Here is all you need to know about AP Calculus BC
First of all, why should you take AP Calculus BC?
At the end of the day, you alone will determine whether or not to enroll in AP Calculus BC. Remember to take into account your personal schedule, the subjects you are most interested in, and how AP Calculus BC will affect your plans in addition to the factors mentioned above as you make your choice. AP Calculus BC is an advanced Calculus class that you could go for if you’re looking at a STEM course for your undergraduate degree like pre-medicine, engineering or natural sciences. Furthermore, passing the AP Calculus BC exam gives you more math credit in college in the vast majority of cases. Here are some of your major options if you choose to study AP Calculus BC:
- Aerospace Engineering
- Applied Mathematics
- Biomedical Engineering
- Civil Engineering
What does it entail:
The College Board offers AP Calculus BC in addition to AP Calculus AB as its two AP Calculus courses. The more difficult of the two courses, AP Calculus BC, builds on what students gained in AP Calculus AB.
Students must have a strong background in math because this is a very advanced course. It might be advantageous for students to have taken AP Calculus AB before AP Calculus BC. In a full-year, two-semester calculus course, AP Calculus BC is designed to cover the material that a first-year college student would learn.
This is what you’ll be learning in Calculus:
|Unit Name||What you’ll learn|
|Limits and Continuity||How limits will allow you to solve problems involving change|
|Differentiation: Fundamentals and Properties||Applying limits to define the derivative and determining derivatives|
|Differentiation: Composite, Implicit and Inverse Functions||Chain Rule, Developing new differentiation techniques and Higher-order derivatives|
|Contextual Applications of Differentiation||Applying derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms|
|Analytical Applications of Differentiation||Exploring relationships among the graphs of a function and its derivatives and applying calculus to solve optimization problems.|
|Integration and Accumulation of Change||Defining definite integrals and how the Fundamental Theorem connects integration and differentiation. Applying properties of integrals and practicing useful integration techniques|
|Differential Equations||Solving differential equations, understanding exponential growth, decay and logistic models|
|Applications of Integration||Net change over an interval of time and to find lengths of curves, areas of regions, or volumes of solids defined using functions|
|Parametric Equations, Polar Coordinates, and Vector-Valued Functions||Solving parametrically defined functions, vector-valued functions, and polar curves using applied knowledge of differentiation and integration. Straight-line motion to solve problems involving curves|
|Infinite Sequences and Series||Convergence and divergence behaviors of infinite series, determining the largest possible error associated with certain approximations involving series.|
This is what you can expect in the exam:
The AP Calculus BC exam is 3 hours long which happens to be one of the longest AP exams, broken down in two sections. The first section is a multiple-choice and the second is a free-response section. They’re essentially 2 sections with a Part A and Part B in each, respectively. You will be allowed to use a graphing calculator only on Part B of Section 1. Calculators are not allowed in the second section.
|Section||Time Duration||About the questions|
|Multiple Choice (50%)||60 minutes (Part A)||This section has 30 multiple choice questions|
|45 minutes (Part B)||This section has 15 multiple choice questions|
|Free Response (50%)||30 minutes (Part A)||This section has 2 free response questions|
|60 minutes (Part B)||This section has 4 free response questions
Various steps in the solving of each problem are given partial credit. A graph is typically required for one of the questions.
Every topic/unit has its individual weightage. The exam may have more questions from one topic than the other as the distribution is not equal. Below is a look at the ten units structured in a sequence recommended by the College Board, along with the weight each unit is given on the AP Calculus BC exam:
|Unit Name||Percentage weightage|
|Limits and Continuity||4%-7%|
|Differentiation: Fundamentals and Properties||4%-7%|
|Differentiation: Composite, Implicit and Inverse Functions||4%-7%|
|Contextual Applications of Differentiation||6%-9%|
|Analytical Applications of Differentiation||8%-11%|
|Integration and Accumulation of Change||17%-20%|
|Applications of Integration||6%-9%|
|Parametric Equations, Polar Coordinates, and Vector-Valued Functions||11%-12%|
|Infinite Sequences and Series||17%-18%|
The table above shows that the majority of the questions from the multiple choice exam are focused around Integration and Accumulation of Change first, and then Infinite sequences and series. Therefore, while you prepare for your exam, you can consider making these concepts a priority so it guarantees you those marks. This subject is essentially Calculus, so, between differentiation and integration, integration is weighed more in terms of percentage.
How’s the exam scored? What were the stats for the last session?
On a scale of 1 to 5, with 5 representing an exceptionally high result, AP exams are graded. If you want college credit, colleges typically require a 4 or 5 on the AP Calculus BC examinations, while some may also accept a 3. Students appear to do pretty well on the AP Calculus BC exam in general. This might be as a result of the extremely strict requirements for prerequisite knowledge, which guarantee that the majority of students enrolling in the course are already prepared for its intensity.
|Score||Percentage of students that scored|
What is the pass rate for AP Calculus BC?
One measure of an AP class’s difficulty is the proportion of students who pass the exam. A passing grade for AP exams is considered to be a 3, and scores range from 1 to 5. By comparing the AP exam pass rate for AP Calculus BC to the overall average, you can get an idea of how difficult the exam is for students. The Calculus BC exam’s pass rate and perfect score rate are contrasted with the average of the other AP subjects in the table below.
|AP Exam||Pass Rate (3 or higher)||Perfect Score (a 5)|
|AP Calculus BC||75.2%||38.3%|
|Other AP classes||64.2%||16.8%|
For AP Calculus BC, the pass rate and percentage of perfect scores are both above average. But AP exam pass rates don’t always accurately reflect how difficult a subject is. Students who take certain AP exams, like AP Calculus BC, typically perform better on them because they have prior knowledge of and preparation in the sciences and are willing to challenge themselves. The level of difficulty you perceive in the course will also depend on a number of additional variables, some of which are specific to you and your school, like the quality of your teacher.
How do you prepare for the AP Calculus BC exam?
Firstly, this is what will be expected from you if you take the subject:
Your subject knowledge is one aspect that can assist you in determining a course’s level of difficulty. Students who excel in math and have a good background in math will probably find AP Calculus BC easier than students who excel in the humanities. Consider your skill set and your preferred courses when deciding whether or not to take AP Calculus BC. Students who are proficient in math may find AP Calculus BC to be simple.
All students should finish the equivalent of four years of secondary mathematics intended for college-bound students before beginning calculus. This includes studying algebra, geometry, trigonometry, analytic geometry, and basic functions. You must be able to graph and solve equations involving the properties of the following functions: linear, polynomial, rational, trigonometric, inverse trigonometric, and piecewise defined.
To boil it down, here are a few ways that you can prepare for the exam:
- Your Calculus notebook could be a delight to look at. But they are also the key to help you understand the concept once you begin revision. Prep books can help all you want but the notes that you write will reflect your understanding. You may have included notes in the side to explain how you got from one step to the next. Therefore, treasure these notes with all that you have. Reading them will definitely help you recollect what was taught in class.
- Utilizing a test prep book is definitely optional but a lot of the AP students use it because the book consists of practice problems and exams unique to each topic be it applications of integration or sequences and series. You will be able to assess your strengths and weaknesses as there will be questions for each aspect of the unit. Some of the most recommended books are Barron’s and Princeton Review’s.
- Practice tests. While this may already be in your prep books, try to find older AP exams so you would truly be ready for anything that comes your way. Practicing past paper AP Calculus BC exams will give you the best idea on how you will perform on the actual exam as the questions are very similar. Your capacity to use a long chain of reasoning to answer problems will be put to the test in the free-response section of the AP Calculus BC exam. You will be required to show that you have a solid understanding of mathematical reasoning and thinking in this section.
Here are a few tips you can keep in mind during the exam:
- Keep a close eye on the time and your calculator. This is so that you have enough time to respond to all of the questions, and be careful not to spend too much time on any one. Before beginning each segment of the free-response section, you might want to review all the questions. You may continue working on the problems from Part A during the second timed section of the free-response section (Part B), but you may not use a calculator at this time. You are allowed to be as exhaustive with your mathematical steps as possible, but try to keep it concise without missing anything out because you’d be on the clock.
- Show the process regardless of whether you use a calculator. On problems requiring calculations, include all the steps you followed to arrive at your result, even if the question does not specifically state that you should. The purpose of the exam is to determine your problem-solving skills. Usually, answers without supporting work are not given credit. Any functions, graphs, tables, or other objects you utilize should have clear labels. The requirements for justifications include providing mathematical justifications and confirming the necessary conditions under which pertinent theorems, properties, definitions, or tests are applied.
- Reading has never been more significant. It is a good idea to read through all of the questions to decide which ones you feel most qualified to answer before starting to answer the free-response questions. For instance, if a question asks for the maximum value of a function, don’t stop after determining the x-value at which the maximum value occurs. If units are specified, be sure to express your response in the appropriate ones, and whenever one is requested, give a justification.
- Do not round up or down answers. Decimals are very important in a Calculus exam, especially if you’re carrying forward the answer in the steps to arrive at a final answer. These partial answers can be written down from the calculator to show the intermediate steps. If you round answers in between, the final answer can turn out to be very different.
Yep! That is all for AP Calculus BC. We’re sure we left no stone unturned so anything you want to know, it’s in this blog!