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- Questions include algebraic, exponential, logarithmic, trigonometric, and general types of functions. Questions include analytical, graphical, tabular, and verbal types of representations. Section II: Free Response 6 Questions | 1 Hour 30 Minutes | 50% of Exam Score Part A: 2 questions; 30 minutes (graphing calculator required).
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Download free-response questions from past AP Calculus AB exams, along with scoring guidelines, sample responses from exam takers, and scoring distributions.
- Question 6
- Question 7
- Question 8
- Question 9
- Question 10
Answer: D Recall the following formula used when converting integrals to limits: ∫abf(x)dx=limn→∞∑k=1nf(a+(b−an)k)⋅b−an. So, in this case, we have that a=3, b=5, and f(x)=x4. Also, b−a=2. Then, ∫35x4dx=limn→∞∑k=1n(3+2kn)4⋅2n, which corresponds to choice D.
Answer: A To solve the differential equation dydt=ky, we’ll first need to divide both sides by yand multiply both sides by dt. This yields dyy=kdt. Since we’ve separated our variables y and t, we can now integrate: ∫dyy=∫kdt. lny=kt+C. To isolate for y, we’ll need to put both sides as a power of e: elny=ekt+C y=ekt+C=ekt⋅eC=ekt⋅C=Cekt. We can now...
Answer: D You should expect to be asked to interpret information on the AP Calculus AB exam. For this question, since H(t) is the temperature of a room (in ºF) t minutes after a thermostat is adjusted, H′(t) would be the changein the temperature of the room per minute, tminutes after the thermostat is adjusted. So, if H′(5)=2means that 5 minutes af...
Answer: B Though this question allows the use of a calculator, we’ll still need to do quite a few calculations by hand. First, recall the relationship between position, velocity, and acceleration: x”(t)=v′(t)=a(t). So, to get to the position function, we’ll need to integrate acceleration twice. v(t)=∫a(t)dt=∫−6t2−tdt=−2t3−12t2+C. From the problem, ...
Answer: A For related rates problems, it’s helpful to start with a familiar formula. In this case, since we’re given information about the volume of a sphere, let’s use that formula: V=43πr3 Now, we can differentiate with respect to time, t: dVdt=4πr2⋅drdt We know that dVdt=2πand r=5, so we can solve for drdt: 2π=4π(5)2⋅drdt⇒drdt=1/50. Next, we’ll ...
The AP Calculus AB Exam has consistent question types, weighting, and scoring guidelines every year, so you and your students know what to expect on exam day. Section I: Multiple Choice. 45 Questions | 1 Hour 45 minutes | 50% of Exam Score. Part A: 30 questions; 60 minutes (calculator not permitted).
Real AP Past Papers with Multiple-Choice Questions. The AP Calculus AB exam has two sections: Section I contains 45 multiple-choice questions for which you are given 105 minutes to complete. Section II contains 6 free-response questions for which you are given 90 minutes to complete.
The AP Calculus AB and AP Calculus BC Course and Exam Description, which is out now, includes that curriculum framework, along with a new, unique set of exam questions.
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The AP Calculus AB Exam will test your understanding of the mathematical concepts covered in the course units, as well as your ability to determine the proper formulas and procedures to use to solve problems and communicate your work with the correct notations.
AP Calculus AB is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore ...
