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Free-Response Questions and Scoring Information Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. If you are using assistive technology and need help accessing these PDFs in another format, contact Services for Students with Disabilities at 212-713-8333 or by email at [email protected] .
- 2007 Scoring Statistics
Scoring statistics for the 2007 AP Calculus AB Exam. AP at a...
- The Exam
The AP Calculus AB Exam has consistent question types,...
- 2007 Scoring Statistics
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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).
College Board AP® Calculus AB Exam Questions Past paper and exam-style questions organised by topic, with student-friendly answers written by teachers and examiners. Unit 1: Limits & Continuity
AP Calculus AB Exam and AP Calculus BC Exam, and they serve as examples of the types of questions that appear on the exam. Each question is accompanied by a table containing the main learning objective(s), essential knowledge statement(s), and Mathematical Practices for AP Calculus that the question addresses.
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This PDF review packet from the College Board includes 16 AP Calculus AB multiple choice questions. All of this material is based on the revised calculus curriculum. Course Description
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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.
