The ENM 503 PretestAn 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

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%

I really enjoyed

that pretest.

Me too! This is going to be one of

my favorite classes.

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

workingwith 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 > 2/3Read me the story again about

changing the direction of an inequality when dividing by a

negative number.

Problem 8

Express in simplest terms: 5 2

6 5

21

3

x z

x z

5 2 3

5 2 6 56 5

21 77

3

x z zx z x z

x z x

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 : w – 2z – 3 = 0

2w + 2z + 6 = 0

3W + 3 = 0

W = -1, Z = -2You nailed this

one Chuck.

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: 3 4 7

?2 3 6

x x x

3 4 7 (3)(3) (2)(4) (1)7 244

2 3 6 6 6

x x x x x x xx

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 = 1809x = 180 x = 20therefore 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 = kx8 = 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)

2 2

3 3 6 6?

a b b a

x y x y

2 2 2 2

3 3 6 6 3 3

6 6

3 1

6( ) 2

a b b a a b x y

x y x y x y b a

a b x y

x y x y b a x y

I like things in simplest terms.

Problem 26

642/3 = ?

22/3 2364 64 4 16

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

400200

2400

1605 / 2

2 360

180mph; 200 180 20mph

x y

x y

x

x y

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) required300 + 300 (.04) t = 33612t = 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 = 202 length + 2(4) = 20length = 6

Area = length x width = 6 x 4 = 24 sq. in.

Problem 32 Perform the indicated operation and simplify:

2 2

2 2

1

2 1 2

x x x

x x x x

2 2

22 2

2 2

1 1 11

2 1 2 2 11

2 1 11

1 2 1 2

2 1 1 2

1 2 1 2

x x x xx x x

x x x x x xx

x x x xx x

x x x x

x x x x

x x x x

Problem 33

Rationalize the denominator (eliminate the radical from the denominator):

5

10 3

5 10 35 10 3

5 10 310 910 3 10 3

It always bothers me to see a radical

in the denominator.

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

Remove parentheses and simplify 2/31/ 2

3

3 8

2 27

x x

y y

2/3 1/31/ 2 1/3 4 /3

3 2 6 2 2 3

3 8 3 64 3 4 2

2 27 2 27 2 3 3

x x x x x x x

y y y y y y y

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

4x + 6y = 7 Why, I can’t find 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…