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These questions come from the 1st pre-test of College Entrance in China.
1.
Cleaned up latex from over running the page - Ricky
Numbers are the essence of the Universe
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2. A circle
has intersections with line at point P and Q,Numbers are the essence of the Universe
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Two functions
have intersections Point A and O .Numbers are the essence of the Universe
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I think the Chinese math exam is a little harsh , Since everyone has to deal with problem like these , no matter what your major is.
Last edited by Stanley_Marsh (2007-03-21 10:28:10)
Numbers are the essence of the Universe
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#2
(1) C is the circle of radius 1 with centre at (1,1). It touches (is tangent to) the y-axis at (0,1). So if M is this point and MP is perpendicular to MQ, PQ must be the diameter of the circle. Thus, the line ℓ passes through the centre of the circle so k = 1.
EDIT:
(2) Still working on the second part. The relationship Ive derived between b and k is
Last edited by JaneFairfax (2007-03-21 12:30:07)
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These are the 3 last questions, the entrance exam just like sat , but only got 120 minute to finish 21 questions.
Yeah , the second is kind of tricky.
Numbers are the essence of the Universe
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Okay, heres I(1).
From which we can see that
If we carry on, we find
From the emerging pattern, we can guess that
It remains to prove our guess by induction. Thats the easy part the hard part is finding the pattern in the first place. Well, not so much hard as laborious.
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Actually there's a shortcut ~
Numbers are the essence of the Universe
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