Exam #1 Information
MATH 166 – Sections 6,7,8,9,10,11
Fall 2014
• Exam Date/Time: Friday, Sept. 19, 2014, 10:00am – 10:50am
• Exam Location: Mol-Bio 1414 (the usual “lecture” room)
You must take the exam on the scheduled date and time unless one of
the following situations applies (see syllabus for details – documentation required):
– You have a medical excuse documented by a note from a doctor
on a prescription pad or equivalent documentation.
– You have a family emergency.
– You are representing ISU at an official university event.
– You are called to military service.
– You have a mandated court appearance (jury duty, etc.).
• Time Limit: 50 minutes
• Plan to get to the test location EARLY! Extra time will not be
extended to students who arrive late.
• At the beginning of the exam:
– You will be required to clear your desk of everything except pens,
pencils, erasers, and a calculator.
– Calculators are allowed (stand-alone calculators only – no smartphone calculator apps or any device with wireless communication
capability).
– All hats must be removed.
– Phones and all electronic devices (other than your calculator) must
be turned completely off and put away.
• During the exam:
– Once the exam starts, you may not leave the room unless you first
turn in your test and then you may not return.
– Show all steps on each problem. Partial credit will be awarded for
correct steps even if the final answer is incorrect. Points will be
deducted for incorrect steps even if the final answer is correct.
– If needed, scratch paper will be provided.
• When you finish the exam:
– You must present your ISU student ID to the person collecting
your exam!
• Covered material: Sections 6.1 - 6.6
• Exam Structure: Computational problems solved on paper with all
work shown (like the quizzes).
• Suggestions for studying:
– This exam is strongly based on homework. Make sure you can do
every homework problem on your own, on paper, without looking
at the book or your notes.
– The sample test is also a good thing to study. Again, make sure
that you can do every problem on the sample test on your own,
on paper, without looking at the book or your notes. Also, the
actual exam is not restricted to the problem types appearing on
the sample test. Any topic in the listed sections is fair game on
the actual exam.
• Key Things to Know (by section):
– Find volume using the slice method (6.1)
– Find volume using the disk method (6.1)
– Find volume using the washer method (6.1)
– Find volume using cylindrical shells (6.2)
– Find arc length given y = f (x). (6.3)
– Find arc length given x = g(y). (6.3)
– Use the Fundamental Theorem of Calculus to set up an arc length
integral. (6.3)
– Find surface area given y = f (x). (6.4)
– Find surface area given x = g(y). (6.4)
– Find surface area by integrating along the axis that is not the axis
of rotation. (6.4)
– Calculate work done by a variable force. (6.5)
– Use Hooke’s Law to calculate the work done to stretch/compress
a spring. (6.5)
– Calculate work done when moving an object of changing mass (i.e.
“hanging rope”, “leaky bucket”). (6.5)
– Calculate work done when pumping fluid from a container. (6.5)
– Find moment(s) and/or center of mass of a thin plate with constant density. (6.6)
– Find moment(s) and/or center of mass of a thin plate with variable
density. (6.6)
– Find moment(s) and/or center of mass of a thin plate bounded by
two curves. (6.6)
– Find moment(s) and/or center of mass of a thin wire with constant
density. (6.6)
Name:
Math 166 A: Calculus II
Exam #1 – SAMPLE – Summer 2014
INSTRUCTIONS: Calculators are allowed, but show all work – including integration details.
Answers without complete work will NOT receive full credit. Clearly indicate final answers. The
maximum possible score is 70 points.
Question 1 (5 points). The base of a solid is the region between the curve y = 3 cos x and the x-axis from
x = 0 to x = π2 . The cross sections perpendicular to the x-axis are isosceles right triangles with one leg on
the base of the solid. Find the volume of the solid.
Question 2 (5 points). Find the volume of the solid generated by revolving the region bounded by y = cos πx
and the x-axis between x = −0.5 and x = 0.5 around the x-axis.
Question 3 (5 points). Find the volume √
of the solid generated by revolving the region in the first quadrant
bounded above by y = 3 and below by y = 3x around the line x = −1.
Question 4 (5 points). Use the shell method to find the volume of the solid generated by revolving the region
bounded by y = 2x, x = 3, and the x-axis around the line x = −4.
3
Question 5 (5 points). Find the length of the graph of x = 32 (y − 1) 2 from y = 16 to y = 25.
Question 6 (5 points). Set up but do not solve an integral giving the arc length of the curve x = 7 tan y
from y = 0 to y = π4 .
Question 7 (5 points). Set up but do not solve an integral giving the surface area generated by revolving
the curve xy = 3 from y = 1 to y = 2 around the y-axis.
Question 8 (5 points). Find the surface area generated by revolving the curve y =
x = 23 around the x-axis.
√
4x − x2 from x =
1
2
to
Question 9 (5 points). A force of 3 N will stretch a rubber band 5 cm. Assuming that Hooke’s Law applies,
how much work is done on the rubber band by a 9 N force?
Question 10 (5 points). A construction crane lifts a bucket of sand originally weighing 145 lb at a constant
rate. Sand is lost from the bucket at a constant rate of 0.5 lb/ft. How much work is done in lifting the sand
70 ft? (Ignore the weight of the bucket and connecting cable.)
Question 11 (5 points). A swimming pool has a rectangluar base 12 ft long and 24 ft wide. The sides are
5 ft high, and the pool is full of water weighing 62.4 lb/f t3 . How much work will it take to lower the water
level 2 feet by pumping the water out over the top of the pool?
Question 12 (5 points). A thin plate with density δ(x) = x covers the trianglular region in the first quadrant
bounded by y = −x + 7. Find the center of mass of the plate.
Question 13 (5 points). Find the moment
√ about the y-axis of of a thin wire of constant density that lies
along the curve y = x2 from x = 0 to x = 2.
Question 14 (5 points). Find the center of mass of a thin plate that is bounded by the graphs of g(x) = x2
and f (x) = x + 12. Assume a constant density of δ = 1.