*#1: The equation we are given ($−at^2 bt c$) is a parabola and we are told to describe what happens when we change c (the y-intercept).From what we know about functions and function translations, we know that changing the value of c will shift the entire parabola upwards or downwards, which will change not only the y-intercept (in this case called the "h intercept"), but also the maximum height of the parabola as well as its x-intercept (in this case called the t intercept).Now, we know that the tablecloth must hang an additional 1$ inches on #5: The position of the a values (in front of the sine and cosine) means that they determine the amplitude (height) of the graphs. Since each graph has a height larger than 0, we can eliminate answer choices C, D, and E.*

These categories are averaged across many students for a reason and not every student will fit into this exact mold.) All that being said, with very few exceptions, the most difficult ACT math problems will be clustered in the far end of the test.

Besides just their placement on the test, these questions share a few other commonalities.

If you’ve got your heart set on that perfect score (or you’re just really curious to see what the most difficult questions will be), then this is the guide for you.

We’ve put together what we believe to be the most 21 most difficult questions the ACT has given to students in the past 10 years, with strategies and answer explanations for each.

We'll take a look at example questions and how to solve them and at what these types of questions have in common, in just a moment.

If you’re just getting started in your study prep, definitely stop and make some time to take a full practice test to gauge your current score level and percentile.Only once you've practiced and successfully improved your scores on questions 1-40 should you start in trying to tackle the most difficult math problems on the test.If, however, you are already scoring a 25 or above and want to test your mettle for the real ACT, then definitely proceed to the rest of this guide.First, distribute out one of your x’s in the denominator.$/$ Now we can see that the $(x^2−1)$ can be further factored.It will always be the second section on the test and you will have 60 minutes to completed 60 questions.The ACT arranges its questions in order of ascending difficulty.As a general rule of thumb, questions 1-20 will be considered “easy,” questions 21-40 will be considered “medium-difficulty,” and questions 41-60 will be considered “difficult.” The way the ACT classifies “easy” and “difficult” is by how long it takes the average student to solve a problem as well as the percentage of students who answer the question correctly.The faster and more accurately the average student solves a problem, the “easier” it is.These are all real ACT math questions, so understanding and studying them is one of the best ways to improve your current ACT score and knock it out of the park on test day.Like all topic sections on the ACT, the ACT math section is one complete section that you will take all at once.

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