MATH 121, Calculus I — Final Exam (Spring 2013)
May 15, 2013 — 4:30pm to 7:00pm
Name:
KU ID No.:
Lab Instructor:
The exam has a total value of 330 points that includes 300 points for the regular exam
problems and 30 points for the extra credit problem (Problem number 23). The exam
contains two distinct parts. Part I contains 18 multiple-choice problems with each problem
worth 10 points. Part II contains 5 show-your-work problems with each problem worth 30
points. The exam contains a total of 23 problems. The exam is strictly closed-book and
closed-notes. THE USE OF CALCULATORS IS NOT ALLOWED.
Score
Problem 1 Problem 13
Problem 2 Problem 14
Problem 3 Problem 15
Problem 4 Problem 16
Problem 5 Problem 17
Problem 6 Problem 18
Problem 7 Problem 19
Problem 8 Problem 20
Problem 9 Problem 21
Problem 10 Problem 22
Problem 11 Problem 23
Problem 12 Total score
1
, Part I — Multiple-Choice Problems
Instructions: Write the letter corresponding to each of your answers in the blank box that
is provided. Correct answers do not require work to receive full credit. However, partial
credit can be awarded for incorrect answers based on the work that is shown in the adjacent
blank spaces. Hence, you are strongly advised to show your work for each problem.
(1) [10 points]
√ Determine which of the following is an equation of the tangent line to the
curve y = x at the point (9, 3).
(A) y = 6x − 51.
(B) y = 3x + 24.
1 3
(C) y = x + .
6 2
√
x 9
(D) y = − √ + 3.
2 2 x
Answer:
dy
(2) [10 points] If x2 y + xy 2 = 3x, then is
dx
x2 + xy 2
(A) .
3
3 − 2xy − y 2
(B) .
x2 + 2xy
(C) 2x2 y + y 2 .
2x + 3
(D) .
x2 + x
Answer:
2
May 15, 2013 — 4:30pm to 7:00pm
Name:
KU ID No.:
Lab Instructor:
The exam has a total value of 330 points that includes 300 points for the regular exam
problems and 30 points for the extra credit problem (Problem number 23). The exam
contains two distinct parts. Part I contains 18 multiple-choice problems with each problem
worth 10 points. Part II contains 5 show-your-work problems with each problem worth 30
points. The exam contains a total of 23 problems. The exam is strictly closed-book and
closed-notes. THE USE OF CALCULATORS IS NOT ALLOWED.
Score
Problem 1 Problem 13
Problem 2 Problem 14
Problem 3 Problem 15
Problem 4 Problem 16
Problem 5 Problem 17
Problem 6 Problem 18
Problem 7 Problem 19
Problem 8 Problem 20
Problem 9 Problem 21
Problem 10 Problem 22
Problem 11 Problem 23
Problem 12 Total score
1
, Part I — Multiple-Choice Problems
Instructions: Write the letter corresponding to each of your answers in the blank box that
is provided. Correct answers do not require work to receive full credit. However, partial
credit can be awarded for incorrect answers based on the work that is shown in the adjacent
blank spaces. Hence, you are strongly advised to show your work for each problem.
(1) [10 points]
√ Determine which of the following is an equation of the tangent line to the
curve y = x at the point (9, 3).
(A) y = 6x − 51.
(B) y = 3x + 24.
1 3
(C) y = x + .
6 2
√
x 9
(D) y = − √ + 3.
2 2 x
Answer:
dy
(2) [10 points] If x2 y + xy 2 = 3x, then is
dx
x2 + xy 2
(A) .
3
3 − 2xy − y 2
(B) .
x2 + 2xy
(C) 2x2 y + y 2 .
2x + 3
(D) .
x2 + x
Answer:
2
