AP Calculus BC is frequently touted as having the easier exam compared to AP Calc AB, even though the overall amount and difficulty of the material is harder.
That's not the case.
Like most advanced placement exams, AP Calculus BC is daunting for the unprepared. However, finding the right materials and tools solves half the problem.
We've examined, tried, and tested all of the books and we got the best ones for you below.
The Ultimate AP Calculus BC Prep List
In order to find the right materials and texts for an exam, it is important to consider the mindset and expectations of the exam creators.
For AP Calculus BC, these expectations are summarized in the course description which states that participants are expected to understand the application of integral and differential calculus, solve problems relating to limits and continuity, functions infinite sequences and series and demonstrate the depth of their knowledge of each topic.
To be of significant value to exam participants, a great AP calculus BC book should.
We considered all the above when creating the below list. If you study hard and use the books below, there's no reason for why you shouldn't get a 5.
For those who are all about getting the optimum value for the money, Barron's AP calculus is a sure winner.
This book makes the cut because it is a two-in-one text, with an impressive coverage of both AB and BC syllabuses. And despite being a compilation of first and second-semester work, it maintains a high standard with sections dedicated to graphing calculator reviews, AB and BC course work as well as a ridiculous number of practice tests for both AB and BC exams -- all of which with keep most learners on their toes.
Most importantly, Barron's AP calculus comes highly recommended by top scorers. And while it is often advised that it is used alongside your textbook due to being unable to explain all concepts in extreme detail, it will no doubt be useful all year long, in the days leading to the exam, and a few more years afterward.
Pros
- It is essentially two books for the price of one
- With 8 practice tests, provides the best bang for your buck
- Solid coverage of both AB and BC course descriptions.
Cons
- It is quite bulky and unwieldy to cart around
- Practice questions are arguably harder than the exams
Like its preceding editions, Five Steps to a 5: AP Calc BC encourages a healthy ambition. It has a 5 point agenda that is aimed at launching readers towards achieving the perfect score.
The textbook starts out with a diagnostic test of your current knowledge of AP Calculus BC.
This is especially useful for customizing the learning process as well as sharpening already acquired skills. Additionally, it provides multiple full-length practice exams, an appendix of theorems and formulas, as well as an accompanying study app which brings online resources and other reading materials within reach.
To top things off, end-of-chapter reviews are shrunk down and easy to digest, while being thorough and extensive enough that you get all the needed information.
Pros
- Comes with a study app and multiple practice tests
- Uses a unique customized-learning system
- Affordable
Cons
- A few minute errors
- Only a supplemental text.
Like Barron's AP Calculus, this book by Kaplan is a condensed combination of both AP calculus courses like the name suggests.
It is reviewed and restructured yearly in order to be up to date with the most current AP exams. The 2020 edition, just like its predecessors is loaded with customizable study plans, diagnostic tests useful for evaluating ability and post-chapter quizzes to constantly monitor your progress.
Most impressive of this book is perhaps the fact that it offers access to full-length practice exams as well as an online tool that evaluates performance on a 1-5 scale. With bite-sized reviews of essential topics, expert exam-taking strategies and over 400 practice questions (and explained answers) the AP Calculus AB & BC Prep Plus by Kaplan guarantees results that certainly surpass its price tag.
Pros
- Concise and thorough
- Offers access to an online scoring tool
- Useful all year round
Cons
- The sheer amount of content might be intimidating
A calculus textbook unlike its peers, these "lecture note" offer a different angle to learning Calc BC with an extensive slew of lecture note that mimics the typical classroom experience.
In place of practice tests and concise reviews, it offers examples and explanations in a detailed manner that makes it ideal for participants with only a basic or intermediate understanding of the course topics.
It goes without saying that the AP Calculus BC Lecture Notes is better suited as supplemental learning materials rather than the main text. Nevertheless, it offers everything from formulas, to updated lessons and theorems such that it can be a worthy rival of most conventional texts.
Naturally, it has garnered an impressive following of high-scorers and tutors alike due to its of its simplicity and interactive layout. What's more, its author has a reputation that more than speaks for itself -- and whether it is the beginning of the year or crunch time, it will provide you with the confidence you need to pass with flying colors.
Pros
- Properly organized, interactive layout
- Easy to understand
- Covers most of the syllabus
Cons
- Best suited for supplementary reading
- No practice exams included
- That cover might not be your favorite
It opens with a thorough explanation of each course topic and provides concise reviews and summaries in a clear, understandable manner. It also breaks down formulas, theorems and concepts such that you can jump on-board even if you didn't listen in class. And then it closes with 4 practice tests that mirror the complexity of actual exams which is useful for evaluating your learning progress and determining whether you're truly ready for the exam.
Overall, Dr Chung’s Advanced Placement Calculus BC helps each user thoroughly unravel each topic at their level of understanding.
Pros
- Useful for any learning level
- Concise coverage of all topics.
- Includes 4 practice tests
Cons
- A few notable typos which might be distracting
- The layout can be a bit disorganized at times
AP Calc Books To Avoid
Cracking The AP Calculus BC Exam by The Princeton Review
While it is true that The Princeton Review has built quite an impressive repertoire of helpful textbooks, the 2019 edition of turned out to be quite a sour disappointment.
From multiple typos, and math errors to the fact that the practice tests are nowhere near the complexity of the actual exam, unknowing students found themselves misled up till the day of the actual test without a hint. Even worse, the diagnostic test questions were found to be blatantly wrong or had none of the crucial exponents required for the exam. So even participants with a fair understanding of the course syllabus found themselves on a wild-goose chase trying to match the answers provided in the text.
Between being plagued with errors, and having misleading answers that made most problems unsolvable, this book was hardly usable. And while we can only hope that the 2020 edition offers a much better experience, it is safer not to take any chances especially since the market is already brimming with error-free, helpful alternatives.
Test Structure
Examines are required to have an extensive knowledge of graphing calculators and demonstrate their understanding of related topics as well as unrelated topics covered in the course overview.
Remember that you are required to bring your own graphing calculator.
The test has a multiple choice section and a free response section, each worth 50%.
For the multiple choice section, participants are required to answer a total of 45 questions in no more than 105 minutes.
Part A of the multiple choice section contains 30 multiple choice questions and does not allow the use of a graphing calculator. Part B of the multiple choice question contains the remaining 15 questions of the section and requires the use of a graphing calculator.
On the other hand, the free response section requires practical demonstration of each participants knowledge. Part A of this section requires a graphing calculator and contains 2 questions which must be solved in 30 minutes or less. Part B of the free response section however has 3 questions which do not permit the use of a calculator and must be solved in under 60 minutes.
As mentioned earlier, the AB Calculus BC exam incorporates concepts of the AB syllabus and evaluates the understanding of topics from both BC and AB course overview. However, examines are also required to consider the knowledge of AB calculus independently of the BC portion, so a thorough knowledge of both courses is pertinent.
Last Time The AP Calculus BC Exam Was Changed
Overall, there are slight modifications made to AP courses and exams on a yearly basis. However, a few key updates were made to AP calculus in 2019 these include:
- Replacing topic outlines with a curriculum framework:
This update aims to align course content with learning objectives as well as make quantitative changes to mathematical practices -- such that they become more explicit. - Adding several topics to the existing program without removing any of the already existing ones:
The added topics aims to broaden the knowledge of participants in concepts relating to limit comparison, the alternating series error bound and absolute conditional convergence. - Adjusting the timing of the multiple-choice section as well as re-distributing the questions based on the counsel of invigilators and tutors.
In the 2020 exam, participants can expect to see questions relating to algebraic, analytical, exponential, graphical, trigonometric, tabular and logarithmic types of functions and representations in the multiple choice section.
On the other hand, the free response section will focus on questions relating to function representation and questions aimed at evaluating the participants ability to incorporate their knowledge in solving real-life problems.
Additional Tips & Resources For Studying
For most participants, tackling an extensive course overview might seem a tad overwhelming unless they incorporate interesting resources and strategies to their study schedule that aid retention. Here are a few that may come in handy:
- Understand the Big Picture
It goes without saying that the performance of each participant will be dependent on their understanding of the topics within the syllabus. By looking at the course overview students can strategize and narrow their focus to the necessities. - Monitor Progress
Textbooks that feature diagnostic and post-chapter quizzes will come in especially handy in this regard. This will help you evaluate their progress as well as highlight problem areas that require attention. - Show The Work
Just like section 2 of the AP Calculus BC exam demands. While it might seem like a tedious process while studying, it helps to sharpen skills of coherency and tidiness and also helps to aid timeliness on the day of the test. - Limit Calculator Use
Participants who choose to restrict calculator use while studying are often at a greater advantage during the test. Frequent use of calculators might create a false send of speed and accuracy, when in fact, the use of calculators is limited to a few sections of the exam. - Incorporate Flash Cards -- Barron's AP Calculus Flash Cards
Flash cards are generally useful for encouraging speed-thinking and in tandem with a great textbook may prove to be a valuable, and somewhat entertaining study aid. Barron's AP Calculus Flash Cards includes 400 flash cards for both review and practice all of which cover formulas, equations, theorems, integrals and derivatives to mention a few. Luckily, students can arrange the flash cards such that their problem areas are given a little more attention than the others. - Use Online Scoring Apps
By using apps that evaluate scores on the 1-5 scale, students can get an accurate evaluate of their abilities in light of the AP scoring scale and eventually work towards their desired goal. A great resource is Albert which has a dedicated AP calculus BC calculator
Additional Materials:
Not everyone learns best from books and text. For those of you who prefer more dynamic learning here are some other options for you:
- Khan Academy - The default for most students when they need an explanation of certain concepts, but it's too important to leave out.
- edX has an entire Calc BC course available for free on their platform.
- CollegeBoard has a list of past free response questions that can be quite useful.
