Math 171
Exam I (with answers)
Fall 2012
1. (a) [5 points] Find a line through the point (6, 3) that is perpendicular to the line
y = 2x + 1.
Solution: The given line has slope 2. The slope of any line perpendicular to it
is the negative reciprocal of 2,
Math 171 Fall 2005
C. Gmez o December 20, 2005
Final Exam
Name:
SOLUTIONS
Sharon Garthwaite
Problem Score 1 2 3 4 5 6 7 8 9 10 Total 12 12 12 12 12 12 12 12 12 12 100
Please circle your TAs name:
Evan (Alec) Johnson Paul Johnson Patrick Rault This exam co
Math 171
Exam II (with answers)
1. [8 points] The graph of x2 + y 2
Fall 2009
2x + 5y + 5 = 0 is a circle. Find its center and radius.
Solution: We complete the square (twice):
x2 + y 2
2x + 5y + 5 = (x2 2x) + (y 2 + 5y ) + 5
= (x 2/2)2 ( 2/2)2 + (y + 5/2
Math 171
Exam I (with answers)
Fall 2013
1. [10 points] Let f (x) =
interval notation.
|3x 1| 4. What is the domain of f ? Write the solution in
Solution: f (x) is dened when |3x 1| 4 0, so when |3x 1| 4. This is true
when either
3x 1 4 or 3x 1 4
3x 3 or
Math 171
Exam II (with answers)
Fall 2012
1. [10 points] Consider a right triangle with angle . If tan = 2 and the length of the
hypotenuse is 3, nd the lengths of the other two sides.
Solution: Let a and b be the lengths of the sides, where a is the side
Math 171
Final Exam (with answers)
1. [6 points] Find the domain of f (x) =
Fall 2009
x2 3x 1.
Solution: f (x) is dened as long as x2 3x 1 0. First we solve x2 3x 1 = 0;
3
941(1)
using the quadratic equation, x =
= 32 13 . Plugging in values we see
2
tha
Math 171
Exam II (with answers)
Fall 2013
1. (a) [8 points] Suppose that a slice from a 12-inch pizza has an area of 42 square inches.
What is the angle of the slice in radians?
Solution: A pizza with diameter 12 has radius 6, so it has area 62 = 36 .
42
Math 171
Final Exam (with answers)
Fall 2013
1. [6 points] The graph of x2 + y 2 + 6x 8y + 6 = 0 is a circle. Find its center and radius.
Solution: We complete the square (twice):
x2 + y 2 + 6x 8y + 6 = (x2 + 6x) + (y 2 8y ) + 6
= (x + 6/2)2 (6/2)2 + (y 8
Math 171
Final Exam (with answers)
Fall 2012
1. Find the following derivatives. Do not simplify.
x5 + 1
d
.
(a) [6 points] Find
dx x2 sin x cos x
Solution: By the quotient and product rules,
d
d
(x2 sin x cos x) dx (x5 + 1) (x5 + 1) dx (x2 sin x cos x)
d
Math 171 Fall 2007
C. Gmez o December 21, 2007
Final Exam
Name: TA's Name Discussion Section Time
Problem 1 2 3 4 5 6 7 8 Total
Score
9 12 10 15 14 16 12 12
This exam contains 10 pages, and 8 problems. Before you begin, please make sure all the pages are