The post My Top SAT/ACT Resources appeared first on Dan's Test Prep.

]]>You don’t have to be a genius to score highly, though. Anyone can reap the benefits of a good score through proper preparation. But in order to do that, you’ll need to know the best resources to prep with and how to use them.

If you want to earn 99th percentile scores like I did, stick around to see my top SAT/ACT resources.

If you’re not using Khan Academy for your test prep, then you need to get on it ASAP. Khan Academy is the number one resource I recommend to all my students, especially if you’re looking to score higher on the SAT. Let’s take a look at why:

- Khan Academy has a total of TEN full practice tests that you can take. For eight of these tests, you are able to input your answers
**directly into Khan**, where it will score and break down the tests for you. Each of these tests also has answer explanations so that you can fully understand each mistake you make. - You can link your CollegeBoard account to Khan Academy on your dashboard. This allows Khan to recommend you
**specific topics**that you missed on your previous PSATs, SATs, and practice tests. - In addition to general tips and strategies, Khan Academy has both math and reading/writing practice questions. Every single skill you’ll need to know is listed on these two pages. Khan also includes
**two example videos**and**dozens of practice questions**per skill.

Not only is Khan Academy great for familiarizing yourself with the general structure of the SAT, but it also has the best source of official practice tests. You want to ensure that you’re prepping with the highest quality materials possible. Khan Academy guarantees this by providing tests made by the CollegeBoard (the creators of the SAT) themselves.

Furthermore, the practice questions for each skill are a godsend for your test preparation journey. No longer are you left guessing what topics pertain to each question. Instead, you are given a breakdown of your skills based on questions you missed, which also helps you keep track of your progress.

If you’re weak on some conceptual knowledge, you can learn by using Khan’s answer explanations and example videos. Even if those don’t help you at first, you’ve at least identified the skill you’re having trouble with. That way, you can do a quick online search for free resources explaining that topic and learn it. Once you’ve filled in that missing knowledge, you can go back to practicing on Khan Academy.

Here’s **one vital tip**, though: don’t just blindly go through practice tests/questions. Whenever you get something wrong, make sure you fully understand why you got something wrong. *Was it a lack of conceptual knowledge? Was it a failure to apply a strategy? Was it just a numerical error?* Learn to identify your mistakes: figure out why they happened and fix them. That way, you won’t make the same mistake twice.

Personally, I did over 1600 practice questions on Khan Academy, and I completed six full practice tests over the course of several months. I got every single skill on there to level 4, and I made sure to understand **every mistake I made**, no matter how long it took.

CrackACT.com is the number one resource I recommend to all students studying for the ACT. Khan Academy is great, and many of the concepts will transfer over to the ACT. However, in order to master the ACT, you have to practice with test material from it. Here’s why I recommended using CrackACT:

- CrackACT has five “ACT Official Guide” Practice Tests along with answer explanations. Not only will you be prepping with reputable materials, but you’ll also be able to understand
**exactly why each answer is correct/incorrect.**This will greatly aid you in fixing your own mistakes. - CrackACT has fourteen full-length “Preparing for the ACT” practice tests. These are created
**directly by the ACT**and even contain “retired” questions from previously administered ACTs. With these tests, you can be confident you’re prepping with extremely high quality questions that mimic the real tihng. - Finally, CrackACT contains
**dozens of previously administered tests**, ranging from Form 1ST (1996) to Form C03 (December 2019). With these tests, you can’t possibly run out of prep material. Plus, the ACT format has not changed much in the past couple of years, so the older materials are okay to practice with.

CrackACT contains a plethora of practice tests from which you can gain valuable practice. I promise you that if you go through the dozens of tests they have, you’ll start to recognize patterns in the questions they ask. Simply being familiar with the questions asked on these exams will make them easier to solve come test day.

Plus, unlike the SAT, the ACT has not had any major changes in content or format over the past couple of years. This means that older practice exams are just as valid as the newer ones. Still, I would consider sticking with the newer exams (2010 and later) just to keep up with those minor differences.

Like with Khan Academy, you’ll want to make sure you understand every mistake you make during your ACT prep. Since there’s more prep material, but less answer explanations, I recommend spacing out when you take the “ACT Official Guide” Practice Tests. This will ensure you don’t blow through all your “answer explanation” tests in one go.

In most cases, though, you can figure out where you went wrong simply by looking at the question and the answer key. For Reading and Science, you’ll need to do a bit of logical reasoning and reading comprehension to figure it out. For Math and English, you may need to figure out what concepts you messed up on and study them. After that, it’s pretty straightforward. Attempt the problem again and try to get the correct answer. Like with the SAT, you should strive for mastery.

If you’re looking to boost your SAT or ACT prep, UWorld is the way to go. Maybe you’ve exhausted the entirety of Khan Academy and CrackACT, or maybe you just want new questions to prep with. Although it isn’t free like the other two on my list, UWorld is a great resource you can use for BOTH of these tests. Let’s take a look at what it has to offer:

- UWorld has an absolute
**abundance of practice questions**to prep with. With over 2100 unique SAT questions and 2100 more ACT questions, your needs for more prep material are absolutely going to be met. It’s likely that you may not even reach the end of the question bank just based on its sheer size. - UWorld contains
**detailed explanations**that guide you through each problem, step by step. You’ll be able to see helpful illustrations and explanations that not only teach you why the correct answer is right, but also why the other answers are wrong. - UWorld
**tracks your performance**and identifies your areas of weakness, so you can focus more on what matters. You’ll be able to see how long you spend answering questions, as well as what concepts you are weakest with. I think that identifies your areas of weakness is absolutely necessary to prepping effectively, and UWorld does it for you.

Most students will never even get close to finishing the massive question bank contained in UWorld. With so many practice questions, you can’t go wrong with choosing this site for extra prep. With their answer explanations and intelligent tracking system, you’ll be able to prep effectively without sacrificing question quality.

I am not affiliated with UWorld in any way. I simply think that their system for practice is extremely well built, and it mimics the way I went about my own test prep. After you’ve learned the content, you also need to know how to apply it in the context of the SAT/ACT. That is a whole separate skill which can only be trained by grinding practice questions, understanding your mistakes, and rinsing/repeating.

You may have noticed that I haven’t listed any books as my top resources for the SAT or ACT. That’s because for most people, I think **these websites are all you need **to score well on the SAT/ACT.

In my opinion, books aren’t really necessary to mastering these tests. Many of the skills and strategies can be obtained by grinding practice questions, and when possible, studying the answer explanations. If you’re missing content knowledge, you can identify the area of weakness and look up the concept online. In some cases, the concepts will even be taught in the answer explanations.

Now, when I say I “don’t recommend any books,” that’s not to say I’m completely against them. I have heard of people who found** great success** using books to learn some of the content and strategies needed to succeed on these tests. Some books I hear thrown around a lot are the Erica Meltzer books for Reading/Writing/English, CollegePanda for Math, and For The Love of ACT Science for Science.

If you’re struggling to learn the concepts you need or you’re having trouble picking up strategies, it may be helpful for you to pick up a book in that area. Some students find it difficult to learn on their own, and that’s totally fine. Other students find it hard to learn even from books and would rather have a tutor guide them through the process. Learning new things is never going to be easy, and for me it was a long, slow grind to get to the level of mastery I am at now. Regardless of whether or not you get a book, you’re going to have to put in hard work.

I’ll be taking a closer look at some books in the near future myself and writing up a post on the ones I feel are most helpful. For now, I recommend trying out these online resources first.

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]]>The post List of SAT Math Cheat Sheets appeared first on Dan's Test Prep.

]]>I’ll be continually updating this page as I develop more math cheat sheets, so be sure to bookmark it!

This cheat sheet is great for anyone who wants to understand the basics of exponents, as well as the rules that exponent operations follow. Download it here.

This cheat sheet is great for anyone who wants to understand how exponents and radicals are related, as well as the rules that roots/radicals follow. Download it here.

This cheat sheet is great for anyone who wants to learn more about circles. I’ve included several helpful formulas, definitions, and visualizations to aid you on those circle problems on the SAT. Download it here.

The post List of SAT Math Cheat Sheets appeared first on Dan's Test Prep.

]]>The post How To Solve Hard SAT Math Problems – Complex Fractions appeared first on Dan's Test Prep.

]]>Recently, I posted a video on TikTok (@danstestprep) showing how you can save valuable time on the SAT Math section.

The video did quite well, and I assume it was because I solved a very difficult-looking problem in just **two seconds**. The question I covered dealt with complex fractions, and you can take a look at it below:

Basically, I was able to recognize that whenever you have a fraction in this form, the answer is always going to be the quadratic expression over the linear expression. In this case, that corresponds to answer choice C.

*But why exactly does this work, and when can you use this trick?*

Keep reading, because I’m going to show you the specific cases in which you can use this trick, as well as **one simple method** that you can use to solve **any complex fraction questions**.

Before we begin, there are some terms you need to know.

Remember that a quadratic term is a term where the highest power on the variable is a 2. This can typically be seen as an x^{2} term.

A linear term is simply a term where the highest power on the variable is a 1. This is typically seen as an x^{1} term, or simply an x (the exponent of 1 is implied).

A constant term is just a term without any variables; therefore its value cannot change.

Let’s begin by analyzing the way our problem is set up. Notice that we have a complex fraction where there is a constant in the numerator, and then the addition of two fractions in the denominator. The fractions nested in the denominator are formatted so that there is a constant in their numerators and a linear term in their denominators.

If you’re confused, here’s an image of what I mean by all that:

This trick can** only be used** under the following conditions:

- The numerator has to be a constant (does not necessarily have to be a 1)
- The denominator must contain two fractions (either being added or subtracted, it doesn’t matter)
- These fractions must have a constant in their numerators (again, can be any constant) and a linear expression in their denominators. This linear expression must be a BINOMIAL, meaning it has two pieces (an x term and a constant).

If these conditions are met, then your answer will simply be the choice with the quadratic expression over the linear expression. That’s really all there is to this trick.

In the next section, I’ll show you why this works, and how you can solve ANY complex fraction problem by just breaking it down.

While solving a question in two seconds would certainly be useful on the SAT, it’s not always feasible to do so. The problem may be presented in a different format or context, requiring you to simplify the complex fractions. I’ll be teaching you exactly how you can tackle those complex fractions no matter where they show up.

Let’s start by taking a look at the expression in our original question:

From here, I suggest that you find the common denominator of all the terms in the complex fraction. The easiest way to do this, in my opinion, is to just take the denominators of each term and multiply them together. The three denominators from our three terms are 1 (from 1/1), x – 3 (from 1/(x – 3)), and x + 4 (from 1/(x + 4)).

We can multiply these three expressions together to get our common denominator: (x – 3) · (x + 4). We could FOIL this out, but I’d like to keep it in this form for now.

Now that we have our common denominator, we can multiply it to both the top and bottom of our fraction:

Make sure you multiply to BOTH the top and the bottom, because otherwise you’d be changing the value of the expression. By multiplying it to both the top and bottom, you’re essentially “multiplying by 1” since (x – 3)(x + 4) divided by itself is equivalent to 1.

Now if we distribute the fraction on the right into our expression, we end up with something that looks like this:

This looks very complex, but it really isn’t. Notice how we can cancel out the (x – 3)’s from the complex fraction on the left. Similarly, we can cancel the (x + 4) terms from the complex fraction on the right. This leaves us with something that looks like this:

This is already looking a LOT simpler. From here, all you have to do is multiply the two terms in the numerator (I like to use FOIL) and add like terms in the denominator. This gives you your final result:

After all that work, you’re left with a quadratic term over a linear term, which is the same result that we got when using the two-second trick above.

By using this method of solving algebraically, you’ll be able to tackle **ANY** complex fraction!

The post How To Solve Hard SAT Math Problems – Complex Fractions appeared first on Dan's Test Prep.

]]>The post How To Solve Hard SAT Math Problems – Right Triangle Trigonometry (Part 1) appeared first on Dan's Test Prep.

]]>Recently, I’ve been tutoring for the SAT, and I noticed one of my students was struggling with some of the SAT math questions. More specifically, they were struggling with Right Triangle Trigonometry questions. Now, I don’t blame them. In my opinion, these are some of the hardest questions that the SAT tests you on. Because of their relatively high difficulty compared to other questions, I felt it was appropriate to address an example of how I’d go about solving one in a blog post.

Let’s take a look at the problem that this student was struggling with.*(Note: If you think you’ve already got a good understanding of trigonometry and just want to see the solution, you can skip ahead to “Solving the Problem.”)*

The question reads: “Side length *t* is 6.43 and *s* is 5.39. Given that s / t ≈ tan(0.697) ≈ sin(0.994) ≈ cos(0.576), approximately what is the measure of angle *β* in radians, to the nearest tenth?”

Looks pretty difficult, right? I took this problem straight from Khan Academy’s SAT prep questions. At first glance, you may have no idea how to solve it. Let’s try and break it down, though, to get a better understanding of what we’re working with here.

It’s clear that the question is asking us to find the measure of the angle *β* (Beta), but the method we’re supposed to use isn’t readily apparent. The only other information that’s given is that the ratio of the two sides, **s / t**, is equal to some angles plugged into some trigonometric functions.

The fact that **s / t** is equal to tan(0.697) and all those other trig values may seem completely abstract, but there’s actually an easy way to conceptualize it. If you recall SOHCAHTOA and your trig/inverse trig relationships…

…it simply means that when a triangle is formed with side length ** s **on the

Likewise, if a triangle is formed with side length ** s** on the

Finally, if a triangle is formed with side length ** s** on the

If you’re still confused as to what that might look like, here’s a visualization I created to help you understand:

In our case, since the angles are changing but the sides being referenced are not, our chart would look a little more like this:

By using all of the information in the chart above, we can actually try to get *β* in place of one of these angles (i.e., replace either 0.994, 0.576, or 0.697 with *β*). This means we must encounter one of three situations in the problem:

- The side OPPOSITE angle
*β*is, and the HYPOTENUSE is*s*.*t* - The side ADJACENT angle
*β*is, and the HYPOTENUSE is*s*.*t* - The side OPPOSITE angle
*β*is**s***β*is.*t*

By definition, if we can get *β* into one of these three positions, then we already have our answer, since the trig relationships for three angles are already defined in the question. Since we’re given three angles to choose from (0.697, 0.994, and 0.576), we could also make a guess here and have a 33% chance of getting it right, but let’s see how we can solve the problem.

Now that we know what we’re looking for, we can go ahead and try to get *β*, *s*, and *t* together in a way that allows us to solve the problem. Believe it or not, we actually have all the information we need to solve this problem. By filling in missing information based on what we already know, we can make this problem a little bit easier to solve.

First, note that the small triangle containing *β* contains a right angle. We’ll label this angle as π / 2, since we’re working in radians, but it’s also equivalent to 90 degrees.

Next, we’ll label the last angle of this triangle as (π / 2) – *β*. We’ll do this because we don’t yet know the measure of this angle, but since we know the measure of the other two angles, we can write the last one in terms of the first two. Since all angles in a triangle add up to 180°, or π, the remaining angle is π – (π / 2) – *β* = (π / 2) – β.

Now that we have those three angles, we can begin labeling the angles of some of the other triangles. Since we know that the vertical line forms a right angle (90°) with the base of the largest triangle, we know that the two angles formed by the diagonal line (between the blue and green sections) are complementary. This means that they will add to 90°, or π / 2. That means that the blue angle is equal to π / 2 – (π / 2 – *β*), or simply *β*.

From here, we can begin to incorporate *s* and *t* into the picture. Note that the quadrilateral formed between *s* and *t* has three right angles, which means that the last angle must also be a right angle. This follows directly from the fact that a quadrilateral has four angles that add up to 360°. Because of this, we know that each pair of opposite sides are equal in length, and we can label the remaining sides of the shape with *s* and *t*.

At this point you may start to see where the answer becomes apparent. Since we have *β*, *s*, and *t* together, we can label the sides according to their position relative to *β*. I didn’t label the hypotenuse because it wasn’t relevant to this particular situation, but if the hypotenuse was *s* or *t* then I would have labelled it as well. Now that we have our sides’ relations to the angle *β*, we can use the original information given to solve the question.

Since the two sides with *s* and *t* were the opposite and the adjacent sides to the angle, we’ll be using a tangent relationship to finish up this problem. We can set up the relation given to us from the problem, where the ratio of the two sides, **s / t**, is the tangent of the angle 0.697. In this case, it is the tangent of the angle *β* as well!

By now you can probably see that *β* is equal to 0.697. However, if you want to go one step further and do it properly, you’d take the inverse tangent of both sides of the equation. This will show you that the inverse tangent of (**s / t**) is equal to 0.697 radians, which is equal to the angle *β*.

And so we arrive at our answer: 0.7 radians. Make sure you pay attention to the wording of the question and round the answer to the nearest tenth, otherwise it would be marked wrong on the SAT!

The biggest takeaway from this example should be that as long as you have the necessary knowledge, any problem on the SAT is manageable when you break it down. (If you’re missing some content knowledge, though, I’d recommend you go and learn those concepts first).

The process I use generally goes as follows:

**Try to figure out what exactly the question is asking you.**In this case, it was pretty clearly stated what the question was looking for. However, it took a bit of thinking to determine how to arrive at such an answer, and what the other information given in the question meant.**Figure out what information is relevant and how it’s relevant.**In this problem, we knew that we’d be using the trigonometric relationships given to solve for the angle*β*. We knew that we had to relate*β*,*s*, and*t*somehow to arrive at our answer.**Use what you’re given to fill in missing information and solve.**In this problem, all the information we needed was given, but not everything was explicitly written on the figure. We had to fill in certain angles and side lengths by logical reasoning as well as implementing some geometry/trigonometry rules.

I hope that you found this post helpful for your SAT prep journey, and hopefully it makes you better with solving right triangle trigonometry questions on the SAT. If anything I wrote was unclear, just let me know and I’ll try to clarify it. Keep on practicing!

The post How To Solve Hard SAT Math Problems – Right Triangle Trigonometry (Part 1) appeared first on Dan's Test Prep.

]]>The post Why Should You Get a Private SAT/ACT Tutor? appeared first on Dan's Test Prep.

]]>Why Get a Tutor?

The realm of college admissions has been getting more and more competitive in recent years, especially with regards to standardized test scores. If you want to stick with the competition, hiring a private SAT or ACT tutor can prove extremely advantageous. Although it’s true that the SAT and ACT have been getting more competitive, the data isn’t very apparent at first. The average SAT and ACT scores vary quite little from year-to-year.** **However, when looking at the top-scoring band (95th percentile and up), there is a clear increase in the number of high-achieving students. In order to be competitive, especially at many top colleges, students need to stand out in terms of test scores.

The number of students scoring highly on the SAT/ACT has only been **increasing** in recent years.

Source: Compass Education Group

To the question of “should I hire an SAT or ACT tutor,” the answer is entirely dependent upon your needs. Indeed, if you’re looking to make yourself more competitive of an applicant, a private tutor can only help you. Not only will you have a better shot at admission, but you might also land a merit scholarship worth thousands. Test prep can be hard to manage on your own, and that’s precisely where tutors come in. Hiring a tutor can make the whole process much easier and more enjoyable for you, among other things. Down below, I’ve compiled a list of the three main benefits I believe you’ll gain by working with a private SAT or ACT tutor.

Accountability

Let’s face it: finding the motivation to study is* *hard. Hiring a tutor cuts out all the excuses for you. With a private tutor, you’ve got a weekly schedule to stick to. In addition to meeting with you weekly, a good tutor will have you practice your skills before the next session. They may assign you some extra homework or readings to reiterate and reinforce your knowledge. While your prep plan may be flexible (and will certainly vary between students), working with a tutor ensures you’re staying on track to earn your target score.

Letting a tutor handle the creation of a test-prep schedule for you takes a huge burden off of your shoulders. With a schedule in place, it becomes much easier to stick to your test prep promises. When you hire a tutor, you enter a commitment to improve your test-taking abilities. Working with someone ensures that you stay dedicated to honoring this commitment. A good tutor will simplify the test-prep process to where you can focus purely on learning, letting them handle everything else.

Guidance

Arguably the most important point on the list is the professional guidance that an SAT/ACT tutor can provide you. When you work with a private tutor, you’re working with a subject-matter expert. As a result, your tutor should be able to answer all of your questions quickly and confidently, in addition to knowing where to get additional resources to help you prep. Furthermore, a good tutor knows exactly what your weaknesses are and how to target them. Often times, students just don’t know what they need to work on. Having a tutor is a great asset: it ensures the student focuses on the right material, maximizing the effectiveness of their test prep.

While free services may have questions and answers to aid in studying, they miss out on other crucial aspects to test prep. These services offer limited (and sometimes confusing) explanations to questions, leaving students stumped and unwilling to proceed with their prep. On the other hand, a tutor can explain a question or concept in multiple ways. They can also offer several strategies to approach a question, allowing the student to choose what’s best for them. Tutors are certainly the way to go if you’re looking for a personalized approach to the test-prep process.

Confidence

Besides for the added focus and guidance you’ll get, working with a tutor can instill a sense of confidence in your test-taking abilities. With the recent increase of top-scoring students on both tests, it’s too easy to feel down about your own scores. However, those students went through a lot of hard work and dedication to get those scores. A private tutor will remind you that anyone (including you!) can achieve a top score like that, as long as they’re willing to put in the work.

When you hire a tutor, you should also be assured that you hired somebody who knows exactly what they’re doing and truly *can* help you improve. Almost every private tutor out there is experienced, knowledgeable, and has a proven track record. They know precisely what you should focus on to maximize your score increase while minimizing time lost. They’ve successfully taught many different students before you, so there’s no reason you should be worried about not improving. All of these qualities should put your nerves at ease, and come test day, enable you to do your best!

If you liked this post, make sure to share it and check out my main page here!

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