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IRS.gov Website
Publication 970
taxmap/pubs/p970-005.htm#en_us_publink1000204370

Who Is an Eligible Student(p14)

rule
To claim the American opportunity credit, the student for whom you pay qualified education expenses must be an eligible student. This is a student who meets all of the following requirements. These requirements are also shown in Figure 2-2, Who is an Eligible Student for the American Opportunity Credit, later.
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Completion of first 4 years.(p14)

rule
A student who was awarded 4 years of academic credit for postsecondary work completed before 2011 has completed the first 4 years of postsecondary education. This student generally would not be an eligible student for purposes of the American opportunity credit.
taxmap/pubs/p970-005.htm#en_us_publink1000204372
Exception.(p14)
Any academic credit awarded solely on the basis of the student's performance on proficiency examinations is disregarded in determining whether the student has completed 4 years of postsecondary education.
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Enrolled at least half-time.(p14)

rule
A student was enrolled at least half-time if the student was taking at least half the normal full-time work load for his or her course of study.
The standard for what is half of the normal full-time work load is determined by each eligible educational institution. However, the standard may not be lower than any of those established by the U.S. Department of Education under the Higher Education Act of 1965.
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taxmap/pubs/p970-005.htm#en_us_publink1000236164
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Example 1.(p14)

Mack graduated from high school in June 2010. In September, he enrolled in an undergraduate degree program at College U, and attended full-time for both the 2010 fall and 2011 spring semesters. For the 2011 fall semester, Mack was enrolled less than half-time. Because Mack was enrolled in an undergraduate degree program on at least a half-time basis for at least one academic period that began during 2010 and at least one academic period that began during 2011, he is an eligible student for tax years 2010 and 2011 (including the 2011 fall semester when he enrolled at College U on less than a half-time basis).
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Example 2.(p14)

After taking classes at College V on a part-time basis for a few years, Shelly became a full-time student for the 2011 spring semester. College V classified Shelly as a second-semester senior (fourth year) for the 2011 spring semester and as a first-semester graduate student (fifth year) for the 2011 fall semester. Because College V did not classify Shelly as having completed the first 4 years of postsecondary education as of the beginning of 2011, Shelly is an eligible student for tax year 2011. Therefore, the qualified education expenses paid for the 2011 spring semester and the 2011 fall semester are taken into account in calculating the American opportunity credit for 2011.
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Example 3.(p14)

During the 2010 fall semester, Larry was a high school student who took classes on a half-time basis at College X. Larry was not enrolled as part of a degree program at College X because College X only admits students to a degree program if they have a high school diploma or equivalent. Because Larry was not enrolled in a degree program at College X during 2010, Larry was not an eligible student for tax year 2010.
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Example 4.(p14)

The facts are the same as in Example 3. During the 2011 spring semester, Larry again attended College X but not as part of a degree program. Larry graduated from high school in June 2011. For the 2011 fall semester, Larry enrolled as a full-time student in College X as part of a degree program, and College X awarded Larry credit for his prior coursework at College X. Because Larry was enrolled in a degree program at College X for the 2011 fall term on at least a half-time basis, Larry is an eligible student for all of tax year 2011. Therefore, the qualified education expenses paid for classes taken at College X during both the 2011 spring semester (during which Larry was not enrolled in a degree program) and the 2011 fall semester are taken into account in computing any American opportunity credit.
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Example 5.(p14)

Dee graduated from high school in June 2010. In January 2011, Dee enrolled in a 1-year postsecondary certificate program on a full-time basis to obtain a certificate as a travel agent. Dee completed the program in December 2011, and was awarded a certificate. In January 2012, she enrolled in a 1-year postsecondary certificate program on a full-time basis to obtain a certificate as a computer programmer. Dee is an eligible student for both tax years 2011 and 2012 because she meets the degree requirement, the work load requirement, and the year of study requirement for those years.