AP 微积分BC 选择题样卷一
AP 微积分BC选择题Section2练习
29) Find the average value of the functionover the interval [0, 4].a)b)c)d)e)30) What is the y-intercept of the line tangent to the curve y = x2 + 7 at x = 3?a)b)c)d)e)31) Which of the following function(s) is continuous and differentiable?I.II.III.a) I and III onlyb) III onlyc) I and II onlyd) I onlye) II only32) Find ma)b)c)d)e)33) The graph of the derivative of f is shown below. Which of the following must be true?a) f is concave down on [0, 4].b) f is increasing on [-2, 2].c) f has a local maximum at x = 0.d) f has a local minimum at x = -2.e) f has a point of inflection at x = 4.34) The sum of two positive integers x and y is 60. Find the value of x that minimizesa)b)c)d)e)35) A particle moves on the curvefind the speed of the particle at time t = .a) 7.1414b) 6.7082c) 7.2801d) 3.3166e) 3.000036) The function f is defined asx 6Which of the following is false?a) f has a horizontal asymptote at y = 1.b) f has a vertical asymptote at x = 6.c) f is decreasing on [3, 6].d) f has a local maximum at x = 3.e) f is concave up for x > 6.37) A particle is moving along the x-axis and its position at time t > 0 is given byWhich of the following is (are) true?I. The particle changes direction at x = 2 and x = 6.II. The particle is slowing down on [0, 2].III. The particle is speeding up on [2, 6].a) II and III onlyb) I onlyc) II onlyd) I and III onlye) I, II and III38) f(x) is a differentiable function and it is decreasing on (,). Ifthen g has a local maximum ata)b)c)d)e)39) The rate at which a bacteria population grows is proportional to the number of bacteria present. Initially, there were 1000 bacteria present and the population doubled in 5 hours. Roughly how many hours does it take for the population to reach 10000?a)b)c)d)e)40) Find the radius of convergence of the seriesa)b)c)d)e)41)for 0 < x < 3The graph of g is shown above. Which of the following must be true? I.II.III.a) II and III onlyb) II onlyc) I and III onlyd) I and II onlye) I only42) If the region bounded by y= tan-1(x), y= and the y-axis is rotated about the y-axis, the volume of the solid formed isa) 0.674b) 0.215c) 1.348d) 0.430e) 0.41343) f (x) is represented by the Maclaurin seriesWhat is the slope of the line normal to the graph of f at x =?a)b)c)d)e)44) What are all values of h for whichconverge?a) h > 1b) h < 1c) h > 1d) h < 1e) -1 < h < 145) The base of a solid is the region bounded bythe x-axis, andthe line x = 7Each cross-section of the solid perpendicular to the x-axis is a square, with one side on the xy-plane. Which of the following expressions represents the volume of the solid?a)b)c)d)e)29.e30.d31.c32.b33.e34.d35.c36.a37.c38.a39.d40.b41.d42.a43.c44.c45.b。
AP 微积分BC选择题样卷二
AP Calculus Practice Exam BC Version - Section I - Part BCalculators ARE Permitted On This Portion Of The Exam17 Questions - 50 Minutes1) The limit of the sequenceas n approaches is -3. What is the value of c?a)b)c)d)e)2) Ifand y = 3 when x = -2, then what is y?a)b)c)d)e)3) The graph of the derivative of f is given below. Which of the following is FALSE about the function f?a) f is increasing on [1,4].b) f is concave down on [1,5/2].c) f is concave down on [-3,0).d) f is not differentiable at 0.e) The funciton is constant on (-,-3].4) Determinea)b)c)d)e)5) Give the area that lies below the x-axis and is contained within the region bounded by the polar curvea)b)c)d)e)6) Give the error that occurs when the area between the curveand the x-axis over the interval [0,1] is approximated by the trapezoid rule with n = 4.a)b)c)d)e)7) LetDetermine f(2/3).a)b)c)d)e)8) Give the length of the curve determined byfor t from 0 to 2.a)b)c)d)e)9) Particles A and B leave the origin at the same time and move along the y-axis. Their positions are determined by the functionsfor t between 0 and 8. What is the velocity of particle B when particle A stops for the first time?a)b)c)d)e)10) The base of a solid is the region in the xy plane enclosed by the curvesover the interval [0,/4]. Cross sections of the solid perpendicular to the x-axis are squares. Determine the volume of the solid.a)b)c)d)e)11) Give the minimum value of the functionfor x > 0.a)b)c)d)e)12) Select the TRUE statement associated with the functiona) The graph of the function passes through the origin.b) The function does not have a horizontal asymptote.c) The function has a vertical asymptote at x = 0.d) The graph of the function is symmetric about the x-axis.e) The graph is always concave up.13) The function g is the derivative ofWhat is the derivative of the inverse of g at x = 3?a)b)c)d)e)14) The half-life of radium-226 is 1625 years. What percentage of a given amount of the radium will remain after 1000 years?a) 65.34%b) 65.20%c) 65.25%d) 65.35%e) 65.30%15) The function f satisfies the equationEvaluate f(/3).a)b)c)d)e)16) A rectangular box with square base and top is to be made to contain 2160 cubic feet. The material for the base costs 30 cents per square foot, the material for the top costs 50 cents per square foot, and the material for the sides costs 20 cents per square foot. Give the length of one side of the base (in feet) so that the cost is minimized.a)b)c)d)e)17) Which expression represents the volume of the solid generated when the region between the curvesover the interval [0,2] is rotated around the x-axis?a)b)c)d)e)1) 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)。
AP 微积分BC选择题Section2练习
29) Find the average value of the functionover the interval [0, 4].a)b)c)d)e)30) What is the y-intercept of the line tangent to the curve y = x2 + 7 at x = 3?a)b)c)d)e)31) Which of the following function(s) is continuous and differentiable?I.II.III.a) I and III onlyb) III onlyc) I and II onlyd) I onlye) II only32) Find ma)b)c)d)e)33) The graph of the derivative of f is shown below. Which of the following must be true?a) f is concave down on [0, 4].b) f is increasing on [-2, 2].c) f has a local maximum at x = 0.d) f has a local minimum at x = -2.e) f has a point of inflection at x = 4.34) The sum of two positive integers x and y is 60. Find the value of x that minimizesa)b)c)d)e)35) A particle moves on the curvefind the speed of the particle at time t = .a) 7.1414b) 6.7082c) 7.2801d) 3.3166e) 3.000036) The function f is defined asx 6Which of the following is false?a) f has a horizontal asymptote at y = 1.b) f has a vertical asymptote at x = 6.c) f is decreasing on [3, 6].d) f has a local maximum at x = 3.e) f is concave up for x > 6.37) A particle is moving along the x-axis and its position at time t > 0 is given byWhich of the following is (are) true?I. The particle changes direction at x = 2 and x = 6.II. The particle is slowing down on [0, 2].III. The particle is speeding up on [2, 6].a) II and III onlyb) I onlyc) II onlyd) I and III onlye) I, II and III38) f(x) is a differentiable function and it is decreasing on (,). Ifthen g has a local maximum ata)b)c)d)e)39) The rate at which a bacteria population grows is proportional to the number of bacteria present. Initially, there were 1000 bacteria present and the population doubled in 5 hours. Roughly how many hours does it take for the population to reach 10000?a)b)c)d)e)40) Find the radius of convergence of the seriesa)b)c)d)e)41)for 0 < x < 3The graph of g is shown above. Which of the following must be true? I.II.III.a) II and III onlyb) II onlyc) I and III onlyd) I and II onlye) I only42) If the region bounded by y= tan-1(x), y= and the y-axis is rotated about the y-axis, the volume of the solid formed isa) 0.674b) 0.215c) 1.348d) 0.430e) 0.41343) f (x) is represented by the Maclaurin seriesWhat is the slope of the line normal to the graph of f at x =?a)b)c)d)e)44) What are all values of h for whichconverge?a) h > 1b) h < 1c) h > 1d) h < 1e) -1 < h < 145) The base of a solid is the region bounded bythe x-axis, andthe line x = 7Each cross-section of the solid perpendicular to the x-axis is a square, with one side on the xy-plane. Which of the following expressions represents the volume of the solid?a)b)c)d)e)29.e30.d31.c32.b33.e34.d35.c36.a37.c38.a39.d40.b41.d42.a43.c44.c45.b。
ap微积分真题答案
ap微积分真题答案【篇一：ap 微积分bc 选择题样卷一】version - section i - part a calculators 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 fis 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 function-1is invertible. give the slope of the normal line to the graph of f atx = 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)【篇二：ap 微积分bc选择题样卷二】17 questions - 50 minutes1) the limit of the sequenceas n approaches is -3. what is the value of c? a)b)c)d)e)2) ifand y = 3 when x = -2, then what is y? a) b) c)d) e)3) the graph of the derivative of fis given below.which of the following is false about the function f?a) f is increasing on [1,4].b) f is concave down on [1,5/2].c) f is concave down on [-3,0).d) f is not differentiable at 0. e) the funciton is constant on (-,-3].4) determinea)b)c) d) e)5) give the area that lies below the x-axis and is contained within theregion bounded by the polar curvea) b) c) d) e)6) give the error that occurs when the area between the curve and the x-axis over the interval [0,1] is approximated by the trapezoid rule with n = 4. a)b)c)d)e)7) letdetermine f(2/3). a)b)c) d) e)8) give the length of the curve determined byfor t from 0 to 2. a)b)c)d)e)9) particles a and b leave the origin at the same time and move along the y-axis. their positions are determined by the functionsfor t between 0 and 8. what is the velocity of particle b when particlea stops for the first time? a) b)c)d) e)10) the base of a solid is the region in the xy plane enclosed by thecurvesover the interval[0,/4]. cross sections of the solid perpendicular to the x-axis are squares. determine the volume of the solid. a)b)c)d)e)11) give the minimum value of the functionfor x 0. a)b)c)d)e)12) select the true statement associated with the function【篇三：ap微积分考试详解】>微积分ap课程包括微积分ab (calculus ab) 和微积分bc(calculus bc)两门课。
AP微积分BC选择题Section1练习
b)
c)
d)
e)
Key
1.e
2.d
3.d
4.b
5.e
6.d
7.c
8.a
9.c
10.a
11.d
12.b
13.d
14.a
15.c
16.c
17.b
18.a
19.b
20.b
21.c
22.a
23.a
24.a
25.e
26.a
27.b
28.b
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AP微积分BC模考卷2023
AP 微积分 BC 模考卷 2023一、选择题（每题1分，共5分）1. 若函数f(x)在点x=a处可导，则f'(a)表示的是（）A. f(x)在x=a处的斜率B. f(x)在x=a处的函数值C. f(x)在x=a处的切线方程D. f(x)在x=a处的曲率A. lim(x→∞) f(x) = LB. lim(x→0) f(x) = LC. lim(x→a) f(x) = ∞D. lim(x→∞) f'(x) = L3. 若函数f(x) = x^3 3x在x=1处的导数为0，则（）A. x=1是f(x)的极大值点B. x=1是f(x)的极小值点C. x=1是f(x)的拐点D. x=1是f(x)的驻点A. ∫(0,1) x dxB. ∫(1,∞) 1/x^2 dxC. ∫(∞,∞) e^(x^2) dxD. ∫(0,2π) sin(x) dx5. 若f(x) = e^(2x)，则f''(x)是（）A. 2e^(2x)B. 4e^(2x)C. e^(2x)D. 2e^x二、判断题（每题1分，共5分）6. 若函数在闭区间上连续，则该函数在该区间上一定可积。
（）7. 若f'(x) > 0，则f(x)是单调递增函数。
（）8. 泰勒公式可以用来近似任何可导函数。
（）9. 第一类间断点处的函数一定不可导。
（）10. 两个函数的导数相等，则这两个函数一定相同。
（）三、填空题（每题1分，共5分）11. 函数f(x) = x^2在x=0处的导数f'(0) = ______。
12. 若f(x) = 3x^3 4x^2 + 2x，则f'(x) = ______。
13. ∫(0,π) sin(x) dx = ______。
14. 函数f(x) = e^x的n阶导数f^(n)(x) = ______。
15. 曲线y = x^3在点(1,1)处的切线方程是______。
AP微积分BC 2023年真题 附答案和评分标准 AP Calculus BC 2023 Real
AP微积分BC 2023年真题附答案和评分标准 AP Calculus BC2023 Real一、选择题1. 问题描述这个问题是关于……2. 解答过程解答过程如下： - 第一步：…… - 第二步：…… - 第三步：……3. 答案和评分标准答案为：A评分标准如下： - 如果只给出了答案，得0分。
- 如果给出了正确的解答过程，得1分。
二、填空题1. 问题描述这个问题是关于……2. 解答过程解答过程如下： - 第一步：…… - 第二步：…… - 第三步：……3. 答案和评分标准答案为：50评分标准如下： - 如果只给出了答案，得0分。
- 如果给出了正确的解答过程，得1分。
三、解答题1. 问题描述这个问题是关于……2. 解答过程解答过程如下： - 第一步：…… - 第二步：…… - 第三步：……3. 答案和评分标准答案为：解答过程如下：解答步骤1解答步骤2解答步骤3评分标准如下： - 如果只给出了答案而没有解答步骤，得0分。
- 如果给出了解答步骤但部分错误，得1分。
- 如果给出了正确的解答步骤，得2分。
四、简答题1. 问题描述这个问题是关于……2. 解答过程解答过程如下： - 第一步：…… - 第二步：…… - 第三步：……3. 答案和评分标准答案为：……评分标准如下： - 如果只给出了答案而没有解答步骤，得0分。
- 如果给出了解答步骤但部分错误，得1分。
- 如果给出了正确的解答步骤，得2分。
五、解决问题1. 问题描述这个问题是关于……2. 解答过程解答过程如下： - 第一步：…… - 第二步：…… - 第三步：……3. 答案和评分标准答案为：……评分标准如下： - 如果只给出了答案而没有解答步骤，得0分。
- 如果给出了解答步骤但部分错误，得1分。
- 如果给出了正确的解答步骤，得2分。
六、总结通过完成这道AP微积分BC 2023年真题的解答，我们学习了……总体而言，这道题目涵盖了……Markdown文本格式的输出使得我们能够清晰地呈现问题描述、解答过程、答案和评分标准，这对于学生来说非常有帮助。
ap微积分bc考试原题
AP微积分BC考试原题及答案一、选择题1.下列函数中，在区间(0, +∞)上是减函数的是( ) A. y = x^2 B. y = 1/x C. y =x^3 D. y = 2/x 答案：D2.若f(x) = ∫ (x^2 + 2x - 5) dx，则f'(x) = ( ) A. x^2 + 2x - 5 B. x^2 + 2x - 4 C.x^2 + 2x - 3 D. x^2 + 2x - 6 答案：D3.已知f(x) = sin x + cos x，则f'(x) = ( ) A. -cos x - sin x B. cos x - sin x C. sinx + cos x D. cos x + sin x 答案：B二、填空题4.若f(x) = (x - 1)/(x^2 + 1)，则f'(x) = _______．答案：f'(x) = \frac{x^2 +1}{(x^2 + 1)^2}5.设f(x) = x^3 + 4x^2 + x，则f'(x) = _______．答案：f'(x) = 3x^2 + 8x + 1三、解答题6.求函数f(x) = (sin x + cos x)^5 的导数．答案：f'(x) = (5\sin{x} \cdot (\sin{x}+ \cos{x})^4 \cdot (\cos{x} - \sin{x}) - 5\cos{x} \cdot (\sin{x} + \cos{x})^4 \cdot (\sin{x} - \cos{x})) / (\sin{x} + \cos{x})^2$7.求函数f(x) = x^3 - 3x^2 在区间(-∞, a) 上的最小值．答案：f'(x) = 3x^2- 6x = 3x(x - 2)，令，令f'(x) > 0，解得，解得x < 0或或0 < x < 2，因此，函数，因此，函数f(x)在在( - \infty,0)上单调递增，在上单调递增，在(0,2)上单调递减，在上单调递减，在(2, + \infty)上单调递增，又上单调递增，又f(0) = 0,f( - 1) = 4,f(1) = -2,f(4) = 16，故当，故当a < 0时，函数时，函数f(x)在区间在区间( - \infty,a)上的最小值为上的最小值为0；当；当0 \leqslant a < 1时，函数时，函数f(x)在区间在区间( - \infty,a)上的最小值为上的最小值为f(a)；当；当a > 1时，函数时，函数f(x)在区间在区间( - \infty,a)上的最小值为上的最小值为- 2$．。
AP考试模拟试题与答案1-微积分BC- AP Calculus-BC
1
14
(A) (B) 1 (C)
(D) 4 (E) 5
2
16
15. Which of the following is an equation of the line tangent to the curve with parametric equations x = 3t2 − 2, y = 2t3 + 2 at the point when t = 1?
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−3
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−2
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(x
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− 3 (x + 2)(x − 3) d x
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−3
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(E) lim n→0 n
III. f < 0 on (0, b)
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(C) II and III only (D) I and III only (E) I, II, and III
y f
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0
x b
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AP微积分_calculus_BC真题答案-048
0
3
1 1 3 f '(t )dt 1 1 2 2 2 2 2
f (3) f (0)
3 9 2 2
4 1 f (4) f (0) f '(t )dt (8 2 2 ) 8 2 0 2 f (4) f (0) 8 2 5 2
2003 AP calculus BC EXAM 答案
1-5 ECADC 6-10 CCBAC 11-15 DEAEB 16-20 CACDD 21-25 BEBDD 26-28 DED 76-80 EACDA 81-85 AAECA 86-90 CCCDB 91-92 BC
Free-response
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QUESTION1 Point of intersection e 3 x x at (T, S) =(0.238734, 0.488604)
(a) Area =
1
T
( x e 3 x )dx 0.442 or 0.443
1
(b) Volume = ((1 e 3 x )2 (1 x )2 )dx 1.423 or 1.424
4.52 2.52 5.147 or 5.148
9
(d) x(9) x (0)
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
x
a
0
b
(A)
y
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(B)
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AP Calculus Practice Exam
BC Version - Section I - Part A
Calculators ARE NOT Permitted On This Portion Of The Exam
28 Questions - 55 Minutes
1) Given
Find 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 that
and
a)
b)
c)
d)
e)
5) The function
is invertible. Give the slope of the normal line to the graph of f -1 at x = 3.
a)
b)
c)
d)
e)
6) Determine
a)
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) Determine
a)
b)
c)
d)
e)
9) Determine
a)
b)
c)
d)
e)
10) Give the radius of convergence for the series
a)
b)
c)
d)
e)
11) Determine
a)
b)
c)
d)
e)
12) The position of a particle moving along the x-axis at time t is given by
At which of the following values of t will the particle change direction?
I) t = 1/8
II) t = 1/6
III) t = 1
IV) t = 2
a) I, II and III
b) I and II
c) I, III and IV
d) II, III and IV
e) III and IV
13) Determine
a)
b)
c)
d)
e)
14) Determine the y-intercept of the tangent line to the curve
at 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 function
on 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 parabola
What is the maximum possible area of this rectangle?
a)
b)
c)
d)
e)
20) Compute
a)
b)
c)
d)
e)
21) Determine
a)
b)
c)
d)
e)
22) Determine
a)
b)
c)
d)
e)
23) Give the exact value of
a)
b)
c)
d)
e)
24) Determine
a)
b)
c)
d)
e)
25) Give the derivative of
a)
b)
c)
d)
e)
26) Give the first 3 nonzero terms in the Taylor series expansion about x = 0 for the function
a)
b)
c)
d)
e)
27) Determine
a)
b)
c)
d)
e)
28) Which of the following series converge(s)?
a) B only
b) A, B and C
c) B and C
d) A and B
e) A and C
1) 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)。