## About ACT Math

The ACT Math Test contains one 60-minute section with 60 questions, and calculators are allowed on the ACT Math Test. If you excel in math, you will find the Math Test the most straightforward section of the ACT.

For the most part, you will be dealing with straightforward math. The math itself is usually really simple, but the questions are always complex, strange, or difficult to understand.

At the same time, we recognize that some students will find the ACT Math Test more of a challenge. For those students, you will substantially improve your score by ensuring you know all the foundational math skills. **You need to know all the facts, formulas, and figures.**

Imagine the ACT Math Test as a house and math facts as your building materials. It doesn’t matter if you’re the best architect in the universe; without the right materials, you’re not going to be able to build much of a home.

The chapters to follow in this book and all of our AP Guru classes will teach you the material that you need to know. It’s important that you document every fact or formula that you do not know or tend to forget.

If you can start to identify each bit of material that makes you uncomfortable or uncertain, you’re well on your way toward mastering the ACT Math Test.

For example, let’s say you’re asked to find the equation of a circle. There’s nothing necessarily hard about this problem. But you either know how to do it, or you don’t. If you know the equation of a circle formula, any problem that asks you to find the equation is going to be simple. If you don’t, the same problem will be impossible.

This is just one of the few hundred little facts that you need to know when taking the ACT Math Test. We can’t emphasize this point enough:** if you don’t put in the work to learn, document and review the math facts that trouble you, you’ll never get a perfect ACT math score.**

#### However, just learning math facts and formulas will not alone do the trick. Like almost any other piece of information you’re trying to retain and recall, a math fact is tough to remember when it’s “floating” in a vacuum. You learn effectively by doing two things:

**Repeating**the information**Using**the information

Repeating is important, but of the two, the second is much more effective. If you see something once and then never repeat it and never use it, there’s almost zero chance that you’ll remember it. If you repeat it a bunch of times but never actually put it to use, it’ll still be tough to remember. It’s only once you use information** in context (repeatedly)** that it really makes any sort of impression on your brain.

**If you get an ACT Math Test problem wrong, there’s a good chance that you may not know the proper procedure to get to the right answer.** You might not know how to find the area of an equilateral triangle, how to set up an average equation, or how to deal with common ratios, or... the list goes on. But you can get there through discipline and a lot of organization.

#### From this day forward, you’re going to use the following procedure **any time you get an ACT Math Test problem wrong or don’t know how to solve it:**

- Immediately go to the answer explanation for the appropriate homework or test
- Read the answer explanation, step by step
- If you do not understand the answer explanation, ask any of us at AP Guru to explain the question and the underlying concept to you
- Follow the recommended procedure yourself and attempt to solve the problem
- Document that fact or formula

This process can seem exhausting at times, but it is well worth it. Many students who thought themselves “bad at math” walk away with an entirely different point of view after using this method. They were never “bad at math” they simply didn’t know many math facts. Once they figured out what they didn’t know and memorized those concepts, their scores and confidence increased!

After teaching ACT to thousands of students, AP Guru can usually categorize students’ aptitude to math into these two categories:

- These students do not count math as one of their favourite subjects and dread the ACT Math Test (especially the non-calculator section of the test).*I hate Math*- These are the students who love math and find the Math Test the easiest section of the ACT. They are invariably aiming for 36 on the ACT Math Test.*I Love Math*

## Group 1: I Hate Math

In a perfect world, you’d know every fact, figure, strategy, and technique for each ACT Math Test problem, and you’d be able to apply this material in under 75 seconds per problem, on average (that’s how time much you’re given to complete the math portion of the test).

This isn’t an unrealistic goal, and it’s one that we’ll be working toward. But in the meantime, **keep in mind that certain problems will always be harder or weirder for you than others.**

As you may already know, the ACT Math Test is generally organized from “easy” to “hard.” So, many students assume that question #30 will always be harder than question #25. But here’s the thing: these problems might be harder statistically, but they might be way easier for you personally!

Have you heard the saying, “One person’s trash is another person’s treasure?” That applies here. The same problems that might be simple for you might be nightmares for someone else, and vice versa. The “easiness” and “hardness” of every problem on the ACT Math Test are totally subjective. It all depends on you: what you know, and what you don’t.

Also, remember that “hard” does not mean “time.” **Hard just means that most students will get the question wrong.** Some of the “hardest” problems take about three seconds to solve if you know the facts behind them. Conversely, some “easy” problems still take a while to solve. Or, they may seem impossible to solve if you don’t know the key facts.

#### Focusing first on the problems you know how to solve is a good use of time. These are your “low hanging fruit” – the questions you can easily pick off without too much effort. Here’s the step-by-step process of how to tackle your low-hanging fruit:

- If you can solve the problem right away (within a minute), go for it
- If you are
**SURE**you can solve a problem, but you think that it might take you a while, circle the problem number and move on.**You'll get to it later.** - If you have
**NO IDEA**how to solve a problem, put a star next to it, then move on.**These are the problem that you’ll solve last.**

Move through all the problems in each section as quickly as possible using this process. **Do not stop. Do not take breaks.**

When you’ve made your way through a section, you’ll have already answered the problems you know. Now it’s time to go back to the start of the section and start answering all the problems you circled the ones you were sure you can answer. **You know how to solve these questions, but they will just take more of your time.** That is okay since you have already solved all the easy questions that were there to be solved in this section. Those were the lowest hanging fruit.

If after you finish all the circled problems time remains, repeat this process and begin attacking all the starred problems.

Make sure you have filled in an answer choice for each and every question on the Math Test. **There are no negative points awarded, so it would be foolish to leave answer choices blank,** even if you are not sure whether the answer you selected is correct. NEVER finish your test without ALL the bubbles filled in.

**That’s all there is to it!**

## Group 2: I Love Math

Every student strives for a perfect score on the ACT. Beyond being “perfect,” have you ever stopped to consider why scoring an 36 on the ACT Math Test is useful? It’s important to know why an 36 Math score is useful since this will fuel your motivation to get a high score.

**Aiming for an 36 on the ACT Math Test helps you compensate for weaknesses in how you perform on other sections of the ACT.** By and large, universities consider your composite score more so than your individual section scores.

#### There are two scenarios where an 36 on the ACT Math Test is important:

- If you’re planning to
**pursue a quantitative or science major**like math, physics, statistics, or chemistry. - If you’re applying to a
**highly selective technical university**like MIT or Caltech.

College admissions are all about comparisons between applicants. A school wants to admit the best, and you’re competing with other students in the same **“bucket”** as you. By applying with the intent of majoring in math or science, you’re competing against other math and science folks: people for whom the ACT Math Test is relatively easy or, in some cases, extremely easy.

Consider these examples: **For Harvard, Princeton, MIT, and Caltech, the 75th percentile ACT Math Test score is 36.** That means at least 25% of all students at these schools achieved an 36 on that portion of the test.

Even more surprising: the **25th percentile score for ACT Math at MIT and Caltech is 34.** This means if you score a 33 on your ACT Math, you’re well below average for these schools!

Working your way to an 36 score shows schools that you’re at an equal level (at least on this metric). Even if it takes you a ton of work, all that matters is the score you achieve at the end.

I’m not going to lie. For many students I teach ACT Math is super easy. Most of them get 36 on pretty much every practice test, and official ACT they ever take. Whether you like it or not, you’re competing against people like them. **And if you apply with a 32 on Math, schools like MIT, Harvard, and Princeton are going to doubt your ability** because ACT Math is supposed to be trivially easy for you.