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Guide to the AP Calculus BC Exam – Expert’s Guide

Mar 16, 2023

Are you wondering how to learn math and at the same time engage in extracurricular activities? Then, the AP Calculus BC Exam is the right choice for you. However, the AP Calculus exam deals with the high school portion of the AP Calculus course. As a result, some may feel taking this exam is a little burdensome, while others enjoy taking this test to boost their mathematical skills. 

Around 125,000 students wrote down the AP Calculus BC Exam 2021 worldwide. However, these numbers are less as, on average, 250,000 students take AP Calculus BC Exam every year. Furthermore, the numbers increase by over 7% each year. This is because students apply theoretical knowledge in practical situations that they learn while taking the course. So, do you want to know more about the AP Calculus BC Exam? 


Knowing about AP Calculus BC Exam 

If you are familiar with the Mean Value Theorem, L’Hospital’s Rule, Squeeze Theorem, and similar topics, then AP Calculus is meant for you. Those who are not familiar with these topics have to thoroughly understand the fundamentals of these chapters. If you are a student, enroll for AP Calculus BC Exam at their official website. And if you are not a student, meaning you are a coordinator, teacher, or administrator, then enroll for the exam at AP Central.
The skills that the students will learn after availing of this course are: 

  • They will learn to connect representations. 
  • Use correct notation, mathematical conventions, and language to communicate solutions and results. 
  • Learn to justify reasoning and solutions. 
  • Determine values and expressions using mathematical procedures and rules. 

The scores of the AP Calculus BC Exam are curved every year. This means that the College Board preserves consistency and standardizes every student’s performance. Are you planning to get a score of 5 on the AP Calculus BC Exam? Then you have to combine tenacity, stick to a plan and commit to learning study material while preparing for the AP Calculus BC Exam. 


How is AP Calculus BC different from AP Calculus AB? 

The AP Calculus exam consists of two parts: AB and BC. These two are not different in terms of difficulty but in terms of content. According to the College Board, AB Calculus is equivalent to a semester of college calculus, whereas BC is equivalent to a year of college calculus. The main difference between AB and BC Calculus is that BC covers some extra theoretical aspects of calculus and a few additional topics than AB Calculus. 

AP Calculus BC Exam Syllabus 

The AP Calculus BC Exam consists of the following topics and their corresponding weighted percentages on the exam score: 

Chapter name Major topics Weighted percentage on the exam score 
Limits and continuity ●      Define limits 

●      Estimate limits from graphs and tables 


●      Determine limits using algebraic properties and manipulation 

●      Application of Squeeze theorem 


●      Types of discontinuities 

●      Understanding asymptotes 


●      Apply intermediate value theorem 

4% – 7% of exam score 
Differentiation: Definition and Fundamental Properties ●      Definition and basic rules 

●      Define average and instantaneous rates of change 


●      Define the derivative of a function 

●      Estimate derivatives at a point 

●      Connect differentiability and continuity 

●      Apply power rule 

●      Product rule 

●      Quotient rule 

●      Determine derivatives of constants, sums, differences, constant multiples, and trigonometric functions, ex, In x 

4% – 7% of exam score 
Differentiation: Composite, Implicit, and Inverse Functions ●      Composite, implicit, and inverse functions 

●      Apply the chain rule 

●      Use implicit differentiation 

●      Differentiate inverse functions 

●      Calculate higher order derivatives 

4% – 7% of exam score 
Contextual Applications of Differentiation ●      Interpret derivatives in the context 

●      Use rates of change in motion and another context 

●      Apply related rates 

●      Approximate using linearization 

●      Apply L’Hospital’s Rule 

6% – 9% of exam score 
Analytical Applications of Differentiation ●      Understand the mean value theorem 

●      Use the extreme value theorem 

●      Find global and local extrema 

●      Apply the first derivative test and second derivative test 

●      Find intervals of increase and decrease 

●      Understand concavity 

●      Sketch graphs 

●      Solve optimization problems 

●      Use implicit relations 

8% – 11% of exam score 
Integration and Accumulation of Change ●      Find accumulations of change 

●      Reimann sums, and definite integrals 

●      Understand the fundamental theorem of calculus 

●      Interpret accumulation functions 

●      Find antiderivatives and indefinite integrals and integrate using substitutions 

●      Long division 

●      Completing the square 

●      Integration by parts 

●      Linear partial fractions 

●      Improper integrals 

17% – 20% of exam score 
Differential Equations ●      Model situations with differential equations 

●      Verify solutions for differential equations 

●      Sketch slope fields 

●      Approximate using Euler’s method 

6% – 9% of exam score 
Applications of Integration ●      Find the average value of a function 

●      Connect position, velocity, and acceleration using integrals 

●      Apply accumulation functions 

●      Find area between curves of functions 

●      Find volumes from cross-sections and revolutions 

●      Finding arc length 

6% – 9% of exam score 
Parametric Equations, Polar Coordinates, and Vector-Valued Functions ●      Polar coordinates, and vector-valued functions 

●      Define and differentiate parametric equations 

●      Find second derivatives of parametric equations 

●      Find arc lengths of parametric equations 

●      Define, differentiate and integrate vector-valued functions 

●      Solve motion problems using parametric and vector-valued functions 

●      Define polar coordinates 

●      Differentiate polar functions 

●      Find the area of regions bounded by a single polar curve or two polar curves 

11% – 12% of exam score 
Infinite Sequences and Series ●      Defining convergent and divergent infinite series 

●      Work with geometric series 

●      Determine convergence and divergence using the nth term test, integral test, comparison test, alternative series test, and ratio test 

●      Work with geometric series and p-series 

●      Determine absolute or conditional convergence 

●      Determine error bound 

●      Finding Taylor polynomials 

●      Find Lagrange error bound 

●      Find radius and interval of convergence of power series 

●      Represent functions as power series 

17% – 18% of exam score 

How long is the AP Calculus BC Exam? 

There are two sections in the AP Calculus BC Exam. Section 1 is multiple-choice, and section 2 is the free-response section. Section 1 is well-understood, while in section 2, students are asked to respond after the AP Calculus BC Exam states a scenario. 

The Task Verbs Used in Section 2 are: 

  • Approximate 
  • Calculate/Write an expression 
  • Determine 
  • Estimate 
  • Evaluate 
  • Explain 
  • Identify/Indicate 
  • Interpret (when given a representation) 
  • Justify 
  • Represent 
  • Verify 

The Following Table Shows the Section-wise Distribution of the AP Calculus BC Exam: 

Section Timing Number of questions % of exam score 
Section 1 Part A: 60 minutes 

Part B: 45 minutes 


Part A: 

● 30 multiple-choice questions 

● A calculator is not permitted in this section. 

Part B: 

● 15 multiple-choice questions 

● Calculator permitted 


Section 2 Part A: 30 minutes 

Part B: 60 minutes 


Part A: 

● 2 free-response questions 

● Calculator permitted 

Part B: 

● 4 free-response questions 

● Calculator not permitted 



AP Calculus BC Exam Score Calculation 

The AP Calculus BC Exam scores are scaled from 1 to 5, where 5 is the highest and 1 is the lowest. AP Calculus BC Exam consists of two sections whose weighted percentages are given below: 

Section of AP Calculus BC Exam Percentage of the overall score 
Section 1, Part A 33% 
Section 1, Part B 17% 
Section 2, Part A 17% 
Section 2, Part B 33% 

MCQs are easier to score than any other section in the AP Calculus BC Exam. There is no penalty in the AP Calculus BC Exam. As a result, students must attempt every question. For getting scores in section 2, students must represent their ideas clearly and accurately on each free-response question. 

Most colleges look for an AP score of 4 or 5, but a few allow 3 too. Here is the list of AP Calculus BC Exam 2021 scores:
Score Meaning Percentage of test-takers 

Score Meaning Percentage of test-takers 
5 Extremely qualified 38% 
4 Well qualified 17% 
3 Qualified 20% 
2 Possibly qualified 18% 
1 No recommendation 7% 

Tips to get a better score in AP Calculus BC Exam 

Here are a few quick tips that will help to improve your AP Calculus BC Exam score: 

  1. The most important tip that students should follow is to focus in class. Students can learn a lot from the class if they pay attention to what is taught and learn simultaneously. The teacher demonstrates new concepts and clears doubts that will help to build a strong foundation for the AP Calculus exam. 
  2. Do take the tuition provided by the school. Do not let opportunities pass by. Grab them and make the best use of them. Moreover, students must take the AP Calculus BC practice exam to measure their preparation levels before the exam. 
  3. Study with friends. Form groups and study together. Work on equations, concepts, and formulas. It can boost morale, build confidence to solve problems and teach how to handle pressure on D-day. 
  4. Go for the AP Calculus BC practice exam. Practice as much as you can. The way to conquer the AP Calculus BC Exam is to practice questions on pen and paper. Take time for the study material and complete the practice problems before the exam. 
  5. Make the graphic calculator your new partner. Aspirants taking the AP Calculus exam must have a good command of the graphic calculator to perform several functions and speed up calculations. 

What are we going to do after the exam? 

Relax and wait for the results. Since you have given all you have got, finally it’s time to relax. Wait for the scores to come. If they are good, it shows you know Calculus. If they are not good enough, do not lose hope and practice for another one.

AP Calculus BC Exam


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