Calculus is the mathematics of change. For instance, calculus is the mathematics of velocities, accelerations, tangent lines, slopes, areas, volumes, arc lengths and a variety of other concepts that have enabled scientists, engineers, and economists to model real-life situations. Therefore, AP Calculus is one very important course of all advanced placement subjects.

AP Calculus Examination divides into AB and BC level. In general, Calculus BC has more topics and more difficult than AB. Math can help the students develop the analyzing ability. Calculus BC has three main areas: differentiation, integration, and series. All of them are totally new to the students. It will take time for students to understand and accept these definitions. In my class, I have been trying to let my students focus on the following three aspects.

Firstly, ask my students to take notes on class. It’s not smart to take either all or no notes that I showed on the blackboard. Just need to take the summary or the knowledge points that are not contained on the textbook.

Secondly, let the students pay attention to the logic and relationship between definitions and theorems. In mathematics the definition is the most important, and all the theorems and rules are based on the definition. Once the students have thoroughly understood the definition, they will find that AP Calculus is easy to learn. In China, many students achieved good scores only by doing a lot of exercise. They only know how to solve the exam problems and cannot understand the logic of the knowledge point or method because they lack the ability of analyzing and summarizing.

Thirdly, focus on master the essence inside the textbooks instead of just memorizing the knowledge. For instance, when I was giving the lectures about finding second derivatives of parametrically defined functions, I want my students to notice that the first derivative is also a parametrically defined function, and the second derivative is the derivative of the first one, so we can deal with the first derivative in the same way. Once you understand the exact logic behind this formula, you will easily get the formula of the second derivatives of parametrically defined functions and will never forget it when you solve problems.

Finally, I ask my students to do the summary after each class, finish the homework on their own and correct the homework in time.

Lily