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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
job/time X job/time2 ... ben take 2h, john takes 3: (1/2)(1/3)=5/6 H together
- n!/(k!(n-k!) 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
not a fraction or decimal.
numerator vs denominator
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:
how do you work your way up factorizations w/prime #'s?
- e.g. find prime of 210?
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
#'s w/exponents in parentheses w/exponents (X^3)^4
multiply exponents x^12
negative exponents 5^-3
adding or subtracting radicals
- only like radicals can be added or subtracted.
multiplying & dividing radicals
- 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=?
choose option divisible by 3 & 6.=C
tips: a>1, ratio of 2a=6 to a^2+2a-3 is
- 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.
probability of rolling six-sided die 4 times, and landing on 3 all 4 times?
probability jar: 10 marbles, 4 blue, 6 red. odds of 2 red marbles in a row, when removing marbles after draw?