How to Succeed in AP Calculus AB

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Last Updated: March 8, 2026 References

AP Calculus AB is one of the math courses offered by the Advanced Placement program. AP Calculus AB and AP Calculus BC are calculus courses you usually take one after the other. If you are signed up to take the first one out of the two courses, here's what you should do to succeed!

Part 1

Part 1 of 3:

Getting the Materials

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Consider buying an AP Calculus textbook. If your school has a designated AP Calculus textbook, use that one. Purchasing an AP Calculus textbook will make studying more organized since each unit has one topic you can focus on. You can also search up PDFs of other AP Calculus textbooks if you want additional practice.
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Get an AP Calculus workbook. Workbooks have dozens of practice problems that are helpful when you are studying for an exam. If you just want to practice your problem-solving skills, buying a workbook is also beneficial. Popular workbooks for this course include The Princeton Review's AP Calculus AB Premium Prep and Barron's AP Calculus.

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Use a designated math notebook for your notes. Just like in previous math classes like algebra and geometry, it is best to take notes. Using a half-lined, half-graph notebook will make it easier for you to switch between drawing graphs and taking regular notes for this class. Unlike algebra class, AP Calculus AB does not focus on drawing detailed graphs. You just need to master sketching approximate graphs. For most of the other content (like solving derivatives, optimization/related rates, implicit differentiation, integrals), you can get away with using lined paper. ^{[1]
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Research source} If you can't purchase this kind of notebook, you can attach graph paper to a lined notebook when it's time to graph. You could also store graph paper in a folder and take notes separately.
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Use online resources to deepen your knowledge. If regular textbooks aren't enough or if you're struggling a bit, searching the web for AP Calc videos can help you! There are several YouTube channels and online courses that can teach you calculus, and they may explain some topics better.
- Khan Academy has a whole course on college calculus I or AP Calculus AB!
- YouTube channels like The Organic Chemistry Tutor, Professor Dave Explains, Khan Academy, and Flipped Math can also help you understand calculus!
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Use flashcards to study vocabulary. There will be some vocabulary terms in this course you'll need to know, like "discontinuity", "L'Hopital's Rule", "derivative", or "integral".^{[2]
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Research source} Some words come with word definitions as well as formulas. Write the word on one side of the card and its definition or a formula on the other side. When you study these terms, quiz yourself on writing its definition with your own words and its formula.
- Using an online flashcard tool like Quizlet is also helpful!
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Get a graphing calculator. It's likely that you'll use a handheld graphing calculator many times in this course, as well as for future calculus courses you may take. Investing in one will make your math journey easier. The TI-84 Plus CE calculator is a popular graphing calculator used by many higher-level math students. Additionally, CollegeBoard allows this calculator during the AP exam. ^{[3]
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Research source}The TI-Nspire CX is another popular choice.

Part 2

Part 2 of 3:

Understanding Calculus

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Understand each unit. There are 8 units in the AP Calculus AB course that build off of each other. The first few units focus on derivatives and the last few focus on integrals. However, you will need to master derivatives to understand integrals. These 8 units include: ^{[4]
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- Unit 1: Limits and Continuity
- Unit 2: Differentiation: Definition and Fundamental Properties
- Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
- Unit 4: Contextual Applications of Differentiation
- Unit 5: Analytical Applications of Differentiation
- Unit 6: Integration and Accumulation of Change
- Unit 7: Differential Equations
- Unit 8: Applications of Integration
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Review your old math skills. You will need a strong foundation in algebra I and algebra II to succeed in AP Calculus AB. There will be trigonometry needed for derivatives and integrals, so you should brush up on this as well. If you can, review these concepts over the summer to see if you still understand them.
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Understand limits. A limit is what a function does as it approaches a value. You read a limit expression as "The limit of f(x) approaches as x approaches (value)". You can find limits by looking at a graph and seeing the value that y approaches as x gets closer to some number, like 0 or infinity. ^{[5]
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Research source} A right-hand limit shows you what value y gets close to as x approaches a number from the positive side, and the left-hand limit shows you what value y approaches as x approaches a number from the negative side. The direction of a limit is indicated with a positive sign (for right) and negative sign (for left). ^{[6]
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- If the two limits are equal, meaning the y-value for both approaches the same number, the limit exists for the function.
- If the two limits are unequal, meaning the y-value for each is different, the limit does not exist. This also means the function is not differentiable at that point, meaning you cannot find its derivative at that x-value.
- A noticeable "break" or "jump" in the graph means there is a jump discontinuity there. An open circle on a function is called a removable discontinuity. Even though there is a gap in the graph, the limit for it still exists because the graph from the left side and from the right side approach the same point.
- An infinite discontinuity occurs when the function has an asymptote. This is when the function extends on forever to positive infinity or negative infinity. ^{[7]
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- When there is any type of discontinuity, it means the function is not differentiable at that x-value.
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Understand derivatives. Remember that the slope of a line is rise over run, or change in y over change in x. This is also called rate of change. If you make the x-values of the 2 points closer to each other, you are closer to finding the instantaneous rate of change of a function. This means finding the slope of a function at one point. To derive means to find the instantaneous rate of change of a graph at one x-value. When you see the apostrophe symbol $(')$ $(')$ , it indicates a derivative, and it is pronounced "prime". $\frac{d}{dx}$ $\frac{d}{dx}$ means the derivative with respect to the variable x. There are a few easy rules to know when finding derivatives of a function:
- The Power Rule: Multiply the exponent and coefficient together, then subtract the original exponent by one. For example, $4x^{3}$ becomes $12x^2$ after it is derived.
- The Product Rule: $f(x)'g(x) + f(x)g(x)'$ . This looks confusing, but with practice, you'll get the hang of it! This is used when 2 functions are multiplied together. Take the 1st function's derivative and multiply it with the 2nd function (not derived yet!). Then you do the same thing but with the 2nd function. Add the two up to get your final derivative! It may be easier to memorize if you switch the order of the addends to match the quotient rule's numerator. ^{[8]
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- The Quotient Rule: $\frac{((f(x)g(x)') - (f(x)'g(x)))}{(g(x)^2)}$ . This is used when 2 functions are divided. You multiply the 1st function by the 2nd function's derivative and repeat this step for the 2nd function. You add the two expressions up. Lastly, you divide the numerator expression with the 2nd function's square.
- The derivative of a linear function (like $y = 3x$ ) is its coefficient. This is because the slope is constant throughout the graph; there is no change in slope at any point. Likewise, the derivative of a horizontal line (e.g. $y = 1$ ) is 0 because horizontal lines have no slope.
- If you have a fraction that evaluates to an indeterminate form (e.g. infinity over infinity) when you try to find its limit, use L'Hopital's rule to derive it. ^{[9]
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  Research source} You derive the numerator and denominator separately until the limit equals a certain value.
- Memorizing common exponential and logarithmic derivatives will also benefit you. ^{[10]
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Remember other derivative rules. After learning all the basic derivative rules, you will need to memorize the ones for trigonometric functions and the inverse function rule. You will also learn something called implicit differentiation. This is used when you can't solve for y in terms of x. Typically with equations like $x^2 + y^2 = 1$ $x^2 + y^2 = 1$ , we treat y as a function of x. You derive every variable normally, but for every derivative with the variable y, you multiply ${\frac {dy}{dx}}$ ${\frac {dy}{dx}}$ with it. Then, you would factor out every derivative containing ${\frac {dy}{dx}}$ ${\frac {dy}{dx}}$ . Lastly, you would move the variables so ${\frac {dy}{dx}}$ ${\frac {dy}{dx}}$ is remaining on one side. Here are some helpful rules to memorize for more complex derivatives:
- The chain rule. This is used when several expressions are "inside" each other, like $(2x + 5)^4$ . The rule is $f'(g(x)) * g'(x)$ . Basically, you separate the expression into several functions and derive each, multiplying everything together at the end. ^{[11]
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  Research source} The 2x + 5 is inside of the power of 4 function. You would derive the outside function first using the power rule, so the expression becomes $4(2x + 5)^3$ . Then, you would multiply it by the inside function's derivative. The derivative of a line (2x + 5) is 2. So, the final derivative of this expression is $2 * 4(2x + 5)^3$ or $8(2x + 5)^3$ . ^{[12]
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- The inverse function rule. To derive a function's inverse, you use the formula $\frac{1}{(f'(f^{-1}(x)))}$ . ^{[13]
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- The trigonometric derivatives. The derivative of $sin(x)$ is $cos(x)$ . The derivative of $cos(x)$ is $-sin(x)$ . Then, the derivative of tan(x) is secant squared $(sec(x))^2$ . There are also a set of derivatives for cotangent, secant, and cosecant you should memorize. ^{[14]
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Understand how to apply differentiation. You can use derivatives to describe a function's behavior. What are the relative maximums and minimums of it? Where are its critical points? At which point does the graph switch from concave up to concave down? There are a few theorems for this topic you should know about. These are called the Mean Value Theorem and the Extreme Value Theorem.
- Mean Value Theorem (MVT): Over a continuous interval [a,b], there will be at least one point c for which $f'(c) = \frac{f(b)-f(a)}{b-a}$ . ^{[15]
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  Research source} In simple terms, this means over a continuous interval, there will be at least one point in which its instantaneous rate of change is equal to the whole interval's slope. A line that intersects a curve at one point is called a tangent line, so you could say that there is at minimum 1 point where the tangent line's slope equals the secant line's slope.
- Extreme Value Theorem (EVT): Over a continuous interval [a,b], a function must obtain a maximum and a minimum value. ^{[16]
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- Extrema: The highest and lowest points of a function. "Relative" extrema are the highest and lowest points of an interval, whereas "absolute" extrema are the highest and lowest points for the entire function. The highest point is a maximum and the lowest point is a minimum.
- Critical point: A point for which $f'(c) = 0$ or $f'(c)$ is undefined. ^{[17]
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- Concavity: The upward bend (like a "U" shape) or the downward bend (like a lowercase "n" shape) of a graph.
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Learn how to interpret the graph of a function and its derivative. Sometimes you will have to sketch the graph of a function's derivative. Other times you'll need to describe the derivative's graph by finding its critical points and determining its extrema (maximums and minimums). You find a function's critical points by finding its derivative ( $f'(x)$ $f'(x)$ ) when it equals 0. There are a few derivative tests you can perform on a graph to determine the function's properties:
- First derivative test: If $f'(x)$ switches from positive (+) to negative (-) over the interval, the point is a relative minimum. Similarly, if $f'(x)$ switches from negative (-) to positive (+) over the interval, the point is a relative maximum. ^{[18]
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- Second derivative test: Substitute your critical points into $f''(x)$ (the function derived twice). If $f''(x)$ is a positive number, the graph is concave up. If $f''(x)$ is a negative number, the graph is concave down. The graph has a maximum when the graph switches from concave down to concave up. The graph has a minimum when the graph switches from concave up to concave down. If the function's concavity changes at a critical point, that point is called an inflection point. ^{[19]
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- You can use either the first or the second derivative test, but choose wisely based on the scenario you are given. There is one case where the 2nd derivative test is inconclusive; this is when $f''(x) = 0$ after substituting the critical point. ^{[20]
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Solve optimization and related rates problems. Optimization is the process of finding a maximum or minimum value of a function with some constraints. For example, a problem may tell you to find the maximum dimensions of a box that can be constructed with a set volume. ^{[21]
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Research source} Related rates questions tell you to solve for the rate of change between 2 variables using the rates of change from other variables. You will need to know your derivative rules as well as implicit differentiation well to ace these problems. ^{[22]
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Learn how to solve integrals. Integrals are a way to find the area under a curve or a function. Integrals and derivatives are inverse operations, meaning they undo each other. In AP Calculus AB, you will learn how to find definite integrals of functions. There are also some rules you should remember for finding integrals of certain functions, especially the trigonometric ones. ^{[23]
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Research source} You write an integral like this: $\int_{a}^{b} f(x) \, dx$ $\int_{a}^{b} f(x) \, dx$ . "a" stands for the lower end of the interval and "b" stands for the higher end of the interval. Basically, you are finding the area of f(x) between x = a and x = b.
- First, you'll be introduced to the concept by estimating the areas with Riemann Sums. You draw rectangles of the same width under a curve to estimate its area. The more rectangles you draw under the curve, the closer your estimate is to the true area.
- Then, you will learn various integral formulas. When functions get complicated, you can use u-substitution to figure out their integrals.
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Understand differential equations. Differential equations explain the relationship between an unknown function and its derivative (e.g. $\frac{dy}{dx} = 4x^2$ ). A slope field visually represents a differential equation. The slope field is a graph with small tick marks each representing the slope of the function at one point. ^{[24]
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Research source} In AP Calculus AB, the problems will tell you to draw a slope field or find the points at which the slope is undefined for the function.
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Use integrals to find volumes of 3D objects. The integral is the area between a function's line and the x-axis. When you revolve this 2D shape around an axis (either the x/y axis or another straight line), you get a 3D solid. In AP Calculus AB, you'll learn how to find the volumes of 3D solids using the disc method and the washer method. ^{[25]
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- Disk/disc method: Imagine a 2D shape revolving around an axis; you'll get a 3D solid. The solid is composed of infinitely many flat "discs" of the same shape. The formula to find this solid's volume is $\int_{a}^{b} π[R(x)]^2 \, dx$ .
- Washer method. Imagine a 2D shape revolving around an axis. There is a gap between the axis and the shape, creating a hole after the revolution, similar to a donut hole or the hole in a washer. The formula for this solid's volume is $π \int_{a}^{b} [R(x)]^2 - [r(x)]^2 \, dx$ . R(x) represents the outer radius and r(x) represents the inner radius. ^{[26]
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Part 3

Part 3 of 3:

Acing the AP Test

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Start studying for the AP exam a few months prior to it. The annual AP Calculus AB exam is administered on the second Monday in May. ^{[27]
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Research source} This means you should start reviewing for the cumulative AP exam in April. Brush up on topics you forgot previously and practice the MCQs and the FRQs.
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Skim through your notes. This helps you look at what important concepts you learned in each unit. Look over the practice examples and graphs you drew to get an idea of what topics you should know for every unit.
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Quiz yourself on important vocabulary words. This is very important because you won't be provided a formula sheet on the AP exam; you need to know these formulas very well. Review the whole set of cards by unit at first. Try to name the word's definition and its formula if it has one. Then, quiz yourself on the key terms you forgot or struggled on every day. This will help you memorize them!
- If you have friends in the same class, you can quiz each other on the words!
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Do a lot of practice problems. Do a set of multiple choice questions and a few free response questions every day. You can search the web for free practice questions for AP Calculus AB. Additionally, even though CollegeBoard has removed past FRQs (actual exam FRQs from 3 or more years ago) from their website ^{[28]
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Research source}, you can still find them by typing "(year) AP Calculus AB FRQ" into a search engine.
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Use Bluebook. Bluebook is CollegeBoard's testing software. Bluebook has many resources for you to practice the AP testing format. It also offers practice tests structured exactly how the actual AP test is (except with fewer questions since it is just a demo). You can install Bluebook through the CollegeBoard website. Try doing some of the questions on Bluebook to get a feel of the software.
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Perform practice AP exam sessions. This will help you get used to the actual testing environment. To simulate the actual AP test exam environment, clear your room of all distractions. Don't access other electronics other than your computer. Grab a pencil or two and an eraser, as well as your graphing calculator. Use a clock or watch to time yourself. Then, find a full set of practice MCQs from one of your study sources to complete in 45 minutes (the allotted time for Parts A and B of the MCQ) ^{[29]
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- Take a quick 10-minute break to get water, have a snack, or chill. There will be an actual break like this on testing day.
- Find past FRQ questions on CollegeBoard and complete the whole section in 1 hour and 30 minutes (the allotted time for the FRQ).