AP Calculus AB: Math can be fun

AP Calculus

The AP Calculus AB examination is going to be held on Tuesday, 5th May, 2020. Before one embarks on a prep course for this AP subject, it is crucial to know the structure of the exam, the themes encompassed and the grading system.

The Syllabus on the Calculus AB exam can be divided into three main topic areas which we call Big Ideas in Calculus: Limits and Continuity, Differential Calculus with applications of differentiation, Integral Calculus with applications of Integration and Analysis of function.

The structure of the examination has not been modified. However, slight changes are made in the course content on your exam. L’Hospital’s Rule is the only addition to the content of the AP Calculus AB exam, and learners must be able to understand and apply it. So, now you have an additional benefit of knowing a specific question type. Got it?

Big Idea 1: Limits and Continuity

  • Evaluating limits, and understanding the features of functions and their graphs.
  • Mathematical rules for abridging and calculating limits and the connection to differentiation
  • Understand whether a limit exists
  • Infer the significance of a derivative in a question.
  • Solve how the sum if infinitely discrete terms can be a finite value represented in a continuous function.
  • Analyze functions for intervals of continuity or points of discontinuity
  • Determine the applicability of important calculus theorems using continuity

Big Idea 2: Differentiation and Application of derivatives

  • Calculation of derivative of a function using a variety of strategies.
  • Evaluate the derivative of a function using (theoretical) limit equation.
  • Derivatives & higher-order derivative evaluation.
  • Understand the behavior of the function.
  • Identify the association relating to differentiability and continuity
  • Understanding instantaneous rates
  • Interpret the idea of a derivative within a question.
  • Crack problems involving the rise/run of a tangent line.
  • Decipher questions relating to rates of change in applied contexts
  • Unravel questions involving related rates, optimization, and related questions.
  • Answer problems involving rates of change in contexts.
  • Authenticate solutions to differential equations.
  • Estimation of solutions using differential equations.
  • The Mean Value Theorem -Evaluation

Big Idea 3: Integrals and the Fundamental Theorem of Calculus

  • An understanding of the concept of antiderivatives
  • Differential equations involving a function’s rate of change and evaluation with integrals to find universal solutions.
  • Interpretation of the integral as the limit of a Riemann sum using definite integrals & Riemann sum.
  • Deduce the idea of a definite integral in a question.
  • Deduce, produce, and elucidate differential equations in context.
  • Approximate a definite integral and calculate a definite integral using areas and properties of definite integrals.
  • Problems involving motion and definite integral correlation and theorems in Calculus.
  • Evaluation of definite integral of a function with a connection with an accumulation of functions with problems involving area, volume using Integration using various methods.

Scoring on the AP Calculus AB Examination

The final score of your examination is composed of MCQ (multiple-choice question) and FRQ (free-response question) each contributing to fifty percent of your total score. 

In the MCQ section, you allow you to score one mark for each correct answer. Marks are not subtracted for wrong answers, so you should never hesitate to attempt any question! You can get a maximum of 45 points in this section which comes first.

For the FRQ, you can get up to 54 points as each of the 6 questions is worth 9 points. However, individual parts of each question can be worth different points (for example, 1 mark for part A, 3 marks for part B, 3 marks for part C, and 2 marks for part D for a single question).

The score which you receive out of a 108 is converted into a standard band score ranging from 1-5. The formula for the conversion can alter marginally from time to time. 

Advice for acing the AP Calculus AB Exam

AP Calculus AB exam can be a difficult examination for many. Use these three tips to make your preparation effective and upsurge your odds of receiving a great score.

Checkpoint 1: Learn Essential Formulas

Of course, as calculus can be quite complex without formulas, mathematicians have developed quite a lot for students to evaluate problems for the AP Calculus AB as there is no formula sheet provided, you are expected to memorize the formulas which you require. Many teachers give out formula sheets for students to memorize. At Option, we provide an exclusive list of cheat sheet which the student can memorize apart from the course materials!!

Fundamental theorems, limits, rules relating to Integration and differentiation are the major formulas involved.

Checkpoint 2: Calculators should be your friend 

Understanding the right time to use and knowing the different functions can save an enormous amount of time during the test. So, master it! Which increases your possibility of getting the right answer.

There are three calculator capabilities you’ll use the most during the exam which are as follows: 

1. Using a specified window, plot the graph of a function.

2. Finding zeroes and equations

3. Calculate the derivative and definite integrals of a function

Practice a lot of questions to increase the pace while working out with a calculator and be sure to know all the shortcuts well beforehand. The mock test series conducted at Option Training Institute can help reinforce your skills in a timed environment.

Checkpoint 3: Write as if the examiner is a student

Yes, you have read it right. For the free-response questions on the AP Calculus AB test, the final answer is awarded only a minor proportion of score when compared with the overall score of a question. For example, a problem is only worth 1 or 2 points out of a total score of  9. This means that the lion’s share of the points is received through the steps of the problem, and if you do not wish to show how you have arrived at the final answer you won’t be able to perform well in this section even if you are a mathematical wizard!

Suppose if you get the right answer by using your calculator, you have to write how you have set up the equation namely derivatives or Integrals and then the answer to get full credit for your work.

NOTE: Students are not used to writing down the intermediate steps which are especially obvious. However, your AP graders will penalize you harshly if you are not explaining your work and approach.

Understand that the evaluators are more interested in evaluating the way and the thought process involved in your calculations. So, be ready to explore the theoretical side of your calculations with proper notations and explanations.

We welcome all the mathematical enthusiasts to appreciate the quality that we have at Option Training Institute, Dubai, and the depth at which Calculus is taught to you. Let’s make math more like fun!