AP Statistics Course Description
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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. -
AP Statistics 2021 Free-Response Questions
2021 AP® Statistics Free-Response Questions © 2021 College Board. College Board, Advanced Placement, AP, AP Central, and the acorn logo are registered trademarks of College Board. Visit College Board on the web: collegeboard.org. AP Central is the official online home for the AP Program: apcentral.collegeboard.org. Formulas for AP Statistics I. Descriptive Statistics 2 1 ∑ x 1 2 ∑( x − x ) x = ∑ x = i s = ∑( x − x ) = i ni n x n − 1 i n − 1 yˆ = a + bx y = a + bx 1 xi − x yi − y sy r = ∑ b = r n − 1 sx sy sx II. Probability and Distributions PA( ∩ B) PA( ∪ B )()()(= PA+ PB − PA ∩ B ) PAB()| = PB() Probability Distribution Mean Standard Deviation µ = E( X) = ∑ xP x 2 Discrete random variable, X X i ( i ) σ = ∑ − µ X ( xi X ) Px( i ) If has a binomial distribution µ = np σ = − with parameters n and p, then: X X np(1 p) n x nx− PX( = x) = p (1 − p) x where x = 0, 1, 2, 3, , n If has a geometric distribution 1 1 − p with parameter p, then: µ = σ = X p X PX( = x) = (1 − p) x−1 p p where x = 1, 2, 3, III. Sampling Distributions and Inferential Statistics statistic − parameter Standardized test statistic: standard error of the statistic Confidence interval: statistic ± (critical value )( standard error of statistic ) (observed − expected)2 Chi-square statistic: χ 2 = ∑ expected III. Sampling Distributions and Inferential Statistics (continued) Sampling distributions for proportions: Random Parameters of Standard Error* Variable Sampling Distribution of Sample Statistic For one population: µ = p p(1 − p) pˆ (1 − pˆ ) pˆ σ pˆ = -
Simple Mean Weighted Mean Or Harmonic Mean
MultiplyMultiply oror Divide?Divide? AA BestBest PracticePractice forfor FactorFactor AnalysisAnalysis 77 ––10 10 JuneJune 20112011 Dr.Dr. ShuShu-Ping-Ping HuHu AlfredAlfred SmithSmith CCEACCEA Los Angeles Washington, D.C. Boston Chantilly Huntsville Dayton Santa Barbara Albuquerque Colorado Springs Ft. Meade Ft. Monmouth Goddard Space Flight Center Ogden Patuxent River Silver Spring Washington Navy Yard Cleveland Dahlgren Denver Johnson Space Center Montgomery New Orleans Oklahoma City Tampa Tacoma Vandenberg AFB Warner Robins ALC Presented at the 2011 ISPA/SCEA Joint Annual Conference and Training Workshop - www.iceaaonline.com PRT-70, 01 Apr 2011 ObjectivesObjectives It is common to estimate hours as a simple factor of a technical parameter such as weight, aperture, power or source lines of code (SLOC), i.e., hours = a*TechParameter z “Software development hours = a * SLOC” is used as an example z Concept is applicable to any factor cost estimating relationship (CER) Our objective is to address how to best estimate “a” z Multiply SLOC by Hour/SLOC or Divide SLOC by SLOC/Hour? z Simple, weighted, or harmonic mean? z Role of regression analysis z Base uncertainty on the prediction interval rather than just the range Our goal is to provide analysts a better understanding of choices available and how to select the right approach Presented at the 2011 ISPA/SCEA Joint Annual Conference and Training Workshop - www.iceaaonline.com PR-70, 01 Apr 2011 Approved for Public Release 2 of 25 OutlineOutline Definitions -
College Majors Requiring Statistics Statistics Is Specifically Required in Some Majors, While It Is a Quantitative Methods Requirement in Others
College Majors Requiring Statistics Statistics is specifically required in some majors, while it is a quantitative methods requirement in others. AGRICULTURAL SCIENCES Kinesiology Chemical Engineering Genetics Agricultural and Environmental Plant Movement and Sport Sciences Civil Engineering Geology Sciences Nursing Computer Information Systems Geophysics Agricultural Business Nutrition Computer Science Hydrogeology Agricultural Communication Occupational Health Computer Software Engineering Marine Sciences Agricultural Education Occupational Therapy Construction Science and Mathematical Sciences Agricultural Mechanization Pharmaceutical Sciences Management Mathematics and Business Physical Therapy Electrical Engineering Meteorology Agricultural Systems Management Pre-Pharmacy Engineering Management and Microbiology Protection Agronomy Pre-Rehabilitation Sciences Neuroscience Environmental and Natural Resources Animal and Veterinary Sciences Respiratory Care Physics Environmental Engineering • Animal Agribusiness Speech Language Hearing Planetary Science Industrial Design • Equine Business Pre-Health • Preveterinary and Science BUSINESS Industrial Engineering Accounting Pre-Veterinary Medicine Crop Science Industrial Management Actuarial Science Statistics Culinary Science Industrial Technology and Packaging Advertising SOCIAL STUDIES Dairy Science Landscape Architecture Aviation Management AND THE HUMANITIES Fisheries and Aquatic Sciences Materials Science and Engineering Business Anthropology Food Science Mechanical Engineering Business -
Advanced Placement® Program (AP®)
Advanced Placement® Program (AP®) CHOOSE AP. STAND OUT. Opening Doors to Universities Worldwide Stand Out at University Admission Flexible Courses on Your Choices What Is AP? The College Board Advanced Placement® Program (AP®) Why Do International Schools enables students to take university-level courses and Embrace AP? exams while they’re still in secondary school. Universities worldwide recognize AP in admissions, and some grant credit. Most universities in the U.S. and Canada award credit IT’S RECOGNIZED GLOBALLY. for advanced coursework taken in high school, allowing In addition to almost all universities in the U.S. and students to skip introductory courses in a given subject Canada, over 4,000 universities in more than 60 and thereby save time and money. Through AP courses, countries use AP Exam scores for admissions, students learn to think critically, construct solid arguments, course credits, and/or advanced placement. and see many sides of an issue—skills that prepare them for college and beyond. Taking AP courses demonstrates to IT’S RIGOROUS. college admissions officers that students have sought the AP courses are designed as introductory-level most rigorous curriculum available to them, and research university experiences, based on a learner-centric, indicates that students who score a 3 or higher on an AP rigorous methodology. Exam typically experience greater academic success in college and are more likely to earn a college degree than IT’S EFFECTIVE. non-AP students. Research shows that AP students are more likely QUICK FACTS to succeed in college: Students who earned a 3 or higher on an AP Exam earned higher first-year and § 38 different AP courses in seven subject areas fourth-year GPAs in college than non-AP students are available. -
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. -
Pathway to a Pre-K-12 Future
Transforming Public Education: Pathway to a Pre-K-12 Future September 2011 This report challenges our nation’s policy makers to transform public education by moving from a K-12 to a Pre-K-12 system. This vision is grounded in rigorous research and informed by interviews with education experts, as well as lessons from Pew’s decade-long initiative to advance high-quality pre-kindergarten for all three and four year olds. The report also reflects work by leading scholars and institutions to identify the knowledge and skills students need to succeed in school and the teaching practices that most effectively develop them. Together, these analyses and perspectives form a compelling case for why America’s education system must start earlier, with pre-k, to deliver the results that children, parents and taxpayers deserve. Table of Contents 2 Introduction 24 Interviewees 6 Envisioning the Future of 25 Sidebar Endnotes Pre-K-12 Education 26 Endnotes 12 Pathway to the Pre-K-12 Vision 29 Acknowledgements 23 Conclusion Introduction More than two centuries ago, as he prepared to retire and attitudes rather than scientific evidence about from the presidency, George Washington counseled the children’s development or their potential to benefit young nation to prioritize and advance public education from earlier educational programs. We know now, because, he wrote, “In proportion as the structure of a from more than 50 years of research, that vital learn- government gives force to public opinion, it is essential ing happens before age five. When schooling starts at that public opinion should be enlightened.”1 Today, kindergarten or first grade, it deprives children of the that our public education system is free and open to chance to make the most of this critical period. -
Hydraulics Manual Glossary G - 3
Glossary G - 1 GLOSSARY OF HIGHWAY-RELATED DRAINAGE TERMS (Reprinted from the 1999 edition of the American Association of State Highway and Transportation Officials Model Drainage Manual) G.1 Introduction This Glossary is divided into three parts: · Introduction, · Glossary, and · References. It is not intended that all the terms in this Glossary be rigorously accurate or complete. Realistically, this is impossible. Depending on the circumstance, a particular term may have several meanings; this can never change. The primary purpose of this Glossary is to define the terms found in the Highway Drainage Guidelines and Model Drainage Manual in a manner that makes them easier to interpret and understand. A lesser purpose is to provide a compendium of terms that will be useful for both the novice as well as the more experienced hydraulics engineer. This Glossary may also help those who are unfamiliar with highway drainage design to become more understanding and appreciative of this complex science as well as facilitate communication between the highway hydraulics engineer and others. Where readily available, the source of a definition has been referenced. For clarity or format purposes, cited definitions may have some additional verbiage contained in double brackets [ ]. Conversely, three “dots” (...) are used to indicate where some parts of a cited definition were eliminated. Also, as might be expected, different sources were found to use different hyphenation and terminology practices for the same words. Insignificant changes in this regard were made to some cited references and elsewhere to gain uniformity for the terms contained in this Glossary: as an example, “groundwater” vice “ground-water” or “ground water,” and “cross section area” vice “cross-sectional area.” Cited definitions were taken primarily from two sources: W.B. -
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. -
Graduate School of Education ❖ Department of Learning And
Graduate School of Education Department of Learning and Instruction Teacher Education Institute Math Education For those who hold a valid NYS Initial Teacher Certificate in Mathematics (grades 7-12) and are seeking the Master of Education degree as well as recommendation for the Professional Teacher Certificate in Mathematics (grades 7-12) and the Professional Extension in Mathematics (grades 5-6). Name: ___________________________________________ Person Number: _____________________________________ III. Professional Certification/Master of Education (Grades 7-12, 5-6 extension) Date Credit Gra de EDUCATION ELECTIVES (6 credits ) LAI 514 Adolescent Writing Across Curriculum (Formerly Language, Cognition, and Writing ) NOTE: If you have taken LAI 414 as a UB undergraduate student, please choose a course from one 3 of the Mathematics Education Electives below in place of LAI 514. LAI 552 Mid dle Ch ildh oo d-Adol escent Literacy Methods 3 MATHEMATICS ELECTIVES (Select 12 credits from the following) LAI 544 Teaching of AP Calculus (May also use as Math Ed elective) 3 LAI 545 Problem Solving & Posing in Mathematics (May also use as Math Ed elective) 3 LAI 643 School Math Advanced Standpoint 1 * 3 LAI 644 School Math Advanced Standpoint 2 * 3 LAI 645 School Math Advanced Standpoint 3 * 3 LAI 64 7 School Math Advanced Standpoint 4 * 3 LAI xxx Teaching & Learning of AP Statistics (May also use as Math Ed elective) 3 Any graduate level course (500 or above) in the Department of Mathematics 3-6 Other electives with advisor approval 3 MATHEMATICS