Bob Koff, Ed.S.
Georgia Perimeter College
INNOVATIONS 2012
March 5, 2012

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BLOOM’S TAXONOMY
EVALUATION
SYNTHESIS
ANALYSIS
APPLICATION
UNDERSTANDING
KNOWLEDGE

Mnemonic:
Greek: mnemonikos ⇒ “mindful”
Mnemosyne: Greek goddess of memory
A device intended to assist memory.

To determine which number in a fraction is the dividend and which is the divisor
Top dog in the house
4
5
5 4

PEMDAS: To determine the order of operations
Parentheses, Exponents, Multiply/Divide, Add/Subtract
P lease
E xcuse
M y D ear*
A unt S ally*
P
E lease ducate
M y D aughters*
A nd S ons*
*on the same line since they have the same priority

(Product of the denominators)

FOIL: To determine the product of two binomial expressions
F irst, O uter or O utside, I nner or I nside, L ast
(a + b) (c + d) = ac + ad + bc + bd

SOAP: To determine the signs of the terms in the factors of the sum or difference of two cubes.
S ame, O pposite, A lways P ositive
(a 3 +b 3 ) = (a+b)(a 2 -ab+b 2 )
(a 3 -b 3 ) = (a-b)(a 2 +ab+b 2 )

Bunny Face: To determine the terms of the sum or difference of two cubes
(a 3 +b 3 ) = (a + b) (a 2 – ab + b 2 )

Definition of slope: Rise over Run;
We say the sun “rises” which implies vertical change while we “run” across or “run” cross country which implies a horizontal change.
The letter repesenting slope is “m” think of a
“m”ountain slope.

Zero Slope
The slope of a horizontal line is Z ero.
The first stroke when writing the letter “Z”
Is a horizontal stroke,

Undefined Slope
The slope of a vertical line is said to be
Undefined, we say it has “No” slope.
The first stroke when writing the letter N is a vertical stroke.
When calculating slope, if a Nonzero Number is obtained over a zerO, the fraction N/O vertically spells “NO” which represents uNdefined.

You can’t stand on a beachball.
You can’t divide by zero

VUX & HOY: To determine the type, slope and equations of certain lines
VUX: Vertical, Undefined, X = a
HOY: Horizontal, zerO, Y = b

Absolute Value Function:
Y = |x|
The shape of the graph is a “V” for “value”

Definitions of complementary and supplementary angles:
Complementary Angles: Two angles whose sum is 90 o
Supplementary Angles: Two angles whose sum is 180 o
Alphabetically C comes before S, numerically, 90 comes before 180
C, S  90 o , 180 o

Area and Circumference of a circle:
A = πr 2 Apple pie “r” square
A = π × r × r Apple pie “r” “r”ound
A circle’s area is pi r squarea
C = π d Cherry pie delicious
C = π d Cherry pie-d

To define the trigonometric ratios;
Sinθ = Opposite/Hypotenuse
Cosθ = Adjacent/Hypotenuse
Tanθ = Opposite/Adjacent
1. SOH-CAH-TOA
2. Some Old Horse Came A-Hopping Through Our Alley
3. Some Old Horse Caught Another Horse Taking Oats Away
4. Some Old Horses Chase And Hunt Till Old Age
5. Some Old Horses Can Always Hear Their Owner’s Approach

6. Some Old Hippie Caught Another Hippie Tripping On Acid
7. Some Old Hippie Caught A High Tripping On Acid
8. Some Old Hippie Came Around Here Tripping On Acid
9. Some Old Hag Cracked All Her Teeth On Asparagus
10. Some Old Hags Can’t Always Hide Their Old Age
11. Some Old Hobos Can’t Aways Hide Their Old Age
12. Some Officers Have Coaches And Horses To Order Around
13. Silly Old Harry Caught A Herring Trawling Off America
14. Silly Old Hippies Can Always Have Tons Of Acid
15. Silly Old Hitler Caused Awful Headaches To Our Airmen

16. Sir Oliver’s Horse Came Ambling Home To Oliver’s Aunt
17. Saddle Our Horses, Canter Away Happily To Other
Adventures
18. See Old Harry Catch A Herring Trawling Off America
19. Snellville’s Old Hospital Can Always Help The Odd Accident
20. Sex On Hard Concrete Always Hurts, Try Other Areas

Definitions of sin, cos, & tan in that order:
1. Oscar Had A Headache Over Algebra
2. Oscar Had A Hangover Over Alcohol
3. Oscar Has A Heap Of Apples (or Acorns)
4. Oscar Had A Hit Of Acid
5. Oscar Had A Hold On Ann
6. Old Hippies Are High On Acid
7. Old Houses Always Have Old Attics
8. Oh Heck, Another Hour Of Algebra

For the definitions in other orders:
1. The Old Aunt Sat On Her Coat And Hat
2. The Old Arab Sat On His Camel And Howled
3. The Cat Sat On An Orange And Howled Horribly
(ratios, numerators, denominators)
4. Old Harry Spills All His Coffee Over Auntie’s Tablecloth

To determine where the trig functions are positive:
Starting in the first quadrant and going counter-clockwise in the order the quadrants are numbered;
All functions are positive in quadrant I
Sine is positive in quadrant II
Tangent is positive in quadrant III
Cosine is positive in quadrant IV

1. All Students Take Calculus
2. All Students Take Chemistry
3. All Schools Teach Crap
4. All Stores Take Cash
5. All Science Teachers Care
6. A Simple Trig Chart
7. Another Stupid Trig Class
8. A Smart Trig Class

9. Aunt Sally Tickles Cobras (Cats, Camels,
Cougars, Chimps, Caribou…)
10. After School To College
11. Add Sugar To Coffee
12. All Silver Tea Cups
13. Albany State Teachers’ College

Which trig functions are odd, which is even, by the numbers:
1. sine
2. cosine
3. tangent
Since 1 & 3 are odd numbers, sine & tangent are odd functions
Since 2 is an even number, cosine is an even function

For derivatives and antiderivatives of sin & cos, use the wheel in a:
Clockwise rotation for a function’s derivative and
Counterclockwise for a function’s antiderivative.
(equate “counter” with “anti”)

-cos
Derivatives sin cos
-cos
Antiderivatives sin cos
-sin
-sin

The Quotient Rule I
If the numerator is “hi” and the denominator is
“ho” and de means the Derivative, we have d(hi/ho) = “ho-de-hi” minus “hi-de-ho over dx ho-ho.

Quotient Rule II
If the numerator is “hi” and the denominator is
“lo” and “de” means the derivative, we have d(hi/lo) = “lo-de-hi” minus ‘hi-de-lo” all over dx lo 2

Measures of Central Tendency
Mean: The sum of the values, divided by the number of values.
The usual method of calculating an “average” by teachers.
Since teachers are “Mean”, this is known as the mean.
Median: The grassy area or wall that runs down the middle of a highway is known as the “Median”. The middle value of a set of values.
Mode: The most frequently occurring value. A four letter word starting with “m-o”. Mode – most.

Primitive Pythagorean Triples: In each case the square of the first value is the sum of the other two values, which differ by one.
3: 4: 5
5: 12: 13
7: 24: 25
9: 40: 41
11: 60: 61

Squaring a number that ends in five:
5 2 = 25
15 2 = 225
25 2 = 625
35 2 = 1225
45 2 = 2025
55 2 = 3025
65
75
85
95
105
115
2
2
2
2
2
2
= 4225
= 5625
= 7225
= 9025
= 11025
= 13225
The digit(s) in front of the 5 times the next integer with a 25 on the end gives the product. For example; 65 2 is 6 times 7 is 42 with a 25 on the end yielding 4225.

Converting some fractions to decimals:
Digits over 9 are repeating decimals of that digit. 5/9 = .555…
Digits over 99, 999, etc. are also repeating decimals of those digits. 23/99 = 232323…,
5/99 = .050505…, 5/999 = .005005…

Remembering Pi:
May I have a large container of coffee?
3.1415926
How I want a drink, alcoholic of course after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard…
3.14159265358979323846264

For some easy multiplying:
Never multiply by 4, just double twice.
Instead of trying to multiply by 25, think in terms of twenty-five cent pieces. For example, what is 17 x 25 ? Ask how much would I have if I had 17 quarters? Since 4 quarters make one dollar, 16 would be 4 dollars and the 17 th quarter is another 25 cents, that’s $4.25 or
425 cents or 17 x 25 = 425

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1. http://www.atlanticwinds.com
2. http://www.sciencejokes.com
3. http://en.wikipedia.org
4. http://wik.ed.uiuc.edu
5. http://faculty.kutztown.edu
6. http://forgetknottripod/com
7. http://mathforum.org
8. http://members.tripod.com
9. http://math.about.com
10. http://results.about.com/math
11. http://.learner.org
12. http://turnbull.mcs.st-and.ac.uk/history
13. laura.lowrey@gpc.edu
14. zacchaeus.oguntebi@gpc.edu