Columbia University Science Honors Program ENTRANCE EXAMINATION

I have the same question^^

What are my chances?

Easy Math:48
Science: 55-65
Challenge:13-14

I am also a freshman

Was the answer to that reciprocal of the sum of the roots of ax^2 + bx + c, -a/b?

It was like e or d… Not sure which. The answer was like (-c/b) or (-b/c) something like that

How? If you divide the expression by a, you get x^2 + b/a x + c/a. The b/a term is the sum of the opposite of the roots, so the sum of the roots is -b/a. And then the reciprocal of that is -a/b

The c term is supposed to be the multiplied roots

That one was easy as long as you knew Vieta’s

@dhusb45 It was -a/b right?

@DankMeme2019:
sum of reciprocals of roots=
1/p+1/q =/= 1/(p+q)

It should be 1/p+1/q=(p+q)/pq so my answer is -b/c

Or was it the reciprocal of the sum of the roots

@dhusb45 I thought it was the reciprocal of the sum of the roots. But i didn’t pay much attention to wording

Ok if it was the other way then I’m wrong

@scietywi which one was it? I don’t remember. I do remember commenting in my mind that the problem was some element of that one question from the easy math. Also that kind of problem is kinda routine for me cause I’m a mather

@dhusb45 Did you pay attention to the wording when reading the question? I’m not certain

@dhusb45 I got the same as you.

@scietywi Did you pay attention to the wording?

Anyone got 3 for the number of (x,y) pairs where x and y is distinct?

@DankMeme2019 I just hate it when I doubt myself after the test…sigh. Well I’m pretty sure I read it correctly, but I wouldn’t be surprised if you were right.

@Tooltooi My argument for that is when you make a mini version of a statue, it should be proportional. To me, its logical to decrease the width and length. I mean how weird would the statue look if only the height was changed? The question itself is really ambiguous so I guess it’s up to interpretation.

@Tooltooi Was that the y = 2xy and x = x^2 + y^2 question?

@scietywi Some other people from my school got the same answer as me, but I’m not sure if i read it correctly

Yeah

Which 3?, Wolfram Alpha says there are 4