When you sit down to take the ACT exam 📚, you will have 4-5 sections on the test 👓 , depending on whether you choose to take the essay section! 

After the English 🤓 section of the test, you'll dive right in to the Math 🧮 section of the ACT! In this study guide, you will learn to MASTER 🤴🏼 the Math section and be on your way to an amazing score!

The Math section is the 2nd section of the ACT standardized test. You will answer 60 questions to answer in 60 minutes ⏰. 

This comes out to be 60 seconds 🕰  or 1 minute per question. It's safe to say that this section will be fast-paced 🏃‍♀️.

Since you're going to be taking the entirety of the ACT exam 📚, we thought it would be beneficial to go over some overall tips and advice for the exam. These tools 🛠 and strategies 👨‍🔬  have worked in the past and have been promoted by many teachers 👩‍🏫. Make sure you pay close attention to common mistakes ⚠️ student make and how you can use these strategies to get the score you want.

The ACT is written in a way that gives you barely enough time to finish every single question if you work with maximum efficiency and minimum distractions 🥵 . Many students say that the hardest aspect of ACT is how fast-paced the exam is. Many students struggle to finish the STEM sections of the ACT, particularly 🧮. So before you even take the test, be in the mindset that you cannot afford to zone out, even for a few minutes. 

There are many exercises like meditation 🧘‍♀️ , slow breathing and simply closing your eyes 👀  that can calm your nerves and help you get in the zone for the exam.

The best way to overcome the timing hurdle is to practice planning and pacing. Practice and plan 🤔 how much time you are going to take on the first half and the second half beforehand (you can divide it up any way you please) 🧠. 

Pacing is the most effective tool 🏃‍♀️ . After every 10 questions or so look up at the clock and see how you are doing time-wise ⏰. If you are going too slow, then pick up speed. If you are doing well on time, continue on with the same momentum. This strategy allows for adjustment 😃 so that you can make quick changes to your approach and attempt all questions, and maximize your score.

This strategy is relatively obvious: you need to work on your skills that need developing more often than ones you are already good at 💕. ACT covers a much bigger umbrella ☂ of math topics compared to SAT and many other standardized test exams. You need to know all math through and including trigonometry and pre-calculus, along with some basic understanding of statistics 🤯. 

Many students find trigonometry tough because they have not worked with it for a long time 😆. So make sure you review some basic trigonometry quantities and identities before the test. Many students also find the geometry section a bit tough because they haven’t worked with geometry for some time 🧠. If there is a chance your geometry skills might be a bit rusty, make sure you take some time to polish them up. 


💡To understand what you need to review, do a practice or diagnostic test, or look through the problems in this guide. Prioritize your review based on what you need help with the most so that you are not wasting time learning things you are already good at 🤔. If you get in a habit of practicing problems, finding your weakness, learning content, and repeating... nothing can stop you from your dream score. 😊 



This sounds so obvious, right? 😁 Why would I read a question incorrectly? Duh! 😄  This strategy does seem obvious. But you’d be surprised to know that when students get back their exams 📖  and they look over what they missed, they realize that they could’ve gotten many more questions right if they had read the question carefully 🔍 . It is natural to skim and look over important details that might be extremely helpful to answer the question. On the English 🤓 section, make sure to look out for words like not, worst, best, etc. For the Math section, 🧮 make sure you answer what the question asks for. Many times students solve for X, but the question wants to know Y, and the students get that question wrong because they did not read it carefully. 
💡So make sure you read 📚 what the question says because the question is the lock 🔒 and the correct answer is the key 🔑 , but you’d have a hard time finding the perfect key if you don't know much about the lock.

Let's get more specific and talk about the math section 🧮 . The tips and strategies discussed above can be applied to any section, including math. However, there are some extra strategies that can help you increase your math score 📈 even further. These strategies are tried and tested for overall test-taking and are especially helpful for the ACT Math section. So let's get started 💃!!

Imagine if you could eliminate possible answers without even solving the problem at all. If you're lucky, you can even find the answer before solving the problem. The close enough strategy is eliminating answers by looking at the problem and asking what type of solutions are the possible. Remembering that the absolute value or a square root of a number is always non-negative can be helpful. 

This strategy is all about logic and reason 🧠. Sometimes you don’t even need to solve the entire question to answer it. The close enough strategy can be a huge time saver and useful to do some challenging problems💡. Some problems cannot have a negative answer, some problems can't have a small answer and some problems can't have a huge answer. This strategy is not perfect, but neither is life or the ACT 😊 . This tool 🧰 can save your score when you get a tough question. The ACT covers such a broad spectrum of topics that you're bound to get a few curveballs ⚽️ . Whenever you get a problem that seems too hard, look at the answer choices and see if they give you a hint. 


💡Sometimes just plugging in random numbers and making up variables can really help give you a feel for what the answer should be. Then, the process of elimination can help you find the correct answer ✅.




All problems in this guide are borrowed from 

Try answering working this question on your own. Check here for answer 💕 


D. You can eliminate ❌A and B because we are taking the absolute value of the final number, 🔢which can never be negative. This automatically gives you a 50% chance at the right answer! Solving the inside we get 44﻿ and 66﻿. The absolute value of 4-64−6﻿ is 22﻿. 💯

This strategy is also told to students all the time 👩‍🎓. However, many students just don't follow it. For some reason, students tend to love 💕  answering questions in the order they are in and forget that they have the option of skipping hard questions.
💡 The key 🔑 to standardized exams is to gain as many points 💰 as you can on the questions you know or the questions you can handle without wasting too much time 🕰  and energy 🔋 on questions that are too challenging. 

One trick 🎩 some students use is to circle tougher questions when they skip them or guess on them so that they know to come back and visit them later. Not wasting all your time ⏰  on some insanely tough problem or on a question with a lot of repetitive arithmetic will allow you to save time and energy ✨ that you can spend on doing questions you feel better about. That being said, leave no questions blanks. 

On the ACT, you are not penalized for a wrong answer. So take your best educated guess 🤔, and if you have no clue just bubble in your letter of choice for the day.

Try answering working this question on your own. Check here for the answer! 💕


G. All you 🧒 have to do in this problem is plug it in 1/2 in for X and solve the expression. You end up getting 4-3 divided by 1/2 which comes out to 2. This is a relatively simple problems so when you're in rush 🏃 try to look for problems like this 😃 . 

On the ACT you are allowed to use a calculator for the entire math section. Unlike other exams, where calculator use is either banned or only permitted partially, you can use a four-function, a scientific or a graphing calculator for the entirety of the exam✅. A graphing calculator is ideal because you might be dealing with some tricky questions regarding trigonometry or precalculus, and your calculator might be able to help you out 🥵 . However, a scientific calculator is just fine for most of the problems. 

With that being said, you need to be extremely strategic with your calculator use. Many students don't prepare enough because they think they can rely on a calculator, but, keep in mind a calculator is a tool, not a magic wand. You still have around 1 minute to answer each question 🏃‍♀️. You will not have time to do each question by hand and check it with the calculator. Use your calculator as a strong and helpful tool. 
💡Questions that seem complex but can be made easier by graphing are perfect for a calculator 🧮. When trying to do several arithmetic steps at once, your calculator can save your life!



E. The formula 🧮  to find periods for sin, cos, sec and csc is $2 \pi /b$. For tan and cot it is $\pi/b$. $b$ is the coefficient in front of the $x$ in the parenthesis. So in this case $b = 4$. Our period is $2\pi/4$ which simplifies to $\pi/2$ 🤯.

Let's say you were to forget how to do that. You could simply plug this equation into a graphing calculator and see how wide a full wave is. 🖥

The ACT writers are testing you on your skills as well as the math content 🤓. Each question tests some aspect of your math ability 💯. Some questions target problem solving, while others want to test your ability to understand concepts. Below, we break down each skill anticipated to be tested on the exam 😃. 

You may notice that the percentages add up to more than 100%. That's not a mistake: the ACT has several questions that test more than one skill at once. Don't worry, this guide will prepare you for the exam and polish the skills you need to ace the ACT 💗.

1. Preparing for Higher Math (~60%)  👨‍🔬 

This section 📚 is related to the recent math you've learned 🧠. Algebra and solving and manipulating equations are at the heart of this skill. You'll be working with all types of functions, equations and expressions to solve problems ❓. This skill is divided into 5 basic topics: algebra, function, geometry, number and quantity, and statistics and probability. We will learn more about each of these 5 topics within this skill in much more detail later‼️


B. This problem might make you reminiscent of the exponents and log units 🥵. But it's not that complicated 😇. Since the bases are the same, for the equation to be true, 2x+7=15. Simplifying that equation gives us x=4 💃. 



This section is kind of a mixed bag of math skills 💼. You can expect to see anything from proportions 🍕 and percentages 🥧  to volume 📦  and surface area 🌍. A lot of the topics tested under this skill are those you've been learning since middle school. These are your fundamentals: the basics ✅. 

This skill doesn't test what you've learned in the last couple of months but rather the skill set you've built in your math career. Keep in mind 🧠 that just because this skill is meant to test the basics, the questions tested 📖 won't always be a walk in the park 🌳. You'll often be asked to apply topics to a complex situation or a problem and perform multiple steps and parts.


C. 8% of 60 is 4.8. To find what number 4.8 is 1/5 of, we multiply 4.8*5 to get 24. Problems like these may test more basic content, but notice how there are many things going on at once 😴. The best way to approach them is to break them down and peel one layer of the onion at a time 🧅.



This is a skill in its purest form 😇 . There isn't any particular content associated with modeling but you can be asked to model any situation 🤓 . These are some of the tougher real life 🌍 word problems. The best way to attack ✨ these problems is to break them down. You need to read each sentence and try to convert the English to math. You need to ask yourself if the sentence adds new information and what the point of the new information might be🕵️‍♀️ . 

Commonly, modeling is tested in conjunction with setting up equations. You could be asked to model anything from the price of X pizzas 🍕 to the population of Wakanda after T years. This is the section where you get to show off how you can apply your skills to solve even the toughest of real-life problems.

H. We set up two equations here. One for the cost of ABC Book Club 📖 and one for the cost of Easy Book Club 📚 .

If we want both costs to be the same (charges for both clubs to equal) we need to set both equations equal 😊 to each other and solve for x. Doing so gives us x=5.

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