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The AP Calculus AB Unit 2 Progress Check FRQ Part A is an important test in AP Classroom that is set up and graded like the real AP exam. It tests basic ideas about differentiation and how ready you are for more advanced units.
This guide has FRQ-style practice questions, full answers, scoring rubrics, calculator rules, and common mistakes, all of which are based on the College Board CED. It will help you get ready for the AP exam and do well on Unit 2
| AP Calculus AB Unit 2 Resource | What’s Included | Practice |
| Unit 2 Progress Check FRQ Part A — AP Calculus AB | Official-style Progress Check FRQ Part A with scoring guidelines, calculator-based questions, and step-by-step solutions | Practice |
| Unit 2 FRQ Part A Practice Questions | Full AP-style FRQs with answers and explanations for how to score them | Practice |
| Derivative Definition Questions | Limit-based derivative problems with full explanations | Practice |
| Average & Instantaneous Rate of Change | Conceptual problems with questions that are like those on the real test | Practice |
| Tangent Line & Differentiability Problems | Finding the slope, the equations for the tangent, and the checks for differentiability | Practice |
| Product & Quotient Rule Practice | Using important rules to solve multi-step derivative problems | Practice |
| Exponential & Trigonometric Derivatives | Questions and answers about e^x and derivatives based on trig functions | Practice |
| Graph-Based Derivative Questions | Understanding graphs, slopes, and rates of change | Practice |
| Common Mistakes Practice Set | The most common FRQ mistakes with explanations and fixes | Practice |
| Full Unit 2 FRQ Mock Test | Full FRQ practice at the exam level (with a calculator) | Practice |
A calculator-based free-response section, the AP Calculus AB Unit 2 Progress Check FRQ Part A assesses fundamental differentiation concepts such as derivative definitions, rates of change, tangent lines, and fundamental rules. Pupils are required to present all of their work, round their answers to three decimal places, and use appropriate notation.
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| AP Calculus AB Unit 2 progress check FRQ answers | AP Calc AB Unit 2 FRQ Part A solutions |
| AP Calculus AB Unit 2 FRQ scoring guide | AP Calc AB differentiation FRQ practice |
| Aspect | Description |
| Overview | The AP Calculus AB Unit 2 Progress Check FRQ Part A checks your understanding of Differentiation: Definition and Fundamental Properties (sub-topics 2.1–2.10). |
| Format | Has one free-response question with more than one part. You need a graphing calculator. You can’t use calculator syntax; all of your work must be shown in standard math notation. |
| Key Rule | Unless otherwise stated, answers must be rounded to three decimal places. Don’t round off the steps in between. |
| Scoring | Answers that don’t have supporting work don’t get any credit. Justifications must include correct math reasoning and check the conditions for definitions or theorems. |
| Part A vs Part B | Part A lets you use a graphing calculator and is mostly about finding derivatives and solving equations. Part B doesn’t let you use a calculator and makes you do algebra by hand. |
The College Board AP Calculus AB CED breaks Unit 2 down into ten smaller topics, from 2.1 to 2.10. Every FRQ Part A question is related to one or more of these sub-topics. You can use this table to find out which skills are being tested on each part of the progress check.
| Sub-Topic | Title |
| 2.1 | Establishing Average and Instantaneous Rates of Change at a Point |
| 2.2 | What the Derivative of a Function Is and How to Use Derivative Notation |
| 2.3 | Finding the Derivatives of a Function at a Point |
| 2.4 | Linking Differentiability and Continuity: Figuring out when derivatives exist and when they don’t |
| 2.5 | Using the Power Rule |
| 2.6 | Rules for derivatives: constant, sum, difference, and constant multiple |
| 2.7 | The derivatives of cos x, sin x, e^x, and ln x |
| 2.8 | The Rule of Products |
| 2.9 | The Rule of Quotients |
| 2.1 | How to Find the Derivatives of the Tangent, Cotangent, Secant, and Cosecant Functions |
There is no formula sheet for the AP Calculus AB exam. You must memorize and use all of the derivative rules below correctly on the Unit 2 Progress Check FRQ Part A. These are the exact formulas that were used to test all of the FRQ Part A questions.
| Rule / Concept | Formula | CED Sub-Topic |
| Average Rate of Change | [f(b) – f(a)] / (b – a) | 2.1 |
| Instantaneous Rate of Change | f'(a) = lim(h→0) [f(a+h) – f(a)] / h | 2.1, 2.2 |
| Limit Definition of Derivative | f'(x) = lim(h→0) [f(x+h) – f(x)] / h | 2.2 |
| Alternate Limit Definition | f'(a) = lim(x→a) [f(x) – f(a)] / (x – a) | 2.2 |
| Power Rule | d/dx [x^n] = nx^(n-1) | 2.5 |
| Constant Rule | d/dx [c] = 0 | 2.6 |
| Constant Multiple Rule | d/dx [c*f(x)] = c*f'(x) | 2.6 |
| Sum and Difference Rule | d/dx [f(x) ± g(x)] = f'(x) ± g'(x) | 2.6 |
| Derivative of sin x | d/dx [sin x] = cos x | 2.7 |
| Derivative of cos x | d/dx [cos x] = -sin x | 2.7 |
| Derivative of e^x | d/dx [e^x] = e^x | 2.7 |
| Derivative of ln x | d/dx [ln x] = 1/x | 2.7 |
| Product Rule | d/dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x) | 2.8 |
| Quotient Rule | d/dx [f(x)/g(x)] = [f'(x)g(x) – f(x)g'(x)] / [g(x)]^2 | 2.9 |
| Derivative of tan x | d/dx [tan x] = sec^2 x | 2.1 |
| Derivative of sec x | d/dx [sec x] = sec x tan x | 2.1 |
| Differentiability implies Continuity | If f is differentiable at x=a, then f is continuous at x=a | 2.4 |
| Category | Details |
| AP Exam Weight (AB) | 10 to 12 percent of the total AP Calculus AB exam score |
| Estimated AP Exam MCQ Questions | Unit 2 has about 5–6 multiple-choice questions and 1 multi-part FRQ. You will need a graphing calculator and have about 15–20 minutes to answer them. |
| FRQ Part A Format | 1–2 multi-part FRQs; no calculator; about 20–25 minutes |
| FRQ Part B Format | Allowed to solve equations, find derivatives at a point, and evaluate definite integrals |
| Calculator Permission (Part A) | You must show how you set up the math; calculator syntax is not acceptable in written work. |
| Calculator Restriction (Part A) | Unless otherwise stated, round final decimal answers to three decimal places. |
| Decimal Rounding Rule | Unless otherwise stated, round final decimal answers to three decimal places. |
| Notation Requirement | Use standard math symbols like dy/dx, f'(x), and d/dx instead of commands for your calculator. |
| Hardest Sub-Topics in FRQ Part A | 2.4 (Differentiability vs. Continuity), 2.8 (Product Rule), 2.9 (Quotient Rule), 2.1 (Average vs. Instantaneous), 2.2 (Limit Definition), 2.5 (Power Rule) |
| Most Frequently Tested Sub-Topics | 2.1 (Average vs Instantaneous), 2.2 (Limit Definition), 2.5 (Power Rule) |
Instructions: A graphing calculator IS required for Part A questions. Show all mathematical setup clearly. Express all work in standard mathematical notation, not calculator syntax. Round decimal answers to 3 decimal places unless otherwise specified.
CED: 2.1, 2.2 | Points: 4
Common Mistake: Confusing average rate with derivative
CED: 2.2 | Points: 3
Common Mistake: Incorrect expansion of (x+h)2(x+h)^2(x+h)2
CED: 2.4 | Points: 4
Common Mistake: Assuming continuity means differentiability
CED: 2.8, 2.9 | Points: 5
CED: 2.7, 2.8 | Points: 4
Common Mistake: Using power rule for exe^xex
To get the most points on the Unit 2 Progress Check FRQ Part A, you need to know how College Board AP readers grade it. The following rules come straight from the College Board’s official AP Calculus AB scoring guidelines.
| Scoring Principle | What It Means | How to Apply It |
| Work without an answer gets partial credit. | Even if the final number is wrong, you get points for a correct setup, derivative rule, or limit expression. | Always show the rule first, then the substitute, and finally the evaluation. Don’t jump to the answer. |
| You won’t get any credit for answering without doing the work. | Most parts get a zero if the final answer is right but no work is shown. | Write down every step: say the rule, use it, plug in values, and find the answer. |
| Decimal answers rounded to three places | The final decimal answers must be correct to three places after the decimal point. | Only round the last answer. In the middle steps, keep the exact values (fractions, e^x, etc.). |
| The syntax for calculators is not okay. | If you write “nDeriv” or “fnInt” in your answer, you get zero points, even if the answer is correct. | You should always write d/dx[f(x)]|x=a or f'(a). Use the calculator to find the answer and write it down in standard math. |
| Justification needs a named theorem | Simply saying “the derivative is positive” isn’t enough. You have to say why. | Write: “By the Product Rule…” “Since f is differentiable at x=a…” “By the definition of the derivative…” |
The two most common ways to lose points on Unit 2 FRQ Part A are (1) using calculator syntax in written answers and (2) writing conclusions without giving a math reason for them. Before the day of the test, fix both
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.
College Board AP Calculus AB Chief Reader Reports and AP educator analysis of the most common mistakes students make on Unit 2 FRQ questions show that these are the most common mistakes.
| Mistake | Why It Loses Points | How to Fix It |
| Using Power Rule on e^x | The derivative of e^x with respect to x is xe^(x-1). The Power Rule only works for x^n. | Remember that d/dx[e^x] = e^x. The derivative of e raised to a variable power is e raised to that power. |
| Reversing Product Rule | Instead of f'(x)g(x) + f(x)g'(x), write h'(x) = f'(x)*g'(x). | Before you substitute, write down the Product Rule formula. Say: “d/dx[fg] = f’g + fg’.” |
| Reversing Quotient Rule numerator | Instead of writing f’g – fg’, write fg’ – f’g. | Remember the order: “HI-dLO minus LO-dHI over HI-HI.” Numerator: (top)'(bottom) – (top)(bottom)’. |
| Confusing continuity and differentiability | Differentiable is not the same as continuous. | Continuity is important, but not enough. Always look at one-sided derivatives on their own. |
| No interpretation in context questions | Just writing a number when asked to explain. | Always say what the derivative value means: slope of the tangent line, rate of change, or whether it is going up or down. |
| Not showing limit definition setup | Going straight to the answer from the question about the definition. | For limit definition FRQs, write out the whole expression lim(h→0) [f(x+h)-f(x)]/h before you simplify it. |
This study plan is based on the College Board Chief Reader Report’s suggestions for preparing for Unit 2 FRQ and a four-week study plan
| Timeline | Study Focus |
| Week 1 (3–4 weeks before test) | Look over sub-topics 2.1–2.3: the difference between the average and instantaneous rate of change, the limit definition of the derivative, and how to use graphs and tables to guess derivatives. |
| Week 2 (2–3 weeks before test) | Learn about differentiability vs. continuity, the Power Rule, the Constant/Sum/Difference Rule, and the derivatives of sin x, cos x, e^x, and ln x. |
| Week 3 (1–2 weeks before test) | Pay close attention to sub-topics 2.8–2.10, which cover the Product Rule, the Quotient Rule, and trig derivatives. Do problems that use the product/quotient rule on a table. |
| Final Week | Practice all of FRQ Part A in a timed setting (15–20 minutes). Look over the scoring rubrics. Correct mistakes in calculator notation. |
| Daily Practice (any week) | 15 to 20 Unit 2 derivative problems with full explanations reviewed every day. Repetition of derivative rules over time. |
The best way to get ready for the Unit 2 Progress Check is to do full FRQ Part A practice under timed conditions and score it using official College Board rubrics.
What is the AP Calculus AB Unit 2 Progress Check FRQ Part A?
In AP Classroom, the AP Calculus AB Unit 2 Progress Check FRQ Part A is a free-response test that covers Differentiation: Definition and Fundamental Properties (sub-topics 2.1–2.10). It tests derivative definitions, average and instantaneous rates of change, differentiability, and basic derivative rules like the Product and Quotient Rules. You need a graphing calculator to do it..
Is a calculator allowed on the Unit 2 Progress Check FRQ Part A?
Yes. You need a graphing calculator for FRQ Part A. Students can use it to figure out how to solve equations, find derivatives at a point, and evaluate definite integrals. But all work must be written in standard math notation, not the way a calculator would do it. You don’t get any credit for writing calculator commands like nDeriv in the solution
What derivative rules are tested on Unit 2 FRQ Part A?
The Power Rule (2.5), the Product Rule (2.8), the Quotient Rule (2.9), the derivatives of sin x and cos x (2.7), and the derivative of e^x (2.7) are the most common derivative rules on Unit 2 FRQ Part A. The limit definition of the derivative (2.2) and the conditions for differentiability (2.4) also come up a lot.
How is the Unit 2 Progress Check FRQ Part A scored?
Each part of the FRQ is scored by points (typically 1–2 points per sub-part). Points are awarded for correct derivative rule application, correct substitution, correct final answer, and written justification. Answers without supporting work receive no credit. Decimal answers must be correct to 3 decimal places.
This resource is created for U.S. high school students by AP-certified educators at TestPrepKart. All sub-topic names, exam weights, and CED references are sourced from the official College Board AP Calculus AB Course and Exam Description. Scoring rubric principles are based on official College Board AP Calculus AB scoring guidelines. For the most current exam information, visit apcentral.collegeboard.org. Last Updated: 2026
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