Score Higher on AP Calculus 2024: MCQ Tips from Students

Multiple Choice Questions

This guide organizes advice from past students who got 4s and 5s on their exams. We hope it gives you some new ideas and tools for your study sessions. But remember, everyone's different—what works for one student might not work for you. If you've got a study method that's doing the trick, stick with it. Think of this as extra help, not a must-do overhaul.

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📌 Overview

• Students are asked to answer mathematical and analytical questions using equations, graphs, tables, word problems, and other representations
• 50% of Exam Score:
  • 45 questions
  • 105 min, or a little over 2 minutes per question
  • Part A of this section includes 30 questions and no calculator for 60 minutes
    • 33% of exam score
    • 2 minutes per question
  • Part B of this section includes 15 questions with a calculator for 45 minutes
    • 17% of exam score
    • 3 minutes per question

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💭 General Advice

Tips on mindset, strategy, structure, time management, and any other high level things to know.

• Don’t get bogged down by questions. If you know it, answer it, if you don’t, mark it to come back if you have time. Every question is worth the same amount of points, so answering all of the easier ones is better than spending too much time on hard ones and running out of time, even if you got those hard ones right!
• There’s no guessing penalty, so if near the end of the time you still have empty questions, make sure to fill all of them out. You might be able to get a few lucky points!
• Your subconscious is an incredible thing—let it work out questions for you! If you don’t know where to start on a question, or you can’t figure it out after a minute, just read it, annotate it, move on, and come back to it later. Odds are, your brain can work it out in the background while you do the rest of the test!
• Keep your pencil moving! Sometimes, (especially with integrals) you may start solving a problem using the wrong method, and if the problem looks worse after around a minute you may need to restart with a different method.
• When it comes to questions with multiple terms, utilize your time wisely. For example, if you are asked to find the derivative or integral of a polynomial, only calculate the first term or two and check your result with the answer choices. You may already have a match, which will save you time!
• Make sure you can recognize when to use what type of method to use when you are solving integrals (partial fractions, trig substitution, splitting an integral, long division before integrating, etc.). This comes with lots of practice.
  • For instance, when the denominator can be split into factors, you’ll want to apply partial fractions OR when the greatest power of the numerator is greater than that of the denominator, you’ll want to perform long division before integrating.
• Get familiar with AP-style questions and the language they use! It can be confusing for a first-time test taker because they aren’t always straight forward. For example, “average rate of change” means you take the derivative, but “average value” means you integrate.

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🫧 Before You Bubble

What should a student do in the first few minutes, before they start answering?

• Underline (or note in the margins) any important words/numbers in the question — this way, you won’t forget any important piece of information.
• Look for key phrases that show what the question is about. For example, “total change” implies that you’ll need to integrate.
• If a lot of the answer choices look similar and there is an odd one out, you can often get rid of it because it’s likely not the answer. This is useful if you find yourself needing to guess on a question!
• Write down all the critical formulas that you can remember in under a minute that may not come intuitively while working on the questions. Important ones might be the double/half angle formulas, Pythagorean identities, inverse trig derivatives/integrals, and arc length.

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❓Choosing the Best Answer

• If all else fails, look for the answer that’s most similar to the rest.
  • For example, if only one answer choice is negative, it’s probably incorrect.
• If you really can’t figure out how to integrate an integral, take the derivative of each of the answer choices until your answer matches the question’s function.
  • Keep in mind that this will take more time than finding the integral, so leave this strategy for the end—only if you have enough time.
• If you are completely lost and cannot figure out how to even begin to address a problem, consider using one of the various ways to approximate answers, like Euler’s Method, Taylor Polynomials, or Riemann Sums. While these may not always be work, and cannot be 100% relied on, they often at least give you a push in the right direction.

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🧮 Using Your Graphing Calculator

• Know how to store values (y1).
• Know how to take a derivative (MATH → 8), an integral (MATH → 9), and do summation (MATH → 0).
• Know how to find intersections (2nd → TRACE → 5) and minimums/maximums (2nd → TRACE → 3 or 4).
• Know how to change window size (window).
• Know how to make your answer a fraction (MATH → 1), insert numbers (2nd → DEL), and type absolute value (MATH → NUM → 1)
• Know how to change your calculator from function mode to parametric or polar mode (MODE).
• Know how to change your calculator from/to decimal mode (Home → Settings → Document Settings → Calculation Mode → Approximate)

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ƒ Formulas to Memorize

Both Calc AB and BC

• Power rule
  • $\frac{\text{d}}{\text{d}x}\ x^n=nx^{n-1}$
• All trig derivatives $\frac{}{}$
• Product rule
  • $\frac{\text{d}}{\text{d}x}(f(x) \cdot g(x))= f'(x)g(x) + f(x)g'(x)$
• Quotient rule
  • $\frac{\text{d}}{\text{d}x}\ \frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}$
• Chain rule
  • $\frac{\text{d}}{\text{d}x}\ f(g(x))=f'(g(x))\cdot g'(x)$
• Volume of rotated solid
  • Washer/Disc Method formulas
• Constant multiple rule
  • $\frac{\text{d}}{\text{d}x}\ c\cdot f(x)=c\cdot \frac{\text{d}}{\text{d}x}\ f(x)$
  • $\int c\cdot f(x)\ dx=c\cdot \int f(x)$

Only Calc BC

• Arc length
  • $2\pi r\left( \frac{\theta}{360\degree}\right)$ (for degrees)
  • $r\theta$ (for radians)
• Taylor polynomial f(n)(a)n!(x-a)n
  • $\sum \frac{f^n(a)}{n!}(x-a)^n$
• Integration by parts
  • $\int u\ \text{d}v=uv-\int v\ \text{d}u$
  • You can remember this formula by thinking of it as “of voodoo”
• Maclaurin Series for $e^x$, $\text{sin}(x)$, $\text{cos}(x)$, $\text{tan}^{-1}(x)$, $\text{ln}(1+x)$, and $\text{ln}(1-x)$.
• Ratio test
  • If $\sum a_n$ is a positive series and $L=\lim_{n\to \infty}\frac{a_{n+1}}{a_n}$, the series is convergent if $L<1$ and divergent if $L>1$. If $L=1$, then the test is inconclusive.
• Integral test
  • If for a series $\sum a_n$ a formula exists such that $a_n=f(x)$, then if $\int f(x) \ dx$ is convergent, the series converges and if $\int f(x)\ dx$ is divergent, the series diverges.
• LaGrange Error Bound
  • This formula tells us how good or bad our Taylor series approximations are.
  • $R_n=\frac{f^{n+1}(z)}{(n+1)!} (x-c)^{n+1}$
• Power reduction formulas
  • $\text{sin}^2(u)=\frac{1-\text{cos}(2u)}{2}$
  • $\text{cos}^2(u)=\frac{1+\text{cos}(2u)}{2}$
  • $\text{tan}^2(u)=\frac{1-\text{cos}(2u)}{1+\text{cos}(2u)}$