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November 17, 2002

                             ET NEWS
================================================================
        NEWS AND INFORMATION FOR ENGINEERING TECHNICIANS
----------------------------------------------------------------
Issue No. 73                                          11-17-2002
================================================================

Contents
--------
- News
- ET Journal
- NICET Test Dates
- AFAA Class Schedule
- Comments and Contacts

================================================================
NEWS
================================================================

The 2003 NICET test schedule has been posted here:
http://63.70.211.210/cfdocs/nicetschedule1.cfm

----------------------------------------------------------------

I'm off to Salt Lake City this week.

Have fun!

Mike

P.S. Because I'm in a different city every week, please use email
mailto:mbbaker@attbi.com if you have a question or comment.

================================================================
ET JOURNAL
================================================================

This section includes material that appears in my NICET Test
Preparation handbooks. For more information about these books and
where to purchase them, please visit my web site:
http://www.etnews.org/index.php?tb=index1&s=11

NICET Fire Alarm Systems Level II
33029^ INTERMEDIATE MATHEMATICS
---------------------------------

33029 is a Level II General Non-Core Work element.

The caret (^) following 33029 means generic crossover credit.
Once you pass this exam element, you will receive credit in other
fields/subfields when you first test in the other field/subfield.
Read the information on crossover work elements on pages 4 and 5
of the Program Detail Manual found at
http://www.nicet.org/nicetmanuals/alarms.pdf.

A crossover table reference document is available at
http://www.geocities.com/michaelbaker/docs/crossover.pdf

33029 DESCRIPTION
Perform mathematical calculations utilizing basic algebra
(fundamental laws, algebraic expressions), geometry, and the
trigonometric functions of triangles. (See basic textbooks on
algebra and trigonometry)

33029 REFERENCES:
Basic textbooks on algebra and trigonometry

33029 DESCRIPTION BREAKDOWN:
"Perform mathematical calculations utilizing basic algebra
(fundamental laws, algebraic expressions), geometry, and the
trigonometric functions of triangles."

Decimals
--------
One decimal place to the right of the decimal point is the
"tenths" place, but one decimal place to the left of the decimal
point is the "ones" place. The "tens" place is two places to the
left. 

To add and subtract decimals, line up the decimal points, use
place-holding zeros.  Note:  Whole numbers are understood to have
a decimal point to the right of the ones place. 

 12.00 
- 4.08
 -----
  7.92

When multiplying decimals, don't consider decimal places until
the problem is solved. Count all places to the right of the
decimal point in the problem. Count that number of places in the
product (the answer) starting from the right. 

  0.004 
x 0.02
  -------
  0.00008

Dividing Decimals: 

If the number in a division box has a decimal, but the number
outside of the division box does not have a decimal, place the
decimal point in the quotient (the answer) directly above the
decimal point in the division box. 

If both the numbers inside and outside of the division box have
decimals, count how many places are needed to move the decimal
point outside of the division box (the divisor) to make it a
whole number. Move the decimal point in the number inside of the
division box  (the dividend) the same number of places. Place
the decimal point in the quotient (the answer) directly above
the new decimal point. 

If the number outside of the division box has a decimal, but the
number inside of the division box does not, move the decimal
place on the outside number however many places needed to make
it a whole number. Then to the right of the number in the
division box (a whole number with an "understood decimal" at the
end) add as many zeros to match the number of places the decimal
was moved on the outside number. Place the decimal point in the
quotient directly above the new decimal place in the division box. 

Rounding Decimals: 

To round a number to the nearest tenth (one place to the right
of the decimal point), compute the number to the hundredths
place (two places after the decimal) . If the number in the
hundredths place is "five" or more , add "one" to the number in
the tenths place and drop the number in the hundredths place. If
the number in the hundredths place is under "five," leave the
number in the tenths place as is and drop the number in the
hundredths place.   

To round a number to any decimal place, just compute the number
one place value position farther to the right. The extra place
is a gauge which indicates whether the number is close to what
it reads (if the next number is less than "5") or is closer to
one number higher (if the next number is "5" or more). 

"Decimals" source: http://www.mccc.edu/~kelld/decff.htm


Linear Equations
----------------
What is a linear equation?

Let's glance at an example: 

The initial cost for setting up a new helipad is estimated to be
50 thousand dollars. The maintenance cost for the helipad
increases with the number of helicopters using it. So if the
number of helicopters using the helipad is H and the maintenance
cost per helicopter is 2.5 thousands dollars per month, the total
amount spent on this project at the end of the first month is
estimated to be:

C = 2.5 H + 50 

where C is the cost in thousands of dollars spent.

If the amount allotted for this project for the first month is
equal to 100 thousand dollars (including the set up cost), how
many helicopters can be allowed to use the helipad during the
first month? 

Let's consider a solution: 

The total cost is equal to the sum of the setup cost plus the
maintenance cost. 

2.5 H + 50 = 100 

Using the properties we learned, we can solve the equation as
follows: 

2.5 H + 50 - 50 = 100 - 50 
2.5 H = 50 
(2.5/2.5) H = 50 / 2.5 
H = 20 

So the number of helicopters allowed during the first month is20. 

A few simple facts that you should know 
 
Did you know that the above example is a linear equation? 

A Linear Equation is an equation of the form:

m * X + c = 0

where X is the unknown.

The name "linear" stems from the fact that the graph of this
equation is a straight line. If we plot a graph of mx + c we
will see a straight line with a slope of m that intersects the
y axis at y = c. Solving the equation means finding the value of
x where the line intersects the x-axis. 

"Linear Equations" source:
http://cne.gmu.edu/modules/dau/algebra/equations/linear1_frm.html


Simultaneous Equations
----------------------
Simultaneous equations are a set of equations which have more
than one value which has to be found.

Example:
A man buys 3 fish and 2 chips for $2.80
A woman buys 1 fish and 4 chips for $2.60
How much are the fish and how much are the chips?

There are two methods of solving simultaneous equations. Use the
method which you prefer.

Method 1: elimination
First form 2 equations. Let fish be f and chips be c.

We know that:
3f + 2c = $2.80  (1)
1f + 4c = $2.60  (2)

Doubling (1) gives:
6f + 4c = $5.60  (3)

(3)-(2) is:

 (6f + 4c) = $5.60
-(1f + 4c) = $2.60
 -----------------
 (5f + 0c) = $3.00

 5f = $3.00

Therefore: f = $3.00/5 = $0.60
The price per piece of fish is $0.60 

Substitute this value into (1):

3($0.60) + 2c = $2.80
$1.80 + 2c = $2.80
2c = $2.80 - $1.80
2C = $1.00

Therefore: c = $0.50
The price of one order of chips is $0.50

Method 2: Substitution
Rearrange one of the original equations to isolate a variable.

Rearranging (2): f = $2.60 - 4c

Substitute this into the other equation:

3($2.60 - 4c) + 2c = $2.80
$7.80 - 12c + 2c = $2.80
$7.80 -10c = $2.80
$7.80 - $2.80 = 10c
$5.00 = 10c
$0.50 = c

Substitute this into one of the original equations to get
f = $.060.

Harder simultaneous equations:
To solve a pair of equations, one of which contains
x², y² or xy, we need to use the method of substitution.

Example:
2xy + y = 10 (1)
x + y = 4    (2)

Take the simpler equation and get y = .... or x = ....

from (2), y = 4 - x    (3)

this can be substituted in the first equation. Since y = 4 - x,
where there is a y in the first equation, it can be replaced by
4 - x

sub (3) in (1), 2x(4 - x) + (4 - x) = 10
8x - 2x² + 4 - x - 10 = 0
2x² - 7x + 6 = 0
2x - 3)(x - 2) = 0
either 2x - 3 = 0 or x - 2 = 0
therefore x = 1.5 or 2

Substitute these x values into one of the original equations.
When x = 1.5,  y = 2.5
when x = 2, y = 2

"Simultaneous Equations" source:
http://www.gcsemaths.fsnet.co.uk/Simultaneous%20Equations.htm


Percentages
-----------
Percent means per hundred. 10 percent is just another way of
saying "ten out of a hundred," or ten hundredths. If exactly 10
percent of your 100 M&Ms are yellow, then 90 of them are some
other color and 10 of them are yellow.

To convert a fraction to a percentage, divide the numerator by
the denominator. Then move the decimal point two places to the
right (which is the same as multiplying by 100) and add a percent
sign.

For example: Given the fraction  5/8  what is the percentage?

     .625     .625 x 100 = 62.5 or 62.5%
   ------
 8 )5.000
    4 8
    ---
      20
      16
      --
       40
       40

So 5/8 of your M&Ms would be 62 1/2 of every 100. 
To change a percentage to a fraction, divide it by 100 and reduce
the fraction or move the decimal point to the right until you
have only integers:

10% = 10/100 = 1/10
62.5% = 62.5/100 = 625/1000
625/1000 = 125/200 = 25/40 = 5/8

"Percentages" source:
http://mathforum.org/dr.math/faq/faq.fractions.html

For more information regarding Percent Increase or Decrease, visit Purplemath:
http://www.purplemath.com/modules/percntof.htm


Areas and Volumes
-----------------
pi = 3.1415926... 

Areas:
------

SQUARE = a^2

+-------+
|       |
|       |
|       |
+-------+
|<- a ->|  


RECTANGLE = ab

+-------+ -
|       | ^
|       | |
|       | |
|       | b
|       | |
|       | |
|       | |
+-------+ -
|<- a ->|


PARALLELOGRAM = bh

    +-------------------+ -
   /                   /  |
  /                   /   h
 /                   /    |
+-------------------+     -
|<------- b ------->|


TRAPEZOID = 1/2(b1 + b2)) x h
  
    |<--- b2 -->|
    +-----------+ ------
   /                  |
  /                   h
 /                    |
+-------------------+ --
|<------- b1 ------->|


CIRCLE = pi*r^2  

    _.-""""-._
  .'          `.
 /              
.                .
|        '<- r ->|
'                '
               /
  `._        _.'
     `-....-'


TRIANGLE = (1/2) b * a  

              B   
          --  .  --
         /   /|   ^
        /   / |   |
       /   /  |   |
      c   /   |   |
     /   /    |   a
    /   /     |   |
   /   /      |   |
  - A +-------+ C -
      |<- b ->|


EQUILATERAL TRIANGLE = (1/4)sqrt(3)a^2


Volumes
-------
CUBE = a^3

CYLINDER = b * h = pi * r^2 * h  

PYRAMID = (1/3) * b * h

CONE = (1/3) * b * h = 1/3 * pi * r^2 * h  

SPHERE = (4/3) * pi * r^3  

Surface Area
------------

CUBE = 6 * a^2  

SPHERE = 4 * pi * r^2  


Pythagorean Theorem
-------------------

a^2 + b^2 = c^2

     .
     |
     | 
     |  
     |   c
     a    
     |     
     |      
     +---b---+

a = height
b = base
c = hypotenuse

EXAMPLE:
NFPA 72-1999 2-2.4.1 Smooth Ceiling Spacing. One of the following
requirements apply:
(1) The distance between detectors will not exceed their listed
spacing, and there will be detectors within a distance of 1/2 the
listed spacing, measured at a right angle, from all walls or
partitions extending to within 18 inches of the ceiling.

(2) All points on the ceiling will have a detector within a
distance equal to 0.7 times the listed spacing (0.7S). This is
useful in calculating locations in corridors or irregular areas.

S = Listed Spacing

a^2 + b^2 = c^2

(0.5S)^2 + (0.5S)^2 = c^2
(0.25)S^2 + (0.25)S^2 = c^2
(0.5)S^2 = c^2
sqrt(0.5)S^2 = c
.707S = c

"Areas and Volumes" source:
http://www.math2.org/math/geometry/areasvols.htm


Trigonometry
------------
http://aleph0.clarku.edu/~djoyce/java/trig/


Trigonometric Functions
-----------------------
I learned a silly phrase to remember the three basic functions
SIN COS TAN:

"Oscar Had A Hairy Old Ass"

Oscar -> Opposite
----     --------   = SIN 
Had   -> Hypotenuse

A     -> Adjacent
-----    --------   = COS
Hairy -> Hypotenuse

Old   -> Opposite
---      --------   = TAN
Ass   -> Adjacent


THE INFORMATION HEREIN IS PROVIDED AS A GUIDE ONLY AND IS
INTENDED TO ASSIST YOU IN PREPARING FOR AN EXAM. IT IS NOT
INTENDED TO BE INCLUSIVE OF ALL INFORMATION THAT MAY BE ON AN
EXAM BUT RATHER IT IS INTENDED TO BE A SMALL SAMPLE OF THE KIND
OF MATERIAL THAT YOU MAY BE EXPECTED TO KNOW.

================================================================
NICET TEST DATES
================================================================

OREGON
------
PCC Sylvania, Portland;
Test 1/25/03. Postmark deadline 12/7/03.
Test 4/26/03. Postmark deadline 3/8/03.

Clackamas Community College, Oregon City;
Test 1/25/03. Postmark deadline 12/7/03.
Test 6/21/03. Postmark deadline 5/3/03.

WASHINGTON
----------
Bates Technical College, Tacoma;
Test 12/14/02. Postmark deadline 10/26/02.
Test 2/22/03. Postmark deadline 1/4/03.

Walla Walla Community College;
Test 2/22/03. Postmark deadline 1/4/03.
Test 5/17/03. Postmark deadline 3/29/03.

Spokane Community College;
Test 2/22/03. Postmark deadline 1/4/03.
Test 5/17/03. Postmark deadline 3/29/03.

These dates are from the NICET web site. For a complete list of
all test centers and test dates, visit
http://63.70.211.210/cfdocs/nicetschedule.cfm

================================================================
AFAA CLASS SCHEDULE
================================================================

------------------
November 19-21, 2002 Salt Lake City, UT
------------------
Intermediate Fire Alarm Seminar.
http://www.afaa.org/afaa/PDF/IntFA_SaltLakeCity_Nov20021.pdf

------------------
December 2-5, 2002 Orlando, FL  
------------------
Fire Alarm System Testing and Inspections Seminar 12/2
http://www.afaa.org/afaa/PDF/INT_TI_Orlando_Dec2002.pdf
Intermediate Fire Alarm Seminar 12/3-5
http://www.afaa.org/afaa/PDF/INT_TI_Orlando_Dec2002.pdf

------------------
December 3-5, 2002 Seattle, WA
------------------
Advanced Fire Alarm Seminar.
http://www.afaa.org/afaa/PDF/ADV_Seattle_Dec2002.pdf

------------------
January 14-16, 2003 Denver, CO - Sponsored by the Rocky Mountain AFAA
------------------
Advanced Fire Alarm Seminar.
http://www.afaa.org/afaa/PDF/ADV_Denver_Jan2003.pdf

------------------
January 21-23, 2003 Oklahoma City, OK - Sponsored by OK AFAA
------------------
Intermediate Fire Alarm Seminar.
http://www.afaa.org/afaa/PDF/IntFA_OKC_Jan2003.pdf

------------------
February 4-6, 2003 Orlando, FL
------------------
Advanced Fire Alarm Seminar.
http://www.afaa.org/afaa/PDF/ADV_Orlando_Feb2003.pdf

------------------
February 19-21, 2003 Raleigh, NC 
------------------
Intermediate Fire Alarm Seminar.
More information will be available soon!

------------------
April 7-9, 2003 New Orleans, LA - Sponsored by LA AFAA   
------------------
Advanced Fire Alarm Seminar.
http://www.afaa.org/afaa/PDF/ADV_NewOrleans_April2003.pdf

================================================================
COMMENTS AND CONTACTS
================================================================

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----------------------------------------------------------------
The NICET acronym found herein refers to: http://www.nicet.org
NATIONAL INSTITUTE FOR CERTIFICATION IN ENGINEERING TECHNOLOGIES
----------------------------------------------------------------
The AFAA acronym found herein refers to: http://www.afaa.org
AUTOMATIC FIRE ALARM ASSOCIATION "We're celebrating 50 years!"
----------------------------------------------------------------
Some information may be found within this email message that is
reprinted with permission from one or more of the following;
NFPA 70 National Electrical Code(r), NFPA 72 National Fire Alarm
Code(r), and NFPA 101(r) Life Safety Code(r), Copyright(c)
National Fire Protection Association, Quincy, MA 02269
http://www.nfpa.org. This reprinted material is not the complete
and official position of the National Fire Protection Association
on the referenced subject, which is represented only by the
standard in its entirety.
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Some information may be found within this web site that is reprinted with permission from one or more of the following: NFPA 70 National Electrical Code®,NFPA 72® National Fire Alarm Code®, & NFPA 101® Life Safety Code®, Copyright© NFPA, Quincy, MA 02269.

This reprinted material is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.