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首页AP MATH CALCULUS AB
AP CALCULUS MATH AB AP courses in calculus consist of a full high school academic year of work and are comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement, or both from institutions of higher learning.
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CALCULUS
CALCULUS AB
CALCULUS BC
Course Description
E f f e c t i v e F a l l 2 0 1 2
AP Course Descriptions are updated regularly. Please visit AP Central
®
(apcentral.collegeboard.org) to determine whether a more recent Course
Description PDF is available.
The College Board
The College Board is a mission-driven not-for-profit organization that connects students to college
success and opportunity. Founded in 1900, the College Board was created to expand access
to higher education. Today, the membership association is made up of more than 5,900 of the
world’s leading educational institutions and is dedicated to promoting excellence and equity in
education. Each year, the College Board helps more than seven million students prepare for a
successful transition to college through programs and services in college readiness and college
success — including the SAT
®
and the Advanced Placement Program
®
. The organization also
serves the education community through research and advocacy on behalf of students, educators,
and schools.
For further information, visit www.collegeboard.org.
AP Equity and Access Policy
The College Board strongly encourages educators to make equitable access a guiding principle
for their AP programs by giving all willing and academically prepared students the opportunity
to participate in AP. We encourage the elimination of barriers that restrict access to AP for
students from ethnic, racial, and socioeconomic groups that have been traditionally underserved.
Schools should make every effort to ensure their AP classes reflect the diversity of their student
population. The College Board also believes that all students should have access to academically
challenging course work before they enroll in AP classes, which can prepare them for AP success.
It is only through a commitment to equitable preparation and access that true equity and
excellence can be achieved.
AP Course Descriptions
AP Course Descriptions are updated regularly. Please visit AP Central
®
(apcentral.collegeboard.org) to determine whether a more recent Course Description
PDF is available.
© 2012 The College Board. College Board, ACCUPLACER, Advanced Placement Program, AP, AP Central, SAT, SpringBoard, and
the acorn logo are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of the College Board and
National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. (Visit the
College Board on the Web: www.collegeboard.org.)
52437_MusicTheory_Covers.indd 4 1/5/12 10:55 AM
i
Contents
About the AP Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Offering AP Courses and Enrolling Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
How AP Courses and Exams Are Developed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
How AP Exams Are Scored . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Additional Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
AP Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
The Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Topic Outline for Calculus AB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Topic Outline for Calculus BC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Use of Graphing Calculators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Graphing Calculator Capabilities for the Exams . . . . . . . . . . . . . . . . . . . . . . . . . 14
Technology Restrictions on the Exams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Showing Work on the Free-Response Sections . . . . . . . . . . . . . . . . . . . . . . . . . . 15
The Exams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Calculus AB Subscore for the Calculus BC Exam . . . . . . . . . . . . . . . . . . . . . . . . 17
Calculus AB: Section I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Part A Sample Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Part B Sample Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Answers to Calculus AB Multiple-Choice Questions . . . . . . . . . . . . . . . . . 27
Calculus BC: Section I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Part A Sample Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Part B Sample Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Answers to Calculus BC Multiple-Choice Questions . . . . . . . . . . . . . . . . . 39
Calculus AB and Calculus BC: Section II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Instructions for Section II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Calculus AB Sample Free-Response Questions . . . . . . . . . . . . . . . . . . . . . . . . 42
Calculus BC Sample Free-Response Questions . . . . . . . . . . . . . . . . . . . . . . . . 48
Teacher Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
AP Central (apcentral.collegeboard.org) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Additional Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
© 2012 The College Board. Visit the College Board on the Web: www.collegeboard.org.
BLANK PAGE ii
1
1
About the AP
®
Program
AP
®
enables students to pursue college-level studies while still in high school. Through
more than 30 courses, each culminating in a rigorous exam, AP provides willing and
academically prepared students with the opportunity to earn college credit, advanced
placement, or both. Taking AP courses also demonstrates to college admission officers
that students have sought out the most rigorous course work available to them.
Each AP course is modeled upon a comparable college course, and college and
university faculty play a vital role in ensuring that AP courses align with college-level
standards. Talented and dedicated AP teachers help AP students in classrooms around
the world develop and apply the content knowledge and skills they will need in college.
Each AP course concludes with a college-level assessment developed and scored
by college and university faculty as well as experienced AP teachers. AP Exams
are an essential part of the AP experience, enabling students to demonstrate their
mastery of college-level course work. More than 90 percent of four-year colleges
and universities in the United States grant students credit, placement, or both on the
basis of successful AP Exam scores. Universities in more than 60 countries recognize
AP Exam scores in the admission process
and/or award credit and placement for
qualifying scores. Visit www.collegeboard.org/ap/creditpolicy to view AP credit and
placement policies at more than 1,000 colleges and universities.
Performing well on an AP Exam means more than just the successful completion
of a course; it is a pathway to success in college. Research consistently shows that
students who score a 3 or higher on AP Exams typically experience greater academic
success in college and are more likely to graduate on time than otherwise comparable
non-AP peers. Additional AP studies are available at www.collegeboard.or g/
apresearchsummaries.
Offering AP Courses and Enrolling Students
This course description details the essential information required to understand the
objectives and expectations of an AP course. The AP Program unequivocally supports
the principle that each school develops and implements its own curriculum that will
enable students to develop the content knowledge and skills described here.
Schools wishing to offer AP courses must participate in the AP Course Audit, a
process through which AP teachers’ syllabi are reviewed by college faculty. The AP
Course Audit was created at the request of College Board members who sought
a means for the College Board to pr ovide teachers and administrators with clear
guidelines on curricular and resource requirements
for AP courses and to help
colleges and universities validate courses marked “AP” on students’ transcripts.
This process ensures that AP teachers’ syllabi meet or exceed the curricular and
resource expectations that college and secondary school faculty have established for
college-level courses. For more information on the AP Course Audit, visit
www.collegeboard.or g/apcourseaudit.
52437_AP_MusicTheory_Press.indd 1 1/5/12 10:44 AM
© 2012 The College Board. Visit the College Board on the Web: www.collegeboard.org.
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