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This is for Question 20 of the ACT G19 test. Yes, this method also works and can be used to eliminate the answer choices one by one.

Unfortunately, I can't share the PDF of the official ACT test due to copyright restrictions.

There is no actual reset for exam 1 and 2. You simply retake these tests using the START TEST button. See the image at this link: imgur.com/a/FYahznK You will only have unique questions if you take each exam 1 and 2 twice. And if you choose to take it beyond two attempts each, there will be repeat questions.

The graph of the function f(x) shown approaches -2 and 2, the range falls between -2 and 2, but never becomes equal to those values. This is then reflected in the domain of the inverse function f^{-1}(x), which then falls between -2 and 2, but excludes the end points. Answer choice G, would imply that the domain includes -2 and 2 along with the values in between.

This is for students who already have a copy of the ACT Z18 test and have attempted it. I can't post the questions because of copyright reasons.

We are given that t falls between 0 and 3, inclusive, and that would mean that t-1 would fall between -1 and 2, inclusive. Note, in the expression for the acceleration the t-1 term is squared and is always positive, and it would be maximum when t-1 is equal to 2, which is what led me to t=3 giving the max value for acceleration. The minimum value of acceleration happens at t=1 with an acceleration of 9(the trap answer here).

@@MathQuantum Thank you for clarifying, I really appreciate it.

It is indeed a hard question. The idea is to become comfortable with finding patterns in sequence type questions. These types of questions come in different flavors, and you will see a couple in the official GRE PowerPrep tests.

Area from 0 to 3 is equal to the area from 3 to 6, because the parabola is symmetric about the line x=3.

The term sinxdx was replaced by -dt.

So then why would you plug cosx back in for t but then not plug in -sindx back into dt

@@andrewgulbrandsen4356 The cosx was replaced with t, and sinxdx was replaced by -dt, and that is why we end up with integral of -t^2dt. I don't think I understand your question.

Because of copyright restrictions. I would love to post the entire question but collegeboard would likely ask youtube to take down my explanations. I would say buy a used copy of the guide from ebay. It probably costs $5 now.

Yes, but only if all they did was to replace 105 with some other number and the rest of the statement stays exactly the same. You are correct that the answer in terms of P is indeed P/4. However, these types questions come in different variations and I personally don't try to memorize these cases. For example, they could have said that 105 was the sum of the one of the radius and the arc of the shaded region, or some other variation, and that would change the answer.

"This result implies that the maximum area of the sector occurs when the arc length is twice the radius." More exploration in this article: kb.osu.edu/server/api/core/bitstreams/be92506f-ff70-4591-98fe-bd309954544f/content

"The parallel of this solution with the one where the square was the maximum area for rectangles with fixed perimeter is worth noting." Another good reference: jwilson.coe.uga.edu/emt725/sector/sector.html

@@MathQuantum Thank you for the very thorough response! I'll try to wrap my head around this problem in other variations but my first and easiest solution to remember is P/4. I'll do some more thinking on it after I get through the rest of the playlist. Thanks again.

Look it up: sin(-x) = -sinx cos(-x) = +cosx tan(-x) = -tanx Their reciprocals are the same. Use this to compute it in the calculator.

The two methods are equivalent, in your case the term with base 2 would stay in the numerator and you would obtain (2^{-10))(5^{13}).

I did finally assemble them in a playlist and here is the link: ruclips.net/p/PLldv_vDcl8CmqddOaYdIOh4JN1dmFABV5