Unit 6: Integration and Accumulation of Change Unit 5: Analytical Applications of Differentiation Unit 4: Contextual Applications of Differentiation Unit 3: Differentiation: Composite, Implicit, and Inverse Functions Unit 2: Differentiation: Definition and Fundamental Properties As always, you have the flexibility to organize the course content as you like. The AP Calculus AB framework is organized into eight commonly taught units of study that provide one possible sequence for the course. The framework also encourages instruction that prepares students for advanced coursework in mathematics or other fields engaged in modeling change (e.g., pure sciences, engineering, or economics) and for creating useful, reasonable solutions to problems encountered in an ever-changing world. The framework specifies what students must know, be able to do, and understand, with a focus on big ideas that encompass core principles, theories, and processes of the discipline. Then be sure to practice on an actual AP Calculus exam.Based on the Understanding by Design® (Wiggins and McTighe) model, this course framework provides a clear and detailed description of the course requirements necessary for student success. Try these ones for starters: AP Calculus AB Free Response Practice Problems and AP Calculus BC Exam Free Response Practice Problems. The best way to understand the AP Calculus free response questions is to do some yourself. Therefore, it is better to completely work out the problems that you know how to answer before trying any that you might have trouble with. The graders are looking for significant progress towards the final answer, rather than a few stabs in the dark. However, I recommend sticking with a free response problem until you can complete all parts. In order to complete all of the questions, you would have to spend an average of 15 minutes per problem or less. Section II of the test consists of 6 free response questions, separated into two parts. How Many Free Response Questions are there on the Exam?īoth the AP Calculus AB and BC tests have the same number of free response problems. However, Part (c) did not depend on Part (b), so this is not a hard and fast rule. Of course, this depends on finding the first derivative (Part (a)).Īs you can see from this example, the parts of the question depend on one another. Finally, Part (c) asks for a second derivative.We need the derivative in order to find the slope of any tangent line. But also notice in this case, part (b) depends on part (a). That’s a clue that you should have more than one answer. Notice the plural equation s and tangent line s. Part (b) asks for the equations of the tangent lines at a specific point.So you’ll have to do implicit differentiation. However the given function is not solved explicitly for y. Part (a) asks for the slope at any point.First of all, the given equation applies to all three parts.We won’t solve it here, but we will build a plan for tackling the problem. Ok, so let’s pick this question apart a little. (b) Find the equations of the tangent lines to the curve at the point x = 2. (a) Write an expression for the slope of the curve at any point ( x, y). ExampleĬonsider the equation x 2 – 2 xy + 4 y 2 = 64. AP Calculus Free Response Question FormatĪ typical free response problem states a scenario and then asks 3-4 questions about that scenario.įor example, the following problem was pulled from a practice Calculus BC exam. In this short article, you’ll discover what to expect on the AP Calculus free response sections. Instead, you will have to work out the problem, showing all steps, and come up with a final answer yourself. What are the AP Calculus free response questions like? Free response means that you will not be given any answer choices.
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