MATH 1432 Review for Test 2
When: September 22 – 26
Do not forget to reserve a seat for Test 2.
Where: CASA - GARRISON GYM.
If this is the first time that you will be taking your exam at CASA and have not registered your finger
scan/picture with CASA (GAR or CBB), please make sure you've completed this registration process
prior to arriving for your exam at CASA-GAR to avoid being deny access to your exam on exam day.
Time: 50 minutes
Number of questions: 10
6 Multiple Choice Questions
4 Free Response Questions
What is covered: Chapter 7
-Integration
-Average Value
-Finding the area of a region.
-Finding the volume of solids (with given cross sections and of revolution)
-Disk/Washer, Shell Methods.
-Finding arc length, surface area, centroid. Pappus’s Theorem.
-Differential Equations, Exponential Growth/Decay.
-Improper Integrals.
Do not be late for your test. Plan to be at the testing center 10-15 minutes before your
scheduled time. If you miss your reserved seat, log in to your CASA account and try to
reschedule; you can do this if there are any available seats.
Remember the make-up policy: NO MAKE-UPS! If you miss your test, you will get a
zero. When you take the final, it will replace ONE missed test.
Take Practice Test – 2!
Do not forget to go to CASA for fingerprint/picture process before your test date.
Do not forget to bring your COUGAR ID when you go to the testing center.
For the free response part, please show your work neatly. Do not skip steps.
When you take the test, you will see a score in your CASA grade sheet right away. That
score is for the multiple choice part only. The grade for the Free Response Part will be
posted later, after the papers are graded.
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Example a) Let f be a positive function. The area bounded by f(x) and the xaxis from x=2 to x=6 is 21/5. Find the average value of this function.
Example b) The acceleration of a particle in one dimensional motion at time t
is given by a(t)=3t−2. Given that the initial velocity of the particle is 0, find the
average velocity of this particle over the first 6 seconds.
2 Example: a) Find the area of the region bounded by f  x   2 x and g  x  
1 2
x .
4
Example: Given that the centroid of a region is (4,12) and its area is 10, find the
volume of the solid formed when this region is rotated about the line y=2.
Example: Set up the formula that gives the arc length of the following curve:
f  x 
2
 x  13 / 2 ,
3
x  1,2
3 Example: Give the general solution:
a)
b)
y' 
y' 
xy  4 y
x2 1
xy 2  x 2 y 2
x y 1
6 Example: Determine if each integral is improper. If it is improper, state why, rewrite it
using proper limit notation, and solve.
27
a.
x
2 / 3
dx
0
4
b.
1

4x
0
9
c.
  x  1
dx
2/3
dx
1
4
d.

e
x
x
0
dx
1
 0 ex dx
6
1
f. 
dx
2
x2

1
g. 
dx
 1 x 2
1
e.
h.
i.
j.
k.

5




2
(x  1)1/2 dx
1

5

0
ex
dx
1  2e x
1
dx
( x  4) 2
1
dx
x +4
2
8 Example: Rewrite the improper integral using proper limit notation, and solve.
k.


0
1
dx
x +4
2
9 y
2
Example: Let R be the region bounded by x  2 y 2 and x  .
a) Graph this region and label the points of intersection.
b) Find the area of the region.
c) If R is the base of a solid such that the cross sections perpendicular to y-axis are
squares, set up the formula for the volume of that solid.
d) Set up the formula that will give the volume of the solid formed when R is rotated
about the y-axis.
e) Set up the integral that will give the surface area of the solid generated when R is rotated
about the y-axis.
4 Example: Let R be the region bounded by f  x   3  x 2 and g  x   2 x .
Set up the formulas that will give the volume of the solid formed when R is rotated
a) about the x-axis.
b) about the y-axis using disc/washer method.
c) about the y-axis using shell method.
5 Example: Given that 10% of a radioactive substance decays in 5 years, give a
formula for the amount of substance in terms of t if the initial amount is 100 grams.
Exercise: The population of a bacteria culture increases by 20% in 10 hours. What
is the population in 24 hours if the initial population is 1000?
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