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Sat Essay Prompts January 2013 Trig

The ACT and SAT are designed for high school juniors. But we know that not all juniors around the world are taking the same math courses. Here’s what students need to know before taking the ACT or SAT.

There is a catch.

Before I declare students are ready for either the SAT or ACT there are a couple caveats:

  • Completion of a course doesn’t always equal retention or mastery of skills. I’ve had students admit they never really learned geometry (or algebra) and just got by on homework grades and cramming. I have other students who are so far advanced (taking Calculus II as a junior for example) that they have forgotten the basics.
  • Both the ACT and SAT are difficult exams written with enough hard questions that not too many students will score in the top 10% (or top 25%.) Math questions are difficult not based on the course sequence, but based on the number of concepts combined into a single problem and the likelihood of making a mistake. In other words, there are hard questions that don’t go beyond junior high school math, but almost no students get these correct due to calculation errors, misleading answer traps, etc.

But there are some basics a student needs to complete before he or she has enough math knowledge to successfully attempt these exams.


ACT math focuses on algebra, geometry, and basic trigonometry. In general I find most students are able to adequately prepare for the exam once they have taken high school algebra and geometry.

Some problems (about 4) include basic trigonometry which most of my students have learned in geometry class. SOH-CAH-TOA is all the trig you need. (If you don’t know it, your student probably does.)

Starting in late 2016, the ACT added some harder probability questions and problems that involve more math typically taught in Algebra II. While Algebra II is not required for success on the ACT, a junior taking Algebra II might want to make sure he or she has a solid understanding of Algebra I. (In some cases a few months of Algebra II is the perfect review for the necessary skills.)


The redesigned SAT (starting in March 2016) goes much deeper into Algebra II concepts than the old SAT or the ACT. In order to be adequately prepared for a majority of SAT math, I’m recommending students complete Algebra II before preparing for the exam.

This means juniors taking Algebra II might want to give serious consideration to the ACT which does not test as many Algebra II concepts or wait until mid-spring to take the SAT.

Tips for math review

I’ve found the free SAT review lessons from Khan Academy to be a good place to start for students taking either exam. You can start here.

For a general overview, skip the diagnostic quiz and scroll down to the videos and practice problems. Start with the basic video for any concept. I like to pause a couple second into the video and see if I can solve the questions quickly and accurately on my own. If I can, I usually fast forward to the end to double check I got it right. Move to the harder example then test your skills on the practice problems.


Whether a student takes the ACT or SAT, it is important to have a solid understanding of the math concepts tested in order to make the most of any additional test preparation activities you may pursue.

/0 Comments/by Megan Dorsey

Whether you're on a budget or just want to see what kinds of ACT Math study materials you can access for free, you've come to the right place. Though the internet is chock-full of ACT resources of dubious quality, we've collected and put together only the highest quality free ACT Math study material available.

So let's jump right in!

Note: For guides and reviews of the best for-pay ACT study, check out our list of ACT study links, which includes all official practice tests, and our top picks for ACT prep books.


Why You Must Use High-Quality ACT Math Materials

Because the ACT is a very specific type of standardized test, it's crucial that you study using the right sources. Studying with the wrong materials is about as bad as not studying at all, and there are, unfortunately, a lot of poorly designed ACT prep materials floating around. So don’t be tempted by the many websites and programs, both free and paid, that provide ACT prep materials of poor quality.

If you spend your time studying from inferior materials, you will not have a clear sense of how you’ll perform on the ACT. Proper test prep is about assessing your current level and improving upon it, but you won’t be able to do this if you get a false sense of your skill level (either higher or lower) based on low-quality study materials. In short, any practice problems that don't properly reflect the types of questions you’ll see on the ACT aren't worth your time!

Knowing this, the absolute best study strategy is to use official ACT materials. The test is designed by ACT, Inc., and their free materials are far and away the best place to start. From here, you can then branch off to programs and resources that utilize (or closely resemble) this official material.

Because you should only be studying from websites and programs that are as close to the source (i.e., the official ACT) as possible, there sadly aren't a whole lot of free materials available.

That said, we've found a couple of solid free ACT Math resources you can use in your prep. Read on to see what these are!


The 4 Best Resources for Free ACT Math Practice

Here are four super helpful websites you can use to help you make the most of your ACT Math studies—and you don't have to pay a cent for any of them!


#1: ACT, Inc.

The creator of the test itself, ACT, Inc., should always be your first go-to website for any and all ACT matters. Luckily, they also have a good deal of free study resources, offering both complete ACT practice tests and individual Math practice materials.


Free Official Full-Length ACT Practice Tests

The five tests linked below are the only free tests available from the past 10+ years. Each ACT test includes an optional Writing section and answer key:

You might notice that there are missing years here (2006-07, 2007-08, etc.). This is because the ACT repeats tests for different years, meaning that the tests for missing years are actually duplicates of the ones above.

Note: If you buy the third edition of the ACT Red Book, you'll have access to five more official ACT practice tests, but this is obviously not free (around $30 on Amazon). You can also buy the more recent 2017-18 edition of the ACT Red Book, but this one only includes three practice tests whose questions often overlap with those in the practice tests above.


Free Official ACT Math Practice

In addition to complete practice tests, the official ACT website provides sample math questions with answer choice feedback. These are a full 60 questions in ascending order of difficulty, just like a real ACT Math section. It's essentially another free complete ACT Math test with which you can study!

We recommend solving all your questions on paper and then checking your work at the end, rather than checking your accuracy after each question. This method will give you a better sense of how you’ll do on the ACT (remember, you won’t get immediate feedback while you’re taking the actual test!).


No need to worry about bills here—most of your ACT studying can be done for free.


#2: PrepScholar ACT Blog

At PrepScholar, we've compiled tons of free resources for all your ACT Math needs, including detailed guides on every ACT math topic. Our articles give definitions and explanations for major math concepts, offer examples of how you’ll see each topic on the test, and provide ACT practice questions with detailed answer explanations.

Below are some of our most helpful content-related resources for the ACT Math section:



Coordinate Geometry

Plane and Solid Geometry



In addition, we have strategy guides to help you solve numerous ACT Math problemsacross the board:

You can also sign up for a free five-day trial for our online ACT prep program. This customizable program assesses your current strengths and weaknesses and adapts to your needs based on your progress. It also gives you practice questions tailored to your areas that need improvement and provides expert answer explanations for all questions.

The questions we use in our program are all based on real ACT test questions, and, though the full program is not free, we guarantee you your money back if you don't improve your ACT score by 4 points.


#3: Ivy Global ACT Practice Test

This company offers a free unofficial ACT practice test. Although the math content overall is solid, some questions are slightly easier than those on the actual ACT. In addition, there are no answer explanations, making it hard to determine how to effectively solve questions you got wrong.

Otherwise, this PDF offers helpful practice and is a great option if you've already used up all official resources. I recommend using it mainly to dig into extra math questions (instead of taking it as a full-length test). This will help you develop a clearer picture of what math concepts and question types are especially difficult for you.

It should also be noted that unlike other ACT websites, Ivy Global does not require you to make an account in order to access its ACT practice material.


#4: Khan Academy

A partner of the College Board (the creators of the SAT—not ACT), Khan Academy is a great website to use for ACT Math practice and review, as long as you know how to use it effectively.

I say that because this free prep website only offers a program for the SAT, so you won't find any official ACT practice questions here. That said, you can still use Khan Academy to drill relevant ACT Math concepts and practice those you've learned.

Since the ACT, like the SAT, has a big emphasis on algebra, you can use the SAT's Heart of Algebra and Passport to Advanced Math sections for relevant practice. For geometry (which makes up 35-45% of ACT Math), use the High School Geometry page to choose specific concepts and watch videos on them. Finally, for trigonometry, go with the trigonometry and SAT Additional Topics sections.


OK, so you've got your study material. Now how do you best use it?


How to Use ACT Math Resources Effectively: 6 Key Tips

In addition to knowing what material to actually use (and what to avoid) for your ACT Math prep, it's important to know how to best utilize the resources you find. The following six tips will help you achieve your highest ACT Math score using the free prep materials available.


#1: Take a Complete Practice Test in One Sitting

Though you're probably mostly concerned about your ACT Math score, you still need to know how you'll fare over the course of the full ACT. Answering one or two ACT questions might not be overly challenging, but the test is a marathon: if you aren't prepared, you'll likely find yourself exhausted by the end of it. And exhaustion can cause anyone to make mistakes!

So before you dedicate your focus to ACT Math alone, see how your Math score fits into the larger test-taking picture. 

Plus, a bonus: by taking a full ACT practice test, you'll also be able to see how your Math score does over the course of the entire Math section (remember, questions get harder and harder over the course of the Math test!).


#2: Use Proper Timing

As you take your complete practice test and any math-specific sections, be sure to follow the proper timing used on the real ACT. 

Here's a brief overview of how much time you'll get on each ACT section as well as how much (estimated) time you should spend per question:

ACT SectionTotal Time# of QuestionsTime per Question
English45 minutes7536 seconds
Math60 minutes6060 seconds
Reading35 minutes4053 seconds
Science35 minutes4053 seconds
Writing (Optional)40 minutes140 minutes


As you can see, you'll have an average of one minute to answer each Math question, and you'll need to know how well you fit into these parameters before test day. It's not worth much if you can answer every question correctly but can't complete the test in time!

Don’t worry if you run out of time while taking your first practice test—this is completely normal and gives you a place from which to begin and improve. If the trend continues, however, consider checking out our guide on how to stop running out of time on ACT Math.


#3: Review Your Mistakes

Taking a practice test is merely the first step. Once you're done with this, focus on identifying any patterns in your correct and incorrect answers so that you can see what and how you need to improve.

For example, do you tend to get the last few questions wrong on Math? Do function questions always throw you for a loop? Whatever your case, dig deep to examine your errors, and tailor your study plan to drill your most challenging areas.


#4: Target Your Areas of Weakness

Your goal is to answer as many questions as accurately as possible, so dedicate the majority of your time to improving your areas of weakness.

For example, if you're struggling to understand a certain concept, such as systems of equations or coordinate geometry, take time to review it and then use practice questions and tests to ensure you're getting it down.

In addition, make an effort to prioritize the first 40 questions or so on ACT Math. Though each question is worth the same number of points, they get more and more difficult as you go through the test. Therefore, it's more efficient in terms of your time and energy to solve two questions in the 20-range than it is to spend twice as much time solving question 60.


#5: Pace Your Studying

Don’t cram all your studying into one day before the test. With a busy schedule, cramming might seem like your only option, but real improvement happens over time.

And yet don't despair, either! No matter how much time you have left before the test, you can make a balanced study program.

Start by looking at the time you have before test day. We generally recommend giving yourself at least three to six months to study for the ACT; this should be enough time for you to identify your weaknesses, take several practice tests, and review key content.

Next, assign yourself at least three full practice tests in addition to your normal studying time, spaced out over the course of your time until the test.

This probably won’t be possible if you only have a week or two before the ACT, but it’s still important to fit in at least one practice test or two wherever you can. If you're on an accelerated or last-minute schedule, check out our guides to studying for the ACT in a month and improving your ACT score in 10 days.


#6: No Improvement? Consider Using a Tutor or Prep Program

Some students want to do all their studying alone, but for others this method is impractical.

If the material doesn't make sense to you and you need extra guidance (or something to get you to make time to study), a tutor or prep program (or both!) can give you the final push you need to do well on the ACT and maximize your score. At PrepScholar, we offer both expert tutoring and a fully customizable online ACT prep program.

As you weigh your options, remember to consider how much you should pay for an ACT tutor and when your ACT test date is so you can come up with a surefire plan that works well for you!


There are many different study paths, and you'll find the right one for your needs! (maramao/DeviantArt)


What’s Next?

Want to best make use of your ACT study materials? Now that you've gathered some ACT Math resources, check out how to get the most realistic ACT experience in your practice.

Bitten by the procrastination bug? Time running out until test day? Check out how to beat the urge to procrastinate and learn how to balance your time for your ACT prep.

Looking to get a perfect ACT score? Take a look at our guides to how many questions you can get wrong and still get a perfect score and how to get a full 36 on ACT Math (written by a perfect scorer!).


Want to improve your ACT score by 4 points? 

Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more.

Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next.

Check out our 5-day free trial:


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