organization of each chapter is more logical. and most of the answer explanations have been edited to be more short and to-the-point.

in its 4th edition, barron’s act remains a very basic book. the book makes for a good introductory warm-up before you move on to longer, more advanced prep books. i may recommend this as a source for students hoping to break into the 30s because they can still practice problem solving strategies and time and stress management. they’ll just need to make sure that they use other sources of questions as well to make sure that they give themselves time to get used to the full range of difficulty. for all sections, the explanations have a good level of detail, which many test prep books do not have.

grade

practice material: b-

answer explanations, strategies and skills: b-

mcgraw-hill act 2021

past reviews have observed that the 2018 book was better than the 2014 version of their book, 10 2022世界杯入门名单s, though it still had flaws. the 2021 edition is a little bit better, but like its predecessors, isn’t perfect. the 2021 edition includes a short section about the new updates to the act test. these updates include the shift to online exams, the retakes of individual sections and the new superscoring policy. the new edition retains the updated explanations from the 2020 version but is otherwise almost a page for page copy of the 2020 edition.

practice materials

mcgraw-hill’s act 2021 offers four print practice tests and access to four more practice tests online. there’s also a diagnostic test at the beginning of the book, and a set of additional practice questions for every section.

so you get a lot of act practice with this book, but is that practice good? act english in the 2021 edition is better than in past editions. the questions are a little on the easy side, but overall are the right length and contain the right mix of topics. act math is similar. it’s a little too easy but will help you learn the topics. not all of the act reading passages are the correct length, and the difficulty is too high. act science is excellent, as it was in past editions. this is the closest you can get to the real thing in a third-party act prep book. finally, the act writing is good, but not great. the essay prompts are good, but the opinions are too long. just something to keep in mind if you use act writing practice from this book.

answer explanations

in the past we called out mcgraw-hill’s answer explanations for being too short and unhelpful. some are still that way, but the explanation quality is also a little better. more explanations go into detail, which is a step in the right direction, but we’d still like them to be clearer.

skills and strategy

the good

mcgraw-hill has some really nice skills building practice materials for english, math, reading, and science. there’s some basic advice throughout their chapters on skills and strategy too, but certain strategies are not going to work for everyone, such as speed reading, or are too obvious to be of much help (“listen to your brain”?!). however, mcgraw-hill has especially good advice for pacing and multiple-choice strategy.

the bad

sometimes the activities are too short, and equal attention is not given to each section and skill. the chapter on act science prep is shorter than the other chapters. and there’s too much focus on easier act math skills like elementary algebra. harder aspects of act math, such as logarithms and trigonometry, are barely explained—and when the math chapter is about three times as long as any of the other chapters, you’d definitely expect more thorough coverage! the writing chapter is better than it’s been in previous editions, but is still a little light. overall, the “advice” portions of this book are written in a confusing, inconsistent way.

act 2021 (mcgraw-hill education): grade

practice materials (act science): a

practice materials (everything else): c+

answer explanations: c

skills and strategy: c

mcgraw-hill 10 2022世界杯入门名单s, 6th edition

there are some things i really like about mcgraw-hill’s 10 2022世界杯入门名单s, 6th edition. but there’s also a lot to dislike. mcgraw-hill’s ability to replicate truly act-like practice varies a good deal, depending on the section of the exam you’re dealing with. and their answer explanations leave much to be desired. it is worth mentioning that the 6th edition is the same as the fifth edition aside from a few reworded explanations.

quality of the practice material

the act english passages are too long, so they’re harder to complete in the time limit. the wrong answers are a little too ambiguous, which can make the questions harder in a confusing way, rather than harder in terms of harder material. also, grammar questions are over-represented in this book, so you don’t get as much practice with other question types. the act reading sections are too short, and are a little harder to understand than those on the real test. the act math questions are a little too easy, and favor pre-algebra and elementary algebra more than on the real test. the act science questions are very good. finally, the act writing is much better than it was in past editions.

quality of the answer explanations

here, mcgraw-hill falls really flat with their 10 practice tests. the answer explanations are maddeningly inconsistent and unhelpful. some answer explanations simply say something like “answer x is correct because it’s the only answer that makes sense.” not useful!

other answer explanations give a little bit of extra information on why an answer is correct, but they usually just reference a concept, without really explaining it. for example, an answer explanation might say “this answer is correct because it follows the rules for quadratics.” but what does that actually mean? moreover, at least half the time, the incorrect answers aren’t addressed at all.

grade

act english and act reading practice: c

act math practice: b-

act science practice: a

answer explanations: d-

princeton review

princeton review has many offerings for the act. here, we are going to give our review of princeton review’s materials in general, and then dive into the specific differences between their main books to help you decide which, if any, will help you in your prep. you may notice that princeton review has even more offerings than we review here, but we’ve decided to focus on these because they are both the most popular and fairly representative of the question style and approach in other books.

act premium prep, 2021

we’ll start with act premium prep, something of a flagship for pr’s act prep. it’s pretty similar to previous versions, so if you happen to have an older version, we would not recommend buying the updated edition. also, the difference between premium and regular is that premium has 8 practice tests whereas regular has 6.

the act reading advice is pretty good, although the text is heavily stamped with princeton review’s branding in the form of specialized terms and acronyms. (the awful acronym pood is back with a vengeance!) the passage itself thankfully has no princeton review buzzwords, and is comparable enough to a real act test.

but—just like previous years’ editions—the added act reading practice questions themselves are abysmally not act-like. most of the new dual passage questions are far too easy, and the “hard” questions are only hard because the answer choices are ambiguous. supposedly “wrong” answers could be right. on the real act, there are no “gray area” possibly right answers like this.

there are a few other flaws in the act writing advice. the sample act writing prompts are slightly more complicated than real act writing prompts, with more complex perspectives. one good update this year is that the princeton review has made some steps towards covering prewriting, a step it previously ignored. the advice about the new act essay is good in some respects. however, once again some branding creeps in. pr gives a pretty strict template for writing the essay, specifying phrases, the structure of individual paragraphs, and the order of content. this princeton review method for this essay isn’t bad per se. but it may not work for everyone. lighter guidance that helps students find their own voice and style would be more helpful.

grade

practice material: c

answer explanations, strategies and skills: b-

crash course for the act 6th edition

the crash course for the act is a shorter offering from pr that focuses on strategies and drills. the strategies are solid, though fairly standard for test prep in general, rather than being act-specific. if you are feeling rusty on standardized tests, this may be a good option for you. the questions are different from cracking the act, so it can be used in combination as well as on its own. the question quality is decent, but not the best, just like with other pr books.

bottom line: a source of additional practice questions as well as general test prep tips that can be helpful to those who aren’t getting those tips from another source.

grade

practice material: c

answer explanations, strategies and skills: b-

princeton review 1,523 act practice questions 2021

princeton review’s 1,523 act practice questions has topic-specific mini drills that would be a useful resource for students who want to focus on one topic at a time. the practice questions aren’t repeated from other books, which is good to know the book has three full-length practice tests and gives you access to pr’s online content. the new edition has the same questions as the previous edition with the exception of 12 new questions. like the others, good, not great.

grade

practice material: c

answer explanations, strategies and skills: b-

kaplan’s act prep plus 2021

just like the 2018 edition, the best part of kaplan’s act prep plus 2021 book is its structure. it lays out act content, question types, skills, and strategies in a complete and straightforward way. by the end of it, you’ll have a very good idea of what the act is all about.

this isn’t to say that kaplan act is perfect. there are strong points and weak points within the book’s largely-good framework. note: the “plus” edition gets you two extra practice tests compared with the regular act prep.

answer explanations, strategies, and skills

the answer explanations in kaplan’s act prep plus 2021 are refreshing in many ways. unlike many act books, this book explains both the right answers and the wrong answers! knowing why the wrong answers are wrong–and how the makers of the act are trying to distract you—is a really important aspect of test strategy.

the explanations are longer and of higher quality than explanations in previous editions, which is another point in kaplan’s favor.

the strategy and skill portions of the book definitely don’t have a problem with incompleteness. here, you get in-depth descriptions of all of the different kinds of questions in each section. there’s also a thorough overview of the major grammar rules and math principles on the exam. similarly, the book gives a very complete explanation of content and strategy in act reading and act science.

still, kaplan—much like its competitor the princeton review—sometimes lets its branding and sales tactics get in the way of its advice.

unfortunately, this edition still includes the smartpoint system. kaplan’s smartpoints system lists each question type in every section as a “smartpoint.” these smartpoint labels can be confusing and inconsistent. some smartpoints are said to be related to other smartpoints, but the connections are vague at best. similarly, the “kaplan method” for each section tends to be fairly obvious. however, the kaplan method for act writing does one thing that’s pretty awesome–it shows students how to brainstorm and write an outline. this is refreshing, since many act prep books don’t cover prewriting sufficiently. regrettably, however, kaplan again applies a flawed, time consuming method. the kaplan method for putting together an act essay includes a prescriptive, highly detailed outline structure that students will have trouble following within the test time limits.

finally, the practice materials all have pretty obvious flaws. here’s a quick rundown, section by section. the act english and reading questions are easier than the real thing. some are way too hard because of ambiguous answer choices, where multiple answers could have been right. real act questions won’t necessarily be easy, but you should be able to narrow down the choices to one. questions on the act math and science are a little easier than the real thing. as for act writing, kaplan’s corrected some of the over-detailed prompts that plagued previous versions of this (um, “kaplan act”) books. these are a lot more solid than they were in previous editions.

grade

practice materials: c-

answer explanations, strategies, and skills: b

the best act prep books that won’t cost you anything!

magoosh’s free act ebook

that’s right! magoosh has a free act ebook!

what will you find in here? strategies for the exam, practice questions, detailed explanations for those practice questions, explanations of the act format and details of all question types.

it’s written by magoosh’s test experts, meaning that it’s not dense or dry like some books. even better, it’s available in a handy pdf so you can study on the go.
magoosh’s sat math formula ebook
(this ebook was written for the sat, but is equally crucial for the act.)

the math formulas you’ll need on the test, plus strategies and practice problems so you can learn how to use them under pressure!

high schooler’s guide to the future

for this ebook, magoosh teamed up with collegexpress to combine our test-prep expertise with their college admissions knowledge. this guide to getting into college provides a timeline to help you navigate the college prep process year-by-year.

going beyond the best act prep books

our best act prep books list grows all the time, so be sure to check back for new reviews! (or send us a request for one!) if you’re interested in adding some online practice to your act prep, complete with videos and interactive tutorials, check out magoosh act prep.

happy studying!

the post best act prep books of 2021 – which book is best for you? appeared first on magoosh blog | high school.