If you were already asking yourself, “should I be taking AP Calculus?”, or “will AP Calculus be too difficult for me?”. Unfortunately, by now you have come across another question, “should I take AP Calculus AB or BC?” This is a fundamental decision you must take before signing up for AP Calculus.
As you can tell by the sets of letters there are two different AP Calculus courses that you can sign up for. If you’ve made it this far in your mathematical and educational journey surely you’ll make the right decision. In the blog, you’ll find out what to expect if you have decided to or are deciding to sign up for AP Calculus AB. We’ll delve into the finer details of the course and what you can do to be successful!
Is AP Calculus AB that different than BC?
To that question, there is a yes and no. There are other articles that can explain the differences between AP Calculus AB and BC, however, in brief, the major difference between the two courses is the pace. AP Calculus and BC cover basically the same kind of material, however, BC covers it at a much faster pace. Taking AP Calculus AB you will study a semester's worth of college of material over a year. Meanwhile, the BC course will be a year's worth of material in that year of AP Calculus BC. Therefore you can expect to cover the material of AP Calculus AB at a more relaxed pace.
What will you review during the course
- Limits and Continuity
- Differential Equations
- Applications of Integration
Limits and Continuity in AP Calculus AB
Understanding limits is one of the most important concepts you’ll need to assure you can take an AP Calculus course. So what exactly are limits? We use limits to figure out continuity, the derivative of a function, and the definite integral of a function. As for the continuity, a function can be one of two things in terms of continuity. The function is continuous or discontinuous. You can use limits to help you define continuity in a pinpoint manner.
The various types of Differentiations
Differentiation is another important concept you’ll need to learn how to handle. You use differentiation to find the derivative of a function. Brace yourself, as it can be a really complex concept in Calculus. Firstly, when it comes to the basics of differentiation you’ll need to be able to define average and instantaneous rates of changes, define the derivative of a certain function, as well as being able to estimate derivatives at a certain point, and use the Power Rule.
You’ll also need to use differentiation to differentiate composite, implicit, and inverse functions. You will need to apply the chain rule, which helps us differentiate composite functions.
You’re also going to learn how to use Contextual Applications of Differentiation. This means learning to use a rate of change in motion, as well as applying related rates, and approximating. Using contextual applications you will also need to apply L’Hospital rule. This rule states that if you have an indeterminate form, 0/0 for example, all that must be done is differentiate the numerator and then differentiate the denominator and finally take the limit.
Analytical applications are understanding the Mean Value Theorem, and applying the Extreme Value Theorem, and searching for extrema, both global and local. Something we all love to do, Sketching graphs, is also part of this concept of Differentiation, as well as using implicit relations.
Integration & Accumulation of Change
This concept of AP Calculus AB is another important one. Some of what you will be studying when you come across this concept in your course will be, understanding the Fundamental Theorem of Calculus, as well as finding antiderivatives and indefinite integrals.
Differential Equations in your AB course
What you will need to do with this concept is using differential equations to model situations. You will also use differential equations to sketch slope fields, and separate variables.
The concept of applying integration is used to find the average value of a function, as well as to connect position, velocity, and acceleration using integrals. Finding the area between the curves of functions, and volumes in cross-sections and revolutions is also what you will study when understanding this concept.
During your AP Calculus AB course, you will be studying these different concepts and applying them to further your knowledge of calculus at an advanced level. If you are able to study these concepts and understand them very well you’ll be well on your well to earning some college credits during your time in high school! Of course, before you can earn those credits, you’ll need to take the AP Calculus AB exam. So let’s break down the exam for you.
AP Calculus AB exam
There are two types of questions, separated into two different sections both worth 50%, that you’ll find on your AP Calculus AB exam. Multiple choice and free-response. In total there are four parts in two sections.
In the first section, you will have to answer 45 multiple-choice questions. In the first part of this section, you will not be allowed to use a calculator, and in the second part, you will be allowed a calculator. Many believe multiple-choice parts of exams are easier, the answer is there of course. However, like any exam with multiple-choice questions, there are going to be tricky answers, where it seems like at least two answers are correct. You will need to be calm and collected and thoroughly look over the question and each possible answer!
In the second section, you will have to answer six free-response questions. Opposite to the first section, you will be allowed a calculator in the first part, and in the second you will not be allowed a calculator. In this section for each question, you’ll need to write the solutions and steps of how you solved the question. In this part, the good news is that partial credit is given.
How are the exams scored?
The grades or scores on your AP Calculus exam are given between a 1 and 5. The grade of one is the lowest score you can have, while five is the highest you can get.
|Score||Meaning||Percentage of Test Takers|
As we can see it can be quite challenging to get a mark where you will be considered for College credits. As a general rule Colleges are looking for applicants who scored a 4 or 5 on their exam. If you exam the table you can see only about 40% managed to scored a mark that would assure them of college credits.
What you can do to help yourself throughout the course
You might be asking yourself now, "Will it be possible to score a 4 or 5"? Of course you want the college credits at the end of the course. The answer to that question is a definite yes! It is definitely possible to get a 4 or 5 on the exam, also don't panic. There are also colleges out there that would give those who scored a 3 on the exam college credits as well. There are quite a few resources one can use to get a high enough score in AP Calculus AB. As you've read there are quite a few different mathematical concepts. One advantage to taking the AP Calculus AB course over the BC course is that you go over everything you will need to learn, however at a slower pace, as mentioned earlier in the post.
This can be key if you did not get amazing marks in Pre Calculus. If you feel confident you can do well in AP Calculus but not ready to take a faster pace BC course, then taking the AB course will be the optimal decision. That decision can also be made between you and your math teachers that you had in Pre Calculus. They've been your teacher and have graded you, so they know your strengths and weaknesses. Your AP Calculus AB teacher will also be a huge help if you have decided to take AP Calculus AB. They can help you prepare for the exam, as well as resources such as tutors.
Using Superprof will help you find a tutor that can help you with concepts that you are struggling with. Make sure you also have the time to study, and continue studying all the different mathematical concepts that are covered over the course of the year. All in all, you can expect a challenging time, taking college-level material before you arrive at college can be a challenge. Knowing what to expect and how you can study, and working with professions will make the challenge much easier.