1969 ap calculus ab multiple choice

Text of AP Calculus Multiple-Choice Question Collection 1969-1998


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AP CalculusMultiple-ChoiceConcern Collection19691998

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Table of Contents

About This Collection vi

Questions 1

1969 AP Calculus AB Exam, Section 1 1

1969 AP Calculus BC Exam, Section 1 10

1973 AP Calculus AB Exam, Section 1 20

1973 AP Calculus BC Exam, Section 1 29

1985 AP Calculus AB Exam, Section 1 38

1985 AP Calculus BC Exam, Section 1 47

1988 AP Calculus AB Exam, Section 1 57

1988 AP Calculus BC Exam, Section 1 67

1993 AP Calculus AB Exam, Section 1 78

1993 AP Calculus BC Exam, Section 1 89

1997 AP Calculus AB Exam, Section 1 100

Part A 100

Part B 108

1997 AP Calculus BC Exam, Section 1 113

Part A 113

Part B 120

1998 AP Calculus AB Exam, Section 1 125

Part A 125

Part B 1331998 AP Calculus BC Exam, Section 1 138

Part A 138

Part B 147

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vi

About This Collection

About This Collection

Multiple-choice inquiries from past AP Calculus Exams administer a wealthy resource forteaching topics in the course and also reviewing for the exam yearly. Over the years,some topics have actually been added or rerelocated, yet almost all of the old concerns still offerinteresting avenues to investigate principles and assess student knowledge.Almethods consult the many current Course Description on AP Central for the currenttopic outlines for Calculus AB and also Calculus BC.

Please note the following:

The solution to each multiple-option question says one possible way to

fix that question. Tright here are often different ideologies that produce thevery same option of answer, and for some concerns such multiple approachesare offered. Teachers are likewise urged to investigate how the incorrectchoices for each question might be derived to assist students understand(and also avoid) common forms of mistakes.

Scientific (nongraphing) calculators were compelled on the AP CalculusExams in 1993.

Graphing calculators have been compelled on the AP Calculus Exams since1995. In 1997 and also 1998, Section I, Part A did not enable the use of a

calculator; Section I, Part B required the use of a graphing calculator. Materials had in this resource might not reflect the existing AP Course

Description and also exam in this subject, and teachers are advised to take thisinto account as they usage these materials to support their instruction ofstudents. For up-to-day information about this AP course and also exam, pleasedownfill the official AP Course Description from the AP Central Internet siteat apmain.collegeboard.com.

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1969 AP Calculus AB: Section I

90 MinutesNo Calculator

Keep in mind : In this examicountry, ln x denotes the herbal logarithm of x (that is, logarithm to the base e).

1. Which of the complying with defines a role f for which ( ) ( )? f x f x =

(A) 2( ) f x x= (B) ( ) sin f x x= (C) ( ) cos f x x=

(D) ( ) log f x x= (E) ( ) x f x e=

2. ( )ln 2 0 if and also only if x (E) 3 x >

3. If2 5 7

( ) , for 2,2

(2)

x x f x x

x f k

+ += =

and if f is consistent at 2 x = , then k =

(A) 0 (B)1

6 (C)

1

3 (D) 1 (E)

7

5

4.8

0 1

dx =+

(A) 1 (B)32

(C) 2 (D) 4 (E) 6

5. If 2 23 2 2, x xy y+ + = then the worth of dy

dx

at 1 x = is

(A) 2 (B) 0 (C) 2 (D) 4 (E) not defined

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1969 AP Calculus AB: Section I

12. If4

( )1

f x = and ( ) 2 , g x x= then the solution collection of ( ) ( )( ) ( ) f g x g f x= is

(A) 13 (B) 2 (C) 3 (D) 1, 2 (E) 1 , 23

13. The region bounded by the x-axis and also the part of the graph of cos y x= between2

x = and

2 x

= is separated into 2 areas by the line k = . If the location of the area for2

k is

3 times the area of the area for ,2

k x then k =

(A) 1arcsin4

(B) 1arcsin3

(C)6

(D)4

(E)

3

14. If the attribute f is characterized by 5 1( ) 1, then f x x f = , the inverse attribute of f , is identified by1( ) f x =

(A)5

11 x +

(B)5

11+

(C) 5 1

(D) 5 1 (E) 5 1 x +

15. If ( ) f x and also ( ) g x exist and also ( ) ( ) f x g x > for all real x, then the graph of ( ) y f x= and also the graphof ( ) y g x=

(A) intersect precisely as soon as.

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(B) intersect no more than as soon as.(C) do not intersect.

(D) might intersect more than when.

(E) have actually a common tangent at each point of intersection.

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1969 AP Calculus AB: Section I

16. If y is a role of x such that 0 y > for all x and also 0 y is given by ln .t vt

=

At what value of t does v obtain its maximum?

(A) 1 (B)1

2e (C) e (D)3

2e

(E) There is no maximum worth for v.

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1969 AP Calculus AB: Section I

20. An equation for a tangent to the graph of arcsin2

y = at the beginning is

(A) 2 0 x y = (B) 0 x y = (C) 0 x = (D) 0 y = (E) 2 0 x y =

21. At 0 x = , which of the following is true of the feature f characterized by 2 2( ) x f x x e= + ?

(A) f is increasing.

(B) f is decreasing.

(C) f is disconstant.

(D) f has actually a loved one minimum.

(E) f has actually a family member maximum.

22. ( )2ln xd edx =

(A) 21 xe

(B) 22 xe

(C) 2 x (D) 1 (E) 2

23. The area of the region bounded by the curve 2 x y e= , the x-axis, the y-axis, and also the line 2 x = isequal to

(A)4

2e

e (B)4

12

e (C)4 1

2 2e

(D) 42e e (E) 42 2e

24. If sin , 0 , y x e x=