AP (Advanced Placement) Calculus is a set of Calculus courses and exams that are offered by the American College Board. This exam/course covers an introduction to limits, derived, and integrals. However, you are likely already aware of this as you are here for an AP Calculus study guide. If you’re looking for a proper AP Calculus AB/BC exam review, we have got you covered.
We’ll be taking a look at the format, some of the topics, Calculus questions, AP Calculus problems, and Calculus math questions. Other than that, we’ll be going over some resources that can help you out, and we’ll try to give you some tips for the exam day. In the end, we’ll summarize everything and you can see for yourself just how prepared you really are.
With all of that said, consider this the definite AP Calculus Review and Study Guide for 2021. Without any further ado, let’s get started.
A Quick Look At This Guide
- Format: We’ll go over things such as how long is the Calc AB Exam, how many calculus questions it has, and the amount of time you are allotted for each section.
- What topics are likely to appear in the exam itself
- What exactly the Calculus Questions appear to be, and how can you tackle them
- How will you be graded/scored on the AP Calculus AB Exam
- What makes the 2021 AP Calculus Exam dissimilar to previous exams
- An effective way to study and retain information for the exam
- Important and Essential Study Tips
- A couple of handy resources
- A synopsis for the entire guide
2021 AP Calculus AB Exam Format
You’re not going to be very well prepared for the 2021 AP Calculus exam if you’re not familiar with the format itself. It’s the first thing you should try to familiarize yourself with. You should know how many calculus questions will appear on the exam, and how much time you will be given to attempt.
Well, allow us to give you a brief overview. In total, there are 51 questions that take place over a testing period of 3 hours and 15 minutes. All of these 51 questions are separated into different sections. There are four sections, out of which you are allowed to use a calculator in only two of them.
Take a look at this table so you can understand how it works.
If you are still confused, you can check here for the Digital Practice page on the AP Central site. It’s a shortened version of the actual exam but will allow you to see how things go down. Next, let’s take a look at the two main sections you’ll need to attempt.
Multiple Choice Questions - Section 1
Section 1 is broken up into two parts. Both parts A and B consist of 45 total questions on the AP Calculus exam. Part A does not require you to use a calculator, neither is it allowed. You will or may be required to use a graphing calculator in Part B of this section. From there, it’s a simple multiple-choice question affair.
Part A: 30 Questions, 60 minutes, No Calculator allowed.
Part B: 15 Questions, 45 minutes, Calculator required.
Each question will have four answer choices, marked as A, B, C and D. Most of these questions will include algebraic, exponential, logarithmic, trigonometric, and general functions. They will also include tabular, analytical, graphical, and verbal representation. You’ll be given an hour and 45 minutes to attempt this section.
The multiple-choice questions will amount to 50% of your final score. Section 1 focused on the first three mathematical practices. Look below to see as to which percentages these practices are accessed with. This way you can get a better identity of the type of questions you are asked to tackle.
Free-Response - Section 2
Next up on the exam you’ll encounter the free-response section. This is the second section and consists of various different calculus math questions. Here is what the format for the AP Calculus AB free-response section looks like. In total, you’ll face six questions, and will be given an hour and 30 minutes to attempt these questions. The free-response section is worth 50% of your total final score.
Part A of this section will have two questions, and you’ll be given 30 minutes in total to answer them. A Calculator will be required here. Part B of this same section will ask you to attempt four questions, and you’ll be given 60 minutes for part B. No calculator is allowed while attempting part B.
This section will include various questions about types of functions and function representations. You’ll also encounter questions related to procedural and conceptual tasks. Expect two of these questions to incorporate real-world scenarios. The free-response section focuses on four mathematical practices. These practices will be scored according to the following weights.
So, you’re given 30 minutes for part A and 60 minutes for part B. If we take the average into account, you’ll be getting around 15 minutes to answer each question. Of course, this will vary depending on how many parts a certain question has. Don’t waste time on a question you’re stuck on. It would be wise to skip that question and come back to it at the end if you have time remaining. And yes, you can return to Part A during the time you are doing Part B.
AP Calculus AB Units
Next up on our AP Calculus AB study guide, we are going to be taking a look at all of the units and what major topics these units cover. Later on in this AP Calculus study guide, we’ll take a look at the three main topics of the course, and how they are mentioned throughout all of the units. All three of these major topics are integrated within all of the units.
But before we get to that point, let’s take a look at the units themselves and what these units discuss with the student.
Unit 1: Limits and Continuity
- Define, evaluate, or estimate limits graphically, numerically, analytically, or verbally
- How to define and confirm continuity
- Connecting limits
- Connecting multiple representations of limits
- Using the Intermediate Value Theorem
- Removing Discontinuities
Exam Weightage (Percentage): 10-12%
Unit 2: Differentiation: Definition and Fundamental Properties
- Define the derivative of a function at a point and as a function
- Define instantaneous rates of change at one point
- Connect differentiability and continuity
- Rules for Derivatives
- Quotient and Product Rule
- Find derivatives of tangent, cotangent, secant, cosecant functions
Exam Weightage (Percentage): 10-12%
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
- Implicit Differentiation
- Calculating Derivatives
- Calculating Higher Order Derivatives
- Chain Rule
- Differentiating Inverse Functions
Exam Weightage (Percentage): 9-13%
Unit 4: Contextual Applications of Differentiation
- Straight-line motion
- Rates of change in applied context rather than motion
- Interpret derivatives in the context
- Solve related rates problems
- Local Linearity and Linearization
- L’Hospital’s Rule
Exam Weightage (Percentage): 10-15%
Unit 5: Analytical Applications of Differentiation
- Mean Value Theorem and Extreme Value Theorem
- Increasing and decreasing intervals
- Using derivative tests for determining relative and absolute extrema
- Determine concavity of functions over their domains
- Graphing functions and derivatives
- Solve optimization problems
Exam Weightage (Percentage): 15-18%
Unit 6: Integration and Accumulation of Change
- Accumulation of change
- Reimann sums, integral notation, summation notation
- Fundamental Theorem Of Calculus
- Accumulation function
- Find antiderivatives and indefinite intervals
- Integrate functions using substitution, long division, and completing the square.
Exam Weightage (Percentage): 17-20%
Unit 7: Differential Equations
- Sketch slope fields
- Model situations and verify solutions with differential equations
- Reasoning via slope field
- Find general and particular solutions using initial conditions and separation of variables
- Exponential modes with differential equations
Exam Weightage (Percentage): 6-12%
Unit 8: Applications of Integration
- Find the average value of the function
- Connect position, velocity, and acceleration of functions
- Use accumulation function and definite integrals in applied contexts
- Find the area between curved
- Volumes with cross-sections
- Find volume with Disc and Washer methods
Exam Weightage (Percentage): 10-15%
Yes, there are a lot of topics covered in AP Calculus AB. Being familiar with all of the calculus questions will help your exam score a lot. It’s a lot to cover, but with prioritization, it’s not an impossible task at all. If you want to see these topics covered in more detail check out this official course guide provided by the college board.
There’s also an official course overview provided by the board so you can see every aspect of the AP Calculus AB and AP Calculus BC exams at a glance.
Three Major Concepts For AP Calculus AB
While the implementation and rules around the AP Calculus exam might have changed, there’s no change in the structure of the exam and the topics that take place. While the pandemic has changed a lot of things for us, the AP Calculus exam still focuses on three main topics. These are also known as the three big ideas of calculus.
In order to keep things brief and clear, we’ll quickly go over three of these ideas. You’ll get a better understanding of what calculus is all about if you haven’t even studied that much. If that’s the case, study up these three major concepts carefully.
Concept Number 1: Change
- You will want to understand how and why change occurs and how to provide reasoning for those changes
- Determine the rate of change that takes place
- Interpret how equations are similar to each other in a structural sense
- Find out or evaluate change over a specific interval of time
- Analyze the functions for intervals of continuity and also discontinuity
- Estimate the rate of change based on the area of the region between the curve and x-axis.
- Model motion that is not constrained to a linear path.
Concept Number 2: Limits
- An understanding of limits, and how to make sense of features of functions plus their graphs
- Understand mathematical properties and rules to simplify and evaluate time limits that apply to differentiation
- How to prove that a limit exists
- Identify the connection between continuity and differentiation
- Find out the meaning of derivative within a problem
- Solve the certain problem that involves the slope of the tangent line
- Solve the certain problem that involves related rates, optimization, and rectilinear motion
- How to solve proves that involve the rate of change in applied contexts
- Solve how a sum that is infinitely discrete terms can be a finite value represented in a continuous function
Concept Number 3: Analyzing Functions
- Eliminate loopholes so that conclusions of functions are true
- Understand how changes of two units of measurement are related to each other. Also, what is the rate at which they change?
- Interpret what numbers indicate about other rates of change
- Apply Mean Value Theorem to justify the conclusion
- Include additional information in a mathematical argument which can optimize a simple equation.
- Calculate derivatives and antiderivatives
- Evaluate or estimate definite integrals
- Analyze graphs by using a parametric equation or polar functions via chain rules
- Apply integrals to problems that involve the average value of function, motion, area, and volume.
- Properly analyze differential equation to obtain solutions
- Interpret and solve differential equations from problems in context.
AP Calculus Exam Scoring Methodology
We’ve already talked about how certain sections of the AP exam are scored. However, to wrap up this AP Calculus AB Study Guide and Exam Review, let’s go a bit in-depth so you can figure out what exactly you are dealing with.
Let us talk about the MCQs section first. You get one point for every answer that is correct. There is no negative marking for incorrect answers, so try to attempt every question. The total possible score for this section is 45.
Next up, we have the free-response section. Each of the six questions here can get you 9 points. In total, that adds up to 54 points that you can get. However, different parts of each question may be worth a different amount of mounts. If Question 1 has three parts: A, B, and C, then you might get 1 point for A, 3 for B, and 5 for C. This could be in any order, of course.
After you’re done with all the sections, you’ll turn in the paper and it will be graded. All the points are summed up, and the score is converted to the AP score scaling of 1-5. The criteria and formula for this exact AP score can vary slightly from year to year. Every AP score correlates to a range of combined scores. We’ll leave a conversion chart below.
A Few Tips to Get A 5
Let’s quickly go over a few tips that you should be aware of when attempting the AP Calculus exam.
- Memorize all the major and important formulas so that you can attempt the questions with ease. Your teacher likely gave out a formula to memorize. Any formula that you often came across in class is worth memorizing.
- Get familiar with your calculator as two of the four exam parts will require you to use it. Determine how and when to use its different functions to save time and get better accuracy.
- Don’t just give answers, show a detailed range of work as to how you got that answer. The final answer is not worth that many points, it’s the amount of work you put in and the steps you take that matter at the end of the day.
Conclusion and Some Helpful Resources.
So, for now, that is all you need to know to get familiar with all of the ins and outs of the AP Calculus exam. Let’s be honest things can get a bit intimidating here. But with a bit of help from our AP Calculus Study Guide, you’ll know what you’re dealing with. Hopefully, you can now go in feeling a bit more confident as to what you’re going to be tackling in the exam itself.
Before we leave, here are a few extra resources. If you want to check out a great website for various other courses and content on mathematics and computer science, Best coding and math website for teenagers. The aforementioned site has a dedicated curriculum for math courses and paths.
Check out the main page of the AP Calculus AB course. If you are curious about the AP Calculus BC Exam as well, here’s a link to that. Other than that, you can download the course and exam description from the official website. The site also has an excellent daily live review feature that is worth checking out. Other than that, good luck on the exam and we hope you do well.