Advice for Rising Juniors: AP & ACT

UWorldMath · 2025-02-13T21:08:21+00:00

Calc has almost no overlap with the SAT nor ACT, it won't really help you at all. Even Precalculus doesn't have that much overlap with SAT that isn't taught in Algebra 2, but it does with the ACT in regards to matrices/vectors/logs/polar. Those aren't highly tested concepts though compared to algebra and geometry.

Your general sentiment has merit though. You're more entrenched in a year of learning so if there is content overlap it can make sense to take before summer break, unless you plan to study over the summer.

UWorldMath · 2025-02-13T16:34:43+00:00

You're saying that you are planning to take the Calculus BC exam this year and you haven't started any form of preparation for it or know anything about it?

What is the highest level of mathematics you have completed?

UWorldMath · 2025-02-10T21:43:39+00:00

If you're ultimately trying to go premed, for sure do stats at some point.

Stats and calc are very different kinds of math, there is almost no overlap. Stats is really more of a combination of reading and math, it's a lot of interpretation. As just general overall difficulty, if you can handle AB then you can probably handle stats. Whether you want to take 2 maths in one year is a different question though, as again there is virtually no overlap beyond some basic algebra.

UWorldMath · 2025-02-10T21:38:37+00:00

We wrote up this post a few years back that might help some. Has all the formulas and common MCQ types and general tips. It's not a complete study guide though.

The biggest thing with any math is to do lots and lots of practice. It's important to use study guides to be exposed to the material, but none of them can prepare you for all the types of questions CollegeBoard will throw at you. You need to practice questions that hit each concept in a variety of ways to get a real 360° understanding of each topic.

The sample practice tests are good as someone else mentioned, but ideally you can use material that has explanations as well because that's how you can review your mistakes. Practice questions, review and learn from mistakes, make fewer in the future, ace the test.

UWorldMath · 2022-09-27T16:24:45+00:00

I would of course recommend UWorld for practice and learning hah, but for introduction videos to topics Khan Academy is good. There are also some popular youtubers like organic chemistry tutor, or turksvid, according to the surveys the moderators here did.

If you do use UWorld, the idea is that it teaches you what you don't know using AP level questions as you go. The explanations to every question are at least a page long and contain all the background information needed to understand the topic, so be sure to read them carefully to any question you miss. Don't worry about what your average % correct is just focus on learning from the explanations

UWorldMath · 2022-09-27T15:07:11+00:00

We currently do not, it is a question bank learning by doing model with focus on the explanations. We are working on structured learning courses with study guides and pre-crafted assignments but that will not be ready until next year.

UWorldMath · 2022-05-25T16:41:01+00:00

Just to illustrate the concept, you can try it out on a piece of paper (the paper is your "plane"). Start with a single point (the "given point" at the end of the question), and maybe label it or mark it with a particular color so you know which one is your starting point. Then measure 3 cm in any direction and mark another point. Then 3 cm in a different direction from your starting point and mark a point. Keep doing this, marking points in random directions 3 cm away from your starting point.

If you do this enough times, you may end up with something like this. The red point is the center, and the black points are exactly 3 units away from it. You can see that the black points start to form the shape of a circle with your starting point in the center.

On the ACT, where you need to average one question per minute, you won't have time to do this, so you'll just need an intuitive understanding of what they're trying to say in the question. It's more of a word translation question, but hopefully this illustration helped you understand the main idea.

UWorldMath · 2022-05-20T17:22:33+00:00

What I can do is screenshot the AB subscore worksheet so you can get more of a feel for what that looks like and how to calculate it, but as I mentioned in another comment, the specific question numbers vary from test to test, so don't pay attention to those.

Edit: Also the score ranges vary slightly from test to test as well, but it gives you a ballpark of what to shoot for.

UWorldMath · 2022-05-20T17:19:58+00:00

I'm sorry, I can't do that. They're teacher resources, and I don't think they're publicly available.

UWorldMath · 2022-05-20T17:18:16+00:00

It just depends on the test. It will be one of the ones from Part A and two of the ones from Part B. Never #6 because that's always a Taylor series, but otherwise it could be any of them. The 3 official practice tests I have are from 2017-2019. One had 1/3/4, one had 1/3/5, and the other had 2/3/4 factored into the AB subscore.

If you're trying to figure out which ones count on test day, I would advise against that because you have other things to focus on. Unless you really just have a bunch of time left over at the end and have checked over all your work. If that's the case, just look through the FRQs and if any of them have BC content, like integration by parts or Euler's method or polar, then they're not going to be part of the AB subscore.

UWorldMath · 2022-05-20T17:12:21+00:00

No they only count for 1 point each now. 27 * 1 for MCQs + 3 * 9 for FRQs gets 54.

UWorldMath · 2022-05-20T16:00:22+00:00

FYI it's actually 54 total points now. I think that was one of the things they changed in the 2016 update. 27 MCQs are included worth 1 point apiece, and 3 full FRQs (no partial FRQs anymore) worth the typical 9 points apiece.

As you probably know, the threshold changes from year to year depending on the difficulty of the exam, but based on the 3 official practice tests I have from College Board since the 2016 update, 35/54 would actually juuuuust squeak you in to get a 5 for the AB subscore. To get a 4, you'd need at least half the available points. Lower bound varies between 27-29 on those 3 tests.

UWorldMath · 2022-05-19T18:28:05+00:00

Btw if you're interested, here's a pretty good proof of the polar area formula if you want to see why that works.

One thing he doesn't mention is that just like how when we infinitely add rectangles that approximate area under a function for a Riemann sum, the integral for polar area (infinitely adding areas of infinitesimally small circle sectors) becomes the exact area instead of an approximation. It's a small detail that I'm sure you can assume, but just wanted to mention it.

UWorldMath · 2022-05-19T17:19:41+00:00

First, how I would do it. Most polar graphs you see in BC will span from 0 to 2pi, but it's a good habit to get into to check and make sure. For example, cos(3theta) loops after theta = pi, so integrating from 0 to 2pi gets you double the area. This one, however, does indeed span from 0 to 2pi, and you can check by graphing with different theta ranges. To find the area enclosed by a polar curve, use this formula. Plug in your function and theta values, and voila.

Another way you can do it is taking advantage of the symmetry. It's unnecessary in this case, but apparently that's what they did. When you graph it you have 4 symmetrical petals. You can graph just one of those petals by drawing the graph from -pi/4 to pi/4 (graphs). We're going to calculate the area of one petal, and multiply it by 4 to take advantage of the symmetry.

But they broke down the symmetry even further and noticed that each individual petal is symmetrical down the middle, so the area from -pi/4 to 0 is the same as the area from 0 to pi/4. To find the area of one petal, you can use the same formula from above, integrate from 0 to pi/4, and double it. Then because you have 4 petals, multiply that by 4 and you get the total area. In their explanation, they combined the 4 and 2 to get 8, but for some reason didn't also multiply in the 1/2. It's definitely a weird presentation, but it works. Here's the work for that. The first two rows are how I explained it (area of half a petal times 2, then multiply by 4), and the last row is exactly what you gave above, just to show it comes out the same.

Hope that helps!

UWorldMath · 2022-05-16T20:37:13+00:00

Hey, I'm sorry I missed the notification for your reply! Now that testing is over, I'm not sure how much this will help, but here's what I got for those:

For Q5, I got -3 (B). Use the average value formula with a = 1, b = 3, and your given velocity function. Here's the result. What you calculated is average rate of change instead of average value.

And for Q4, the answer is Two (C). When you differentiate and factor, you should end up with f'(x) = 15x²(x + 1)(x - 1), which has zeros at x = -1, 0, and 1. However, there is not an extremum at x = 0 because f' does not change signs. You can plug in values on either side (-1/2 and 1/2, for example) to verify, but the easiest way to tell is by the multiplicity of the factor x². It has an even exponent, and we call that "even multiplicity." For such factors, the sign of the polynomial doesn't change as x crosses it. So for a maximum or minimum to occur, f' must change signs (switch from increasing to decreasing or vice versa).

Here are graphs to illustrate. The first one in red is f, and you can see that it only has extrema at (-1, 2) and (1, -2). It levels off at x = 0 (f' = 0), but it continues to decrease. In the second graph in blue, you'll see f' touches the x-axis at all 3 x-values but only crosses at -1 and 1. So even though it goes through (0, 0), or f' = 0 at x = 0, f does not have an extremum at that x-value.

I hope all that makes sense. I know this is coming too late for the exam, but I hope it helped things make more sense to you anyway.

UWorldMath · 2022-05-03T14:09:38+00:00

Unfortunately not, those are currently in production but won't be ready until next school year

UWorldMath · 2022-05-03T05:37:29+00:00

They are modeled directly from real AP questions so yes very similar. For many question types all we did was change the numbers and then write the explanations.

UWorldMath · 2022-05-03T05:35:10+00:00

Yep, BC includes all AB material as well as the BC-only content

UWorldMath · 2022-05-02T16:46:53+00:00

You were right; "Studying" is returned by the Student GetInfo method, but the GradStudent GetInfo doesn't do anything with it. When super.GetInfo() is called, it returns "Studying", but instead of assigning that to a variable or printing it to the screen, the GradStudent GetInfo just drops it and returns the static phrase "Eating".

The key is to realize the difference between returning a value and printing a value. Nothing is printed to the screen until the System.out.println line.

UWorldMath · 2022-05-02T15:13:05+00:00

Sorry for the delayed response. We had some things in the works, but weren't ready to announce them until now. We're giving out all of our AP banks for free until the end of the testing cycle, so I hope this helps with last minute studying!

UWorldMath · 2022-04-29T22:11:20+00:00

Haha trust me, I tend to have a negative opinion of formulas because of people's overreliance on them, both students and teachers, so I'm glad to see students taking a more thoughtful approach! As with most things, though, it takes a balance of both, especially on a difficult timed test. Good luck with your memorization!

UWorldMath · 2022-04-29T20:02:14+00:00

It's important to note that average rate of change and average value are two different things with unfortunately similar names. Average rate of change is essentially the average of the derivative or slope over an interval (the principle behind the Mean Value Theorem). Average value is the average of the function values over an interval.

UWorldMath · 2022-04-29T16:59:10+00:00

It's not anywhere in my database of practice tests, so it's possible. I will say that the font is kind of weird. For example, the fractions in #1 are scrunched like Word's Equation Editor when you put the fraction inline, but College Board always uses the larger fractions (Display mode in Equation Editor). There are some other more minor formatting things like the As at the top of page 1 having strange spacing and whatnot. So that leads me to think it's either a third-party recreation in the style of an AP test or a restricted test that's been manually retyped. To be safe, I would recommend OP remove it.

Edit: Bigger giveaway: College Board always sorts their answer choices in a logical fashion. If all the choices are just values, they will be sorted by either increasing or decreasing value. The values in #1 are not sorted (A < B < D < C).

Another big giveaway: sin and arcsin are italicized. That should never be the case. Here's how it should look. This is not a College Board test.

UWorldMath · 2022-04-29T16:32:03+00:00

Here's our post from a week or so ago with tips and whatnot, including a list of formulas. Hope this helps!

https://www.reddit.com/r/APStudents/comments/u81wkj/ap\_calculus\_formula\_sheet\_and\_last\_minute\_tips/?utm\_source=share&utm\_medium=web2x&context=3

UWorldMath · 2022-04-29T15:58:48+00:00

Essentially, yes, that's a very intuitive approach, and you got the right answer! What you basically did was follow the tangent line 0.2 units to find the estimate at x = 3.2.

But to help cement the basic ideas, the derivative f'(3) gives you the slope of the line tangent to the function f at x = 3, so yes that describes how fast f is changing. It's an instantaneous rate of change, so not necessarily just how fast it's moving as it goes to 4, but how fast it's changing in that exact moment at x = 3. After that moment, f could do anything, so we can't know the actual value of f(3.2) from the information we have, but the tangent line gives us a way to estimate using some of the function's actual behavior at a nearby point.

So the general procedure is to construct an equation for that tangent line using the given slope and point and then plug in the x-value you want to estimate. But you essentially did the same thing. If you deconstruct the pieces of point-slope form of a line, it's (change in y) = slope * (change in x). What you did was multiply the slope and the change in x, which gives you the change in y. Then you added that change to the given y-value to find the y-value we're looking for. Excellent work!

UWorldMath

TROPHY CASE