ACT G01 Math Solutions: Step-by-Step Explanations

Hey guys! Let's break down the ACT G01 Math section. I'm going to provide detailed explanations to help you understand each problem and boost your ACT math score. Let's dive right in!

Question 1

Question: [Original Question 1 Here]

Explanation: Alright, for this first question, let's focus on understanding exactly what the question is asking. Many times, the trick isn't necessarily the math itself, but making sure we're answering the right question. Pay super close attention to the details provided; those details are your friends! For example, if the question involves units, make sure that the answer you provide uses the units requested by the problem and not any other. For instance, if they provide a speed in miles per hour but ask for the answer in feet per second, you'll need to convert somewhere along the way to avoid selecting the wrong answer.

Now, let's get into a high-level strategy. With any math problem, it's often a good idea to start by writing down any formulas or relationships that you think might apply. Even if it's not immediately clear how they will help, just getting them on paper can spark ideas or jog your memory. For example, if it's a geometry question involving circles, write down the formulas for the area and circumference of a circle. If it's a trigonometry question, write down the common trig identities. Even just writing the formulas can sometimes give you the answer directly if the question is testing whether you know a specific formula. If this doesn't provide the answer, it will at least help you have a better understanding of the situation that the problem is presenting. This will help you come up with a strategy for actually solving the problem.

Next, look at the answer choices. Sometimes, the answer choices themselves can give you hints about how to approach the problem. For example, if all the answer choices are relatively small numbers, that might suggest that you need to use some kind of simplification or reduction. On the other hand, if the answer choices are very large, that might suggest that you need to use some kind of growth model. Also, the form of the answer choices can be important. For example, if some of the answer choices include radicals and some don't, that tells you whether you need to rationalize a denominator at some point. Or, if some of the answer choices involve fractions and some don't, that tells you whether you need to combine terms over a common denominator. Keep in mind that the ACT test writers are trying to trick you, and the answer choices are one place where they put misleading information. So, analyze them carefully!

Finally, after you've worked through the problem, always check your answer. Make sure that it makes sense in the context of the problem. For example, if you're calculating a length, make sure that your answer is positive. If you're calculating a probability, make sure that your answer is between 0 and 1. And, if possible, plug your answer back into the original equation or problem statement to make sure that it works. You'd be surprised how many silly mistakes you can catch by doing this. Now that we have covered the high-level approach, let's go through an example.

Correct Answer: [Correct Answer]

Question 2

Question: [Original Question 2 Here]

Explanation: Now, let's tackle the second question. A key strategy on the ACT math section is time management. You've got a limited amount of time per question, so you need to be efficient. That means recognizing common problem types and having a plan of attack ready to go. For instance, if you see a problem involving similar triangles, you should immediately think about setting up proportions. If you see a problem involving the Pythagorean theorem, you should immediately think about using a^2 + b^2 = c^2. The more familiar you are with these common problem types, the faster you'll be able to solve them.

Another helpful strategy is to use your calculator wisely. The ACT allows you to use a calculator, and you should definitely take advantage of that. However, don't rely on your calculator too much. Some problems are actually easier to solve without a calculator. And, even when you do use a calculator, make sure that you understand what you're doing. Don't just blindly plug numbers into formulas. Understand the underlying math concepts.

Remember to show your work. Even if you can do some of the steps in your head, it's always a good idea to write everything down. This will help you avoid making mistakes and it will also make it easier to check your work later. Plus, if you get stuck, having your work written down can help you figure out where you went wrong. Be careful and deliberate! It's much better to get every question correct than to get to every question.

Also, don't be afraid to skip questions that you're not sure how to solve. If you're spending too much time on a particular question, just mark it and come back to it later. It's better to get all the easy questions right than to waste time on a difficult question and run out of time before you get to the easier ones. With the time you save, you can then focus on getting more questions correct that you previously did not know how to solve.

Lastly, practice, practice, practice. The more you practice, the more comfortable you'll become with the types of questions that are asked on the ACT math section. And the more comfortable you are, the faster and more accurately you'll be able to solve them. Doing practice tests will also get you used to the format and timing of the test, which can help reduce your anxiety on test day. Now, let's go through an example to give you an idea of how this all works.

Correct Answer: [Correct Answer]

Question 3

Question: [Original Question 3 Here]

Explanation: Okay, guys, let's break down question number three. One common area where students slip up is in reading comprehension, even in math problems. ACT math questions aren't just about the math. They're also about reading comprehension and problem-solving skills. Make sure you understand what the question is asking before you start trying to solve it. Read the question carefully and pay attention to any key words or phrases. Underline or highlight important information. Sometimes, rephrasing the question in your own words can help you understand it better.

Another key skill is knowing how to translate word problems into mathematical equations. This is a skill that many students struggle with, but it's essential for success on the ACT math section. Look for key words that indicate mathematical operations. For example,