1969 AP Calculus BC Multiple-Choice Questions with Answers

1969 AP Calculus BC Multiple-Choice Questions with Answers

The 1969 AP Calculus BC exam features multiple-choice questions designed to assess students' understanding of advanced calculus concepts. This exam includes a variety of topics such as limits, derivatives, integrals, and the Mean Value Theorem. Students preparing for the AP Calculus BC exam will find valuable practice questions that reflect the style and rigor of the actual test. Each question is accompanied by an answer key for quick reference, making it an essential resource for effective study and review. Ideal for high school students aiming for college credit through AP exams.

Key Points

  • Includes 40 multiple-choice questions from the 1969 AP Calculus BC exam.
  • Covers key calculus topics such as derivatives, integrals, and limits.
  • Provides an answer key for all questions, facilitating self-assessment.
  • Designed for students preparing for the AP Calculus BC exam to enhance their understanding.
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AP Calculus Multiple-Choice Question Collection 10
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.
1969 AP Calculus BC: 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. The asymptotes of the graph of the parametric equations
1
,
1
t
xy
tt
==
+
are
(A) 0, 0xy== (B)
0x
=
only (C) 1, 0xy
=
−=
(D)
1x =−
only (E) 0, 1
x
y
=
=
2. What are the coordinates of the inflection point on the graph of (1)arctan?yx x
=
+
(A)
()
1,0− (B)
()
0,0 (C)
(
)
0,1 (D) 1,
4
π
⎛⎞
⎜⎟
⎝⎠
(E) 1,
2
π
⎛⎞
⎜⎟
⎝⎠
3. The Mean Value Theorem guarantees the existence of a special point on the graph of yx=
between
()
0,0 and
()
4,2 . What are the coordinates of this point?
(A)
()
2,1
(B)
()
1,1
(C)
()
2, 2
(D)
11
,
2
2
⎛⎞
⎜⎟
⎝⎠
(E) None of the above
4.
8
0
1
dx
x
=
+
∫
(A) 1 (B)
3
2
(C) 2 (D) 4 (E) 6
5. If
22
32 2,xxyy++= then the value of
dy
dx
at
1
x
is
(A) –2 (B) 0 (C) 2 (D) 4 (E) not defined
AP Calculus Multiple-Choice Question Collection 11
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.
1969 AP Calculus BC: Section I
6. What is
88
0
11
88
22
lim ?
h
h
h
→
⎛⎞⎛⎞
+−
⎜⎟⎜⎟
⎝⎠⎝⎠
(A) 0 (B)
1
2
(C) 1 (D) The limit does not exist.
(E) It cannot be determined from the information given.
7. For what value of k will
k
x
x
+
have a relative maximum at 2?x
=
−
(A) –4 (B) –2 (C) 2 (D) 4 (E) None of these
8. If
22
() () (), () (),hx f x g x f x gx
′
=− =− and () (),gx fx
′
=
then ( )hx
′
=
(A) 0 (B) 1 (C) 4 ( ) ( )
f
xgx−
(D)
()()
22
() ()gx f x−−
(E)
(
)
2()()gx f x−− +
9. The area of the closed region bounded by the polar graph of 3cosr
=
+θ is given by the integral
(A)
2
0
3cosd
π
+θθ
∫
(B)
0
3cosd
π
+
θθ
∫
(C)
()
2
0
23cosd
π
+
θθ
∫
(D)
()
0
3cos d
π
+θθ
∫
(E)
2
0
23cosd
π
+
θθ
∫
10.
2
1
2
0
1
x
dx
x
=
+
∫
(A)
4
4
−π
(B) ln 2 (C) 0 (D)
1
ln 2
2
(E)
4
4
+
π
AP Calculus Multiple-Choice Question Collection 12
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.
1969 AP Calculus BC: Section I
11. The point on the curve
2
20xy+=
that is nearest the point
1
0,
2
⎛⎞
−
⎜⎟
⎝⎠
occurs where y is
(A)
1
2
(B)
0
(C)
1
2
−
(D)
1−
(E) none of the above
12. If
2
0
() ,
x
t
Fx e dt
−
=
∫
then ( )Fx
′
=
(A)
2
2
x
x
e
−
(B)
2
2
x
x
e
−
− (C)
2
1
2
1
x
e
e
x
−+
−
−+
(D)
2
1
x
e
−
− (E)
2
x
e
−
13. The region bounded by the x-axis and the part of the graph of cosyx
=
between
2
x
π
=−
and
2
x
π
= is separated into two regions by the line
x
k
=
. If the area of the region for
2
x
k
π
−≤≤ is
three times the area of the region for
,
2
kx
π
≤
≤ then
k
=
(A)
1
arcsin
4
⎛⎞
⎜⎟
⎝⎠
(B)
1
arcsin
3
⎛⎞
⎜⎟
⎝⎠
(C)
6
π
(D)
4
π
(E)
3
π
14. If
2
2 and 2 1,yx u x=+ =− then
dy
du
=
(A)
()
2
2
224
21
xx
x
−+
−
(B)
2
624
x
x
−
+ (C)
2
x
(D)
x
(E)
1
x
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End of Document
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Faqs of 1969 AP Calculus BC Multiple-Choice Questions with Answers
What topics are covered in the 1969 AP Calculus BC exam?
The 1969 AP Calculus BC exam covers a wide range of topics essential for advanced calculus understanding. Key areas include limits, derivatives, integrals, sequences, and series. The exam also emphasizes the application of the Mean Value Theorem and the Fundamental Theorem of Calculus. Students will encounter problems that require both conceptual understanding and computational skills, making it a comprehensive assessment of their calculus knowledge.
How can students use the 1969 AP Calculus BC questions for exam preparation?
Students can utilize the 1969 AP Calculus BC multiple-choice questions as a practice tool to familiarize themselves with the exam format and question types. By working through these problems, students can identify their strengths and weaknesses in calculus concepts. The accompanying answer key allows for immediate feedback, enabling students to focus their study efforts on areas needing improvement. This practice can significantly enhance their readiness for the actual AP exam.
What is the significance of the Mean Value Theorem in calculus?
The Mean Value Theorem is a fundamental concept in calculus that establishes a connection between the derivative of a function and its average rate of change over an interval. It states that if a function is continuous on a closed interval and differentiable on the open interval, there exists at least one point where the derivative equals the average rate of change. This theorem is crucial for understanding the behavior of functions and is often applied in solving real-world problems involving motion and optimization.
What types of questions can students expect from the AP Calculus BC exam?
Students can expect a variety of question types on the AP Calculus BC exam, including conceptual questions that test understanding of calculus principles and computational questions that require solving problems. The exam typically includes questions on limits, derivatives, integrals, and series. Some questions may involve graphical interpretations, while others may require analytical reasoning. This diverse range of questions ensures that students demonstrate a comprehensive understanding of calculus.