CALCULUS AB



|CALCULUS AB |

|SECTION I, Part A |

|Time – 30 minutes |

|Number of Questions – 15 |

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|A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION |

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|Directions: Solve each of the following problems, using the available space for scratchwork. After examining the form of the choices, |

|decide which is the best of the choices given and put your answer on the separate answer sheet. No credit is given for any work written on |

|the test. Do not spend too much time on any one problem. |

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|In this test: |

|(1) Unless otherwise specified, the domain of the function f is assumed to be the set of all real numbers x for which f(x) is a real |

|number. |

| |If [pic], then [pic] = |

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| |(A) [pic] |

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| |(B) [pic] |

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| |(C) [pic] |

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| |(D) [pic] |

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| |(E) [pic] |

| |If [pic], then when [pic], the value of [pic]is |

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| |(A) [pic] (B) 0 (C) -8 (D) -3 (E) [pic] |

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| |[pic] |

| |[pic] |

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| |[pic] |

| |[pic] |

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| |If [pic], which of the following features does the graph of [pic] have? |

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| |a local minimum at x = 2 and a local maximum at x = 3. |

| |a local maximum at x = 2 and a local minimum at x = 3. |

| |a point of inflection at x = 2 and a local minimum at x = 3. |

| |a local minimum at x = 2 and a point of inflection at x = 3. |

| |a local maximum at x = 2 and a point of inflection at x = 3. |

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| |[pic] |

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| |(A) [pic] (B) [pic] (C) 1 (D) 2 (E) nonexistent |

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| |[pic] |

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| |[pic] |

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| |[pic] |

| |[pic] |

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| |[pic] |

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| |[pic] |

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| |[pic] |

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|CALCULUS AB |

|SECTION I, Part B |

|Time – 27 minutes |

|Number of Questions – 9 |

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|A GRAPHING CALCULATOR IS REQUIRED FOR SOME QUESTIONS ON THIS PART OF THE EXAMINATION |

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|Directions: Solve each of the following problems, using the available space for scratchwork. After examining the form of the choices, decide |

|which is the best of the choices given and put your answer on the separate answer sheet. No credit is given for any work written on the test. |

|Do not spend too much time on any one problem. |

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|In this test: |

|The exact numerical value of the correct answer does not always appear among |

|the choices given. When this happens, select from among the choices the number |

|that best approximates the exact numerical value. |

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|Unless otherwise specified, the domain of the function f is assumed to be the set |

|of all real numbers x for which f(x) is a real number. |

| |[pic] |

|[pic][pic] |[pic] |

| |[pic] |

| |The total area of the regions bounded by the graphs of [pic] and [pic] is |

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| |(A) 0 (B) 0.262 (C) 0.316 (D) 0.523 € 0.632 |

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| |The radius of a sphere increases at a constant rate of 2 cm/min. At the time when the volume of the sphere is 40 cm3, what is the |

| |rate of increase of the volume in cm3/min? [pic] |

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| |2.122 (B) 9.549 (C) 56.562 (D) 113.124 (E) 293.954 |

| |Find all values c that satisfy the Mean Value Theorem for the function [pic] |

| |on the interval [pic]. |

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| |(A) 0.050 (B) -0.050 (C) 0.102 and 1.801 |

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| |(D) 0.050 and 2.449 (E) None exist in the interval. |

| |[pic][pic] |

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|[pic] | |

| |[pic] |

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|CALCULUS AB |

|SECTION II, Part A |

|Time –30 minutes |

|Number of Questions – 2 |

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|A GRAPHING CALCULATOR IS REQUIRED FOR SOME QUESTIONS ON THIS PART OF THE EXAMINATION |

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|Directions: Write your solution to each part of each problem in the space provided. On Part A, you are permitted to use your calculator|

|to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must |

|clearly indicate the setup of your problem, namely the equation, function, or integral you are using. If you use other built-in features|

|or programs, you must show the mathematical steps necessary to produce your results. |

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|General Instructions for Section II Part A and Part B |

|All problems are given equal weight, but the parts of a particular problem are not necessarily given equal weight. |

|Be sure to write clearly and legibly. If you make an error, cross out the work rather than try to erase it. Erased or crossed-out work |

|will not be graded. |

|Show all of your work. Clearly label any functions, graphs, tables, or other objects that you use. You will be graded on the |

|correctness and completeness of your methods as well as your answers. Answers without supporting work may not receive credit. |

|Justifications require that you give mathematical (non-calculator reasons) |

|Your work must be in standard mathematical notation rather than in calculator syntax. |

|Unless otherwise specified, answers (numeric or algebraic) need not be simplified. |

|If you use decimal approximations, you will be graded on accuracy. Unless otherwise specified, your final answers should be accurate to |

|three places after the decimal point. |

|Unless otherwise specified, the domain of the function f is assumed to be the set of all real numbers x for which the f(x) is a real |

|number. |

| |[pic] |

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| |[pic] |

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| |[pic] |

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| |[pic] |

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| |[pic] |

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|CALCULUS AB |

|SECTION II, Part B |

|Time – 30 minutes |

|Number of Questions – 2 |

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|A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION |

| |[pic] |

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| |[pic] |

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