# AP Calculus AB Free Response Questions

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This is 15 questions styled after the released AP questions. Eight of these questions are calculator and 7 are non-calculator.

Each of these questions is 3 parts: the question, the scoring guidelines, and a blank answer sheet for students to use. All are out of 9 points. (They are all posted separately also.)

These questions are on subjects such as: area/volume, velocity/acceleration, slope fields, related rates, trapezoidal sums, rates, implicit differentiation, continuity, and critical and inflection points.

3 questions are area/volume - 2 of these are calculator questions that ask for area, volume when rotated about a line, and volume when the shape is a square and perpendicular to the axis. The non-calculator question also asks for area and to set up volume equations, but also asks students to find k where y=k divides the area into equal parts.

2 questions are trapezoidal sums - both calculator questions - students determine rate of changes, averages using the trapezoidal sums, difference between 2 objects, and explaining the meanings.

2 rate questions - both calculator and give rate equations. One of the questions uses km/h and has students determine the number of km, the number of liters/time (chain rule), and the number of liters/km. The second question is water leaking out of a pool and being put back into the pool. Students will determine the rate of gallons per hour per hour, how much the pool is losing and the maximum in the pool.

2 velocity/acceleration - both calculator questions - Students are given a velocity equation and they are to determine total distance, speed, acceleration, where a particle is changing direction, and increasing and decreasing.

1 slope field - non-calculator - Students will sketch the direction field, describe slopes, and determine a particular solution.

2 Related Rates - non-calculator - One question gives a rate equation where students will determine increasing, decreasing, second derivative, describe a graph, and find a particular solution. The second question has a cylindrical candle where students have to show the rate of the change in height, find a particular solution, and how many hours it will take to burn out.

1 implicit - non-calculator - Students will show the derivative, write an equation of the tangent line, a horizontal tangent line, and determine the second derivative.

1 Derivatives using the natural log - non-calculator - Students will write an equation of the tangent line, determine critical points, maximum and minimums, and find points of inflection.

1 Continuity using Limits - Students will find the derivative of a square root function, write an equation of a tangent line, determine if it is continuous using the definition of continuous (limits), and integrate using u-substitution.
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60 pages
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