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Math 200 - Exam 1 - April 27, 2016 - Prof. Ronald K. Perline, Exams of Calculus

Drexel University Calculus

Prof. Ronald K. Perline

The instructions and problems for the math 200 exam 1 held on april 27, 2016. The exam consists of free response and multiple choice questions covering topics such as finding the area of triangles, equations of planes, distance between a point and a line, acute angles between planes, equations of tangent lines, and spheres. Students are not allowed to use books, notes, or electronic devices during the exam.

Typology: Exams

2015/2016

Uploaded on 10/18/2016

krj1126 🇺🇸

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Math 200 - Exam 1 - 4/27/2016

Name: Section:

The following rules apply:

•This is a closed-book exam. You may not use

any books or notes on this exam.

•For free response questions, you must show

all work. Answers without proper justification

will not receive full credit. Partial credit will be

awarded for significant progress towards the cor-

rect answer. Cross off any work that you do not

want graded.

•For multiple choice questions, circle the let-

ter of the best answer. Make sure your cir-

cles include just one letter. These problems will be

marked as correct or incorrect; partial credit will

not be awarded for problems in this section.

•You have 50 minutes to complete this exam.

When time is called, stop writing immediately and

turn in your exam to the nearest proctor.

•You may not use any electronic devices in-

cluding (but not limited to) calculators, cell phone,

or iPods. Using such a device will be considered

a violation of the university’s academic integrity

policy and, at the very least, will result in a grade

of 0 for this exam.

Page Points Score

2 20

4 15

5 10

6 15

7 10

8 10

9 10

10 5

11 5

Total: 100

Discover Exams of Calculus Drexel University

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Download Math 200 - Exam 1 - April 27, 2016 - Prof. Ronald K. Perline and more Exams Calculus in PDF only on Docsity!

Math 200 - Exam 1 - 4/27/

Name: Section:

The following rules apply:

This is a closed-book exam.any books or notes on this exam. You may not use
For free response questions, you must showall work. Answers without proper justification will not receive full credit.awarded for significant progress towards the cor- Partial credit will be rect answer.want graded. Cross off any work that you do not
For multiple choice questions, circle the let-ter of the best answer. Make sure your cir- cles include just one letter. These problems will bemarked as correct or incorrect; partial credit will not be awarded for problems in this section.
You have 50 minutes to complete this exam. When time is called, stop writing immediately and turn in your exam to the nearest proctor.
You may not use any electronic devicescluding (but not limited to) calculators, cell phone, in- or iPods.a violation of the university’s academic integrity Using such a device will be considered policy and, at the very least, will result in a gradeof 0 for this exam.

Page Points Score 2 20 4 15 5 10 6 15 7 10 8 10 9 10 10 5 11 5 Total: 100

Part I: Free Response

(20 points) Consider the three points A(1, 1 , −1), B(2, 2 , 3), and C(0, 1 , 2). (a) Find the area of the triangle with vertices A, B, and C.

(15 points) Find the distance between a pointand B(3, 2 , 0). P (4, 3 , −1) and a line containing points A(1, 2 , 1)

(10 points) Compute the acute angle between the two planes P 1 and P 2 : P 1 : x + 2y + 2z = 0 P 2 : 2x − 3 y + z = 0

Part II: Multiple Choice

(a) x^2 + y^2 + z^2 = 5. (5 points) Which of the following is the equation of a sphere that has a center at the point(1, 2 , 3) and is tangent to the xz-plane?
(b) (x + 1)^2 + (y + 2)^2 + (z + 3)^2 = - (c) (x + 1)^2 + (y + 2)^2 + (z + 3)^2 =
(d) (x − 1)^2 + (y − 2)^2 + (z − 3)^2 = - (e) (x − 1)^2 + (y − 2)^2 + (z − 3)^2 =
- (a) t ≥ 6. (5 points) Which of the following is the domain of −→r (t) = ln(t + 5)−→ i − et−→ j − √ 10 − t−→ k?
(b) t ≤ −10 or t > - (c) t ≤ −5 or t ≥
(d) − 10 ≤ t < - (e) − 5 < t ≤

(5 points) Which of the following is a vector of length 2 that makes an angle of π 3 with the positive x-axis? (a) 〈√ 3 , 1 〉 (b) 〈√ 3 , − 1 〉 (c) 〈 1 , √ 3 〉 (d) 〈 1 , −√ 3 〉 (e) 〈√ 2 , √ 2 〉
(5 points) Which of the following is the equation of the plane that contains a point (1and is parallel to the plane 2x − y + 3z = 2? , 1 , 1)

(a) 2x − y + 3z = 0 (b) 2x − y + 3z = 1 (c) 2x − y + 3z = 2 (d) 2x − y + 3z = 3 (e) 2x − y + 3z = 4

(5 points) Which of the following best represents −x^2 − y^2 + z^2 = −1? (a) (d)

(b) (e)

(c)

(5 points) Which of the following graphs is the level curve ofthrough P (− 2 , 0)? f (x, y) = x^2 − 4 y^2 which passes

(a) (d)