SAT Practice Test Question

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Jeff463
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Joined: Fri May 13, 2011 1:42 am UTC

SAT Practice Test Question

Postby Jeff463 » Sat Sep 03, 2011 12:19 am UTC

Hey everybody. I'm currently in 11th grade and preparing for the SATs, so I've been taking some practice tests. I'm an advanced math student, so I wasn't expecting to have any trouble with math, but as it turns out I have a problem.

If m=3+2p^2 and n=4+p√2
then what is m in terms of n?

I thought I got the correct answer but it isn't any of the choices. Due to the fact that I'm not really good at posting math on these forums, I'm not gonna post what the answers are right away. I also want to see what some people get as their answers.

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imatrendytotebag
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Re: SAT Practice Test Question

Postby imatrendytotebag » Sat Sep 03, 2011 12:25 am UTC

Well, we can solve the second equation for p, then put that into the first equation:

Spoiler:
First we get p = (n - 4)/sqrt(2), this gives m = 3 + 2((n-4)/sqrt(2))^2 = 3 + (n-4)^2 = n^2 - 8n + 19.
Hey baby, I'm proving love at nth sight by induction and you're my base case.

Jeff463
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Joined: Fri May 13, 2011 1:42 am UTC

Re: SAT Practice Test Question

Postby Jeff463 » Sat Sep 03, 2011 12:32 am UTC

Which is the correct answer. I thank you. I feel like an idiot for messing that one up. What I did originally is I tried squaring the bottom equation to get rid of p(squarert2) which I assumed would be n^2=16+2p^2, and from there I could just have 2p^2=n^2-16 and plug that into the first equation for the 2p^2. I should have known to separate the (squarert2), but I was so stuck in my ways after i initially saw the problem. So yeah, thanks again.

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Dopefish
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Re: SAT Practice Test Question

Postby Dopefish » Sat Sep 03, 2011 12:43 am UTC

Squaring both sides of the expression for n, and subbing in stuff to that result should work out (and is my prefered route), you just have to square things properly.

Namely, keep in mind that (4+p*sqrt(2))^2 =/= (4)^2+(p*sqrt(2))^2, as theres the cross term to deal with.


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