Testing Tips

The Do’s and Don’ts of the SAT Essay

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Now that we’re a few years into the “new” SAT (which was completely overhauled in 2016), I’ve started to see more of my students opting to take it over the ACT. One major difference between the tests that often gets overlooked, however, is the essay. If you’re considering both tests, I’d recommend practicing each test with the essay — which you can (and should!) do during the diagnostic process here at LP. And to get you started with thinking about the SAT essay, here’s a couple of quick tips based on the SAT essays that I’ve seen.

First, let’s take a look at an SAT essay prompt. Before the passage, you’ll see this box:

And after the passage, you’ll see this box (just replace “Jimmy Carter” and “the Arctic…” with whatever your passage is about):

Notice how, unlike the ACT, the SAT does not ask you to argue your opinion on a topic; instead, you are asked to analyze how effectively someone else makes their points.

Here are some do’s and don’ts to consider when writing the SAT essay:

DO paraphrase or quote from the most important parts of the passage to demonstrate your reading comprehension. A full third of your score is “reading,” and your grader can only evaluate how well you’ve read from your writing.

DO try to fill close to two handwritten pages, and try to leave yourself a couple of minutes to revise your work for spelling and grammar mistakes. Now, according to the rubric, your ideas should matter much more than length and spelling. But think about your grader, who’s probably going through hundreds of essays very quickly. These types of things can end up mattering more than they probably should.

DO consider a “three-prong” thesis statement to clearly lay out your essay’s structure — something like “Through his X, Y and Z, Jimmy Carter makes a persuasive case that the Arctic National Wildlife Refuge should not be developed for industry.” Sure, it’s not the most “sophisticated” thesis statement. But you have 50 minutes to read and write your essay, and your grader knows that. However, this leads straight into my one big “don’t,” based on the essays that I’ve seen...

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DON’T cram “rhetorical devices” into your thesis or topic sentences unless they are a major, recurring part of the passage. Honestly, it’s stronger to say “at the close of his argument, the author appeals to carefully selected facts and statistics to underscore his point” than to try to force “the author’s use of logos” into your essay and make it sound natural. There might be one or two devices that are present enough to warrant an entire paragraph (appeals to emotion and personal anecdote are two common examples) — and in that case, go for it! But if you feel like you’re “forcing it,” take another approach.

INSTEAD, pick a broader, more descriptive category for your topic sentence, and explain how this category functions for the author’s argument: rather than “the author uses diction to make his point,” say “the author richly describes the natural world, helping the reader to visualize what’s at stake.”

Now, this isn’t to say you should avoid mentioning rhetorical devices entirely. When you notice rhetorical devices, show off what you know! For example, when analyzing a specific piece of evidence in a body paragraph, you can say something like, “Carter’s description of nature in this quote edges on hyperbole” (before going on to further explain how that likely affects a reader). Just don’t let rhetorical devices become a “crutch” for your topic sentences. Your topic sentences should allow you to talk about all the most important parts of the passage, not constrain you to a list of rhetorical devices that you’ve memorized.

3 Easy ACT English Tips to Boost Your Score

The following tips offer strategic approaches to specific question types on the ACT English section. For more thorough explanations of these topics, reach out to your LogicPrep tutor!

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1. When choosing between who and whom, use prepositions as a shortcut.

Prepositions are words that demonstrate the relationship between two things such as with, to, for, in, and on. When you get to a question where you have to choose between options that use who and whom, just look at the word right before it. If it’s a preposition like those listed above, choose whom. Otherwise, choose who. This shortcut works more than 95 percent of the time, so make sure to ask your LogicPrep tutor for an explanation that will cover the other 5 percent of cases.

2. The period and the semicolon are used interchangeably.

The ACT English section considers the semicolon and period interchangeable. As long as you’re connecting what could be considered two separate sentences, either punctuation mark can be used. So if you get to a question that offers two options, one with a period and one with a semicolon —and all else is equal— you can immediately consider both incorrect; no question can have two right answers.

3. For transition word or phrase questions, be strategic and immediately eliminate any equivalent options.

Similar to the prior tip, you should be strategic and eliminate options with equivalent answers since it would be impossible to have two correct answers. Most of the transition words or phrases on the ACT can be categorized into a few broad categories: contrast (however, on the other hand, nevertheless, etc.), similarity (likewise, similarly, additionally, etc.), or consequence (thus, consequently, therefore, etc.). When you get to such a question, look at the options and if two of them fall under the same category, you can confidently eliminate both, even without analyzing the context.

How Learning to Work Deeply Can Improve Your Test Scores

The New York Times recently published an article that caught my eye: “How to Actually, Truly Focus on What You’re Doing.” Needless to say, I read it while also answering emails. On the subway.

The article features a conversation with Cal Newport, the author of a 2016 book called Deep Work, whose title is also a term he’s coined for “the activity of focusing without distraction on a cognitively demanding task.” Newport argues, rather convincingly, that there’s a cost to switching continuously between tasks -- even if it’s just to quickly switch between browser tabs to check your email. This cost is a psychologically recognized phenomenon called attention residue, and it can significantly reduce your productivity.

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Newport goes on to describe four rules for deep work; the one I found most fascinating was to “embrace boredom.” He notes that if you immediately reach for your phone and start scrolling every time a task begins to bore you, you’re effectively telling your brain it will never have to tolerate tasks that aren’t immediately interesting.

But as we might know from test-taking, homework, and the like, that’s not always the case. Sometimes you have to work through a tough task. And Newport’s research shows that doubling down on the task at hand by working deeply will bear much more fruit than trying to multitask or shifting to a new task halfway through. Fortunately, learning to work deeply is something we can train and work at improving, much like a muscle. So, I’m starting now. As soon as I’m off the subway.

Cognitive Offloading is the Most Important Test Tip You Didn’t Know Existed

Forgive me, dear reader, for this incredibly gimmicky-sounding title, but understanding cognitive offloading will improve your life — and subsequently, your test taking ability. Before I drown you in psychology jargon, I ask this:

Do you know that satisfying feeling when you write out a to-do list? The way your thoughts flow more clearly once you start typing or writing them? Have you ever asked someone (or set your phone alarm) to remind you about something later so you don’t have to hold mental space for it?

These are all everyday examples of cognitive offloading. In short, your brain can only juggle so many things at once — whether it’s keeping information in the background (like remembering something you need to do later) or actively handling a complex task (like planning out an argument for a paper).

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Cognitive offloading is anything you do to reduce the cognitive demands of a task: basically, to make it take up less mental space. You can then use that extra mental space to live your daily life less burdened by background stressors and focus on the task at hand, or to engage more deeply with a cognitively demanding task.

A favorite example: if all of your thoughts seem to be spinning around in your head with no clear way to corral them, offloading the responsibility of memory and organization from your abstract headspace onto a concrete piece of paper (or computer screen, if you must) makes things much easier to process.

My unsolicited life advice to you is to buy a journal and use it! This can be especially helpful if you are reading this as someone engaged in the test prep process yourself, in an incredibly formative stage of life rife with excitement, confusion, and anxieties. In the interest of full disclosure, you should know that I’m not entirely sure when, if ever, that stage ends.

I understand you may have many questions — What does this have to do with test taking? Why is a 23-year-old giving me life advice? Why is the sun setting at 4pm in New York? I promise it’s all related and important somehow.

The good news is it’s fairly simple to apply this concept wherever your test-taking needs carry you. Every test — especially if it has a time limit — is a mind game and cognitive offloading should be a part of your psychological toolkit. Hopefully you’ve already heard or practiced these strategies and can now more fully contextualize them.

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In a test-taking context, cognitive offloading can accomplish two main goals: making challenging tasks easier and minimizing the cognitive demand of simple tasks.

The first is easy: write out your work, especially on math tests. If you don’t know how to get the answer, start writing what you know; if applicable, write the simplest equations you are confident in and integrate them on paper instead of in your head. Even the trickiest word problems can often be broken down into a few simple equations, but students get stuck trying to synthesize all of the information into the most comprehensive equation possible before putting pencil to paper. Psychologically speaking, writing more will actually make it easier for you to think

As for the second, the simple task of watching your timing can become incredibly cognitively draining, especially when there’s test anxiety involved. While mitigating test anxiety is a much longer and more complex process, offloading thoughts about time onto a watch is the simplest thing you can do. Any watch with a (silent!) stopwatch or timer will do, but if you’re an LP student you should have our watch, which is pre-programmed with timers for each section of the ACT or SAT. Trusting that the watch is keeping time, only a glance at your wrist away, allows you to release much of the pressure to be thinking about pace as you’re also trying to remember how to calculate arc length or wade your way through a fiction passage. It seems simple, but my students always report feeling less anxious about timing after practicing with their watch — and this lessened anxiety translates to better overall performance on the test.

If this topic is of interest to you, I’d recommend reading Daniel Kahneman’s Thinking, Fast and Slow, or simply becoming more mindful of the ways in which you already use, and may further integrate, cognitive offloading in your everyday life. Alternatively, track me down at the LP office and I’m happy to ramble about psychology in person.

Solving the Mysteries of Subject Tests

The SAT Subject Tests have been produced by the College Board since 1937, though over the years they have gone by several different names and seen several redesigns of the tests. As the tests themselves have changed, so have the ways in which schools use them in the admissions process. In the current landscape, many colleges have shifted from requiring Subject Tests for admission to either recommending them or considering them. Even as this shift occurs, it is important for students and parents to understand how Subject Tests can work to their advantage in the admissions process.

For highly achieving students in school, the Subject Tests offer an opportunity to show a more specialized level of knowledge than either the general SAT or ACT would. Though many schools have removed the requirement of Subject Test scores because of the financial burden they place on lower-income students, many of these same schools still recommend or consider these tests, meaning they can help boost your profile for admission or help you earn merit-based scholarships from the school. For certain test-optional schools, Subject Tests may actually be submitted in place of an SAT or ACT score on the application. Most schools that consider the Subject Tests will ask for scores from two subjects, and a full list of universities that use Subject Test scores can be found here.

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As students start to consider what colleges they may be interested in, it makes sense to start to develop a plan for how and when to tackle Subject Tests. As freshmen or sophomores, some students take their first AP classes, such as AP Biology or AP World History. As a freshman or sophomore taking AP classes, I would recommend exploring a practice Subject Test as you start to prepare for the AP in the spring. The May Subject Test date tends to coincide well with the AP testing dates, so if you are feeling strong in your AP classes, you could get a head start on these exams. However, the vast majority of students who take these tests will do so in their junior year, while some will even wait until senior year.

For juniors who are interested in schools that consider Subject Tests, there are a few possible paths for getting them done. Though most students will simply wait until the May and June Subject Test dates because they line up with the AP testing dates, this can create an overwhelming spring workload for students who are in multiple AP classes and taking multiple Subject Tests. Though waiting for the spring dates makes the most sense for the Subject Tests that relate to specific class material, the Math and Literature Subject Tests are not directly tied to a curriculum. For students looking to alleviate some of the anxiety of spring, tackling these Subject Tests in October, November, or December of junior year can be a great way to get ahead. For students who may not have realized they needed or wanted Subject Tests until later in the process, taking them in May or June of junior year may not be an option since the focus may still be on the ACT or SAT. In this case, the Math and Literature Subject Tests offer a great alternative, as you can take the summer between junior and senior year to prepare for them. Like with the SAT or ACT, the Subject Tests are highly predictable in their content, so the best way to tackle them is to start thinking about your planned schedule early and to give yourself plenty of time to study and prepare.

The Power of Elimination - Mastering Multiple Choice

It’s one of the oldest tricks in the book -- but is a very powerful, underrated strategy!

“So, what can you eliminate?”

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My students will tell you that I must say this phrase at least 100 times each lesson, but there is a method to my madness. In almost every question on the ACT Math section, there is usually one answer that is completely out of left field. As soon as you see that answer, crossing it off immediately will ensure that you won’t accidentally choose it if it comes down to guessing. It will also help lead your brain to the right answer by narrowing your focus to the other answer choices. In the case of “plug and chug” questions, having to plug in 3 numbers versus 5 can save you precious seconds in the race against the clock.

Eliminating will not only help you increase your chances of selecting the correct answer, but it will exercise your intuition and confidence. Knowing the wrong answer can be just as useful as knowing the right one!

My Favorite (Free!) Website for ACT Reading Preparation

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Most of my students struggle with the ACT Reading section not because they can’t read, but because it is so difficult to manage the short time given. This is entirely understandable, the ACT is a unique experience that is hard to prepare for. Think about it this way, in the real world people normally don’t open up the New York Times and give themselves 5 minutes to read the top front page article. That would be just weird. Even if you wanted to do this, you wouldn't know how long the article should take you to read anyway. With every second counting, guessing an article should take you 6 minutes to read when it really should be 5 minutes can be quite costly.

This is why I love JSTOR’s, the world’s leading digital library of academic journals, daily (free!!!) blog based on the papers they publish.

Sourced and written by their own high-quality writers, the content is on par with what you may see in an ACT Reading section. Even better, they divide the website topically so you can practice the passage type (expect fiction) that gives you the most trouble. Best of all, each article is listed with a reading time so you can time yourself even if don’t have time for a full section. Perfect for when you just have 5 minutes to practice.

JSTOR’s blog is the best free website out there to help you prepare for reading the ACT’s deep academic content under time pressure.

You can find the link here: https://daily.jstor.org/   

Good luck and enjoy!

The Other Half of the Test, and How to Master It

We all know there is a lot of material to learn on the path to mastering the SAT or ACT – formulas, grammar rules, reading strategies. But there is another skill to master: the mind game.

During the nearly four-hour test, pacing, endurance, and fatigue become huge factors in our mental performance. These hurdles make up the mind game: the psychological prowess needed in partnership with the material to maintain rigorous concentration during the test’s unique conditions. Rather than being learned in a lesson, these skills come from building the muscle of focus. And like any muscle, it needs to be trained. 

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Training is not something that happens over night – at our second trip to the gym, we don’t run a marathon. Instead, we take active steps to train this muscle during our practice.

Practice. Interesting word, that. What do we know about practice?

We are taught that practice makes perfect. This is not true. An aspiring pitcher who practices by bowling the baseball probably isn’t going to be very successful, even if they practice all day every day.

The truth is: Practice makes permanent. Perfect practice makes perfect.

This means when we prepare for the test but do not exercise the mind game, we are making permanent the limited focus and energy we are bringing to our practice. That is why it is so important to push ourselves to improve focus during all of our SAT/ACT practice.

There are steps we can take to train our focus and improve our mind game when we study for the tests:

THE ENVIRONMENT

Just like test day, your practice space needs to be distraction free. Find a quiet space, preferably with as few people around as possible. This isn’t always as easy as it sounds. If kid brother is always practicing his air guitar and mom always has an endless number of phone calls, tell your family “Hey, I’m going to be studying for the SAT/ACT at 7 tonight, can I have an hour of quiet-time in the house?”

Most importantly, put your phone away. In another room, preferably. Practicing with it buzzing at the other end of the table is going to make permanent that little voice in your head wondering what your friends are texting you. It won’t be there on test day, so get it outta there.

Or better yet, head to LogicPrep anytime, and we’ll set you up in a distraction-free study space or an empty room. We’ll even hold your cell phone behind the front desk for you.

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THE BODY

Given the intensity of high school, it is understandable that sometimes SAT/ACT homework happens later at night than we might want. But attempting these endurance-based tests when we’re losing our energy to stay focused is bad practice, and builds bad mental habits. If you feel yourself losing steam, it might be best to call it a night and start up again in the morning.

Hunger can be just as distracting as tiredness. Stock up on brain foods to snack on before you begin your SAT/ACT practice, like nuts or berries. Just like with our phones, we do not want to make permanent the state of distraction that an empty stomach brings.

THE MIND

You know the feeling when you’ve read the same paragraph for the third time but still can’t remember what it is about? That’s your mind’s signal telling you that your focus is temporarily low and needs a little reset. There’s no use reading it a fourth time – we don’t want to make that mental state permanent. Instead, take a micro break. Try moving your body: walk up and down the stairs or do ten jumping jacks. Use this moment to wipe your slate clean and return to the question at hand as if it’s the first question you’re working on today. Slowly, our mental muscles improve, and we can reset and focus by simply taking a deep breath. But until then, note when your mind is drifting, and take active, physical steps to correct it.

In order to build the mental muscles required for staying focused during these large tests, it is important that you study in test conditions. Remember, practice makes permanent. Perfect practice makes perfect.

Tips for Succeeding on the Spanish Subject Test

For many speakers of Brazilian Portuguese, taking the SAT Subject Test in Spanish seems like a no-brainer. After all, Spanish and Portuguese have upwards of 80% lexical similarity, and the infamous portuñol has long allowed Latin Americans of both linguistic backgrounds to communicate with some degree of ease.

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Yet Brazilians should not think of the SAT Subject Test in Spanish as a cakewalk. There are crucial differences between the two languages that can bring down your test score if you aren't careful. I for one learned Spanish growing up, and after two years of study, continue to find Portuguese both familiar and challenging. While understanding written Spanish may not be difficult for Brazilian students, the SAT Subject Test asks questions about very specific grammar topics -- pronouns and irregular conjugations, for instance -- that require some preparation.

Remember, the biggest difference between Spanish and Portuguese is phonetics. Since you won’t be speaking on the test, don’t fret! Do, however, review these key concepts before jumping into the Spanish test cold turkey:

Articles & Demonstrative Pronouns

Definite articles

Feminine -- La, las
Masculine -- El, los

Indefinite articles

Feminine -- una, unas
Masculine -- un, unos

Note that in Spanish, there are far fewer contractions with prepositions than in Portuguese. Only de and el contract (to “del”).

Demonstrative pronouns also resemble Portuguese, but watch the spelling! None of these will ever contract with any prepositions.

Feminine: Esta, esa, aquella
Masculine: Este, ese, aquél
Neutral: Esto, eso, aquello

Personal Pronouns & Possessives

Brazilian Portuguese is a very colloquial (informal) language, meaning that many of its grammatical rules tend to be disregarded in everyday speech. Spanish tends to retain a more formal linguistic structure even in informal contexts. Pronouns and possessives are one area where this difference is evident. Take a look at this chart:

*For reflexive verbs  ªIf you’ve studied Spanish, you might be familiar with the pronouns “vos” (common in certain countries in South America) or “vosotros” (common in Spain). Don’t worry about learning either of these for the sake of the SAT Subject Test.

*For reflexive verbs

ªIf you’ve studied Spanish, you might be familiar with the pronouns “vos” (common in certain countries in South America) or “vosotros” (common in Spain). Don’t worry about learning either of these for the sake of the SAT Subject Test.

It might be helpful to review the difference between subject and object pronouns in English (a classic ACT/SAT topic) before jumping into the differences between Spanish and Portuguese. Notice, however, the surface level similarities between the cousin languages.

Subject pronouns are straightforward: we use them to replace nouns that are in subject position, meaning that they come before a verb.

Object pronouns are a bit more complicated. In Spanish, there are three different types of object pronouns: direct, indirect, and prepositional.

Direct Object Pronouns

These replace nouns that are being directly acted upon. For instance:

I met her at the beach yesterday.
Eu a conheci na praia ontem.
(Colloquial Portuguese: Eu conheci ela na praia ontem.)
Yo la conocí en la playa ayer.

Indirect object pronouns replace nouns (usually people) that are not being acted upon directly, but are receiving the direct object of the sentence:

I give him homework after every class.
Eu lhe dou liçāo de casa depois de cada aula.
(Colloquial Portuguese: Eu dou liçāo de casa para ele depois de cada aula)
Yo le doy tarea después de cada clase.

Here, homework is the direct object -- the thing being given -- while him is the person being given that item, hence the indirect object.

Notice that in Portuguese, the difference between the direct and indirect object pronouns is often ignored in everyday speech; Brazilians use subject pronouns no matter the noun’s position vis-à-vis the verb, and they often make use prepositional phrases to avoid using the object pronoun, as shown above. Spanish behaves more like English or French in its retention of the distinction between subject pronouns, direct/indirect object pronouns, and even prepositional pronouns:

This is very hard for you.
Isto é muito difícil para você.
Esto es muy difícil para tí

Moreover, be sure to not forget that genitive pronouns (possessive pronouns) exist in Spanish, as in English and French! In Portuguese, the genitive form is constructed by adding a definite article to the possessive adjective, whereas Spanish has a different form. This distinction is an important one:

This test is mine.
Essa prova é a minha.
Esa prueba es mía.

Essential Logical Connectors

A lot of prepositions, introductory phrases, and logical connectors in Spanish will be familiar to speakers of Portuguese. Some, however, are quite different. Be sure to know the ones that differ most from Portuguese:

Luego – don’t confuse this one with logo! “Luego” in Spanish means “then” or “next,” not necessarily “quickly” or “very soon” as in Portuguese.

ES — PT
Todavía – ainda
Sin embargo – porém
Aunque – embora
Hace falta – é preciso
Ademas — além disso
Pero — mas
Así que — assim que, entāo
Entonces — então, pois

Verb Tenses

In general, Spanish and Portuguese verbs behave relatively similarly in their written form. One major difference lies in the subjunctive. For one, Spanish does not have a future subjunctive; in cases where the future subjunctive is used in Portuguese, hispanohablantes will usually substitute the present or imperfect subjunctive. Sometimes, Spanish speakers forgo the subjunctive altogether, especially when talking about hypotheticals or plans for the future:

“Se for para o Brasil, você precisa visitar o Rio de Janeiro.” (future subjunctive)
“Si vas a Brasil, tienes que visitar Rio de Janeiro” (present indicative)

Overall, however, speakers of Portuguese should be relatively familiar with Spanish verbs. That said, Spanish has a lot of "stem-changing" verbs that complicate mutual intelligibility, particularly in the subjunctive. These verbs behave a bit erratically, changing in spelling and thus deviating significantly from the Portuguese equivalent.

Make sure you know the meaning of these twelve essential irregular verbs. Don’t forget how to conjugate them in the present and imperfect* subjunctive tenses:


Infinitive  / present subjunctive (3rd person sing) / imperfect subjunctive (3rd person sing)
Estar / esté / estuviera
Ser / sea / fuera
Haber / haya / hubiera
Tener / tenga / tuviera
Hacer / haga / hiciera
Poder / pueda / pudiera
Conocer / conozca / conociera
Saber / sepa / supiera
Venir / venga / viniera
Pedir / pida / pidiera
Querer / quiera / quisiera  
Decir / diga / dijera

Note: don’t be overwhelmed(!), but the imperfect subjunctive in Spanish actually has two forms. The one listed above is more common, but you might see the other form on the SAT. All you do is swap out the -era ending for -ese: estuviese, fuese, hubiese, etc.

False Cognates

While context clues and shared Latin roots will help a lusophone tremendously on the Spanish SAT Subject Test, there are lots of false cognates between the two languages. Here are the eight words most likely to trip you up on the SAT Subject Test:

Tirar
BR-PT: to take away, to steal, or to obtain (as in tirar a 36 on the ACT!)
ES: to throw
(quitar is the Spanish verb for “to take away” – but you would not say “quité un 36 en el ACT;” instead, try the verb sacar)

Pronto
BR-PT: ready, done, finished (ES: listo/a)
ES: fast, quickly, right away

Concertar
BR-PT: to fix, to mend, to repair (ES: arreglar)
ES: to schedule

Acordarse
BR-PT: to wake up (ES: despertarse)
ES: to remember

Pasta
BR-PT: folder (ES: carpeta)
ES: pasta (e.g. al dente, primavera, with pesto, etc.)

Sitio
BR-PT: farm, ranch (ES: granja or finca)
ES: site, place

Cena
BR-PT: scene (ES: escena)
ES: dinner

(Des)envolver
BR-PT: to develop (ES: desarrollar), to involve (ES: involucrar)
ES: to (un)wrap (e.g. a package)

6 Math Formulas to Know Before Taking the ACT

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For many students, the ACT math section is the final frontier on the journey to their dream score. While the section can sometimes feel daunting — those word problems can go on forever — there’s some easy prep that can save you some time and earn you some major points. By far, the one thing that makes the biggest difference for my students is getting familiar with the most common formulas. Because the ACT math section is relatively short (just about a minute per question) and you don’t get a formula sheet, knowing these formulas can be the difference between feeling like a champ after your test and leaving the test center scratching your head. Here are my top six formulas to know before the ACT:

1. Special Right Triangles

One of the first things I ask my students to memorize. For some people, the meaning of life is happiness, or success; for the ACT, it’s special right triangles. It feels like half of the geometry problems are really just triangle problems in disguise, so knowing the sets of side lengths (or angles) that always make perfect right triangles definitely comes in handy.


2. Area of a Trapezoid

This one might seem a bit random, but there’s always at least one trapezoid problem on the ACT, and it’s an easy way to guarantee yourself a point. It’s also one of the easiest to memorize, since it’s so close to the triangle area formula.

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Watch out here- sometimes you’ll be need to find the height, where the Pythagorean Theorem (or your knowledge of special right triangles) will be a big help.

3. Distance and Midpoint

Two very popular questions in coordinate geometry:

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...are easily solved when you have the equations for distance and midpoint between two points. (there’s also a nifty program, Points, that can do this for you- know the formulas, but don’t be afraid to take advantage of the technology!).

4. Slope of a Line

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Slope. Gradient. Rise over run. A slope by any other name works just as well- as long as you remember that your change in Y always goes above your change in X.

5. Slope-Intercept Form of a Line

Speaking of slopes, remembering how to find the slope-intercept form of a line is a must. While the ACT doesn’t play as many tricks as other, similar tests (see: SAT), one thing the test writers love to do is hand you an equation that looks like this:

...and ask you for the slope. Proceed with caution! Most students pull the coefficient off the X (in this case, that would give us C), but this only works when your line is in slope-intercept form:

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2x + 3y + 6 = 0

3y = -6 - 2x

y = -6 -2/3x

Here, it’s evident that the answer is actually D. My advice? Anytime you get an equation that looks like this, rearrange it so it’s in slope intercept. You’ll still be able to plug and chug if you need to, and you’ll save yourself one of those.

6. SOHCAHTOA

Not really a formula as much as it is a mnemonic device, but an essential one, especially on the second half of the test. Most of the right triangle trig questions on the test are pretty straightforward— just remember to double check which angle you’re using when you’re figuring out your opposite vs. adjacent sides.

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P.S. don’t forget- tan can be rewritten a fraction (sin/cos)!

These formulas are a great start for anyone starting their ACT math prep, or a good refresher for anyone looking to bulk up on some math knowledge mid-program. Learn these, and you’ll be flying through the math section in no time!