AP Calculus BC Exam Format



AP Calculus BC Exam Format

Multiple Choice (Section 1)

Part A

28 questions…………………………………………………..55 minutes

No calculator allowed.

Part B

17 Questions …………………………….…………………..50 minutes

Graphing calculator required.

Number correct multiplied by 1.2 to get score/54

Free Response (Section II)

Part A

2 Questions ………………………………………………...30 minutes

Graphing calculator required

Part B

4 Questions ……………………………………………….60 minutes

No calculator allowed.

Total points /54

Section 1 + Section 2 = score/108

If you complete part A of the FR before the 30 minutes is over, you may not begin part B until you are told that you may do so. In other words, you have to wait until the 30 minutes is up before you can begin part B.

After the completion of part A for the FR, you may go back and work on the problems in part A but you may not use your calculator.

All free-response questions appear in the Section II: Free Response exam booklet.

Part B questions (calculator not permitted) are sealed within the Section II exam booklet. After students complete Part A (graphing calculator required), calculators are put away. Then students are instructed to break the seals on the portion of the exam booklet that contains Part B questions and complete those questions. Students may go back to Part A questions if they wish, but they may not use their calculators.

Students write their responses in the spaces indicated in the Section II exam booklet. Notes may be written in the areas of the exam booklet not designated for answers.

Calculus AB Subscore for the Calculus BC Exam

A Calculus AB subscore is reported based on performance on the portion of the exam devoted to Calculus AB topics (approximately 60 percent of the exam). The Calculus AB subscore is designed to give colleges and universities more information about the student. Although each college and university sets its own policy for awarding credit and/or placement for AP Exam scores, it is recommended that institutions apply the same policy to the Calculus AB subscore that they apply to the Calculus AB score. Use of the subscore in this manner is consistent with the philosophy of the courses, since common topics are tested at the same conceptual level in both Calculus AB and Calculus BC.

Tips for Students from the College Board Website

Show all work.

Remember that the grader is not really interested in finding out the answer to the problem. The grader is interested in seeing if you know how to solve the problem.

Do not round partial answers.

Store them in your calculator so that you can use them unrounded in further calculations.

Do not let the points at the beginning keep you from getting the points at the end.

If you can do part (c) without doing (a) and (b), do it. If you need to import an answer from part (a), make a credible attempt at part (a) so that you can import the (possibly wrong) answer and get your part (c) points.

If you use your calculator to solve an equation, write the equation first.

An answer without an equation will not get full credit, even if it is correct.

If you use your calculator to find a definite integral, write the integral first.

An answer without an integral will not get full credit, even if it is correct.

Do not waste time erasing bad solutions.

If you change your mind, simply cross out the bad solution after you have written the good one. Crossed-out work will not be graded. If you have no better solution, leave the old one there. It might be worth a point or two.

Do not use your calculator for anything except:

(a) graph functions, (b) compute numerical derivatives, (c) compute definite integrals, and (d) solve equations. In particular, do not use it to determine max/min points, concavity, inflection points, increasing/decreasing, domain, and range. (You can explore all these with your calculator, but your solution must stand alone.)

Be sure you have answered the problem.

For example, if it asks for the maximum value of a function, do not stop after finding the x at which the maximum value occurs. Be sure to express your answer in correct units if units are given.

If they ask you to justify your answer, think about what needs justification.

They are asking you to say more. If you can figure out why, your chances are better of telling them what they want to hear. For example, if they ask you to justify a point of inflection, they are looking to see if you realize that a sign change of the second derivative must occur.

Top Ten Student Errors

1. [pic]is a point of inflection.

2. [pic] is a maximum (minimum) [pic]

3. Average rate of change of f on [a, b] is [pic]

4. Volume by washers is [pic].

5. Separable differential equations can be solved without separating the variables.

6. Omitting the constant of integration, especially in initial value problems.

7. Graders will assume the correct antecedents for all pronouns used in justifications.

8. If the correct answer came from your calculator, the grader will assume your setup was correct.

9. Universal logarithmic antidifferentiation: [pic].

10. [pic]and other Chain Rule errors.

FAQ: What happens if a student provides two different solutions for the same question?

Answer: If it is not clear that the student has abandoned one solution attempt for another, Readers are usually instructed to score both solutions, find the arithmetic mean of the two scores, and round the resulting mean down to the nearest whole number. For example, if the two solutions are scored 1 and 4 points, respectively, the student is awarded 2 points (the mean, 2.5, is rounded down).

FAQ: What happens if a student provides a perfectly correct final answer with no supporting work?

Answer: Questions on the free-response section of the exam usually require supporting work to obtain an answer. On this section of the exam, students are expected to show the reasoning and methods that lead to an answer. Therefore, an isolated or separate answer without any supporting reasoning or computations usually earns no credit. In addition, an incorrect answer without supporting work will not earn any partial credit.

Comment: When instructed to justify an answer, students are expected to provide an explanation of the mathematical basis for their results or conclusions. For example, to justify the location of a relative extremum of a function, a student could invoke the First or Second Derivative Test accompanied by evidence that the hypotheses are satisfied. In other cases, a student could show that the hypotheses are satisfied for the relevant theorem, such as the Intermediate Value Theorem or the Mean Value Theorem. Statements of the form “from my calculator I can see that ...” are not sufficient.

FAQ: Are there any computations that a student can perform with the calculator without need for showing intermediate computational steps?

Answer: Yes. On Part A (the first two free-response questions), students are assumed to have a graphing calculator that can 1) graph a function, 2) numerically solve an equation, 3) numerically compute the value of a derivative at a point, and 4) numerically calculate the value of a definite integral. A student can freely use a calculator for any of these purposes without showing any intermediate work, as long as the student clearly indicates using mathematical language (not calculator syntax) how the calculator was used (referred to in the directions as the “setup”). With respect to the four capabilities just mentioned, this means: 1) labeling the function, the axes, and the scaling for a graph sketched from the calculator, 2) stating the equation that was solved, 3) stating the function and the point at which its numerical derivative was calculated, and 4) stating the definite integral that has been calculated. Note, however, that a graph reproduced from a calculator is not sufficient as the basis of a mathematical argument. (E.g., a graph obtained from a calculator is not sufficient justification for the existence of an extremum.) Although there are multiple calculator methods for solving an equation, it is recommended that students look at the graphs of functions to help orient themselves toward identifying the possible solutions or the number of solutions. This method provides students with a visualization of all the solutions, which makes finding the appropriate solution more efficient. On the graph screen, students should use “intersect” or “root/zero” commands. Students should avoid the use of tracing along a graph, which might not produce the required accuracy. Information from this graphical approach to solving an equation should be used before utilizing the calculator’s numerical or symbolic “solver” commands.

FAQ: Are sign charts acceptable in justifying either a local or an absolute extremum of a function?

Answer: A sign chart is an annotated number line that relates the graphical behavior (increasing/decreasing, concave up/down) of one function with the sign behavior (positive/negative) of another. Sign charts are a useful tool to investigate and summarize the behavior of a function. However, sign charts, by themselves, will not be accepted as a sufficient response when a question asks for a justification for the existence of either a local or an absolute extremum of a function at a particular point in its domain.

FAQ: Does a definite integral count as an unsimplified final numerical answer?

Answer: No. Unless the question specified that the answer be reported as an integral expression without further evaluation, a student would be expected to compute the value of a definite integral.

FAQ: MUST answers reported in decimal form be rounded to only three decimal places?

Answer: Definitely not—reporting more accuracy is not penalized! The standard refers to the minimal accuracy expected in a final decimal answer. It should not be read as a requirement to round or truncate decimal answers, but rather to record decimal answers accurately to at least three places after the decimal point.

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