The ENM 503 Pretest
An exercise in frustration
Let’s see now. I
remember that a log is
associated with the
lumber industry and a
radical favors extreme
change?
The ENM 503 Pre-Test Results
I really
enjoyed that
pretest.
Me too! This is
going to be one of
my favorite classes.
Statistics:

Mean and median – 60 percent

Average number missed: 16 out
of 40

Median number missed: 16

Minimum number missed: 9

Maximum number missed: 24

Standard deviation: 12.5%
Engineering management students
enjoy reminiscing about today’s class.
Problem 2
If an automobile averaged 40 miles per (mph)
for 45 minutes and 50 mph for 1.5 hours, how
far did it travel?
40 x 45/60 + 50 x 1.5 = 30 + 75 = 105 miles
Problem 3

Subtract (-2a + 7x – 5c2) from (-2x + 8a + c2)
(-2x + 8a + c2) - (-2a + 7x – 5c2) = -2x + 8a + c2 +2a - 7x + 5c2
= -9x + 10a +6c2
Problem 5
log2 8 = ?
Loga x = y
ay = x
2y = 8; y = 3
working
with
logs
Problem 6
Multiply: (-3st2) (2s2t3) (-2s2t2) = ?
(-3st2) (2s2t3) (-2s2t2) =12s5 t7
We know how to
multiply.
Problem 7
Find the values for x for which -3x + 2 < 0.
-3x < -2
X > 2/3
Read me the story again about
changing the direction of an
inequality when dividing by a
negative number.
Problem 8
5 2

21x z
Express in simplest terms:
6 5
3x z
5 2
21x z
7 z
5 2
6 5
 7 x z  x z  
6 5
3x z
x
3
Problem 9



Factor into two binomial expressions:
x2 – xy – 2y2
x2 – xy – 2y2 =(x+y)(x-2y)
Problem 11




Solve for y: y – (1/3) y + 1 = 3 – (2/3) y
(2/3)y + 1 = 3 – (2/3)y
(4/3)y = 2
Y = 2(3/4) = 6/4 = 1.5
Problem 12
Solve for w and z :
You nailed this one
Chuck.
w – 2z – 3 = 0
2w + 2z + 6 = 0
3W
+3=0
W = -1, Z = -2
Problem 13

An equilateral triangle is one whose sides are
all the same length. If the perimeter of an
equilateral triangle is 36 inches, what is its
height?
Side (hypotenuse) = 12; 144 – 36 = 108
108  6 3  10.4in
Problem 14

Add:
3x 4 x 7 x


?
2
3
6
3x 4 x 7 x (3)(3) x  (2)(4) x  (1)7 x 24 x




 4x
2
3
6
6
6
Problem 15

Simplify:
2 18 2  ?
2 18 2  2 (2)(9) 2
 2(3) 2 2  (2)(3)(2)  12
Problem 17



Solve for x: 2x2 – 13 = x2 + 12
x2 = 25
x = 5
I forgot the
minus sign.
Problem 18

A man has a rope 180 feet long that he
wishes to cut into three parts in the ratio of
2:3:4. How long in feet will each piece of the
rope be?
2x + 3x + 4x = 180
9x = 180
x = 20
therefore ratio is 40:60:80
Problem 19

If y varies directly with x (i.e. y is directly
proportional to x), and y = 8 when x = 4, what
is the value of y when x = 6?
y = kx
8 = k4
k=2
y = 2x = 2(6) =12
Problem 22

A man has a car with a 6 gallon radiator filled with a
solution containing 10 percent coolant. He drains
off a certain amount and replaces it with a solution
that contains 70 percent coolant. How much was
drained off if the solution then contained 20 percent
coolant?
Let x = gallons drained
.70x + .10(6-x) = .20(6)
.7x - .1x = 1.2 - .6 = .6
x = 1 gallon
Problem 25

(reduce to simplest terms)
3a  3b 6b  6a

?
2
2
x y
x y
3a  3b 6b  6a 3a  3b x  y

 2

2
2
2
x y
x y
x  y 6b  6a
3 a  b
x y
1



 x  y  x  y  6(b  a) 2  x  y 
I like things in
simplest terms.
Problem 26

642/3 = ?
64
2/3


3
64

2
 4  16
2
Problem 27

Two airfields A and B are 400 miles apart and B is due east of
A. A plane flew from A to B in 2 hours and then returned to A
in 2.5 hours. The wind blew with a constant velocity from the
west during the entire trip, find the speed of the plane in still
air and the speed of the wind.
Let x = speed of the airplane and y = speed of the wind
recall that distance/ rate = time
400
x y 
 200
2
400
x y 
 160
5/ 2
2 x  360
x  180 mph; y  200  180  20 mph
Problem 28




Expand: (x – 2y)3 = ?
(x-2y)(x-2y)(x-2y) = (x-2y)[x2 – 4xy + 4y2]
= x3 – 4x2y + 4xy2 -2x2y + 8xy2 – 8y3
= x3 - 6x2y + 12xy2 – 8y3
Press the button
Problem 29

The amount of money available at simple interest is
equal to the principle plus the product of the
principle, the rate, and the time. Find the time
required for a principle of $300 to accumulate to
$336 at 4 percent per year.
t = amount of time (years) required
300 + 300 (.04) t = 336
12t = 36
t = 3 years
Problem 31

The perimeter of a rectangle is 20 inches and
one side is 4 inches. What is its area?
Perimeter = 2 length + 2 width = 20
2 length + 2(4) = 20
length = 6
Area = length x width = 6 x 4 = 24 sq. in.
Problem 32

Perform the indicated operation and simplify:
x2  x
x2 1
 2
2
x  2x 1 x  x  2
x  x  1  x  1 x  1
x2  x
x2 1
 2


2
2
x  2 x  1 x  x  2  x  1
 x  2  x  1
x
x  1 x  x  2    x  1 x  1



x 1 x  2
 x  1 x  2 

x 2  2 x   x 2  1
 x  1 x  2 
1 2x

 x  1 x  2 
Problem 33

It always bothers me
to see a radical in
the denominator.
Rationalize the denominator
(eliminate the radical from the
denominator):
5
10  3


5
10  3 5 10  3


5
10  9
10  3 10  3

10  3

Problem 34



Factor completely: 2x4 y – 32y = ?
2y (x4 – 16) = 2y (x2 + 4) (x2 - 4)
2y (x2 + 4) (x - 2) (x+2)
I just ran out
of time.
Problem 35
3x  8 x 
Remove parentheses and simplify

3 
2 y  27 y 
1/ 2

3x  8 x 


2 y  27 y 3 
1/ 2
2/3
1/ 3
3x  64 x 



2 y  27 2 y 6 
3x  4 x1/ 3  2 x 4 / 3

 2 2 
2 y  3 y  3 y3
2/3
Problem 36




Solve for x: log10 x3 – 2 log10 x = 2
3 log10 x – 2 log10 x = 2
log10 x = 2
x = 102 = 100
My head hurts.
Problem 38
The following system of equations has how
many solutions?
2x + 3y = 10
Why, I can’t find
4x + 6y = 7
any solution to
these equations.
Tune in again next week,
same place, same time…
The Block 1 Exam
This ought to be
good. Come-on…