AP Calculus AB Exam Guide | Fiveable (2024)

Your Guide to the 2024 AP Calculus AB Exam

We know that studying for your AP exams can be stressful, but Fiveable has your back! We created a study plan to help you crush your AP Calc AB exam. This guide will continue to update with information about the 2024 exams, as well as helpful resources to help you do your best on test day.Unlock Cram Modefor access to our cram events—students who have successfully passed their AP exams will answer your questions and guide your last-minute studying LIVE! And don't miss out on unlimited access to our database of thousands of practice questions.

Format of the 2024 AP AP Calculus AB Exam

Going into test day, this is the exam format to expect:

• • Multiple Choice - 50% of your score- - 30 questions - no calculator- - 15 questions - calculator
• • Free Response - 50% of your score- - 2 Questions - require a calculator- - 4 Questions - no calculator

When is the 2024 AP Calculus AB Exam and How Do I Take It?

**The exam is on paper at your school on Monday, May 13, 2024 at 8:00 AM, your local time.**

How Should I Prepare for the Exam?

• • First, download theAP Calculus AB Cheatsheet PDF - a single sheet that covers everything you need to know at a high level. Take note of your strengths and weaknesses!
• • Review every unit and question type, and focus on the areas that need the most improvement and practice. We’ve put together this plan to help you study between now and May. This will cover all of the units and essay types to prepare you for your exam- - Practice problems are your best friends! Both the FRQs and MCQs had several questions that were similar toprevious FRQs and the open-sourced multiple-choice questions on College Board (essentially the same questions with different numbers).
• • We've put together the study plan found below to help you study between now and May. This will cover all of the units and essay types to prepare you for your exam. Pay special attention to the units that you need the most improvement in.
• • Study, practice, and review for test day with other students during our live cram sessions viaCram Mode. Cram live streams will teach, review, and practice important topics from AP courses, college admission tests, and college admission topics. These streams are hosted by experienced students who know what you need to succeed.

Pre-Work: Set Up Your Study Environment

Before you begin studying, take some time to get organized.

🖥 Create a study space.

Make sure you have a designated place at home to study. Somewhere you can keep all of your materials, where you can focus on learning, and where you are comfortable. Spend some time prepping the space with everything you need and you can even let others in the family know that this is your study space.

📚 Organize your study materials.

Get your notebook, textbook, prep books, or whatever other physical materials you have. Also, create a space for you to keep track of review. Start a new section in your notebook to take notes or start a Google Doc to keep track of your notes. Get yourself set up!

📅 Plan designated times for studying.

The hardest part about studying from home is sticking to a routine. Decide on one hour every day that you can dedicate to studying. This can be any time of the day, whatever works best for you. Set a timer on your phone for that time and really try to stick to it. The routine will help you stay on track.

🏆 Decide on an accountability plan.

How will you hold yourself accountable to this study plan? You may or may not have a teacher or rules set up to help you stay on track, so you need to set some for yourself. First, set your goal. This could be studying for x number of hours or getting through a unit. Then, create a reward for yourself. If you reach your goal, then x. This will help stay focused!

🤝 Get support from your peers.

There are thousands of students all over the world who are preparing for their AP exams just like you! JoinRooms🤝 to chat, ask questions, and meet other students who are also studying for the spring exams. You can even build study groups and review material together!

AP Calculus AB 2024 Study Plan

👑UNIT 1: Limits and Continuity

Big takeaways:

Unit 1 is the basic idea of all of Calculus. The limit is the concept that makes everything click. You ask someone what they learned in calculus and they will most likely answer “derivatives and integrals”. help us to understand what is happening to a function as we approach a specific point. Limits can be one or two sided, but the sides have to match in order for the limit to exist from both directions! Well without the limit, we wouldn’t have either. A major concept used throughout the curriculum and within theorems is . We prove continuity using limits and learn how to do that within this unit. We also learn about the and the , although this topic most likely won’t be directly tested on this year’s exam, it’s the bread and butter of what’s to come.

Content to Focus On:

• Methods of Finding Limits
  • From a table
    • Be able to estimate values not given in a table by using values that were given in a table.
  • From a graph
    • Be able to use a graph to interpret a limit at an x value.
  • Algebraically
    • Limit Properties
    • Some limits look unsolvable, (00 or ), but using algebraic manipulation, you can solve them! In unit 4 we learn about another helpful tool for this, L’Hospital’s rule!
  • Infinite Limits
• Squeeze Theorem
  • The squeeze theorem helps us to find limits of functions that we do not know, by using the limits of a function that is greater than or equal to and a function that is less than or equal to. If we can find the limits of those two functions and they are equal, then our function should have that limit too!
• Continuity and Discontinuity
  • Students should be able to prove if a function is continuous as a point, and know the different types of discontinuity! Removable, jump, infinite.
• First existence theorem:
  • Intermediate Value Theorem
    • This theorem helps us to prove points exist given certain information. Don’t forget to always state or prove the conditions! In this case, it would be that the function is continuous on [a,b].

Resources to use:

📰 Read these Fiveable study guides:

• • 1.0Unit 1 Overview
• • 1.1Introducing Calculus: Can Change Occur at An Instant?
• • 1.2Defining Limits and Using Limit Notation
• • 1.3Estimating Limit Values from Graphs
• • 1.4Estimating Limit Values from Tables
• • 1.5Determining Limits Using Algebraic Properties of Limits
• • 1.6Determining Limits Using Algebraic Manipulation
• • 1.7Selecting Procedures for Determining Limits
• • 1.8Determining Limits Using the Squeeze Theorem
• • 1.10Exploring Types of Discontinuities
• • 1.11Defining Continuity at a Point
• • 1.12Confirming Continuity over an Interval
• • 1.13Removing Discontinuities
• • 1.14Connecting Infinite Limits and Vertical Asymptotes
• • 1.15Connecting Limits at Infinity and Horizontal Asymptotes
• • 1.16Working with the Intermediate Value Theorem (IVT)🎥 Watch these videos:

• Defining Limit and using Limit Notation: Introduction to limits

• Graphical Limits: Finding limits given a graph.

• Algebraic Limits: How do you find a limit algebraically?

• : Defining a continuous function

• Limits at Infinity: Using limits at infinity to demonstrate function behavior

• Working with the Intermediate Value Theorem: There are two theorems that are related to Unit 1: The Intermediate Value Theorem and The . Learn about the Intermediate Value Theorem here.

🤓UNIT 2: Differentiation: Definition and Basic Derivative Rules

Big takeaways:

Unit 2 introduces the first of the 2 major halves of calculus: , or the instantaneous rate of change of a function. We start off with defining the derivative and applying it to our old friend, the limit. This unit also sets up the rules so that you can figure out the derivative of most simple functions you will find on the FRQ section! We will additionally discuss the difference between average and instantaneous rates of change and how they appear differently. One thing is for sure, you should still follow order of operations!

Content to Focus On:

• Average Rate of Change vs Instantaneous Rate of Change
  • If we apply a limit to an average rate of change, we are looking at an instantaneous rate of change!
• Definition of the Derivative
• Estimating The Derivative
• Connecting differentiability and continuity. Remember, differentiability implies continuity, but not the other way around! Make sure you know how to tell if a function is differentiable. No cusps or corners, polynomials are always differentiable!
• Finding Simple Derivatives using:
  • Derivative Properties
  • Trigonometric Derivatives
  • Exponential and Logarithmic Derivatives
• Product and Quotient Rules

Resources to use:

📰 Read these Fiveable study guides:

• • 2.0Unit 2 Overview
• • 2.1Defining Average and Instantaneous Rates of Change at a Point
• • 2.2Defining the Derivative of a Function and Using Derivative Notation
• • 2.3Estimating Derivatives of a Function at a Point
• • 2.4Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
• • 2.5Applying the Power Rule
• • 2.6Derivative Rules: Constant, Sum, Difference, and Constant Multiple
• • 2.7Derivatives of cos x, sinx, e^x, and ln x
• • 2.8The Product Rule
• • 2.9The Quotient Rule
• • 2.10Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions🎥 Watch these videos:

• The Limit Definition of the Derivative: The derivative from first principles

• • Introduction to Finding Derivatives: The power rule and trigonometric derivatives, a must watch!
• • The Product and Quotient Rules: The product and power rules, a powerful tool in your derivative-finding toolkit!
• • Practicing Derivative Rules: Applying what you’ve learned in finding derivatives so far!

🤙🏽UNIT 3: Differentiation: Composite, Implicit & Inverse Functions

Big takeaways:

In Unit 3, we expand on the methods of finding derivatives from Unit 2 in order to evaluate any derivative that Collegeboard can throw at you! This section includes the very important . is a big take away from this unit as well. It allows us to find derivatives of any variable when we may be finding the derivative with respect to something else.

Content to Focus On:

• Chain Rule
  • Chain rule allows us to differentiate composite functions. But make sure you see every function! Sometimes chain rule can be more than one chain! For example: (sin(x2))2. We have 3 functions to consider here!
• Implicit Differentiation
  • Implicit differentiation gives us the tools to derive any variable with respect to any variable. The main concept is that if the variable you are deriving is not the same as the variable you are taking the derivative of, chain rule applies and you must also multiply by the derivative of that variable. For example, the derivative of y2 with respect to x is 2ydydx.
• (Including Trigonometric Functions)
  • Remember how to find an inverse? Switch x and y and solve for y? Well then take the derivative of that! or follow the formula we have! The important part to remember on problems like this is the x and y values. If you are supposed to be using the x value of an inverse function, that means it was the y value of your original function!

Resources to use:

📰 Read these Fiveable study guides:

• • 3.0Unit 3 Overview
• • 3.1The Chain Rule
• • 3.2Implicit Differentiation
• • 3.3Differentiating Inverse Functions
• • 3.4Differentiating Inverse Trigonometric Functions
• • 3.5Selecting Procedures for Calculating Derivatives
• • 3.6Calculating Higher-Order Derivatives🎥 Watch these videos:

• The Chain Rule: The chain rule, used to evaluate the derivative of composite functions, is very important!

• • Implicit Derivatives: Derivatives of implicitly defined functions/curves
• • Practicing Derivative Rules II: Applying what you have learned through the previous 2 units!
• • Using Tables to Find Derivatives: Finding derivatives when the equation may not be present

👀UNIT 4: Contextual Applications of Differentiation

Big takeaways:

Unit 4 allows you to apply the derivative in different contexts, most of which have to do with different rates of change. You will also learn how to solve problems containing multiple rates, how to estimate values of functions, and how to find some limits you may not have known how to solve before! is a very popular topic in the FRQ section of the exam. It is very important you label every variable you use! Limits that you didn’t know how to solve can now be solved using L’Hospital’s rule, but make sure you know the requirements!

Content to Focus On:

• Rates of Change
  • , ,
    • Velocity is the derivative of position, and acceleration is the derivative of velocity. Velocity has a direction. If the velocity and acceleration match signs, the particle is speeding up. If their signs are opposite, the particle is slowing down. Speed is the absolute value of velocity and does not have direction. On the AP test, you can be asked to map out the path of a particle, which direction it is going and if it is speeding up or slowing down.
  • Related Rates
    • Related Rates have to do with nothing other than relating rates! There are a set of steps to follow when solving a related rate:- 1. Assign letters to quantities and label their derivatives with respect to time. If you have A= area, then dA/dt would be the rate of change of the area.- 2. Identify the rates that are known and the rate that needs to be found.- 3. Find an equation that relates the variables whose rates of change you need in step 2. Draw a picture to help you find this equation!- 4. Differentiate the equation with respect to time. Remember it is necessary to think about this as implicit differentiation.- 5. Substitute in all known values and variables, and solve for the unknown rate of change.
• One special type of related rate is that of a cone. You should practice a related rate problem with a cone, because it is necessary to write r, the radius, in terms of h before differentiating.
• and
  • In these types of problems, we use a tangent line approximation for one value that we know and use it to approximate another very close value. Let’s say, x0 is the one we know about, and x1 is the one we need. Then we would use: f(x1)-f(x0)=f'(x0)(x1–x0) to find f(x1).
• L’Hopital’s Rule- When using L’Hospital’s rule, we have a few things we need to remember! To apply L’Hospital’s rule, your limit needs to be in one of two forms: 0/0 or ∞/∞. To show this in a free response question, you need to show the limits in the numerator and the denominator go to either 0 or infinity separate from each other, then you can use L’Hospital’s rule, which says: xaf(x)g(x)=xaf'(x)g'(x).

Resources to use:

📰 Read these Fiveable study guides:

• • 4.0Unit 4 Overview
• • 4.1Interpreting the Meaning of the Derivative in Context
• • 4.2Straight-Line Motion: Connecting Position, Velocity, and Acceleration
• • 4.3Rates of Change in Applied Contexts other than Motion
• • 4.4Intro to Related Rates
• • 4.5Solving Related Rates Problems
• • 4.6Approximating Values of a Function Using Local Linearity and Linearization
• • 4.7Using L'Hopitals Rule for Determining Limits in Indeterminate Forms🎥 Watch this video:
• • Related Rates: How to solve related rates problems

✨UNIT 5: Analytical Applications of Differentiation

Big takeaways:

Unit 5 continues our discussion on the applications of derivatives, this time looking at graphs and how the value of the first and second derivatives of a graph influences its behavior. We will review two of the three existence theorems, the mean and extreme value theorems. We’ll also learn how to solve another type of problem commonly seen in the real world (and also on FRQ problems): .

Content to Focus On:

• Two of the three Existence Theorems
  • It is important to make sure their conditions are met before you use them!
  • • In order to use the Mean Value Theorem, the functions must be continuous on a closed interval and differentiable on that same interval, but open. Once you can say for sure that these things are true, the mean value theorem tells us that there must be a point in that interval where the average rate of change equals the instantaneous rate of change, or the derivative, at a point within the interval. f'(c)=f(b)-f(a)b-a.
  • Extreme Value Theorem
    • For this existence theorem, the condition is that the function continuous on a finite closed interval. If it is, that means there must be an absolute maximum and an absolute minimum.
• and The First Derivative
  • If the derivative of a function is positive, then the function is increasing! If the derivative is negative, then the function is decreasing!
• Local and Global Extrema
  • First and Second Derivative Tests for Local Extrema
  • for Global Extrema
• , , and The Second Derivatives
  • If the second derivative is positive, the function will be concave up. If the second derivative is negative, the function will be concave down. Whenever the second derivative changes sign, there will be an inflection point, a change in concavity, on the original function.
• • All of the information you learned from how the first and second derivatives relate to the original function can help you to sketch graphs based on the information you have about their derivatives!
• Optimization Problems
  • These are also known as applied maximum and minimum problems. They are problems about finding an absolute maximum and an absolute minimum in an applied situation. When trying to find an absolute max or min, you must find all critical points (f'(x)=0 or undefined). Then plug those and the endpoints into the original function to find out which has the highest or lowest value, depending on what you are looking for.

Resources to use:

📰 Read these Fiveable study guides:

• • 5.0Unit 5 Overview
• • 5.1Using the Mean Value Theorem
• • 5.2Extreme Value Theorem, Global vs Local Extrema, and Critical Points
• • 5.3Determining Intervals on Which a Function is Increasing or Decreasing
• • 5.4Using the First Derivative Test to Determine Relative (Local) Extrema
• • 5.6Determining Concavity
• • 5.7Using the Second Derivative Test to Determine Extrema
• • 5.8Sketching Graphs of Functions and Their Derivatives
• • 5.10Introduction to Optimization Problems
• • 5.11Solving Optimization Problems🎥 Watch these videos:

• Interpreting Derivatives Through Graphs: Graphical interpretation of derivatives

• • Existence Theorems: Mean Value Theorem, Extreme Value Theorem, Intermediate Value Theorem
• • Increasing and Decreasing Functions: Using the first derivative to show where function increases and decreases
• • Concavity: Using the second derivative to find concavity
• • f, f’, and f”: Relating a function and its
• • Optimization Problems: How to solve optimization problems

🔥UNIT 6:

Big takeaways:

Unit 6 introduces us to the integral! We will learn about the integral first as terms of an area and Reimann sums, then working into the fundamental theorem of calculus and the integral's relationship with the derivative. We will learn about the definite integral and the indefinite integral. We will additionally learn about methods of integration from basic rules to substitution. In some cases the integral is called the antiderivative, and if f is the function, then F would be the antiderivative of that function.

Content to Focus On:

• • When given a graph, we can find the area under the curve and between the x axis to find the integral. However, if an area is underneath the x-axis, that would be considered negative.
• Riemann Sums
  • A way of evaluating an area under a curve by making rectangles to find the area of an adding them up. This is useful with a table of values or with a curve that we do not know the exact area of its shape. There are four kinds: Left, Right, Midpoint, and Trapezoidal sum. Depending on the function, these may be over or under estimates of the actual area.
  • Students should also be able to write a Riemann sum in summation notation and integral notation.
• The Fundamental Theorem of Calculus
  • This theorem tells us two very important things:
    • abf(x)dx=F(b)-F(a)
    • ddx(axf(t)dt)=f(x), where a is a constant.
  • We use this theorem very often when working with integrals.
• Definite vs.
  • Integrals must always include a dx (if not x, whichever variable you are using) at the end.
  • If an integral is indefinite, it has no bounds. This means it cannot be evaluated using the fundamental theorem of calculus. Instead, we add on a +C, to make it know that there could have been a constant at the end of the function, and that there are lots of possibilities for what that constant would be.
  • have bounds and we use the fundamental theorem of calculus often with them. The bounds let us know the endpoints of the integral, or in terms of a graph, what two points we are finding the area under the curve between.
• • Make sure you remember how to integrate and its connection to deriving!
  • You can check an integral by taking its derivative to see if you get back to where you started.
• • When you have a composition of functions in an integral, it is necessary to use u-substitution to make sure you are integrating each part. It is usually the inside function which is chosen. Sometimes it can be hard to tell. You will know once you try! If you find yourself going in circles and needing to substitute more, I would try using a different piece of the function as u.

Resources to use:

📰 Read these Fiveable study guides:

• • 6.0Unit 6 Overview
• • 6.1Integration and Accumulation of Change🎥 Watch these videos:

• The Fundamental Theorem of Calculus: Explains the Fundamental Theorem of Calculus and its uses as the most important theorem in calculus

• • Some Integration Techniques: How to do integration techniques found in Calculus AB

💎UNIT 7: Differential Equations

Big takeaways:

• Unit 7 takes us to a great connection between integrals and derivatives in differential equations. We will learn how to model and solve differential equations using . This always requires separation of variables when it comes to free response questions! We will also learn how to identify differential equations from their and how to draw those fields as well.

Content to Focus On:

• Differential Equations
  • Modeling - If you are given information, can you write a differential equation from it?
  • Verifying Solutions - Being able to plug in given information and deduce if the solution is true.
  • Separation of variables
    • This appears often in the FRQ section. Students are given a differential equation and need to put all of the terms for one variable on one side and for the other variable on the other, then they integrate both sides and solve for y, usually y, but really whichever the dependent variable it.
    • NOTE: If you skip the step of separating variables on AP exams in the past, they have offered you no credit for the rest of that section of the problem.
  • Using initial conditions
    • Once you have done your separation of variables, don’t forget to have a +C! This is where the initial condition comes in. You plug in the terms given from x and y in your initial condition, then you solve for C, rewriting the function at the end with C plugged in!
• Slope fields
  • Slope fields are coordinate planes of 1 by 1 sections of slopes at each x and y value. If given a differential equation and asked to find a slope field, you plug in an x and y pair into the differential equation, the value it outputs is the slope at the point, and is the steepness you use to draw a line at that particular pair.

Resources to use:

📰 Read these Fiveable study guides:

• • 7.0Unit 7 Overview
• • 7.2Verifying Solutions for Differential Equations
• • 7.3Sketching Slope Fields
• • 7.4Reasoning Using Slope Fields
• • 7.6Finding General Solutions Using Separation of Variables
• • 7.7Finding Particular Solutions Using Initial Conditions and Separation of Variables🎥 Watch this video:
• • Separable Differential Equations: How to solve separable differential equations

🐶UNIT 8: Applications of Integration

Big takeaways:

Unit 8 teaches us more useful applications of the integral as we enter the 3D graph world! We learn how to find the and the particle motion according to an integral. We also use cross sections and disks and washers to find volume of shapes as functions are revolved around either a vertical or horizontal line. We put our spatial reasoning and geometry skills to use in this section.

Content to Focus On:

• Average Value of a function
  • The average value of a function is denoted by 1b-aabf(x)dx. We can only find the average value of a function that we have a definite integral for.
• Position, Velocity, Acceleration
  • Position is the integral of velocity, and velocity is the integral of acceleration! If you take the absolute value of velocity, you are able to find speed.
  • Distance is the integral of the absolute value of velocity
  • Displacement is the integral of velocity
    • To remember this, I think about a track! After one lap around, your distance is 400m, but your displacement is 0. Make sure if you are asked for distance, you remember to use absolute value!
• • If given two curves on a coordinate plane and endpoints, students should be able to integrate those functions, either with respect to the x or y axis, in order to determine the area between them. When talking about the x axis, all functions should be in terms of x, the bounds should be in terms of x, and it will be the integral of the upper functions minus the lower. When talking about with respect to the y-axis, all functions should be in terms of y, the bounds should be in terms of y, and it will be an integral of an outer function minus the inner.
• Finding the area between curves that intersect at more than two points.
  • Sometimes, your function will have different parts where you may need to split the area and add your answers together, because the upper functions changes, or another function changes.
  • When in doubt, break it up into pieces you know how to work with, and add those together.
  • Area under the x axis is already accounted for as negative when evaluating using an integral, so don’t worry about that!
• • When using cross sections, you integrate the area of whatever shape is given to you (this could be a square, rectangle, triangle, or semicircle).
  • You will integrate the area on a given interval, but it is important that you interpret the function for the variable in the shape that it represents.
  • If it says perpendicular to the x-axis, all should be in terms of x.
  • Perpendicular to the y-axis, all should be in terms of y.
• • In this case we are integrating an area again, but this time the shape will always be a circle, so we will always be using the area formula for a circle. The variable that changes here is r, the radius, which you can interpret using the function.
  • If the rotation is around just the x axis, all should be in terms of x (bounds and functions) and the radius will be your function.
  • If the rotation is around just the y axis, all should be in terms of y (bounds and functions) and the radius will be your function.
  • If it is rotated around any other vertical or horizontal line, you may need to add or subtract value from your function to find the radius.
  • A washer is when two functions are used, and you must subtract out the volume the inner function would have added into your total volume to account for the missing piece.

Resources to use:

📰 Read these Fiveable study guides:

• • 8.0Unit 8 Overview
• • 8.1Finding the Average Value of a Function on an Interval
• • 8.2Connecting Position, Velocity, and Acceleration of Functions Using Integrals
• • 8.3Using Accumulation Functions and Definite Integrals in Applied Contexts
• • 8.4Finding the Area Between Curves Expressed as Functions of x
• • 8.5Finding the Area Between Curves Expressed as Functions of y
• • 8.6Finding the Area Between Curves That Intersect at More Than Two Points
• • 8.7Volumes with Cross Sections: Squares and Rectangles
• • 8.8Volumes with Cross Sections: Triangles and Semicircles
• • 8.9Volume with Disc Method: Revolving Around the x- or y-Axis
• • 8.10Volume with Disc Method: Revolving Around Other Axes
• • 8.11Volume with Washer Method: Revolving Around the x- or y-Axis
• • 8.12Volume with Washer Method: Revolving Around Other Axes🎥 Watch these videos:

• Interpreting the Meaning of the Derivative and the Integral: Showing derivatives and integrals applied in different contexts

• • Position, Velocity, and Acceleration: Exploring the relationship between position, velocity, and acceleration

Key Terms to Review (39)

Acceleration: Acceleration refers to the rate at which an object's velocity changes over time. It measures how quickly an object is speeding up, slowing down, or changing direction.

Approximating an integral as an area: Approximating an integral as an area involves dividing a region into smaller rectangles and summing up their areas to estimate the total area under a curve. It is a method used to find the value of definite integrals when exact calculations are not possible.

Average Value of a Function: The average value of a function over an interval is the total change in the function divided by the length of the interval.

Candidates Test: The Candidates Test is a method used to determine the behavior of a function at critical points. By evaluating the sign of the derivative on either side of a critical point, you can determine if it is a local maximum, minimum, or neither.

Chain Rule: The chain rule is a formula used to find the derivative of a composition of two or more functions. It states that the derivative of a composite function is equal to the derivative of the outermost function times the derivative of the innermost function.

Concavity: Concavity describes whether a graph opens upward (concave up) or downward (concave down). It indicates whether the graph is curving upwards like an "U" shape or downwards like an "n" shape.

Continuity: Continuity describes whether or not there are any breaks, holes, or jumps in a function. A continuous function has no interruptions and can be drawn without lifting your pen from the paper.

Curve/Derivative Sketching: Curve/derivative sketching involves analyzing the behavior of a function and its derivative to determine key features such as critical points, inflection points, and concavity.

Definite Integrals: Definite integrals are used to find the exact value of the area under a curve between two points on the x-axis. It represents the accumulation of infinitesimally small areas and can be thought of as finding the total "signed" area.

Derivatives of Inverse Functions: Derivatives of inverse functions refer to finding the rate at which an inverse function changes at any given point on its graph. This can be done by swapping x and y in the original function's derivative formula.

Differentiation: Differentiation is the process of finding the rate at which a function changes. It involves calculating the derivative of a function to determine its slope at any given point.

Extreme Value Theorem: The Extreme Value Theorem states that if a function is continuous on a closed interval, then it must have both a maximum value and a minimum value on that interval.

Finding area between curves: Finding area between curves involves calculating the area enclosed by two or more curves on a graph.

First Derivative Test: The First Derivative Test is a method used to determine the intervals on which a function is increasing or decreasing, and to identify local extrema (maximum or minimum) points.

Implicit Differentiation: Implicit differentiation is a technique used to differentiate an equation implicitly without explicitly solving for one variable in terms of another.

Increasing/Decreasing Functions: An increasing function is one in which the values of the function increase as the input increases. A decreasing function is one in which the values of the function decrease as the input increases.

Indefinite Integrals: Indefinite integrals, also known as antiderivatives, represent families of functions whose derivatives match a given function. They do not have specific limits but rather include an arbitrary constant (C).

Inflection Points: Inflection points are points on a graph where the concavity changes. In other words, they mark the spots where a curve transitions from being concave up to concave down, or vice versa.

Initial Conditions: Initial conditions refer to the values or states of a system at the starting point of a problem or scenario. They are used to determine the specific solution or behavior of the system.

Integral Rules: Integral rules are formulas or techniques used to evaluate definite and indefinite integrals. They provide shortcuts for finding antiderivatives or calculating areas under curves without having to resort to basic integration from scratch.

Integration and Accumulation of Change: Integration involves finding antiderivatives and calculating areas under curves. It represents accumulation of change over an interval.

Intermediate Value Theorem: The Intermediate Value Theorem states that if a continuous function takes on two values, say "a" and "b", at two points in its domain, then it must also take on every value between "a" and "b" at some point within that domain.

L'Hopital's Rule: L'Hopital's Rule is a method used to evaluate limits of indeterminate forms, such as 0/0 or ∞/∞. It states that if the limit of the ratio of two functions is an indeterminate form, then taking the derivative of both functions and evaluating the limit again can help determine the original limit.

Limits: Limits are used in calculus to describe the behavior of a function as it approaches a certain value or point. It helps determine what happens to the output of a function when the input gets closer and closer to a specific value.

Linearization: Linearization is an approximation method used to estimate values of functions near a particular point by using their tangent lines.

Mean Value Theorem: The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on an open interval (a, b), then there exists at least one point c in (a, b) where the instantaneous rate of change (derivative) equals the average rate of change over the interval.

Optimization Problems: Optimization problems involve finding maximum or minimum values for certain quantities within given constraints. These problems often require using calculus techniques such as differentiation to determine critical points.

Position: Position refers to an object's location in space relative to a reference point. It is usually described using coordinates or distances from fixed points.

Power Rule: The power rule is a calculus rule used to find the derivative of a function that is raised to a constant power. It states that if f(x) = x^n, where n is a constant, then the derivative of f(x) with respect to x is equal to n*x^(n-1).

Rationalization: Rationalization is the process of eliminating radicals from the denominator of a fraction by multiplying both the numerator and denominator by an appropriate expression. It helps simplify fractions and make them easier to work with.

Related Rates: Related rates is a concept in calculus that deals with finding the rate at which one quantity changes with respect to another related quantity. It involves using derivatives to solve problems involving changing variables.

Second Derivative Test: The second derivative test is used to determine whether critical points correspond to local maxima, minima, or neither. It involves analyzing the concavity of a function at those critical points.

Slope Fields: Slope fields are graphical representations of differential equations that show the slope at various points on a plane. They help visualize the behavior and solutions of differential equations.

Squeeze Theorem: The Squeeze Theorem states that if two functions, g(x) and h(x), both approach the same limit L as x approaches a certain value c, and another function f(x) is always between g(x) and h(x) near c (except possibly at c itself), then f(x) also approaches L as x approaches c.

Tangent Line Approximations: Tangent line approximations involve estimating the value of a function at a specific point by using the equation of its tangent line at that point. It provides a close approximation when working with small intervals around that point.

U-Substitution: U-substitution is a technique used to simplify integrals by substituting a new variable for part of the original expression.

Velocity: Velocity is the rate at which an object's position changes with respect to time. It includes both speed and direction.

Volumes by disks and washers: Volumes by disks and washers is a method used to find the volume of a solid by integrating cross-sectional areas. It involves slicing the solid into thin disks or washers perpendicular to an axis, calculating the area of each disk or washer, and then summing up these areas using integration.

Volumes of cross sections: Volumes of cross sections refer to calculating three-dimensional volumes by integrating cross-sectional areas along a given axis.