2.Evaluate and Leave No Negative Exponents. (2X3)(5X4)(7X)0
Name: ______
Summer 2004 – Math 233
Midterm 1b
Instructions: The following exam may be completed with the use of a single 8.5" x 11" note card. The card 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. 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. 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.Simplify the following: -3 | 3 45 | 6 + 2
[-5 (-1)] + -22 + 8
2.Evaluate and leave no negative exponents. (2x3)(5x4)(7x)0
5x –3y5
3.Evaluate.
a) -8 b) -64c) x14 y 7
125
4.Solve. Give the solution set using interval notation (use union symbol where
appropriate) or roster form.
a)| x + 2 | + 5 6
b)| x 5 | = | 2x + 1 |
c) 3x 1 + 1 > 5
2
5.Solve.
a)1/3 x 1/6 (x ½) = 1/4 (x + 1/3)
b)2(x + 5) + 3x = 5(x + 2)
6.Simplify.1/4 x2 2/5 (1/4 x2 2/5x) 1
7.Is the following a function?
a)b) {(2,6), (2,7), (3,7), (4,8)}c)14
25 3
46
8.How many liters (L) of a 20% salt solution must be added to 68 L of a 61% salt
solution to get a 37% salt solution?
9.A train traveling at 40 mph leaves for a certain town. Four hours later a bus
traveling at 50 mph leaves for the same town and arrives at the same time as the
train. If both the train and bus travel in a straight line, how far is the town from
where they start?
10.Which is most likely the graph of 5x 7y = 35
a)b)c)d)
11.Give the equation for any horizontal line.
12.Give the slope of any vertical line.
13.Find the following when f(x) = 5x + 1 and g(x) = 2
x + 1
a)f (2)
b)(f + g)(1)
14.Which is most likely the graph of y = x2 + 5
a)b)c)d)
15.Which is most likely the graph of y = | x | 2
a)b)c)d)
16.Which is most likely the graph of y = x 3
a)b)c)d)
17.Which is most likely the graph of y = x3 3
a)b)c)d)
18.For each give the equation in slope-intercept form (where possible) for the line
described by the given scenario.
a)Through (-5, 4) and (-6, 8)
b)Parallel to y = 5x 4 through the point (2, 3)
c)Perpendicular to the line 2x + 3y = 6 through (0, 4)
d)Through the points (5,-9) and (6, -9)
e)Vertical line through (-5, -2)
19.The solution to a system of 2 linear equations in 2 unknowns is
a)a pointb)a linec) d)All of the above
20.Solve the following systems
a)3x y = 2
y = 3x + 2
b)y = 2x 1
y = 5/2 x 2
c)2y 14x = -4
2y = 14x 4
21.Solve the following system:x + y + z = -9
2x y + z = 13
x 2y z = 1
22.Factor each of the following completely
a)3x2 21x 15
b)x2 (x + 1) + 4x (x + 1) 3(x + 1)
c)x2y + 6xy 7y
d)6x2 15x 2xy + 5y
e)x2 9xy + 18y2
23.The sum of three numbers is 161. The second number is 7 more than the first
number and the third number is 5 times the first number. Set up a system of 3
equations in 3 unknowns that could be used to solve the problem for the second
number. Define each variable clearly and any needed expressions as well.
24.Which of the following best describes the graph of 8x 3y > 24
a)b)c)d)
25.For the following sets:A = {a, b, c , d, e} and B = {b, d, l, t}
a) Find A B
b)Find A B
26.Write in standard notation:
a)1.502 x 10 3
b)5.25 x 10-5
27.Write in scientific notation:
a)552,000
b)0.0001025
28.Multiply using exponents rules & write in scientific notation. Do not multiply in
standard form.
(1.5 x 108)(-3 x 10-3)
1