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hypotenuse (the side opposite the right angle)
adjacent (the side "next to" θ)
opposite (the side furthest from the angle)
Triangle: Side 1 opposite to Angle 1*: 1/sin1*=2/sin2*=3/sin3*
Sin θ = Opposite/Hypotenuse,
Cos θ = Adjacent/Hypotenuse, and
Tan θ = Opposite/Adjacent

Issue writing goals
 1) write issues in own words
 2) base position on evidence, historic events, personal experience.
 3) Lead w/best argument

Paragraph structure of issue task
 P1: paraphrase issue, state position, summarize goal
 P2: state strongest point
 P3 & 4 if time: State another point
 P5: address opposite & refute
 P6: conclusion/summary address instructions.

read critically by identifying:
1) Note: topic, scope, purpose, key ideas

argument construction structure
 1)identify evidence needed.
 2) outline intro: states argument.
 middle: id flaws/assumptions
 provided examples of needed evidence
 conclusion:I'm not persuaded w/o evidence. Link to related ideas.

Goals of argument task
 assess concency (clarity)
 analyze chain of reason/evidence
 critique argument instead of develop it.

time, distance, seed formula
T=D/S, S=D/T, D=ST

Work formula
job/time X job/time2 ... ben take 2h, john takes 3: (1/2)(1/3)=5/6 H together

combination formula
 n!/(k!(nk!) n=# of items, k=# combinations !=factorial.
 4 awards, 7 competitors. combo's of awards for possible winners? n!=(7*6*5*4)/(4*3*2*1)

prime # def
only divides by self & 1

interger def
not a fraction or decimal.


numerator vs denominator
numerator/denominator

operations
parenthesis, exponents, multiply<>divide, add<> subtract

determining divisibility of large numbers
 2=ends w/digit divisible w/2
 3=digits add up to a multiple of 3
 4=last 2 digits are a multiple of 4
 6=divisible by 2 &3
 9=digits add up to multiple of 9

methods of factorization:
 1) Work your way up w/prime #'s
 2) Word your way down to prime factors.

list of prime factors:
1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59

how do you work your way up factorizations w/prime #'s?
 e.g. find prime of 210?
 210/2=105
 105/3=35
 35/5=7
 7/7=1

how do you work your way up factorization w/primes
keep dividing numbers until you get to primes.

How do you change inequality signs X≥4
add 1 to both sides X≤4

multiplying #'s w/exponents
add the exponents.

dividing #'s w/exponents
subtract exponents

#'s w/exponents in parentheses w/exponents (X^3)^4
multiply exponents x^12

negative exponents 5^3
invert 1/(5^3)


adding or subtracting radicals
2√3+4√2√23√3=?
 only like radicals can be added or subtracted.
 =3√2√3

multiplying & dividing radicals
6√2(2√5)=?
 multiply numbers outside first. Then inside.
 (6)(2)=12, 2x5=10: 12√10
 simplifying: factor out perfect square: √72=6√2

fast comparison of fractions
5/6 or 7/9 is larger?
cross fractions denominator of one x numerator of the other. 5/6 is larger

tips for solving X^2+10X+25=0 formula name
Polynomial: (x+5)(x+5), so X=5

tip: (5x/3)+9=(x/6)+18, x=?
a)12
b)8
c)6
d)5
e)4
choose option divisible by 3 & 6.=C

tips: a>1, ratio of 2a=6 to a^2+2a3 is
a) 2a
b) a+3
c) 2/(a1)
d) 2a/3(3a)
e(a1)/2
 1) pick a number <1, like #2 plug it into ans
 2) see which ones yield #'s greater than 1, if 2 ans do, pick another number & continue.

probability of tossing penny 4 times, and getting heads only once.
 2*2*2*2=16 possibilities
 4 possible tosses it could land on heads once.
 4/16=.25

probability of rolling sixsided die 4 times, and landing on 3 all 4 times?
1/6x1/6x1/6x1/6x1/6x1/6=1/1296

probability jar: 10 marbles, 4 blue, 6 red. odds of 2 red marbles in a row, when removing marbles after draw?
(6/10)(5/9)=3/9

