Math 10A Winter 2009 Precalculus Review
The following questions review precalculus material from Sections 1.1 1.6 of our
textbook, e.g., 1.1.14 refers to Exercise (or Problem) 14 in Section 1.1. I strongly suggest
that you review this material by carefull
Section 4.5 Exponential and Logarithmic Equations
Exponential Equations
An exponential equation is one in which the variable occurs in the exponent.
EXAMPLE: Solve the equation 2x = 7.
Solution 1: We have
2x = 7
log2 2x = log2 7
x log2 2 = log2 7
x = log2
Macasieb
Sample Exam 1
Sections 2.1-2.4, 3.1-3.4
Calculus for Life Sciences
MATH 130 Sections 01*
These are typical problems that could be on the exam, though there are certainly other types of problems
that could also appear. Also note that the wording o
Cayla Walker
Mr. Michael Floren
Math 120
22 Sept 2013
Unit 2 Reflection
In Unit two (Sections 2a and 2b in the book), the class covered conversions first.
The most common example of this was miles per hour, second, minute, etc. A great
example of this wou
Math 131 Fall 2013
1
CHAPTER 2 EXAM (PRACTICE PROBLEMS - SOLUTIONS)
Problem 1. Let f ( x ) = 2 x3 8 .
(a) Use the limit of difference quotients to find the instantaneous rate of change of the function
at the point x = 3 .
(b) Find an equation of the tange
MATH 131
Oehrtman
Fall 2013
Exam 1
Name (print): _
(25 points)
1. The function f graphed below is decreasing and has a removable discontinuity at x = 2.5.
y
4.31
4.23
y = f ( x)
2.4
2.5
x
2.6
a. Explain how you know that lim f ( x ) exists (without relyin
MATH 131
Fall 2012
Exam 2
Name (print): _
(15 points)
1. State the limit definition of the derivative of a function f.
(25 points)
2. Fill in the following blanks with appropriate expressions from the definition of the derivative to
label the quantities m
MATH 131
Oehrtman
Fall 2012
Exam 1
Name (print): _
Depth below ocean floor (m)
(15 points)
1. The graph of f (t) below represents the depth in meters below the Atlantic Ocean floor where t
million-year-old rock can be found.*
140
*
Data of Dr. Murlene Cla
Math 131 Fall 2013
1
CHAPTER 5 EXAM (PRACTICE PROBLEMS - SOLUTIONS)
Problem 1. A skydiver jumps from an airplane and her velocity is then v (t ) ft/s after t seconds
of freefall in a tucked position, so that she continually speeds up.
a. Use an integral t
Math 131 Fall 2013
1
CHAPTER 5 EXAM (PRACTICE PROBLEMS)
Problem 1. A skydiver jumps from an airplane and her velocity is then v (t ) ft/s after t seconds
of freefall in a tucked position, so that she continually speeds up.
a. Use an integral to express th
MATH 131
Fall 2013
Exam 2
Name (print):
Solutions
(30 points)
1. Fill in the following blanks with appropriate expressions from the definition of the derivative
f ( x) = lim
x 0
f ( x + x) f ( x)
x
to label the quantities marked on the graph of y = f ( x
MATH 131
Fall 2013
Exam 2
Name (print): _
(30 points)
1. Fill in the following blanks with appropriate expressions from the definition of the derivative
f ( x) = lim
x 0
f ( x + x) f ( x)
x
to label the quantities marked on the graph of y = f ( x ) as ill
MATH 131
Fall 2013
Chapter 5 Exam
Name (print): _
Show all of your work.
1. The table below gives the speed, v(t ) in meters per second, of a device dropped from a weather
balloon for 80 seconds. Assume that the speed was increasing the entire time it fel
MATH 131
Final Exam
Fall 2012
Name (print): _
Instructions: There are 8 numbered questions worth a total of 250 points. Make sure you have a
complete copy of the exam before beginning. You must show all of your work to receive full credit
for every questi
MATH 131
Fall 2013
Chapter 5 Exam
Name (print): _
Show all of your work.
1. The table below gives the speed, v(t ) in meters per second, of a device dropped from a weather
balloon for 80 seconds. Assume that the speed was increasing the entire time it fel
MATH 131
Fall 2012
Chapter 5 Exam
Name (print): _
Show all of your work.
1. The table below gives the expected growth rate, g (t ) , in ounces per week, of the weight of a baby
in its rst 54 weeks of life (which is slightly more than a year). Assume for t
MATH 131
Fall 2012
Chapter 4 Exam
Name (print): _
Show all of your work.
2
1. Let f ( x) = e x . In the following, do not substitute a numerical value for the constant e.
a. For what values of x is f concave up and decreasing? Fully justify your answer.
b
MATH 131
Fall 2013
Chapters 3-4 Exam Solutions
Name (print): _
(30 points)
1. Find all of the critical points of y = ( x 1)3 ( x + 3)2 . Classify each one as a relative maximum,
relative minimum, or neither and justify your answers.
y = 3( x 1)2 ( x + 3)2
MATH 131
Fall 2013
Chapters 3-4 Exam
Name (print): _
(30 points)
1. Find all of the critical points of y = ( x 1)3 ( x + 3)2 . Classify each one as a relative maximum,
relative minimum, or neither and justify your answers.
MATH 131
(30 points)
2. Suppose