Download Intermediate Algebra Exam IV—Take-Home

Intermediate Algebra Exam IV—Take-Home Component
Name____________________________________________
Vosbury
Rules: You are allowed to help each other. You may receive help from anyone.
Your responsibility is to learn how to do the problems and understand them. The
help you receive should be in the form of hints and explanations showing you how to
do the problem. It should not involve someone doing the problem for you
completely. You should write up your own solutions independently even if you have
worked together with others on all the problems. You will be required to solve some
of the problems (or nearly identical problems) in class or in my office. You can
reduce the extent of this requirement if I observe you working on problems in the
classroom (before or after class or during designated class time) or in the E-Building
conference room or Academic Success Center and you turn in the test at least one
day before the last night of class.
Show a solution method for each problem
2x
8
1. Simplify.
 2
2
x  2x x  4
2. Two people are able to work on a job together with each working at the same speed
at which he could work alone. One can do the job alone in 8 hours and the other can
do the job alone in 6 hours. How long would it take them to do the job working
together?
EC If the time to do the job alone is “a” hours for one man and “b” hours for the other
man, how long will it take the two to do the whole job working together in terms of a and
b?
3. Simplify.
274 3
4. Simplify.
x5 2  x3 2
x2
5. Simplify.
 1024 
25
6-12 Write in simplified radical form. All variables are positive real numbers.
72x 3 y 4
6.
7.
3
32x 6 y11
8.
6
64x 3 y 6
9.
10.
11.
12.
8 xy 3
2 x5
3
16
xy 2
4
6 2
2 x 2 xy  32 x3 y  x 8 xy
13-15 Solve each equation.
13.
2 x2  4  x  2
14.
x  7  3x  3
15.
x
2
 15  4
13
16. Two trains are 480 miles apart and traveling toward each other. One of the trains is
traveling at an average of 10 miles per hour faster than the other train. They will pass
each other in 4 hours. Find the average speed of each train. You must state what
your variable stands for and show an equation in your solution even though the
answers are “nice” numbers.
17. A red boat and a green boat each depart from the same location traveling in directions
that form a right angle. The red boat is traveling at 15 nautical miles per hour and the
green boat is traveling at 10 nautical miles per hour. The green boat leaves 2 hours
before the red boat leaves. In how many hours after the green boat leaves will the
distance between the two boats be 50 nautical miles. You must state what your
variable stands for and show an equation in your solution even though the answer is a
“nice” number.
18. The price per pound of a certain delicious specialty chocolate in a candy store varies
directly as the monthly demand for it during the previous month. The price per pound
for the chocolate was $5.23 in July and the demand in June was 1046 pounds. What
would the price per pound be in August if the demand in July was 1188 pounds?
19. A 25 foot ladder is leaning against a wall. The top of the ladder is initially 23 feet
above the ground which is slippery. The top of the ladder begins sliding down the
side of the wall at 2 feet per second. In how many seconds will the bottom of the
ladder be 20 feet from the wall? You must state what your variable stands for and
show an equation in your solution even though the answer is a “nice” number.
20. Express the following power of i as a real number.
i 62
21. Write the following complex quotient in the form a + bi. Reduce.
2i
3i
22. Solve the following quadratic equation by completing the square.
3x 2  24 x  15  0
23. Solve the following quadratic equation by any method.
2 x2  9 x  7  0
24. A total of 18 meters of fencing is going to be used to build a rectangular fenced in
area and then construct 3 interior fences in order to produce 4 adjacent rectangular
fenced in regions (see the picture demonstrated in class). The total area of the fenced
in regions is to be 8 square meters. Find the dimensions of the total fenced in area.
You must state what your variable (or variables) stand for and show an equation in
your solution even though the answers are “nice” numbers.
25. Find the midpoint and length of the line segment whose endpoints are the points
(-4,6) and (-9,18).
26. Find the equation of the line that is the perpendicular bisector of the line segment
with endpoints (-10,4) and (-2,0). Write your answer in the form y = mx + b.