2015年AP微积分BCfree-response-questions
AP 微积分BC 选择题样卷一
AP Calculus Practice ExamBC Version - Section I - Part ACalculators ARE NOT Permitted On This Portion Of The Exam28 Questions - 55 Minutes1) GivenFind dy/dx.a)b)c)d)e)2) Give the volume of the solid generated by revolving the region bounded by the graph of y = ln(x), the x-axis, the lines x = 1 and x = e, about the y-axis.a)b)c)d)e)3) The graph of the derivative of f is shown below.Find the area bounded between the graph of f and the x-axis over the interval [-2,1], given that f(0) = 1.a)b)c)d)e)4) Determine dy/dt, given thatanda)b)c)d)e)5) The functionis invertible. Give the slope of the normal line to the graph of f -1 at x = 3.a)b)c)d)e)6) Determinea)b)c)d)e)7) Give the polar representation for the circle of radius 2 centered at ( 0 , 2 ).a)b)c)d)e)8) Determinea)b)c)d)e)9) Determinea)b)c)d)e)10) Give the radius of convergence for the seriesa)b)c)d)e)11) Determinea)b)c)d)e)12) The position of a particle moving along the x-axis at time t is given byAt which of the following values of t will the particle change direction I) t = 1/8II) t = 1/6III) t = 1IV) t = 2a) I, II and IIIb) I and IIc) I, III and IVd) II, III and IVe) III and IV13) Determinea)b)c)d)e)14) Determine the y-intercept of the tangent line to the curveat x = 4.a)b)c)d)e)15) The function f is graphed below.Give the number of values of c that satisfy the conclusion of the Mean Value Theorem for derivatives on the interval [2,5].a)b)c)d)e)16) Give the average value of the functionon the interval [1,3].a)b)c)d)e)17) A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 20 square feet. Give the rate of change of the width (in ft/sec) when the height is 5 feet, if the height is decreasing at that moment at the rate of 1/2 ft/sec.a)b)c)d)e)18) The graph of the derivative of f is shown below.Give the number of values of x in the interval [-3,3] where the graph of f has inflection.a)b)c)d)e)19) A rectangle has its base on the x-axis and its vertices on the positive portion of the parabolaWhat is the maximum possible area of this rectanglea)b)c)d)e)20) Computea)b)c)d)e)21) Determinea)b)c)d)e)22) Determinea)b)c)d)e)23) Give the exact value ofa)b)c)d)e)24) Determinea)b)c)d)e)25) Give the derivative ofa)b)c)d)e)26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the functiona)b)c)d)e)27) Determinea)b)c)d)e)28) Which of the following series converge(s)a) B onlyb) A, B and Cc) B and Cd) A and Be) A and C1) d)2) e)3) b)4) b)5) e)6) a)7) c)8) c)9) b)10) d)11) c)12) c)13) c)14) e)15) a)16) d)17) a)18) b)19) a)20) d)21) b)22) b)23) a)24) c)25) d)26) b)27) b)28) c)。
AP微积分七大考点总结
AP微积分七大考点总结AP频道为大家带来AP微积分七大考点总结一文，希望对大家AP备考有所帮助。
Free Response 考点分析根据对以往真题的分析，解答题(Free Response)所考察的知识点比较集中，共可分为七个专题：定积分求面积体积弧长变限积分(Variablelimit integral)运动(直线运动与平面运动)图表题蓄水池模型微分方程(Differentialequation)级数(Series)定积分求面积体积弧长【必考知识点】利用定积分求几何图形的面积、体积、周长，有时也会与运动结合在一起进行考察。
变限积分(Variable limit integral)【必考知识点】利用变限积分定义一个新的函数，考察该函数的各种性质，主要是增减性、凹凸性，以及该函数的最大值最小值等等。
运动(直线运动与平面运动)【必考知识点】AB考察直线运动，BC考察平面运动，其中主要考点是加速减速区间的判断、运动方向的判断、position 与distance 的求法。
ABBC图表题【必考知识点】给出函数的局部特征，利用局部来推测整体。
主要考察点在中值定理、连续性、黎曼和等。
蓄水池模型【必考知识点】这一部分我们同学小学的时候就可能接触过，给一个水池，一边往里接水一边往外放水，基本原理很简单，某一时刻水池中的水量等于初始时刻的水量加上这段时间放进来的水量再减去放出去的水量。
微分方程(Differential equation)【必考知识点】微分方程这部分题型很固定，欧拉估值、斜率场、解微分方程基本就会构成一道大题。
级数(Series)【必考知识点】这是每年的压轴题，不是特别难，但是我们同学经过漫长的考试，精力与体力在这道题上基本已经处于最低值，因此这道题往往成为同学最后的一个噩梦。
考点包括幂级数求收敛半径、收敛域，函数的泰勒展开，泰勒估值及其余项。
此外还有极坐标的题目，每年也是重点考察的部分，请考生注意!以上就是AP频道为你带来的AP微积分七大考点总结。
ap微积分考试题型_
ap微积分考试题型
AP微积分考试通常包含两个部分：多项选择题（Multiple-Choice Questions，MCQs）和开放性问题（Free-Response Questions，FRQs）。
下面是这两个部分的一些常见题型：
1. 多项选择题（MCQs）：
-求极限：给出一个函数或数列，要求计算其极限。
-导数和微分：给出一个函数，要求计算其导数或微分。
-积分：给出一个函数，要求计算其不定积分或定积分。
-解微分方程：给出一个微分方程，要求找到满足条件的特解或通解。
-曲线分析：给出一个函数的图像或方程，要求根据图像或方程进行分析，如找极值点、拐点、渐近线等。
-高阶微积分概念：涉及高阶导数、泰勒级数、参数方程、极坐标等概念。
2. 开放性问题（FRQs）：
-解题和证明：给出一个问题或命题，要求解答并给出证明过程。
-应用问题：给出一个实际问题，要求建立数学模型并求解。
-推导公式：给出一个函数或关系，要求通过推导得到相应的公式。
-分析函数性质：给出一个函数或图像，要求分析其性质，如极值点、拐点、渐近线等。
在备考AP微积分考试时，建议你掌握以下几点：
1. 熟悉微积分的基本概念、公式和定理，包括极限、导数、积分、微分方程等。
2. 理解微积分的几何和物理意义，将数学概念与实际问题联系起来。
3. 多做练习题和模拟考试，熟悉题型和考试时间，提高解题速度和准确性。
4. 学会运用不同的解题方法和策略，灵活应用数学工具解决问题。
5. 注意细节和计算精度，避免常见的计算错误。
AP 微积分BC 选择题样卷一,DOC
AP Calculus Practice ExamBC Version - Section I - Part ACalculators ARE NOT Permitted On This Portion Of The Exam28 Questions - 55 Minutes1) GivenFind dy/dx.a)b)c)d)e)2) Give the volume of the solid generated by revolving the region bounded by the graph of y = ln(x), the x-axis, the lines x = 1 and x = e, about the y-axis.a)b)c)d)e)3) The graph of the derivative of f is shown below.Find the area bounded between the graph of f and the x-axis over the interval [-2,1], given that f(0) = 1.a)b)c)d)e)4) Determine dy/dt, given thatanda)b)c)d)e)5) The functionis invertible. Give the slope of the normal line to the graph of f -1 at x = 3.a)b)c)d)e)6) Determinea)b)c)d)e)7) Give the polar representation for the circle of radius 2 centered at ( 0 , 2 ).a)b)c)d)e)8) Determinea)b)c)d)e)9) Determinea)b)c)d)e)10) Give the radius of convergence for the seriesa)b)c)d)e)11) Determinea)b)c)d)e)12) The position of a particle moving along the x-axis at time t is given byAt which of the following values of t will the particle change direction?I) t = 1/8II) t = 1/6III) t = 1IV) t = 2a) I, II and IIIb) I and IIc) I, III and IVd) II, III and IVe) III and IV13) Determinea)b)c)d)e)14) Determine the y-intercept of the tangent line to the curveat x = 4.a)b)c)d)e)15) The function f is graphed below.Give the number of values of c that satisfy the conclusion of the Mean Value Theorem for derivatives on the interval [2,5].a)b)c)d)e)16) Give the average value of the functionon the interval [1,3].a)b)c)d)e)17) A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 20 square feet. Give the rate of change of the width (in ft/sec) when the height is 5 feet, if the height is decreasing at that moment at the rate of 1/2 ft/sec.a)b)c)d)e)18) The graph of the derivative of f is shown below.Give the number of values of x in the interval [-3,3] where the graph of f has inflection.a)b)c)d)e)19) A rectangle has its base on the x-axis and its vertices on the positive portion of the parabolaWhat is the maximum possible area of this rectangle?a)b)c)d)e)20) Computea)b)c)d)e)21) Determinea)b)c)d)e)22) Determinea)b)c)d)e)23) Give the exact value ofa)b)c)d)e)24) Determinea)b)c)d)e)25) Give the derivative ofa)b)c)d)e)26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the functiona)b)c)d)e)27) Determinea)b)c)d)e)28) Which of the following series converge(s)?a) B onlyb) A, B and Cc) B and Cd) A and Be) A and C1) d)2) e)3) b)4) b)5) e)6) a)7) c)8) c)9) b)10) d)11) c)12) c)13) c)14) e)15) a)16) d)17) a)18) b)19) a)20) d)21) b)22) b)23) a)24) c)25) d)26) b)27) b)28) c)。
AP统计学常见的11个问题
AP统计学常见的11个问题1.AP统计学的课程大纲分为4大部分第一部分：数据分析，占考试的20-30%。
学生应该使用绘图计算器来分析数据分布，包括单变量、双变量数据，和分类数据。
第二部分：包括试验设计占考试的10-15%。
学生必须学会通过抽样或实验来进行数据收集，并从中得出结论。
第三部分：概率论，包括预测数据分布。
该部分占考试的20-30%。
第四部分：考试的30-40%，包括基于点估算的推论统计学、置信区间、显著性差异等。
重点内容：包括数据的分布，相关性与回归，样本的选择，实验的设计，二项分布，正态分布，中心极限定理，置信区间，显著性检验等。
2. AP统计学都有什么题型?(真题举例)题型分类AP统计学考试题型分为选择题(multiple-choice)和自由问答题(free-response question)。
选择题部分：40道题，每题有5个选项问答题部分：6道问答题，题目很长，分为几道小题真题举例Multiple-choice 2008年的真题Free response 2015年的真题3. AP统计学大题一般考什么内容?有答题技巧么?AP统计问答题是综合题，经常由几个小题共同组成，考查的知识涉及几个章节。
AP统计学考试中各个知识点所占点比例还是比较均衡，绝不会出现某一个知识点一家独大的情况。
一般情况下问答题涉及到的知识点：最小二乘回归线应该一个题，画图解释一个题，抽样和实验设计一个题，随机变量的概率分布以及独立随机变量的组合一个题，参数估计和假设检验应该各有一个题。
问答题切记一定要先看问题进行考点定位。
并且一定记住：某一个问项的题干只能往前找，而不能使用该问题下面的信息。
以2014年AP统计学部分为例，考查知识点结构如下虽然AP统计学考试各个知识所占比例相对稳定，但是在考试深度不变的前提下，要求学生对知识点的掌握有相当的广度。
4.大题的论述重要还是数据重要?论述有个别语法错误会扣分么?会影响下一问得分么?AP统计学的每一个大题都由4-5个小题组成，每个小题目都有三个等级的评分标准(correct, partially correct, incorrect)，并不是你给出正确答案就可以得到满分。
AP微积分-Integral Test-260
y 2.
e) Find the volume of the solid whose base is the region and whose cross-sections cut by planes
y axis and x 3.
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3. Suppose f (x)dx 2 and f (x)dx 1 , and 3 f (x)dx 6 . What is f (x)dx
t (hours)
0
R(t) (gallons per hour)
AP微积分AB与AP微积分BC考试应该如何选择
AP微积分AB与AP微积分BC考试应该如何选择AP微积分AB、AP微积分BC，这两门有什么差别?AP频道为大家带来AP微积分AB 与AP微积分BC考试如何选择一文，希望对大家AP备考有所帮助。
由于微积分AB和BC 的考试时间是同一个时间，很多学生为了避免考试的冲突，都在纠结，无从选择。
今天我们就来说一说微积分AB和BC，其实这两门的差别不大。
AP微积分课程包括微积分AB (Calculus AB) 和微积分BC(Calculus BC)两门课。
微积分AB需要1年的课程学习时间，其内容大约占了大学一年的微积分课程内容的三分之二，而微积分BC需要1年多的课程学习时间，其内容包括了大学一年的微积分课程内容的全部。
开设Calculus AP课程的学校或者自学的同学，应该在高一高二进行合理安排，确定课程计划，以保证把学习微积分应具备的基础知识先行学习完毕。
由于AP微积分是一门大学水平的课程，具有挑战性，因此想要学习的学生必须具有扎实的数学基础。
微积分BC是微积分AB的延伸和扩展，但是，对共同内容的理解深度和要求却是一致的。
微积分BC课程的主要内容除了包括微积分AB课程的全部内容之外，还增加了以下内容：参数方程、向量方程、极坐标方程各自的求导和求积分的方法，分部积分，反常积分，欧拉方法，级数等;在积分的应用中，增加了物理模型、经济模型、生物模型等。
在2016年之前，BC还比AB多洛必达法则这个知识点，但是新出来的2017年的AB 大纲中显示，洛必达法则也成为了AB的必考项目。
中国学生的理科属于强项，建议选择微积分BC学习，并且BC在大学的认可度及能够转换学分的概率都相对较高。
另外，如果大家参加了微积分BC的考试，最后可以拿到两个分数，一个BC的，一个AB的。
微积分BC拿到满分5分的情况下，也会获赠微积分AB的满分成绩，这就是常常出现的微积分双5分的情况;是不是顿时觉得很划算啊;所以，相比较而言，微积分BC对中国学生来说会是更优的选项。
AP考试模拟试题与答案1-微积分BC- AP Calculus-BC
1
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AP考试模拟试题与答案1-微积分BC- AP Calculus-BC
6. The graph of the function f is shown in Figure 1T-3. Which of the following statements is/are true?
I. f (0) = 0
II. f has an absolute maximum value on [a , b]
Use the answer sheet provided on the previous page. All questions are given equal weight. Points are not deducted for incorrect answers and no points are given to unanswered questions. Unless otherwise indicated, the domain of a function f is the set of all real numbers. The use of a calculator is not permitted in this part of the exam.
GO ON TO THE NEXT PAGE
(C) e 2
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AP 微积分BC 选择题样卷一
AP Calculus Practice ExamBC Version - Section I - Part ACalculators ARE NOT Permitted On This Portion Of The Exam28 Questions - 55 Minutes1) GivenFind dy/dx.a)b)c)d)e)2) Give the volume of the solid generated by revolving the region bounded by the graph of y = ln(x), the x-axis, the lines x = 1 and x = e, about the y-axis.a)b)c)d)e)3) The graph of the derivative of f is shown below.Find the area bounded between the graph of f and the x-axis over the interval [-2,1], given that f(0) = 1.a)b)c)d)e)4) Determine dy/dt, given thatanda)b)c)d)e)5) The functionis invertible. Give the slope of the normal line to the graph of f -1 at x = 3.a)b)c)d)e)6) Determinea)b)c)d)e)7) Give the polar representation for the circle of radius 2 centered at ( 0 , 2 ).a)b)c)d)e)8) Determinea)b)c)d)e)9) Determinea)b)c)d)e)10) Give the radius of convergence for the seriesa)b)c)d)e)11) Determinea)b)c)d)e)12) The position of a particle moving along the x-axis at time t is given byAt which of the following values of t will the particle change direction?I) t = 1/8II) t = 1/6III) t = 1IV) t = 2a) I, II and IIIb) I and IIc) I, III and IVd) II, III and IVe) III and IV13) Determinea)b)c)d)e)14) Determine the y-intercept of the tangent line to the curveat x = 4.a)b)c)d)e)15) The function f is graphed below.Give the number of values of c that satisfy the conclusion of the Mean Value Theorem for derivatives on the interval [2,5].a)b)c)d)16) Give the average value of the functionon the interval [1,3].a)b)c)d)e)17) A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 20 square feet. Give the rate of change of the width (in ft/sec) when the height is 5 feet, if the height is decreasing at that moment at the rate of 1/2 ft/sec.a)b)c)d)e)18) The graph of the derivative of f is shown below.Give the number of values of x in the interval [-3,3] where the graph of f has inflection.a)b)c)e)19) A rectangle has its base on the x-axis and its vertices on the positive portion of the parabolaWhat is the maximum possible area of this rectangle?a)b)c)d)e)20) Computea)b)c)d)e)21) Determinea)b)c)d)e)22) Determinea)b)c)d)e)23) Give the exact value ofa)b)c)d)e)24) Determinea)b)c)d)e)25) Give the derivative ofa)b)c)d)e)26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the functiona)b)c)d)e)27) Determinea)b)c)d)e)28) Which of the following series converge(s)?a) B onlyb) A, B and Cc) B and Cd) A and Be) A and C1) d)2) e)3) b)4) b)5) e)6) a)7) c)8) c)9) b)10) d)11) c)12) c)13) c)14) e)15) a)16) d)17) a)18) b)19) a)20) d)21) b)22) b)23) a)24) c)25) d)26) b)27) b)28) c)。
AP 微积分BC考试技巧
The AP Calculus ExamHow, not only to Survive, but to Prevail…The AP Calculus exam is the cumulation of all of the years you’ve spent in high school studying mathematics. It’s all led up to this. The calculus you study in the last year completes the prior years of preparation. If you are reading this at the beginning of the year keep these things in mind as you go through the year. If you are reading this only a few weeks before the test think back and see how these things fit together.Everything in calculus, and mathematics in general, is best understood verbally, numerically, analytically (that is, through the use of equations and symbols) and graphically. Look at everything from these perspectives. Look at the relationships among them — how the same idea shows up in words, in equations, in numbers and in graphs.For example: numerically a linear function is one which when written as a table of values, regular changes in the x-values produce regular changes in the y-values. Graphically a linear function has a graph that is a straight line. Analytically it is one=+. And the three way are interrelated: The ratio whose equation can be written as y mx bof the changes in the table is the number m in the equation; the graph can be drawn using the number m by going up and over from one point to the next. The idea of the slope as “rise over run” expresses this verbally. Everything in mathematics and in the calculus works that way.Learn the concepts — the exam emphasizes conceptsLearn the procedures and formulae — even though the concepts are more important than the computations you still have to do the computations. Like it or not, learn to do the algebra, the arithmetic and the graphs.Learn to be methodical — work neatly and carefully all year.Think about what you are doing. Watch yourself work. It is natural to concentrate on the material you know and can do, but you need to concentrate on the things you donot (yet) know how to do. You can learn much from your mistakes. Look at a wrong answer as a green light to go in that direction until you’ve reached the right answer.Reviewing for the ExamIn the few weeks before the AP Exam you will need to review what you have studied, firm up what you have learned, work on your areas of weakness and yes, memorize some formulas. You also need to prepare for the exam itself by learning what kinds of questions will be asked and how to best answer them. Specifically Understand the format of the exams. (See below). Know how your knowledge will be tested.STUDY WHAT YOU DO NOT KNOW. That may seem obvious but many people enjoy getting the right answers so much that they only review the stuffthey know. The time to concentrate on what you know is when you are takingthe test.Practice writing Free-Response answers. The College Board publishes copies of student answer from past years. If your teacher has some of these, look atthem and learn what is expected and what is not needed.Plan your review carefully. Don’t try to cram the weekend before the exam.The day before the test: relax, get psyched, and get a good night’s sleep. Theday of the test eat a good breakfast. The test is grueling, even though you’reup for it. Bring a snack for the brief break between the multiple-chose andFree-response sections.CalculatorsThe reason calculators are so important in learning mathematics is that they allow you do the graphical and numerical work easily, quickly and accurately. You should use your calculator all year, on homework, tests and when studying. Learn how to use it efficiently. Learn its strengths and weaknesses.You may use your calculator any way you wish. There are four types of things you should definitely know how to do. They arePlot the graph of a function within an arbitrary viewing window,Find the zeros of functions (solve equations numerically),Numerically calculate the derivative of a function, andNumerically calculate the value of a definite integral.You may have programs in your calculator; but you will not be asked to use them. The questions on the exam are designed so that someone with a program, or a more expensive calculator, has no advantage over someone who does not. This includes many of the built-in programs.Be sure your calculator is set in Radian mode.Numerical answers may be left unsimplified and in terms of π, e, etc. There is no reason to change an answer to a decimal if you don’t have to. (Why take the chance on pushing the wrong button?)Install fresh batteries before the exam.The Format of the ExamsThere are two parts to the AP exams: a multiple-choice section and a Free-response section.. The number of questions and timing may change slightly from year to year. Be sure you check the current College Board publications for your exam.Both sections count equally towards your final grade. Both sections cover the full range of topics. It is natural to expect that different classes will cover some topics in greater detail than others; the exam will evaluate your knowledge of the calculus. It is not necessary to answer all the questions to get a good score. In fact the exam is made so that the average score will be about 50%, is usually a score of three.The Current AP Calculus Exam format isSection I Part A (55 minutes) 28 multiple-choice questions for which you may not use a calculator.Section I Part B (50 minutes) 17 multiple-choice questions. You may use your calculator on this section. Some of these questions require the use of a graphing calculator others do not.Section II Part A(45 minutes) Three Free-Response questions. You may use your calculator on this section. In this section you will find longer questions with several related parts. You are required to show your work in this section. You may continue work on this section without a calculator after you start part B.Section II Part B (45 minutes) Three Free-Response questions. You may not use your calculator on this section. In this section you will find longer questions with several related parts. You are required to show your work in this section. You may use part of this time to work on Section II, Part A without a calculatorMultiple Choice QuestionsRead each question carefully and look at the answer choices. Do the ones you are sure of. Don’t struggle over one that isn’t working out. Remember your time is limited and you do not need to answer all of the questions. There is a penalty for guessing, so don’t guess blindly. You receive one point for each correct answer. One-quarter point is deducted for each wrong answer. Nothing is deducted for a question that is left blank. Guessing may improve your score only if you can eliminate one or more of the choices. Be sure to bubble your answer in the correct space on the answer sheet.Types of Multiple Choice QuestionsOne type of question may ask for a computation (a limit, a derivative, a definite or indefinite integral) and give five possible answers: be aware thatanswers which result from predictable mistakes are among the choices —work carefully, just because your answer is there doesn’t mean it's correct.Another type may ask you only to set up a problem: looking at the answer choices may keep you from doing too much work.Some questions ask you to choose the one true or one false statement from a list of five statements: be sure you know if you are looking for a true or a falsestatement.Another type of question asks which of three statements is true (or false): the answer may be any one or some combination of the statements.Another type may ask you to choose the correct table or graph from among five choices.Free-Response QuestionsThe general directions for Section II require you to show your work and indicate the methods you use to arrive at your answers. In addition, parts of questions may say, “Justify your answer” or “Show the analysis that leads to your conclusion.” Your answers will be read by calculus teachers who will judge your work. It is important that you clearly show how you arrived at your answer. Unsupported answers lose points even if the final answer is correct.The questions are designed to show the breadth and depth of your knowledge. There are some common types of questions that are asked. There will also be questions asked in new and original ways.Some things to keep in mind about Free-Response Questions:Don’t write a long essay: it's not necessary. Do show the work that you do, so that the reader will understand you. You may use common terms and names,like “the first derivative test.” You do not need to name theorems. You mayshow a number line as your analysis of the sign of the derivative — be sure tolabel it appropriately, for example y' or y''.The Free-Response section of the exam rarely requires long complicated computation; if you find yourself doing a long complicated computationyou’ve probable gone wrong somewhere and should start over.Do not explain how to do the problem you cannot do. A general explanation without work will receive no credit. You must do the problem you are given.Avoid simplifying numerical answers . Answers may be left unsimplified as fractions, radicals, powers of e , in terms of ,πetc . Do not take a chance of pushing the wrong button once you have an acceptable answer. If you do arithmetic it must be done correctly. Every year students find the correct answer, change it to a decimal incorrectly and lose a point. Decimal answers (for example a definite integral on a calculator) are acceptable even if an exact answer is possible.If you make a mistake cross it out. Crossed out work is not read or graded. If you leave wrong work on your paper (not crossed out) it will be read and may affect your score.If you work the problem two different ways, choose the best one and put an X through the other. If both are left, they will both be scored and the scores will be averaged. This can lower your score even if one solution is perfect.Standard notation must be used. Don’t use calculator notation. (For example: fnInt(x2,x,0,2) is not acceptable, use the standard 220x dx ∫. Answers without work do not receive full credit. Don’t do work on a calculator without indicating what you are doing. For example if you are evaluating a definite integral write the integral on your paper and put the calculator answer next to it; you do not need to show the work in between (the antiderivative).Different calculators have different built-in utilities (for example the ability to find points of inflection, or maximum values of a function). You may have programs in your calculator to do things such as the Trapezoidal Rule. However, if you use such a built-in utility or a special program to do something other than the four things listed previously, you must show the complete set-up (the terms of the Trapezoidal Rule, the computation and analysis of the second derivative required to find a point of inflection etc.) on your paper. Only the four things listed may be done without further explanation.Don’t put things where they are not needed. Work must be shown on the part of the answer booklet where it is used. For example, if you need a derivativein part (b) of a question and you have it in part (a) where it is not needed, youwill not get credit for finding the derivative (in either part). Either copy it inpart (b) or draw an arrow over to where you wrote it. You must show youknow where you need the derivative as well as your ability to find it.Likewise, do not put work on the graph or drawing. It will not be read unlessyou specifically refer to it in the part of the answer booklet where you used it.Finally the parts of a Free-Response question are related to each other. This can help you in two ways:o Sometimes each part may be answered without reference to the other parts. Read and try of all the parts: if you cannot do part (a) maybe youcan do part (b). Perhaps doing part (b) will give you a hint on how to dopart (a).o Other times the one part will lead to the next: this is done to help you find your way through the problem. Keep in mind that this may be the case andwork your way from part (a) to part (b) to part (c) even if you’re not surewhere the problem is heading.Try all of the Free-Response questions. They are written so that the first parts are easier in order to help you get started. Even if you don’t get the entireproblem, some points are better than no points.Common Free-Response MistakesAlgebra and arithmetic mistakes.Missing limits of integration.Not considering the end points of an interval (for example, when looking for the absolute maximum value of a function).Giving answers from points outside the given interval.Not giving both coordinates of a point when required.Giving both coordinates when only one is asked for; remember “value of a func-tion” means the y -value.Having the calculator in degrees mode.Not answering the question that was asked even though all the work is correct. If it is a yes or no question, say “yes” or “no.”Ignoring units of measure.Family of function problems: Questions that start with a phrase like, “This question deals with functions defined by ()1sin()f x b x =+ where b is a positive constant...” are meant to be done in general, not for a specific value of b. Even if you get the correct answer using a specific value of b , you may lose points. The reason is that, because you used a particular value, you have no way to be sure that your answers are true for all values of b.Don’t Curve Fit: Occasionally, a function is given as a graph or a table of values with no equation. You are being asked to demonstrate that you can work from the graphical or numerical data. The questions that follow can be answered without an equation. You may have learned to approximate functions using various curve fitting (regression) operations built into your calculator. This should be avoided. While this is a perfectly good approach in the real world, you may lose points because you are not working with the function you were given (only an approximation of it), and this is not one of the four allowed calculator operations. Using a built-in calculator utility or a program without showing all the work and justification for what you are doing. You may do only the four things you are allowed to do with a calculator on the exam.A Word About Three-Decimal Place Accuracy.Some answers, the evaluation of definite integrals is a prime example, must be written as decimals because they are found using a graphing calculator. These answers, and other answers that you choose to change to decimals, must be correct to three placespast the decimal point. This means that the answer may be rounded to three decimal places, truncated after the third decimal place or left with more than three decimal places as long as the first three are correct. An answer of π, which should be left as π, may be given as 3.1415926535898…, 3.142, 3.141, or even 3.14199999. If the number ends in zeros, they may be omitted; thus 17.320 may be given as 17.32 and 56.000 may be given as 56.Too often, students may choose to give decimal answers when they are not required. Once a Free-Response answer is entirely in terms of numbers there is no need to change the number to a decimal. For example, 1999 AB 1(c) does not require a decimal answer: 7122cos 4−+ is sufficient. If the decimal is correct (to three decimal places) thestudent will receive the credit. However, if you change a correct answer to an incorrect decimal (including one with too few decimals) then you will lose credit. The moral is: avoid arithmetic, avoid decimals; give them only if you cannot give anything else.Rounding too soon is another common mistake made by students. Computations should be done with more decimal places than is required in the final answer. Learn how to store the intermediate values in your calculator and recall them when you need them in a computation. If premature rounding affects the three decimal place accuracy of the final answer, you will not be given the answer point. However, a rounded answer used in the next part of a problem will not be held against you.Good Luck!。
AP物理C真题2015
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c q b 90° a
VECTOR PRODUCTS A B AB cos q AB AB sin q
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d f du du dx
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d n x dx d ax e dx d ln ax dx
【最新!】AP化学真题2015
少年向上，真善美伴我行800字作文少年向上，真善美伴我行|800字作文无论是在学校还是在社会中，大家都有写作文的经历，对作文很是熟悉吧，写作文可以锻炼我们的独处习惯，让自己的心静下来，思考自己未来的方向。
那么问题来了，到底应如何写一篇优秀的作文呢？以下是小编整理的少年向上，真善美伴我行|800字作文，欢迎阅读与收藏。
能让我们向上的是什么？能让我们成长的是什么？能让我们走向成功的是什么？其实，这些问题都有一个共同的答案，就是“真善美”。
两年前的某个夏日，中午放学，我一出教室就瞧见了一轮骄阳悬挂高空，犹如一团火。
我大汗淋漓，口干舌燥，正好校门口不远有个奶茶铺。
我从口袋里掏出几块钱，皱巴巴的。
我如同行走在大漠里的人见了水和绿洲，急匆匆跑到奶茶铺前。
慈眉善目的'阿姨摆弄着那些瓶瓶罐罐，见又有顾客了，笑得眼睛眯成缝儿，问：“要喝什么呀？”我不假思索回答：“巧克力味的奶茶，不要珍珠、不要椰果，冰镇。
”“好咧！”顾客渐渐多了。
我接过阿姨给我的奶茶，拿了根吸管，蹙眉穿过人群。
插上吸管，我端起了奶茶慢慢喝着，心满意足。
喝完了，我回想起刚刚的场景，不由得一拍脑袋，懊恼道：“坏了！真是个榆木脑袋，竟然忘了给钱了！”我回头看了看路程，又望了望天上骄阳，打消了现在回去付钱的想法，心想：算了，还是下午再给吧。
整个午休时间，我的心一直惴惴不安。
老师和父母从小教育我要真诚、讲信用，现在我却买东西不给钱不付账，哪是什么真诚？哎！哎！哎！下午，走到学生附近，渐渐靠近那家奶茶铺，我却踌躇着不敢前行了，内心生出了胆怯。
我是个极好面子的家伙，但祖辈一代一代流传下来的传统美德更不能忘啊！鱼和熊掌不可兼得，怎么办，怎么办？！我简直无助极了，我多么希望能有一位智者来引导我的方向呀！此时，我想起了“油条哥”刘洪安的故事。
“油条哥”卖油条不用复炸油，还教顾客验油。
这位诚实守信的“油条哥”不正是我的榜样吗？我给自己加油，鼓起勇气迈开步伐，走上前递钱，低下头羞愧地说道：“对不起，我上午忘了给钱……”阿姨一愣，眯起眼细细打量我。
AP 微积分BC 选择题样卷一
AP Calculus Practice ExamBC Version - Section I - Part ACalculators ARE NOT Permitted On This Portion Of The Exam28 Questions - 55 Minutes1) GivenFind dy/dx.a)b)c)d)e)2) Give the volume of the solid generated by revolving the region bounded by the graph of y = ln(x), the x-axis, the lines x = 1 and x = e, about the y-axis.a)b)c)d)e)3) The graph of the derivative of f is shown below.Find the area bounded between the graph of f and the x-axis over the interval [-2,1], given that f(0) = 1.a)b)d)e)4) Determine dy/dt, given thatanda)b)c)d)e)5) The functionis invertible. Give the slope of the normal line to the graph of f -1 at x = 3.a)b)c)d)e)6) Determinea)b)c)e)7) Give the polar representation for the circle of radius 2 centered at ( 0 , 2 ).a)b)c)d)e)8) Determinea)b)c)d)e)9) Determinea)b)c)d)e)10) Give the radius of convergence for the seriesa)b)c)d)e)11) Determinea)b)c)d)e)12) The position of a particle moving along the x-axis at time t is given byAt which of the following values of t will the particle change direction?I) t = 1/8II) t = 1/6III) t = 1IV) t = 2a) I, II and IIIb) I and IIc) I, III and IVd) II, III and IVe) III and IV13) Determinea)b)c)d)e)14) Determine the y-intercept of the tangent line to the curveat x = 4.a)b)c)d)e)15) The function f is graphed below.Give the number of values of c that satisfy the conclusion of the Mean Value Theorem for derivatives on the interval [2,5].a)b)c)d)e)16) Give the average value of the functionon the interval [1,3].a)b)c)d)e)17) A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 20 square feet. Give the rate of change of the width (in ft/sec) when the height is 5 feet, if the height is decreasing at that moment at the rate of 12 fta)b)c)d)e)18) The graph of the derivative of f is shown below.Give the number of values of x in the interval [-3,3] where the graph of f has inflection.a)b)c)d)e)19) A rectangle has its base on the x-axis and its vertices on the positive portion of the parabolaWhat is the maximum possible area of this rectangle?a)b)c)d)e)20) Computea)b)c)d)e)21) Determinea)b)c)d)e)22) Determinea)b)c)d)e)23) Give the exact value ofa)b)c)d)e)24) Determinea)b)c)d)e)25) Give the derivative ofa)b)c)d)e)26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the functiona)b)c)d)e)27) Determinea)b)c)d)e)28) Which of the following series converge(s)?a) B onlyb) A, B and Cc) B and Cd) A and Be) A and C1) d)2) e)3) b)4) b)5) e)6) a)7) c)8) c)9) b)10) d)11) c)12) c)13) c)14) e)15) a)16) d)17) a)18) b)19) a)20) d)21) b)22) b)23) a)24) c)25) d)26) b)27) b)28) c)。
ap微积分考试题型
AP微积分考试通常由两个部分组成：多项选择题和自由响应题。
多项选择题部分（Multiple Choice Questions, MCQs）由 45 道题目组成，使用 1.5 小时时间完成。
这些题目分为两部分：常规多项选择题和计算机单元答案问题。
常规多项选择题通常包括简答、图形和函数概述等类型的问题。
计算机单元答案问题是先提供一个问题，然后要求学生从五个答案中选择最正确的答案。
自由响应题（Free-Response Questions, FRQs）由 6 道问题组成，包含两个部分：解答问题和应用问题，每个部分各有三道问题。
解答问题一般包括证明、证明方法、函数拟合等，应用问题则要求学生应用微积分的概念和技能解决实际问题。
在自由响应题中，考生需要对每个问题写出清晰且完整的解答。
考试规定只有在指定的答题空间中，才会被评分。
答题空间可以是特定的网格纸、特定的表格或特定的响应空间页面。
在答题时，学生需要表述解题思路，清晰地阐述想法，展示问题解决过程，并用数学语言表述答案。
请注意，这里所述的考试结构仅适用于适用于一般情况下的AP微积分考试，不同辖区可能会有不同的考试格式，并且考试安排随时间而变化，请参考您所在辖区或总部的具体考试规定。
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f x be the particular solution to the differential equation with the initial condition f 2 (c) Let y Does f have a relative minimum, a relative maximum, or neither at x 2 ? Justify your answer.
(d) Find the values of the constants m and b for which y
3.
mx b is a solution to the differential equation.
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4, so that f x
neither at x
1 . Determine whether f has a relative minimum, a relative maximum, or x 4x 2. Justify your answer.
2
(c) Find the value of k for which f has a critical point at x (d) Let k Find
2
x 2 kx
2
.
(a) Let k
3, so that f x
1 . Write an equation for the line tangent to the graph of f at the point x 3x
2
whose x-coordinate is 4. (b) Let k
2. At time t 0, a particle moving along a curve in the xy-plane has position x t , y t with velocity vector
v t
cos t 2 , e0.5t . At t
6, so that f x
2
5.
1 . Find the partial fraction decomposition for the function f. x 6x
Ô f x dx .
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1, the particle is at the point 3, 5 .
(a) Find the x-coordinate of the position of the particle at time t
2.
(b) For 0 t 1, there is a point on the curve at which the line tangent to the curve has a slope of 2. At what time is the object at that point? (c) Find the time at which the speed of the particle is 3. (d) Find the total distance traveled by the particle from time t
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2015 AP® CALCULUS BC FREE-RESPONSE QUESTIONS
dy dx
4. Consider the differential equation
2 x y.
(a) On the axes provided, sketch a slope field for the given differential equation at the six points indicated.
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2015 AP® CALCULUS BC FREE-RESPONSE QUESTIONS
0 to time t
1.
END OF PART A OF SECTION II
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3 hours? Give a reason for your
(c) At what time t, 0 t 8, is the amount of water in the pipe at a minimum? Justify your answer. (d) The pipe can hold 50 cubic feet of water before overflowing. For t ! 8, water continues to flow into and out of the pipe at the given rates until the pipe begins to overflow. Write, but do not solve, an equation involving one or more integrals that gives the time w when the pipe will begin to overflow.
(b) Find
d2y in terms of x and y. Determine the concavity of all solution curves for the given differential dx 2 equation in Quadrant II. Give a reason for your answer.
2015 AP® CALCULUS BC FREE-RESPONSE QUESTIONS CALCULUS BC SECTION II, Part B
Time— 60 minutes Number of problems—4 No calculator is allowed for these problems.
out the other end of the pipe at a rate modeled by D t 0.04t 3 0.4t 2 0.96t cubic feet per hour, for 0 t 8. There are 30 cubic feet of water in the pipe at time t 0. (a) How many cubic feet of rainwater flow into the pipe during the 8-hour time interval 0 t 8 ? (b) Is the amount of water in the pipe increasing or decreasing at time t answer.
AP Calculus BC 2015 Free-Response Questions
®
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2015 AP® CALCULUS BC FREE-RESPONSE QUESTIONS CALCULUS BC SECTION II, Part A
Time— 30 minutes Number of problems— 2 A graphing calculator is required for these problems.
Find Bob’s acceleration at time t
5.
(d) Based on the model B from part (c), find Bob’s average velocity during the interval 0 t 10.
© 2015 The College Board. Visit the College Board on the Web: .
1. The rate at which rainwater flows into a drainpipe is modeled by the function R, where R t
È t2 Ø 20sin É Ù Ê 35 Ú cubic feet per hour, t is measured in hours, and 0 t 8. The pipe is partially blocked, allowing water to drain
B t t 3 6t 2 300, where t is measured in minutes and B t is measured in meters per minute.
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40
v t dt in the context of the problem.
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40
v t dt using a right Riemann sum with the four subintervals indicated in the
t (minutes)