1969, 1973, 1985, 1993, 1997, 1998 AP Multiple Choice Sections, AB and BC, Solutions (620)

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Unformatted text preview: ions still offer interesting opportunities to investigate concepts and assess student understanding. Always consult the most recent Course Description on AP Central® for the current topic outlines for Calculus AB and Calculus BC. Please note the following: • The solution to each multiple-choice question suggests one possible way to solve that question. There are often alternative approaches that produce the same choice of answer, and for some questions such multiple approaches are provided. Teachers are also encouraged to investigate how the incorrect options for each question could be obtained to help students understand (and avoid) common types of mistakes. • Scientific (nongraphing) calculators were required on the AP Calculus Exams in 1993. • Graphing calculators have been required on the AP Calculus Exams since 1995. In 1997 and 1998, Section I, Part A did not allow the use of a calculator; Section I, Part B required the use of a graphing calculator. • Materials included in this resource may not reflect the current AP Course Description and exam in this subject, and teachers are advised to take this into account as they use these materials to support their instruction of students. For up-to-date information about this AP course and exam, please download the official AP Course Description from the AP Central Web site at apcentral.collegeboard.com. AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. vi 1969 AP Calculus AB: Section I 90 Minutes—No Calculator Note: In this examination, ln x denotes the natural logarithm of x (that is, logarithm to the base e). 1. Which of the following defines a function f for which f (− x) = − f ( x) ? (A) (B) f ( x) = sin x (D) 2. f ( x) = x 2 f ( x) = log x (E) f ( x) = e x ln ( x − 2 ) < 0 if and only if (A) x<3 (B) 0< x<3 (D) 3. x>2 (E) x>3 ⎧ 2x + 5 − x + 7 , for x ≠ 2, ⎪ f ( x) = If ⎨ x−2 ⎪ f (2) = k ⎩ 8 ∫0 dx 1+ x (A) 1 5. 2< x<3 and if f is continuous at x = 2 , then k = 1 6 (C) 1 3 (D) 1 (E) 7 5 (B) 3 2 (C) 2 (D) 4 (E) 6 (D) 4 (E) not defined = If 3 x 2 + 2 xy + y 2 = 2, then the value of (A) –2 (C) (B) (A) 0 4. f ( x) = cos x (C) (B) 0 dy at x = 1 is dx (C) 2 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 1 1969 AP Calculus AB: Section I 8 6. (A) 0 (E) 7. 1 2 For what value of k will x + (C) 1 (D) The limit does not exist. k have a relative maximum at x = −2? x (B) –2 (C) 2 (D) 4 (E) None of these If p ( x) = ( x + 2 )( x + k ) and if the remainder is 12 when p( x) is divided by x − 1, then k = (A) 2 9. (B) It cannot be determined from the information given. (A) –4 8. 8 ⎛1 ⎞ ⎛1⎞ 8⎜ + h ⎟ − 8⎜ ⎟ 2 ⎠ ⎝2⎠ ? What is lim ⎝ h →0 h (B) 3 (C) 6 (D) 11 (E) 13 When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is (A) 1 4π (B) 1 4 (C) 1 π (D) 1 (E) π (E) ln x 10. The set of all points (et , t ) , where t is a real number, is the graph of y = (A) 1 ex (B) 1 ex (C) 1 xex (D) 1 ln x 1⎞ ⎛ 11. The point on the curve x 2 + 2 y = 0 that is nearest the point ⎜ 0, − ⎟ occurs where y is 2⎠ ⎝ 1 1 (B) 0 (C) − (D) −1 (E) none of the above (A) 2 2 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 2 1969 AP Calculus AB: Section I 12. If f ( x) = (A) 4 and g ( x) = 2 x, then the solution set of f ( g ( x) ) = g ( f ( x) ) is x −1 ⎧1 ⎫ ⎨⎬ ⎩3⎭ (B) {2} (C) {3} (D) {−1, 2} (E) ⎧1 ⎫ ⎨ , 2⎬ ⎩3 ⎭ 13. The region bounded by the x-axis and the part of the graph of y = cos x between x = − π and 2 π π is separated into two regions by the line x = k . If the area of the region for − ≤ x ≤ k is 2 2 π three times the area of the region for k ≤ x ≤ , then k = 2 x= ⎛1⎞ (A) arcsin ⎜ ⎟ ⎝4⎠ (D) ⎛1⎞ arcsin ⎜ ⎟ ⎝3⎠ (E) π 4 (B) π 6 π 3 (C) 14. If the function f is defined by f ( x) = x5 − 1, then f −1 , the inverse function of f , is defined by f −1 ( x) = (A) (D) 1 5 x +1 5 x −1 (B) (E) 1 5 x +1 5 (C) 5 x −1 x +1 15. If f ′( x) and g ′( x) exist and f ′( x) > g ′( x) for all real x, then the graph of y = f ( x) and the graph of y = g ( x) (A) intersect exactly once. (B) intersect no more than once. (C) do not intersect. (D) could intersect more than once. (E) have a common tangent at each point of intersection. AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 3 1969 AP Calculus AB: Section I 16. If y is a function of x such that y′ > 0 for all x and y′′ < 0 for all x, which of the following could be part of the graph of y = f ( x) ? 17. The graph of y = 5 x 4 − x5 has a point of inflection at (A) (0, 0) only...
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This note was uploaded on 12/29/2010 for the course MATH 214 taught by Professor Smith during the Fall '10 term at Oregon Tech.

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