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1. Issue writing goals
• 1) write issues in own words
• 2) base position on evidence, historic events, personal experience.
2. 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
1) Note: topic, scope, purpose, key ideas
4. argument construction structure
• 1)identify evidence needed.
• 2) outline intro: states argument.
• -middle: id flaws/assumptions
• -provided examples of needed evidence
• -assess concency (clarity)
• -analyze chain of reason/evidence
• -critique argument instead of develop it.
6. time, distance, seed formula
T=D/S, S=D/T, D=ST
7. Work formula
job/time X job/time2 ... ben take 2h, john takes 3: (1/2)(1/3)=5/6 H together
8. combination formula
• 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)
9. prime # def
only divides by self & 1
10. interger def
not a fraction or decimal.
11. whole #
not negative
12. numerator vs denominator
numerator/denominator
13. operations
14. 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
15. methods of factorization:
• 1) Work your way up w/prime #'s
• 2) Word your way down to prime factors.
16. list of prime factors:
1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59
17. 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
18. how do you work your way up factorization w/primes
keep dividing numbers until you get to primes.
19. How do you change inequality signs -X≥-4
add -1 to both sides X≤4
20. multiplying #'s w/exponents
21. dividing #'s w/exponents
subtract exponents
22. #'s w/exponents in parentheses w/exponents (X^3)^4
multiply exponents x^12
23. negative exponents 5^-3
invert 1/(5^3)
24. exponent 0
always =1
2√3+4√2-√2-3√3=?
• =3√2-√3
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
27. 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
28. tips for solving X^2+10X+25=0 formula name
Polynomial: (x+5)(x+5), so X=-5
29. 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
30. tips: a>1, ratio of 2a=6 to a^2+2a-3 is
a) 2a
b) a+3
c) 2/(a-1)
d) 2a/3(3-a)
e(a-1)/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.
31. 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
32. probability of rolling six-sided die 4 times, and landing on 3 all 4 times?
1/6x1/6x1/6x1/6x1/6x1/6=1/1296
33. 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