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AP Calculus BC
Mathematics Fairfield Public Schools AP Calculus BC AP Calculus BC BOE Approved 04/08/2014 1 AP CALCULUS BC Critical Areas of Focus Advanced Placement Calculus BC consists of a full year of college calculus. This course is intended for students who have demonstrated exceptional ability and achievement in mathematics, and have successfully completed an accelerated program. To be successful, students must be motivated learners who have mathematical intuition, a solid background in the topics studied in previous courses and the persistence to grapple with complex problems. Students in the course are expected to take the Advanced Placement exam in May, at a fee, for credit and/or placement consideration by those colleges which accept AP credit. The critical areas of focus for this course will be in three areas: (a) functions, graphs and limits, (b) differential calculus (the derivative and its applications), and (c) integral calculus (anti-derivatives and their applications). 1) Students will build upon their understanding of functions from prior mathematics courses to determine continuity and the existence of limits of a function both graphically and by the formal definitions of continuity and limits. They will use the understanding of limits and continuity to analyze the behavior of functions as they approach a discontinuity or as the function approaches ± . 2) Students will analyze the formal definition of a derivate and the conditions upon which a derivatve exists. They will interpret the derivative as the slope of a tangent line and the instantaneous rate of change of the function at a specific value. Students will distinguish between a tanget line and a secant line. -
The Relationship of PSAT/NMSQT Scores and AP Examination Grades
Research Notes Office of Research and Development RN-02, November 1997 The Relationship of PSAT/NMSQT Scores and AP® Examination Grades he PSAT/NMSQT, which measures devel- Recent analyses have shown that student per- oped verbal and quantitative reasoning, as formance on the PSAT/NMSQT can be useful in Twell as writing skills generally associated identifying additional students who may be suc- with academic achievement in college, is adminis- cessful in AP courses. PSAT/NMSQT scores can tered each October to nearly two million students, identify students who may not have been initially the vast majority of whom are high school juniors considered for an AP course through teacher or and sophomores. PSAT/NMSQT information has self-nomination or other local procedures. For been used by high school counselors to assist in many AP courses, students with moderate scores advising students in college planning, high school on the PSAT/NMSQT have a high probability of suc- course selection, and for scholarship awards. In- cess on the examinations. For example, a majority formation from the PSAT/NMSQT can also be very of students with PSAT/NMSQT verbal scores of useful for high schools in identifying additional 46–50 received grades of 3 or above on nearly all of students who may be successful in Advanced the 29 AP Examinations studied, while over one- Placement courses, and assisting schools in deter- third of students with scores of 41–45 achieved mining whether to offer additional Advanced grades of 3 or above on five AP Examinations. Placement courses. There are substantial variations across AP subjects that must be considered. -
Calculus Terminology
AP Calculus BC Calculus Terminology Absolute Convergence Asymptote Continued Sum Absolute Maximum Average Rate of Change Continuous Function Absolute Minimum Average Value of a Function Continuously Differentiable Function Absolutely Convergent Axis of Rotation Converge Acceleration Boundary Value Problem Converge Absolutely Alternating Series Bounded Function Converge Conditionally Alternating Series Remainder Bounded Sequence Convergence Tests Alternating Series Test Bounds of Integration Convergent Sequence Analytic Methods Calculus Convergent Series Annulus Cartesian Form Critical Number Antiderivative of a Function Cavalieri’s Principle Critical Point Approximation by Differentials Center of Mass Formula Critical Value Arc Length of a Curve Centroid Curly d Area below a Curve Chain Rule Curve Area between Curves Comparison Test Curve Sketching Area of an Ellipse Concave Cusp Area of a Parabolic Segment Concave Down Cylindrical Shell Method Area under a Curve Concave Up Decreasing Function Area Using Parametric Equations Conditional Convergence Definite Integral Area Using Polar Coordinates Constant Term Definite Integral Rules Degenerate Divergent Series Function Operations Del Operator e Fundamental Theorem of Calculus Deleted Neighborhood Ellipsoid GLB Derivative End Behavior Global Maximum Derivative of a Power Series Essential Discontinuity Global Minimum Derivative Rules Explicit Differentiation Golden Spiral Difference Quotient Explicit Function Graphic Methods Differentiable Exponential Decay Greatest Lower Bound Differential -
Should You Take AP Calculus AB Or
Author: Success Pathway Email: [email protected] Calculus AB and BC’s significant distinction lies in the range of what you'll learn, not the difficulty level. Although both AP Calculus classes are intended to be university-level courses, Calculus AB utilizes one year to cover the equivalent of one semester of Calculus in a college semester. Calculus BC covers a total of two semesters. Both courses follow curriculum created by The College Board and requires students to take the AP exam in May. A student cannot take both AP Calculus AB and BC in the same year. AP Calculus AB teaches students Precalculus (A) and the beginning part of Calculus I (B). AP Calculus BC will also cover Calculus I (B) and part of Calculus II (C). Some of the topics covered in Calculus AB include functions, graphs, derivatives and applications, integrals and its application. On the contrary, Calculus BC will cover all of the above topics, along with polynomial approximations, Taylor series, and series of constants. AP Calculus BC Taking Precalculus and Calculus BC can prove to be a hard challenge. If a student is doing well in Precalculus and wants to pursue a degree in any math dominant career such as Engineering, they may want to consider taking Calculus BC. They will need to continue into more advanced math courses and Precalculus is a great prerequisite. They may want to consider taking AP Statistics, if their schedule allows. Taking AP Calculus BC will give students the opportunity to challenge their math skills. Provided a student passes the Calculus BC exam, they can transfer more credits to their future college than if they took Calculus AB. -
AP Macroeconomics: Vocabulary 1. Aggregate Spending (GDP)
AP Macroeconomics: Vocabulary 1. Aggregate Spending (GDP): The sum of all spending from four sectors of the economy. GDP = C+I+G+Xn 2. Aggregate Income (AI) :The sum of all income earned by suppliers of resources in the economy. AI=GDP 3. Nominal GDP: the value of current production at the current prices 4. Real GDP: the value of current production, but using prices from a fixed point in time 5. Base year: the year that serves as a reference point for constructing a price index and comparing real values over time. 6. Price index: a measure of the average level of prices in a market basket for a given year, when compared to the prices in a reference (or base) year. 7. Market Basket: a collection of goods and services used to represent what is consumed in the economy 8. GDP price deflator: the price index that measures the average price level of the goods and services that make up GDP. 9. Real rate of interest: the percentage increase in purchasing power that a borrower pays a lender. 10. Expected (anticipated) inflation: the inflation expected in a future time period. This expected inflation is added to the real interest rate to compensate for lost purchasing power. 11. Nominal rate of interest: the percentage increase in money that the borrower pays the lender and is equal to the real rate plus the expected inflation. 12. Business cycle: the periodic rise and fall (in four phases) of economic activity 13. Expansion: a period where real GDP is growing. 14. Peak: the top of a business cycle where an expansion has ended. -
The Relationship Between AP® Exam Performance and College Outcomes
RESEaRch REpoRt 2009-4 The Relationship Between AP® Exam Performance and College Outcomes By Krista D. Mattern, Emily J. Shaw, and Xinhui Xiong VALIDITY College Board Research Report No. 2009-4 The Relationship Between AP® Exam Perfomance and College Outcomes Krista D. Mattern, Emily J. Shaw, and Xinhui Xiong The College Board, New York, 2009 Krista D. Mattern is an associate research scientist at the College Board. Emily J. Shaw is an assistant research scientist at the College Board Xinhui Xiong was a graduate student intern at the College Board. Researchers are encouraged to freely express their professional judgment. Therefore, points of view or opinions stated in College Board Reports do not necessarily represent official College Board position or policy. About 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. © 2009 The College Board. College Board, Advanced Placement Program, AP, SAT and the acorn logo are registered trademarks of the College Board. -
Ap Calculus Ab 2018 Elite Student Edition 4Th Edition Pdf, Epub, Ebook
5 STEPS TO A 5: AP CALCULUS AB 2018 ELITE STUDENT EDITION 4TH EDITION PDF, EPUB, EBOOK William Ma | 9781259864001 | | | | | 5 Steps to a 5: AP Calculus AB 2018 Elite Student Edition 4th edition PDF Book Home Learning. Let me know what you think in the contact link below!. The AP score distributions are added live to this page as they are Tweeted. Free delivery worldwide. Want to know my take? Popular Features. Show More. Get ready to ace your AP Microeconomics Exam with this easy-to-follow, multi-platform study guide5 Steps You can find the question. In any economy, the existence of limited resources along with unlimited wants results in the need to make choices. McGraw-Hill Professional Publishing. User account menu. Andrew White 4 months ago 34 minutes views Solution video to the second set of free response , questions ,. High school students studied Newtonian mechanics, electricity and magnetism, fluid mechanics, and thermal physics, waves and optics, and atomic and nuclear physics in preparation for a cumulative exam given each May. Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for Home 1 Books 2. Over AP macroeconomics practice questions to help you with your AP macroeconomics exam prep. You need to take the test seriously but it is a practice test. Sign in to Purchase Instantly. Video Project - See iLearn for Details. Ecology practice questions answers. All of those questions require you to have sufficient knowledge. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. -
Babson Curriculum / Ap Exam Equivalents /Class of 2025
BABSON CURRICULUM / AP EXAM EQUIVALENTS / CLASS OF 2025 Scores of 4 or 5 Only AP INFORMATION BABSON EQUIVALENT COURSE INFORMATION Exam # Exam Title Code Credits Course Title Requirement 14 Art: Studio Art-Drawing Portfolio N/A N/A No Babson Equivalent No Babson Equivalent 15 Art: Studio Art-General Portfolio N/A N/A No Babson Equivalent No Babson Equivalent 20 Biology N/A N/A No Babson Equivalent No Babson Equivalent 66 Calculus AB N/A N/A No Babson Equivalent No Babson Equivalent 69 Calculus AB: subscore grade N/A N/A No Babson Equivalent No Babson Equivalent 68 Calculus BC N/A N/A No Babson Equivalent No Babson Equivalent 25 Chemistry N/A N/A No Babson Equivalent No Babson Equivalent 28 Chinese Language CHN 1200 4 AP Chinese Lang Free Elective 31 Computer Science A N/A N/A No Babson Equivalent No Babson Equivalent 33 Computer Science AB N/A N/A No Babson Equivalent No Babson Equivalent 35 Economics: Macroeconomics ECN 2000 4 AP Macroeconomics Principles of Macroeconomics 34 Economics: Microeconomics SME 2031 3 AP Microeconomics Principles of Microeconomics 36 English Language and Composition WRT 1001 4 AP English Lang&Comp Writing Across Context WRT 1001 or Writing Across Context or 37 English Literature and Composition 4 AP English Lit&Comp LVA 2050 1 2 LVA Intermediate 40 Environmental Science N/A N/A No Babson Equivalent No Babson Equivalent 43 European History HSS 2050 2 4 AP EuroHistory HSS Intermediate 48 French Language FRN 1200 4 AP French Lang Free Elective 51 French Literature FRN 1200 4 AP French Lit Free Elective 55 German -
AP Calculus AB Cram Sheet
ABCramSheet.nb 1 AP Calculus AB Cram Sheet Definition of the Derivative Function: f xh f x f ' (x) = limh0 cccccccccccccccchccccccccccccccc + / + / Definition of Derivative at a Point: f ah f a f ' (a) = limh0 cccccccccccccccchccccccccccccc (note: the first definition results in a function, the second definition results in a number. Also f ah f a note that the difference quotient, cccccccccccccccchccccccccccccc , by itself, represents the average rate of change of f from x = a to x = a + h) + / + / + / + / Interpretations of the Derivative: f ' (a) represents the instantaneous rate of change of f at x = a, the slope of the tangent line to the graph of f at x = a, and the slope of the curve at x = a. Derivative Formulas: (note:a and k are constants) d cccccccdx k 0 d cccccccdx (k·f(x))= k·f ' (x) + / d n n1 cccccccdx f x n f x f ' x d cccccccdx [f(x) ± g(x)] = f ' (x) ± g ' (x) + + // + + // + / d cccccccdx [f(x)·g(x)] = f(x)·g ' (x) + g(x) · f ' (x) d f x g x f ' x f x g ' x cccccccdx cccccccccccg x ccccccccccccccccccccccccccccccccg x 2 cccccccccccccccccc d + / + / + / + / + / ccccccc sin(f(x))+ / = cos (f(x))+ + // ·f ' (x) dx , 0 d cccccccdx cos(f(x)) = -sin(f(x))·f ' (x) d 2 cccccccdx tan(f(x)) = sec f x º f ' x d 1 cccccccdx ln(f(x)) = cccccccccccf x º f ' x + + // + / d f x f x cccccccdx e e +º /f ' x + / d f+x/ f+ x/ cccccccdx a a º ln a º f ' x + / cccccccd sin+/1 f x + / ccccccccccccccccf ' xcccccccccccc dx 2 1 f x + / + / d 1 r f ' x ccccccc cos f x cccccccccccccccc+ + // cccccccccccc dx + / 1 f x 2 + / r + / + + // ABCramSheet.nb 2 d tan1 f x f ' x cccccccdx cccccccccccccccc1 f xcccccc2 d 1 + / 1 ccccccc f x at x +f + a// equals cccccccccccccc at x a dx + / f ' x L'Hopitals's Rule: + / + + // + / f x 0 f ' x If limxa cccccccccccg x cccc0 or cccccc and if limxa ccccccccccccccg ' x exists then f x + / f ' x + / limxa cccccccccccg x + / limxa ccccccccccccccg ' x + / + / + / 0 f x The same+ /rule applies if +you/ get an indeterminate form ( cccc0 or cccccc ) for limx cccccccccccg x as well. -
Ap Calculus Formula List
AP CALCULUS FORMULA LIST 1 n Definition of e:e = lim 1 + n→∞ n ____________________________________________________________________________________ x if x ≥ 0 Absolute Value: x = −x if x < 0 ____________________________________________________________________________________ Definition of the Derivative: fxxfx()()+−∆ fxhfx()() +− fx'() = lim fx '() = lim ∆x→∞ ∆xh →∞ h fa()()+ h − fa fa'() = lim derivativeatxa = h→∞ h fx()()− fa fx'() = lim alternateform x→ a x− a ____________________________________________________________________________________ Definition of Continuity: f is continuous at c iff: (1)f() c is defined (2) limf() x exists x→ c (3) lim fx()()= fc x→ c ____________________________________________________________________________________ fb( ) − fb( ) Average Rate of Change of fx() on [] ab, = b− a ____________________________________________________________________________________ Rolle's Theorem: If f is continuous on [] ab, and differen tiable on ()()() ab, and if fafb= , then there exists a number c on ()() ab, such that fc' = 0. ____________________________________________________________________________________ Mean Value Theorem: If f is continuous on [] ab, and differen tiable on () ab, , then there fb()()− fa exists a number c on ()() ab, such that fc'= . b− a Note : Rolle's Theorem is a special case of The Mean Valu e Theorem fa()()− fb fa()() − fa If fa()()() = fb then fc' = = = 0. ba− ba − Source: adapted from notes by Nancy Stephenson, presented by Joe Milliet at TCU AP Calculus Institute, July 2005 AP Calculus Formula List Math by Mr. Mueller Page 1 of 6 Intermediate Value Theorem: If f is continuous on [] abk, and is any number between fafb()() and , then there is at least one number c between ab and such that fck() = . ____________________________________________________________________________________ Definition of a Critical Number: Let f be defined at cfcf. If '() = 0 or ' is is undefined at cc, then is a criti cal number of f . -
AP Macroeconomics: Updates for 2019-20
AP Macroeconomics: Updates for 2019-20 § To bring you and your students new classroom resources and supports, we’re making updates to AP® Macroeconomics for the 2019-20 school year. § These updates will give you a clearer sense of the content and skills that will be tested on the AP Exam. They’ll also ensure that the exam format remains consistent from year to year. § You won’t need to update your syllabus in the AP Course Audit. § Starting in August, you’ll need to complete a simple digital activation process to access the new resources and help your students register for their exams. Course Updates The CED organizes the course into six commonly taught units. AP Macroeconomics has been updated for the 2019-20 § school year to make things clearer for you and your students. This series of units represents a sequence that is found in widely adopted college textbooks and that many Course and exam information is now clearly AP Macroeconomics teachers have told us they follow: w presented in a course and exam description (CED). Unit 1: Basic Economic Concepts § w Currently, a course description booklet—a very general Unit 2: Economic Indicators and the Business Cycle overview of course content, with a topic outline—is w available to help you plan your instruction. Unit 3: National Income and Price Determination § w Starting in late May 2019, you’ll have access to a course Unit 4: Financial Sector w and exam description (CED) for AP Macroeconomics Unit 5: Long-Run Consequences of that clearly outlines all required course content and Stabilization Policies defines how that content will be assessed on the exam. -
AP Economics/ 10Th - 12Th Grade ______
SCHOOL DISTRICT OF THE CHATHAMS CURRICULUM ______________________________________________________________________________ CONTENT AREA(S): Social Studies COURSE/GRADE LEVEL(S): AP Economics/ 10th - 12th Grade ______________________________________________________________________________ I. Course Overview Advanced Placement Economics provides students with a thorough understanding of the principles and applications of microeconomics and macroeconomics. This rigorous, college-level course, prepares students for both the AP Microeconomics exam and AP Macroeconomics exam. The purpose of microeconomics is to give students a thorough understanding of the principles of economics that apply to the functions of individual decision makers, both consumers and producers, within the economic system. It places primary emphasis on the nature and functions of product markets and includes the study of factor markets and the role of government in promoting greater efficiency and equity in the economy. The purpose of macroeconomics is to give students a greater understanding of the principles of economics that apply to an economic system as a whole. The course places particular emphasis on the study of national income and price-level determination, and also develops students’ familiarity with economic performance measures, the financial sector, stabilization policies, economic growth, and international economics. Advanced Placement Economics students will be challenged to master economic theory in order to analyze and evaluate current economic issues using supply and demand analysis. II. Units of Study Microeconomics Unit 1: Basic Economic Concepts (1.5 weeks) [SC1, SC8, SC9] a. Scarcity b. Three Fundamental Economic Questions c. Factors of Production d. Opportunity Cost and Trade-offs e. Benefits of trade versus being self-sufficient f. Import versus export g. Different Types of Economic Systems h.