AP Calculus AB Review Sheet PDF | Complete Study Guide

There is a lot of material covered in the AP calculus AB Review Sheet, but studying is made easier with a clear and concise review sheet. The most crucial formulas, ideas, and shortcuts that students need to increase their confidence and score higher on test day are highlighted in this guide.

How do I get the free AP Calculus AB Review Sheet?

Good news – we’ve got everything organized for you, and it’s all free:

What topics will I actually learn in AP Calculus AB?

Okay, let’s talk about what you’re getting into. AP Calculus AB has 8 units, and honestly, some matter way more than others for the exam:

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Pro tip: Notice how Units 5, 6, and 8 add up to about half your exam score? Yeah, spend extra time there.

My advice: Print the big review sheet and keep it on your desk. Use the cheat sheet the week before the exam when you’re freaking out. And actually DO the workbook problems – reading doesn’t teach calculus, doing does.

What formulas do I absolutely need to memorize?

Let me be real with you – there are A LOT of formulas. But some are way more important than others. Here are the ones that’ll save your life on exam day:

The Derivative Rules Everyone Uses

The Big Four:

Power Rule: d/dx[x^n] = nx^(n-1)

Product Rule: d/dx[f·g] = f’·g + f·g’

Quotient Rule: d/dx[f/g] = (f’g – fg’)/g²

Chain Rule: d/dx[f(g(x))] = f'(g(x))·g'(x)

Trig Derivatives (yes, you need all six):

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Other Important Ones:

d/dx[e^x] = e^x (it’s its own derivative – cool, right?)

d/dx[ln(x)] = 1/x

d/dx[arcsin(x)] = 1/√(1-x²)

d/dx[arctan(x)] = 1/(1+x²)

Integration Formulas (The Reverse)

∫x^n dx = x^(n+1)/(n+1) + C (as long as n ≠ -1)

∫1/x dx = ln|x| + C (those absolute value bars matter!)

∫e^x dx = e^x + C

∫sin(x) dx = -cos(x) + C (negative again!)

∫cos(x) dx = sin(x) + C

∫sec²(x) dx = tan(x) + C

The Two Theorems You Can’t Escape

Fundamental Theorem of Calculus: This is THE big deal in calculus. It connects derivatives and integrals:

• Part 1: If F(x) = ∫[a to x] f(t)dt, then F'(x) = f(x)
• Part 2: ∫[a to b] f(x)dx = F(b) – F(a)

Mean Value Theorem: Basically says: at some point, your instantaneous speed equals your average speed.

f'(c) = [f(b) – f(a)]/(b – a)

What does the actual exam look like?

Alright, here’s what you’re walking into on exam day:

What scores actually mean:

Real talk: About 60% of students score 3 or higher. And here’s a secret – you only need to get about 60-70% of the questions right to score a 5. The curve is your friend!

How should I actually study for this?

Three Months Out

• Go through one unit each week
• Do 5-10 practice problems every day
• Make your own formula sheet (writing helps you remember)
• Watch YouTube videos when you’re confused

One Month Out

• Take a full practice test every week
• Look at this review sheet for 15 minutes every day
• Focus extra time on Units 5, 6, and 8 (they’re worth the most)
• Practice ALL your calculator functions

One Week Out

• Light review only – don’t burn yourself out
• Practice calculator stuff for 10 minutes daily
• Look over common mistakes (I’ve got a list below)
• Sleep 8 hours every night – seriously, it matters

What mistakes should I avoid?

Let me save you some pain. Here are the mistakes I see students make over and over:

On Multiple Choice

• Rushing through easy ones – Slow down on the “gimmes”
• Spending forever on hard ones – Skip it, come back later
• Calculator is in degrees instead of radians – Check this!
• Not eliminating obviously wrong answers – Use process of elimination
• Basic math errors – The pressure makes you mess up simple stuff

On Free Response

• Not showing your work – Even if your answer is right, no work = fewer points
• Forgetting units – “The velocity is 5” ≠ “The velocity is 5 m/s”
• Sloppy notation – Write clearly, even when stressed
• Giving up on part (a) – Later parts often don’t need (a) to be right
• Rounding too early – Keep those decimals until the end

Bottom line: Show your work, use proper notation, include units, and double-check your calculator mode!

What calculator should I use and how?

Most students use the TI-84 Plus. It’s reliable, your teacher probably uses it, and you can find help videos everywhere.

Other good options:

• TI-83 or TI-83 Plus
• TI-Nspire (but NOT the CAS version – that’s banned)
• Casio fx-9750GII

Calculator Functions You MUST Know

Exam day checklist: ✓ Brand new batteries in your calculator ✓ Memory cleared (they might check) ✓ You’ve practiced these functions until they’re automatic ✓ Backup batteries in your bag

What concepts show up the most?

Not all topics are created equal. Focus your energy here:

1. Chain Rule (it’s EVERYWHERE) Seriously, this shows up in like 40% of problems. Any time you have a function inside another function, you need it.

Example: Taking the derivative of (3x² + 5)⁷? Chain Rule time.

2. Fundamental Theorem of Calculus This connects derivatives and integrals. It’s on every single exam.

3. Related Rates Those word problems about ladders sliding down walls? Yeah, those are related rates.

4. Optimization Finding maximum or minimum values in real situations.

5. U-Substitution It’s the reverse Chain Rule for integration. Master it.

Strategy: If you only have time to master 5 things, make it 5

Why should I choose TestprepKart?

Look, I know you’ve got options for test prep. Here’s why students pick us:

Our Results:

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Free AP Calculus AB Exam Study Guide

AP Calculus AB is easier to learn when you have the correct Study Resources. To help students improve their comprehension and test performance, TestprepKart provides a number of free downloadable e-books that cover every essential idea and formula required to succeed in AP AP Calculus AB and other AP science courses.

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Frequently Asked Questions (FAQs) –AP Calculus AB Review Sheet PDF

1.What should be on a review sheet for AP Calculus AB?

Limit rules, derivative formulas, integration shortcuts, theorems (MVT, IVT, and FTC), graph behavior, and applications like optimization and related rates are all essential components of a quality review sheet. Students in the United States favor one-page summaries that only cover topics covered in exams.

2. Is a review sheet sufficient for an AP Calculus AB score of five?

A review sheet aids in memory and rapid review, but it needs to be used in conjunction with FRQ drills and practice problems. Particularly in Units 3–6, students who combine a review sheet with daily practice see the largest improvement in their scores.

3. How should AP Calculus AB be studied the week before the test?

Pay attention to calculator shortcuts, derivative rules, integrals, FRQ strategies, and typical errors. To strengthen weak areas, use your review sheet every day, take at least one timed mock exam, and go over all of the wrong questions.

4. Does the AP Calculus AB exam come with a formula sheet?

No, a formula sheet is not provided by the College Board. Every derivative, integral, and theorem must be committed to memory by the students. For this reason, during exam season in the United States, a lot of people look for review and cheat sheets.