Name: ______
New Material – Ch. 5-8, w/ 1-4 selectively
Final – Math 233
Summer 2004
Instructions: The following exam may be completed with the use of an 8 ½ " x 11"sheet of notes. The notes may not have any complete problems or definitions and must be handed in with the exam (please staple to the back). You may use your calculator. For all non-multiple choice problems, please show all work neatly and clearly. Please recall that a correct answer does not guarantee full or even partial credit; this is especially true with word problems. For word problems, algebra must be used to achieve the answer and all variables must be defined and the equations used must be shown. For multiple choice problems please circle the best answer. This test is designed to be two hours long. The point value is 300 points, although the actual points may vary, and if so they will be scaled to 300, using percentages. Good luck!
1.Solve the system of linear inequalities by graphing.
Use either substitution or elimination to find the point of intersection of the
boundary lines. Work must be shown and be valid in yielding the point.
x + 2y 6
-2x + y > -2
2.Simplify each of the following:
a)(2.3x3 5.6x2 2) (5.5x3 7.4x2 + 2)
b)(x + 2)(x 2)(2x 3)
3.Using long division, find the quotient(2x3 x2 7) (x 2)
4.Using synthetic division, find the quotient(3x3 x2 + 4x + 8) (x + 2)
5.Using f(x) = x + 2, g(x) = 2x2 + x 1,
simplify the following h(x) = 2x 1
x + 1
a)(f + g)(x)
b)h(-1)
c)(g h)(x)
d)(g f)(x)
6.Factor each of the following completely
a)8x3 + cxy + 4cx2 + 2x2y
b)4x2 + 25
c)4x2 8x 6
d)8x2 + 10x 12
e)27x3 1
f)54x6 + 2
g)16x4 40x2y + 25y2
h)x2 + 2xy + y2 144
7.Solve the following using the zero factor property, not completing the square,
the quadratic formula or square root property!
7x2 + 2x = 3x(x 4)
8.Simplify 2y 46 + 4
2y2 2y 40 2y 10
9.In solving any type of equation, if you have made no mathematical errors and get
the answer 0x = 1, what does this mean?
a)nothingb)No solutionc)d)x = 1
10.In solving any type of equation, if you have made no mathematical errors and get
the answer x = x, or 1 = 1, what does this mean?
a)nothingb)No solutionc)d)x = 1
11.Solve the following.4 8x = 8
x + 1 x + 1
12.Which equation would best be used to solve the following? Assume that r = rate.
A car and a train leave DC at the same time traveling to NY, 390 miles away. If
the speed of the car averages twice the speed of the train and the car arrives 6.5
hours before the train, find the speed of the car and the speed of the train.
a)390/2r = 390/r 6.5b)2r r = 6.5
c)2r/390 = r/390 + 6.5d)780r = 390r 6.5
13.Which equation would you find best to use in solving the following?
Assume m = Mac's time alone.
Joan and Mac build cabinets. Joan can make a set of cabinets in 10 hours.
Together Mac and Joan can do the same job in 6 hours. How long will it take
Mac working alone?
a)1/10 + 1/6 = 1/mb)1/10 + 1/m = 1/6
c)3/5 + 6/m = 1d)1/m + 1/6 = 1
14.Which equation would best be used to solve the following? Assume that
x = height from the ground where the wire is attached.
A tent has wires attached to it to help stabilize it. A wire is attached to the ground
12 feet from the tent. The length of wire used is 8 feet greater than the height
from the ground where the wire is attached. How long is the wire?
a)x2 + 12 = (x + 8)2b)x2 16x 80 = 0
c)-16x + 80 = 0d)x2 + 144 = x2 + 64
15.Which best describes the following:W is directly proportional to the square of L
and inversely proportional to A.
a)W = kAL2b)W = kA2L
c)W = k L2 d)W = k L2
A2 A
16.Which is the best solution for m, in the formulaV = mv
m + M
a)m = Vm + VM b)m = VM
v v V
c)m = VM V d)m = 1
v v
17.Use exponent rules to simplify. a7 c6
32a2c -7
18.Simplify completely.Write in radical form. No rational exponents & no radicals
in denominators.
a) -16x6 y3 z12
b) 2
3x2
c) 4
3 + 2
d)212 3
e)(7 + 4x )(27 + 3x )
19.Solve the following
a)10x + 5 1 = 2x
b)2y + 5 y 1 = y + 2
20.Simplify the following and write your answer as a complex number (a + bi)
a) - 144
b)(7 8i) + (-12 4i)
c)(2 + 3i)(2 i)
d)i21
e)i83
f)i30 + i28
21.Solve using the square root property.4x2 = -16
22.Solve by completing the square.x2 5x 24 = 0
23.Solve by using the quadratic formula.x2 + 8x = -3
24.Solve the following by seeing it in quadratic form.2b-2 = 7b-1 3
25.Circle all that apply.
Which represent inverse functions?
a){(1,4), (2,5), (-3,-5)} b)x = 5y
{(-4,-1), (-5,-2), (-5,-3)}y = log 5 x
c)f(x) = x 1/x + 1d) {(1,4), (2,5), (-3,-5)}
g(x) = x/x 1 {(4,1), (5,2), (-5,-3)}
26.What 3 points do you need to graph a logarithmic function?
27.What 3 points do you need to graph an exponential function?
a)(1/a, -1), (1,0) & (a, 1)b)(-1, 1/a), (0,1) & (1,a)
c)(-1/a, 1), (-1,0) & (a, 1)d)(1, -1/a), (0,-1) & (1,a)
28.Which is the correct logarithmic form for:125 = 53
a)log 3 5 = 125b)log 5 3 = 125
c)log 5 125 = 3c)log 125 5 = 3
29.Which is the correct exponential form for:6 = log 2 x
a)2x = 6b)26 = xc)x6 = 2 d) x2 = 6
30.Evaluate
a)log z 100 = 2
b)log 4 64 = y
c)log 25 x = ½
EC #1The area of a triangle is 104 square meters. If the base of the triangle is 10 greater
than 2 times the height, find the base and height of the triangle.
EC #2Solve the following using a system of 3 equations and 3 unknowns.
A total of 300 people attended the high school play. The admission prices
were $5 for adults, $3 for high school students and $2 for any kids under high
school age. The ticket sales totaled $1010. The school principal suggested that
next year they raise prices to $7 for adults, $4 for students and $3 for kids. He
said that if exactly the same number of people attended next year as this year, the
ticket sales would total $1390 based upon the higher prices. How many adults,
students and kids attended this year?
EC #3Solve the following system using Cramer's Rule. You must show all work.
4x + y + 2z = 6
x + y + z = 1
-x + 3y z = -5
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