Pre-Calculus Topics: 2013

Thursday, December 12, 2013

Solutions to the EXAM - Form A

Below are problems that you use

a CALCULATOR to solve:

Friday, December 6, 2013

Dear Pre-Calculus students,
I am sure that your snow day comes with mixed feelings. Extra time to prepare
for all your exams is great, but you now feel pretty much on your own for my exam.
The exam is Wed., Dec. 11th, from 2:45 pm to 4:35 pm.
The best I have to offer to assist you is two-fold:
Option #1) I have an appointment in Fairfield Ohio on Wednesday morning until shortly after 1:00 pm
As soon as I am finished I plan to go to my Office at the Mount. I can help anyone that
stops in from about 2:00 pm until the exam.
Option #2) You can email me a problem number and page and I will work out the problem
in detail and post it on the blog: knepfle.blogspot.com
You can scan a problem and email it.
You can take a picture of a problem and email it.
Sincerely,
Mr. Chuck Knepfle
*******************************
How to study for the final exam:
1) review the 3 tests we have had
2) review the announced quizzes
3) If you need individual help, I am in my office
on Monday, Wednesday and Friday of the first week of December.
(about 12:00 p.m. to 12:50 p.m.)
4) Know the Special Trig values
5) Be able to graph all the TRIG FUNCTIONS
Click here for the Trig Graphs http://knepfle.blogspot.com/2013/08/using-unit-circle-71.html
plus: linear functions, x squared, x cubed, e to the x, log of x

Monday, December 2, 2013

Final Exam and last week of the term

How to study for the final exam:
1) review the 3 tests we have had
2) review the announced quizzes
3) If you need individual help, I am in my office
on Monday, Wednesday and Friday of the first week of December.
(about 12:00 p.m. to 12:50 p.m.)
4) Know the Special Trig values
5) Be able to graph all the TRIG FUNCTIONS
plus: linear functions, x squared, x cubed, e to the x, log of x

Sunday, August 18, 2013

General Information

General information:
YOU MUST KNOW THIS STUFF:

I am in my Math Dept. Office from 12:00 until class on Mon., Wed., and Friday.
Please stop in for help! - I am more than glad to:
- Re-teach a topic OR - Help on a homework problem
- Help with a Math technique that I may have assumed that you knew before entering the class
- We can do more example problems from a topic that seems to be troubling you
****************3rd EXAM - TEST on FRIDAY, NOV. 8th******************
Possible Questions:

Find the RADIAN measure of the angle with the given degree measure.
36 degrees
72 degrees
900 degrees
1200 degrees
-120 degrees
-225 degrees

Find the DEGREE measure of the angle with the given radian measure.
4pi/5
3pi/4
13pi/6
13pi/12

The measure of an angle in standard position is given in DEGREES.
Find the coterminal angle with the given condition.

GIVEN: (-120 degrees) -> Find a coterminal partner between zero and 360 degrees. ____________
GIVEN: (-150 degrees) -> Find a coterminal partner between zero and 360 degrees. ____________
GIVEN: (780 degrees) -> Find a coterminal partner between zero and 360 degrees. ____________
GIVEN: (650 degrees) -> Find a coterminal partner between zero and 360 degrees. ____________

Find an angle between 0 and 2pi RADIANS that is coterminal with:
7pi/3
15pi/4
-13pi/4
-9pi/4

Find the length of an arc that subtends a central angle of 30 degrees
in a circle of radius 8 meters.

Find the length of an arc that subtends a central angle of 3pi/2 radians
in a circle of radius 8 meters.

Find the area of a sector that is formed in a circle of diameter 14 meters.
This sector subtends a central angle of 120 degrees.

Find the area of a sector that is formed in a circle of diameter 14 meters.
This sector subtends a central angle of pi/4 radians.

**********PLUS some from the last double quiz*******************

1) If $7896 is invested at 6%. The interest is compounded monthly.
How much money will be available after 7 years?
2) What is the PRESENT VALUE of $8976 under the conditions that
the money would be invested at 8% for 11 years and compounded daily?
(In other words: What would I need to invest at 8% now to have $8976 in 11 years?)
3) Starting with 2500 units of substance, find the amount remaining after
8 years with continuous compounding under a decomposition of 4%
4) Find the Annual Percentage Yield for 8% compounded continuously.
5) Switch each Logarithmic Form to the corresponding Exponential Form.

6) Switch each Exponential Form. to the corresponding Logarithmic Form.
7) Find the value of "z" in each equation

***********Find the Final Amount or Find the Initial Amount
another name for this finding the PRESENT VALUE***************
1) $7000 - at 4% - compounded yearly - for years - results in $8516.570317
2) $7000 - at 4% - compounded monthly - for 5 years - results in $8546.976158
3) $7000 - at 4% - compounded daily - for 5 years - results in $8549.72561
4) $3658 - @ 5% - compounded daily - for 7 years - becomes $5190.824665
5) $3658 - @ 5% - compounded monthly - for 7 years - becomes $5187.175879
6) $3658 - @ 5% - compounded yearly - for 7 years - becomes $5147.17334
7) $8,187.39725 - at 4% - compounded daily - for 5 years - results in $10,000
8) $4,493.4866 - at 4% - compounded daily - for 20 years - results in $10,000
*** With Continuous Compounding any of the four variables can be found given the other 3
**(e = 2.71828182...)*****
9) $3658 - @ 5% - compounded continuously - for 7 years - becomes $5190.949093
10) 9876 - Decaying continuously - @ 6% - for 10 years - becomes 5420.063718
11) $7000 - at 4% - compounded Continuously - for 5 years - results in $8549.819307
12) $8187.307531 - at 4% - compounded Continuously - for 5 years - results in $10,000
13) $4493.289641 - at 4% - compounded Continuously - for 20 years - results in $10,000

A Function is ... (3.1)

A DIFFERENCE QUOTIENT EXAMPLE:

A FUNCTION is...
a "RULE" that explains what mathematical operations will be APPLIED to:
- an INPUT (an "X") to produce the OUTPUT (the "Y" value)
- "X" (the INDEPENDENT VARIABLE)
- a NUMBER from the DOMAIN
- to get the VALUE for Y (the DEPENDENT VARIABLE) from a given "X" VALUE

the DOMAIN is the set of possible "X" values
the RANGE is the set of "Y" values
use letters like "f" or "g" or "h" ... to represent a function

f can also be thought of as a MAPPING (Arrow diagram)
showing how (CONNECTS) each
value from the DOMAIN is
matched to a PARTNER in the RANGE

f can also be pictured as a MACHINE that takes
a given INPUT and produce a SINGLE OUTPUT
using a UNIQUE RULE
"x" is an INPUT and
"y" or "f(x)" is the OUTPUT value

f(x) is read as
- f of x
- f operating on x
- f evaluated at x
- the value of f at x
- the image of x under f

An employee for ACME INDUSTRY earns $9 for each hour worked.
To calculate the EARNINGS for a certain individual we
"Multiply the NUMBER OF HOURS (x) by 9"
g(x) = 9 times x
g(x) = 9x
suppose the DOMAIN is {20,30,40}
then the RANGE will be {180, 270, 360}
g(20) = 9(20) = 180
etc.

If ACME INDUSTRY changes the pay rate to $360 for any
employee that works less than or equal to 40 hours in a given week.
When an employee works more than 40 hours they receive an
additional $10 for each hour over 40. This creates the need for a
special type of function called a PIECEWISE DEFINED FUNCTION.
Two different rules are needed. One rule for less than or equal to 40 hours
and a second rule for over 40 hours.

g(x) = 360 ..................... if 0< x <= 40
g(x) = 360 + 10(x-40) .... if 40 < x

REPRESENTING A FUNCTION:
1) VERBALLY (using words)
2) ALGEBRAICALLY (using a formula ... f(x) = 9x )
3) VISUALLY (use a GRAPH)
4) NUMERICALLY (by use of TABLE)

Function Graphing (3.2)

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Information from a Graph (3.3)

Information from a Graph (3.3)

HW for Section 3.3
#5, 7, 19, 21, 31, 33, 47

Topics for this section:
GIVEN A GRAPH:
1) Find the y value for a given x
2) Find the x value(s) for a certain y
3) On what intervals does the graph INCREASE?
4) On what intervals does the graph DECREASE?
5) Are there any RELATIVE MAXIMUMS?
Where do they occur? (x value)?
What are the VALUES THERE (y value)?