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2008-04-22 23:33:03
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT
So I took an SAT practice test today and missed a couple math problems. When I looked over the answers, I had absolutely no idea how they got them, which was disconcerting and annoying. Obviously, as this is a study test, I would like to know how the answers are attained. Could someone explain the correct answers for each of the problems? Karma for constructive answers...

1.

(a+b)1/2 = (a-b)-1/2

Which of the following must be true?

A. b = 0
B. a + b = 1
C. a - b =  1
D. a2+b2 = 1
E. a2 - b2 = 1

Its E.

2.

The graph of x = y2 - 4 intersects line 'l' at (0, p) and (5, t). What is the greatest possible value of the slope of 'l'?

I got 1/5, the answer book says 1.

Last edited by nukchebi0 (2008-04-22 23:34:10)

2008-04-22 23:37:23
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY
1.  a2-b2=1 => (a-b)(a+b)=1, divide by (a-b), take square root.

Edit:  I flipped a sign.  Fixed.

2.  It's a sideways parabola.  y = +/- sqrt(x+4), so the slope eq. is:  3-(-2) / (5-0) = 1

Last edited by SenorToenails (2008-04-22 23:42:45)

2008-04-22 23:39:11
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT
I was thinking it had something to do with differences of squares. Thanks.

So working from the source, you would square both, multiply to isolate 1, and then simplify?

For two...

Oh,  I forgot about doing that. I just took the positive square root. Thanks again.

Last edited by nukchebi0 (2008-04-22 23:46:35)

2008-04-22 23:44:47
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY

nukchebi0 wrote:

I was thinking it had something to do with differences of squares. Thanks.

So working from the source, you would square both, multiply to isolate 1, and then simplify?
Yep.

SAT questions are meant to have an apparent easy answer, but actually trick you.  These are two good examples.
2008-04-22 23:49:05
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT

SenorToenails wrote:

nukchebi0 wrote:

I was thinking it had something to do with differences of squares. Thanks.

So working from the source, you would square both, multiply to isolate 1, and then simplify?
Yep.

SAT questions are meant to have an apparent easy answer, but actually trick you.  These are two good examples.
I see. Of course, the 'easy' ones you can do in your sleep.

Example:

Company A produced 300 of a product in week one. They received more machinery, and consequently produced 50% more of the product in week two. How much of product two did they make in this second week?
2008-04-22 23:51:21
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY

nukchebi0 wrote:

I see. Of course, the 'easy' ones you can do in your sleep.

Example:

Company A produced 300 of a product in week one. They received more machinery, and consequently produced 50% more of the product in week two. How much of product two did they make in this second week?
I'm betting '150' was a choice, right?
2008-04-22 23:53:53
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT
It was student-response question, so unfortunately no. If it was, that is probably a safe guess.

Try this:

x + (2/x) = 5 + (2/5)

What could x be equal to?

A. 1/5
B. 4/5
C. 1
D. 5/2
E. 5
2008-04-22 23:57:49
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY

nukchebi0 wrote:

Try this:

x + (2/x) = 5 + (2/5)

What could x be equal to?

A. 1/5
B. 4/5
C. 1
D. 5/2
E. 5
x = 2/5 or 5, so E.
2008-04-22 23:58:22
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT
How long did it take you?
2008-04-23 00:02:24
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY

nukchebi0 wrote:

How long did it take you?
I figured it was '5' by looking at it.  2/5 is not as obvious, but that isn't saying much.

When they ask "what could it be", there might be more than 1 correct answer, so I looked for the other to make sure it wasn't on the list.

Last edited by SenorToenails (2008-04-23 00:03:30)

2008-04-23 00:04:46
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT

SenorToenails wrote:

nukchebi0 wrote:

How long did it take you?
I figured it was '5' by looking at it.  2/5 is not as obvious, but that isn't saying much.

When they ask "what could it be", there might be more than 1 correct answer, so I looked for the other to make sure it wasn't on the list.
You analyzed even more than I did.

Regardless, it was an easy question, no?
2008-04-23 00:07:00
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY

nukchebi0 wrote:

You analyzed even more than I did.

Regardless, it was an easy question, no?
Incredibly.

Sometimes its nice to look at math that can be done in under 5 minutes. 
2008-04-23 00:10:33
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT

SenorToenails wrote:

nukchebi0 wrote:

You analyzed even more than I did.

Regardless, it was an easy question, no?
Incredibly.

Sometimes its nice to look at math that can be done in under 5 minutes. 
Yes. Going from AP Calculus to this provides a nice relief.
2008-04-23 00:15:38
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY

nukchebi0 wrote:

Yes. Going from AP Calculus to this provides a nice relief.
AB or BC?
2008-04-23 00:20:04
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT

SenorToenails wrote:

nukchebi0 wrote:

Yes. Going from AP Calculus to this provides a nice relief.
AB or BC?
AB, I'm only a junior.

The free response questions take 5-10 minutes apiece, as you should remember.
2008-04-23 00:22:36
David.P
Banned
+649|6747
Fuck i'm doomed!
2008-04-23 00:26:57
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY

nukchebi0 wrote:

AB, I'm only a junior.
You are a year ahead of me.  My school didn't offer AP Calc BC, and my 'accelerated' sequence brought me to AB by my senior year.

nukchebi0 wrote:

The free response questions take 5-10 minutes apiece, as you should remember.
The SAT has changed a bit since I took it.  I don't recall if the free response question time has changed at all.  I only took them once, and it was 6 year ago.
2008-04-23 00:31:09
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT

SenorToenails wrote:

nukchebi0 wrote:

AB, I'm only a junior.
You are a year ahead of me.  My school didn't offer AP Calc BC, and my 'accelerated' sequence brought me to AB by my senior year.
Is 'accelerated' normal smart people in your grade, or you a year ahead of these normal smart people?

If the former, then our 'accelerated' sequence does the same thing. I skipped basic Algebra in 6th grade, and went with the normal smart people of the grade above me.

nukchebi0 wrote:

The free response questions take 5-10 minutes apiece, as you should remember.
The SAT has changed a bit since I took it.  I don't recall if the free response question time has changed at all.  I only took them once, and it was 6 year ago.
I meant the free response questions on the AP exam, just to specify how I could identify with your sentiments about not having to do lengthy problems.
2008-04-23 00:38:25
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY

nukchebi0 wrote:

Is 'accelerated' normal smart people in your grade, or you a year ahead of these normal smart people?

If the former, then our 'accelerated' sequence does the same thing. I skipped basic Algebra in 6th grade, and went with the normal smart people of the grade above me.
Same, only I skipped 8th grade math.

I meant the free response questions on the AP exam, just to specify how I could identify with your sentiments about not having to do lengthy problems.
I long for those days.  Now I get stuck with a 3 question test and 4 hours to do it.
2008-04-23 00:44:56
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT

SenorToenails wrote:

nukchebi0 wrote:

Is 'accelerated' normal smart people in your grade, or you a year ahead of these normal smart people?

If the former, then our 'accelerated' sequence does the same thing. I skipped basic Algebra in 6th grade, and went with the normal smart people of the grade above me.
Same, only I skipped 8th grade math.
So the majority of the 'smart people' in your high school didn't take AP Calculus, if you were a year ahead of them?

I meant the free response questions on the AP exam, just to specify how I could identify with your sentiments about not having to do lengthy problems.
I long for those days.  Now I get stuck with a 3 question test and 4 hours to do it.
Oh. So doing a 5 minute free response question in Calculus AB is nothing to you anymore? I didn't realize it got that complex in college.
2008-04-23 01:00:21
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY

nukchebi0 wrote:

So the majority of the 'smart people' in your high school didn't take AP Calculus, if you were a year ahead of them?
Yes, my calculus class was ~30 people in a graduating class of ~400.  I don't think half the class took the exam, since my district didn't pay for them.

Oh. So doing a 5 minute free response question in Calculus AB is nothing to you anymore? I didn't realize it got that complex in college.
It's to be expected.  I went to college specifically for math and physics, which gets complicated, though it really depends on the subject matter.  The actual math that is covered on the calc AB test is simple, especially when every class I took used calculus in some form.  Physics and engineering get that way...

You want to go to college for engineering of some form, right?  Wait until your third or fourth year, then go and try some calc AB or SAT questions.  I guarantee you'll understand my point of view.
2008-04-23 01:06:54
nukchebi0
Пушкин, наше всё
+387|6797|New Haven, CT

SenorToenails wrote:

nukchebi0 wrote:

So the majority of the 'smart people' in your high school didn't take AP Calculus, if you were a year ahead of them?
Yes, my calculus class was ~30 people in a graduating class of ~400.  I don't think half the class took the exam, since my district didn't pay for them.
I see.

Oh. So doing a 5 minute free response question in Calculus AB is nothing to you anymore? I didn't realize it got that complex in college.
It's to be expected.  I went to college specifically for math and physics, which gets complicated, though it really depends on the subject matter.  The actual math that is covered on the calc AB test is simple, especially when every class I took used calculus in some form.  Physics and engineering get that way...

You want to go to college for engineering of some form, right?  Wait until your third or fourth year, then go and try some calc AB or SAT questions.  I guarantee you'll understand my point of view.
Yes, I do. Will the transition be much different than revisiting the FOIL problems of 7th grade (which took 2 minutes apiece then) now, and being able to do them entirely in my head within ten seconds?
2008-04-23 01:11:32
SenorToenails
Veritas et Scientia
+444|6603|North Tonawanda, NY

nukchebi0 wrote:

Yes, I do. Will the transition be much different than revisiting the FOIL problems of 7th grade (which took 2 minutes apiece then) now, and being able to do them entirely in my head within ten seconds?
haha, probably.

 

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