weirdness in the ap calculus ab exam

someone asked me recently about some problems in the college board's advanced placement calculus ab exam. they were in a non-calculator section, and required one to find indefinite integrals. they were all multiple-choice questions. i found that to be weird. do you?

btw, i think that the ap calculus ab exam is generally a good test of one's understanding of basic calculus, not merely of one's ability to apply canned formulas.

WillyNilly wrote:someone asked me recently about some problems in the college board's advanced placement calculus ab exam. they were in a non-calculator section, and required one to find indefinite integrals. they were all multiple-choice questions. i found that to be weird. do you?

btw, i think that the ap calculus ab exam is generally a good test of one's understanding of basic calculus, not merely of one's ability to apply canned formulas.

i don't see a problem with this. indefinite integrals do not require a calculator. they are multiple choice questions because the examiner wants the student to check the answer he is obtaining with the four or five given answers, one of which is the correct answer. this is to avoid the student making some silly mistake. it also helps the examiner by making it quicker to check the answer sheets and also avoiding the need to give partial marks (in the case of some silly mistakes) which can involve subjectivity.
Incidentally, the Voyage 200 calculator from Texas Instruments will compute indefinite integrals. I do not know of any other tool (including MATLAB) which can compute indefinite integrals--they can all compute definite integrals.

Rashmun wrote:

WillyNilly wrote:someone asked me recently about some problems in the college board's advanced placement calculus ab exam. they were in a non-calculator section, and required one to find indefinite integrals. they were all multiple-choice questions. i found that to be weird. do you?

btw, i think that the ap calculus ab exam is generally a good test of one's understanding of basic calculus, not merely of one's ability to apply canned formulas.

i don't see a problem with this. indefinite integrals do not require a calculator. they are multiple choice questions because the examiner wants the student to check the answer he is obtaining with the four or five given answers, one of which is the correct answer. this is to avoid the student making some silly mistake. it also helps the examiner by making it quicker to check the answer sheets and also avoiding the need to give partial marks (in the case of some silly mistakes) which can involve subjectivity.
Incidentally, the Voyage 200 calculator from Texas Instruments will compute indefinite integrals. I do not know of any other tool (including MATLAB) which can compute indefinite integrals--they can all compute definite integrals.

to choose the correct answer, one only needs to find the answer choice whose derivative is the integrand, the function that is to be integrated. thus it doesn't necessarily test the student's skill in integration, but it can test his/her understanding of the fundamental theorem of calculus.

WillyNilly wrote:

Rashmun wrote:

WillyNilly wrote:someone asked me recently about some problems in the college board's advanced placement calculus ab exam. they were in a non-calculator section, and required one to find indefinite integrals. they were all multiple-choice questions. i found that to be weird. do you?

btw, i think that the ap calculus ab exam is generally a good test of one's understanding of basic calculus, not merely of one's ability to apply canned formulas.

i don't see a problem with this. indefinite integrals do not require a calculator. they are multiple choice questions because the examiner wants the student to check the answer he is obtaining with the four or five given answers, one of which is the correct answer. this is to avoid the student making some silly mistake. it also helps the examiner by making it quicker to check the answer sheets and also avoiding the need to give partial marks (in the case of some silly mistakes) which can involve subjectivity.
Incidentally, the Voyage 200 calculator from Texas Instruments will compute indefinite integrals. I do not know of any other tool (including MATLAB) which can compute indefinite integrals--they can all compute definite integrals.

to choose the correct answer, one only needs to find the answer choice whose derivative is the integrand, the function that is to be integrated. thus it doesn't necessarily test the student's skill in integration, but it can test his/her understanding of the fundamental theorem of calculus.

I see your point. One other thing to consider though would be time constraints in the exam. Your method means integrating the function and then differentiating it again. This is suitable for assignment problems but may not be appropriate for a quiz or an exam in which every minute is important.

Rashmun wrote:

WillyNilly wrote:

Rashmun wrote:

WillyNilly wrote:someone asked me recently about some problems in the college board's advanced placement calculus ab exam. they were in a non-calculator section, and required one to find indefinite integrals. they were all multiple-choice questions. i found that to be weird. do you?

btw, i think that the ap calculus ab exam is generally a good test of one's understanding of basic calculus, not merely of one's ability to apply canned formulas.

i don't see a problem with this. indefinite integrals do not require a calculator. they are multiple choice questions because the examiner wants the student to check the answer he is obtaining with the four or five given answers, one of which is the correct answer. this is to avoid the student making some silly mistake. it also helps the examiner by making it quicker to check the answer sheets and also avoiding the need to give partial marks (in the case of some silly mistakes) which can involve subjectivity.
Incidentally, the Voyage 200 calculator from Texas Instruments will compute indefinite integrals. I do not know of any other tool (including MATLAB) which can compute indefinite integrals--they can all compute definite integrals.

to choose the correct answer, one only needs to find the answer choice whose derivative is the integrand, the function that is to be integrated. thus it doesn't necessarily test the student's skill in integration, but it can test his/her understanding of the fundamental theorem of calculus.

I see your point. One other thing to consider though would be time constraints in the exam. Your method means integrating the function and then differentiating it again. This is suitable for assignment problems but may not be appropriate for a quiz or an exam in which every minute is important.

one only needs to differentiate the function given in each answer choice, then check whether or not the result is the same as the integrand, the function given within the integral; one would not need to integrate anything at all.

yes, time is a factor because, in the worst case, one may need to check five answer choices. on the other hand, one usually needs more time to integrate than to differentiate, and there's no certainty of ever finding a given integral.

WillyNilly wrote:

Rashmun wrote:

WillyNilly wrote:

Rashmun wrote:

WillyNilly wrote:someone asked me recently about some problems in the college board's advanced placement calculus ab exam. they were in a non-calculator section, and required one to find indefinite integrals. they were all multiple-choice questions. i found that to be weird. do you?

btw, i think that the ap calculus ab exam is generally a good test of one's understanding of basic calculus, not merely of one's ability to apply canned formulas.

i don't see a problem with this. indefinite integrals do not require a calculator. they are multiple choice questions because the examiner wants the student to check the answer he is obtaining with the four or five given answers, one of which is the correct answer. this is to avoid the student making some silly mistake. it also helps the examiner by making it quicker to check the answer sheets and also avoiding the need to give partial marks (in the case of some silly mistakes) which can involve subjectivity.
Incidentally, the Voyage 200 calculator from Texas Instruments will compute indefinite integrals. I do not know of any other tool (including MATLAB) which can compute indefinite integrals--they can all compute definite integrals.

to choose the correct answer, one only needs to find the answer choice whose derivative is the integrand, the function that is to be integrated. thus it doesn't necessarily test the student's skill in integration, but it can test his/her understanding of the fundamental theorem of calculus.

I see your point. One other thing to consider though would be time constraints in the exam. Your method means integrating the function and then differentiating it again. This is suitable for assignment problems but may not be appropriate for a quiz or an exam in which every minute is important.

one only needs to differentiate the function given in each answer choice, then check whether or not the result is the same as the integrand, the function given within the integral; one would not need to integrate anything at all.

yes, time is a factor because, in the worst case, one may need to check five answer choices. on the other hand, one usually needs more time to integrate than to differentiate, and there's no certainty of ever finding a given integral.

you are right.