sat 2 math level1c

[swq]

now i know that this exam is only about basics and so, but still i wanna test my self in math, id say i know about 65% math and i excel in trigonometry, so start the questions id be happy to answer em.

[Notorious]

now i know that this exam is only about basics and so, but still i wanna test my self in math, id say i know about 65% math and i excel in trigonometry, so start the questions id be happy to answer em.

http://forums.narutofan.com/showthread.php?t=271222


^Post there for help, but I'll give you a question.

If x + y = 10 and xy = 18, find x^2 + y^2

[swq]

;10689847']http://forums.narutofan.com/showthread.php?t=271222


^Post there for help, but I'll give you a question.

If x + y = 10 and xy = 18, find x^2 + y^2

thats easy.. first of all (x+y)^2=x^2 + 2xy + y^2 => (10)^2 = x^2 + 2(18) + y^2 => 100 = x^2 + 36 + y^2 => x^2 + y^2 = 64. thnx

[The_Unforgiven]

try this:

if ax^2 + 12x + 9 = 0 has -3/2 as its only solution, what is the value of a?

(BTW, this is from the book I told u about)

[Notorious]

These are good questions for math 1C, but I recommend you buy either PR or barron's for good practice tests. You only need basic trig for it...although knowing your identities would be useful...so that's what I am asking you. Name the 3 fundamental trig identities.

[swq]

kk first of all u know that if the quadratic equation has only one solution then in the formula of X=-b^2+or-radical(b^2-4ac)/2a. that b^2-4ac = 0, so just replace and ull c that a = 4.

the three iden. are sin, cos, tan.
thnx for the warmup. :d

[Notorious]

kk first of all u know that if the quadratic equation has only one solution then in the formula of X=-b^2+or-radical(b^2-4ac)/2a. that b^2-4ac = 0, so just replace and ull c that a = 4.

the three iden. are sin, cos, tan.
thnx for the warmup. :d
No man, this is what i was getting at:

sin^2 + cos^2 = 1
1 + cot^2 = csc^2
1 + tan^2 = sec^2

[Commander Red]

Try this one:

Show that the inequality: "|a-b| >_ ||a|-|b||" holds for all real numbers a nd b.


"|x|" means absolute value of x, so |-x| = x. and |x||y| = |xy|.
"x >_ y" means x more than or equal to y.
I'm posting these definitions, because it's impossible to write the inequalities clearly on the forum. If I wanted to say "more than" then I would have used the ">" symbol.

[swq]

woh!! easy man, well one of the things im bad at is eniqualties so.. i wont even try coz im just seeing chinese :P .. hit me with another thing

[Commander Red]

woh!! easy man, well one of the things im bad at is eniqualties so.. i wont even try coz im just seeing chinese :P .. hit me with another thing

Huh? Aren't inequalities almost identical with equations just with slight minor difference in answering them? It's almost like solving an equation.

[swq]

Huh? Aren't inequalities almost identical with equations just with slight minor difference in answering them? It's almost like solving an equation.

yeah but still i can't understand them, because an absolute value in an inequality has two answers positive and negative.. that confuses me alot, id appreciate it if u explained it to me, seems u well known to the subject :)

[Commander Red]

yeah but still i can't understand them, because an absolute value in an inequality has two answers positive and negative.. that confuses me alot, id appreciate it if u explained it to me, seems u well known to the subject :)

Well you don't have to solve, but you have to proof it, that's true for each a and b. To do so, there are several ways;
one way is to show that if a > 0 & b > 0 are true, then with a < 0 & b > 0 is true, and so on untill you showed all four possibilities are true. If it's correct then you've proved that |a - b| >_ ||a| - |b|| is correct for all real numbers a and b.

The other way is to make use of the triangle inequality: "|a + b| _< |a| + |b| holds for all real numbers a and b."
More information about the triangle inequality and the proof can be found here:
http://en.wikipedia.org/wiki/Triangle_inequality But yes, this is I think, a bit difficult.

Do you get proof questions just like this one on your test?

[Notorious]

Nope. SAT MathIC is multiple choice. You will only see proof questions in advanced college classes and the USAMO, really.

[Commander Red]

Right, I see. Alright then, I've asked totally the wrong questions for this... My apologies.

[Notorious]

Lol, yeah. In US High schools its all about concepts. Problem solving and proofs are done in specialized math contests.

[swq]

thxn for the link it'll be helpful someday, i like math and expanding would be good

[Commander Red]

Hehe, alright then. Goodluck!

Would like to see the proof, or do you want to try it out for yourself?

[swq]

i'll try to asnwer it myself, if i give up ill ask u.

[Commander Red]

Alright then, Goodluck!

[Notorious]

If you want to get good at math:


www.artofproblemsolving.com


Best resources. Get the two volumes with the same name and you'll be a pro.

[Bakalakadaka]

Here, I'll just throw some problems from my PR practice Math SAT2 book at you (i took the Math 2 last year):

In 1900, the population of Malthusia was 120,000. Since then, the population has increased by exactly 8 percent per year. If population growth continues at this rate, what was the population in the year 2000?

a. 216,000
b. 2,599,070
c. 1,080,000
d. 5.4 x 10^7
e. 2.6 x 10^8

[AbnormallyNormal]

d or e, since there is a trick whree to find out how many units of time it takes some quantity to double, you divide 70 by the constant percentage rate of increase, in this case something a little above 9 (years). so in other words you double 120,000 ten times to get the answer

[vanh]

Not exactly 2.6 x 10^8 though, but close.

Let's call the population in year t A.

In year t+1 , the population is : A + A x 0.08 = A x 1.08
In year t+2 , the population is : A x 1.08 + A x 1.08 x 0.08 = A x (1.08^2)
In year t+3 , the population is : A x 1.08^2 + A x 1.08^2 x 0.08 = A x 1.08^3

After 100 year, the population is : A x (1.08)^100 = 120,00 x 1.08^100 = 263,971,350.

[The_Unforgiven]

i remember learning a formula on compound population growth, but I don't remeber it. Can anyone post it here?

[AbnormallyNormal]

uh i think i just did? basically if there is a constant rate of increase, a neat trick is to divide 70 by that rate expressed as a percentage, and thats the # of units of time (probably in years) for the amount to double overall

[Bakalakadaka]

Yeah, lacking got it right.

Here's an easier one:

Which of the following is the positive difference between 10^18 and 9^19?

a. 5.3 x 10^16
b. 1.0 x 10^17
c. 3.5 x 10^17
d. 1.1 x 10^18
e. 7.3 x 10^18

[The_Unforgiven]

that's easy. Just grab the calculator. The answer is C.

[Commander Red]

So, you're allowed to grab a Calculator during SATs?

[myle]

I don't think so.

[swq]

yeah u are, plus the percentage problem is easy there is a formula in the sat 2 book, i think it goes like if it was increasing by 8 percent, in the equation u write (1+8/100).