Challenge: sample question from Chinese university entrance tests

<p>Show off your talent...:)</p>

<p><a href=""&gt;;/a&gt;&lt;/p>

<p>FYI: Chinese university entrance tests are subject tests taken by high school seniors and given only once a year; admission to college/major is based almost entirely on exam scores (even your high school grades don't really matter).</p>

<p>hahaha that's insane.</p>

<p>it's not insane...if i had it on paper then it'll b much easier to solve the prism one...the second one is ridiculously easy.</p>

<p>oo btw dun think that im lame spending time doing this on a friday...but i broke my foot so i haven't been outside</p>

<p>That article was actually created quite a while ago, and when I saw it, I asked a friend at Cambridge University what he thought. He says that the Royal Society is attempting to mislead its audience. Though why they're attempting to do so, I don't remember his reasons.</p>

<p>First of all, the easy trig question used by "an English university" isn't something set up by the government, whereas the Chinese question was approved by the government. We could go to the local community college and see their placement exams and then compare them to an elite college in Africa and make the conclusion that African schools are much better than those of the United States. In addition, it's obvious that in placement exams, the questions vary in difficulty. The question on the Chinese entrance test is most likely the hardest question on the test, whereas the question on the English entrance test is probably among the easiest.</p>

<p>Finally, the maths curriculum of the two nations could vary significantly, and the Chinese could focus more on geometry, whereas the English focus more on analysis. Just a note so you won't take that article so seriously. Have a go at the problem, though.</p>


<li><p>Actually, the exam isn't an entrance exam for a elite Chinese college. It's an annual public exam taken by all seniors. It's like SAT II subject tests.</p></li>
<li><p>Chinese curriculum actually goes pretty deep into numerical analysis. I will post the link to one of the actual exam.</p></li>
<li><p>You are right that the media tries to exaggerate the contrast. I studied the O-level in Hong Kong, and we practiced many problems from past GSCE. In other textbooks, we usually have problems classified into level I, level II, and level III. The GSCE problems are definitely harder than the one shown on the article. However, they are almost never classified as level III. The math O-level exam in Hong Kong is harder than GSCE and that's where level III questions appear. I don't know how Hong Kong's A-level math is compared to China as I left after 10th grade; all I know is one of my friends got a D on "pure math" and got 800 on SAT math.</p></li>

<p><a href="****i/2007/0613/115203050.html%5B/url%5D"&gt;****i/2007/0613/115203050.html&lt;/a&gt;&lt;/p>

<p>There are 11 filling in the blank ones, 4MCs, and 6 questions that look like the one in the BBC article where you have to show steps and rationale. Time limit is 2 hours.</p>

<p>My Chinese is pretty shaky, but here are some of what I can translate:<br>
1. The domain of f(x) = ln(4-x)/(x-3) is?
2. Given L1: 2x + my +1 and L2: y =3x -1 are parallel, what's m?
3. What's the inverse function of f(x) = x/(x-1)?
4. What are the solutions of the equation 9^x-6*3^x-7 = 0?
5. f(x) = what's the minimum value of period T of sin (x + pi/3) * sin (x + pi/2)
6. Given x,y E R+, and x+4y=1, what are the maximum value of x and y
7. If you pick 3 numbers out of 1,2,3,4,5 randomly, what's the probability that 2 remaining are odd number?</p>

<p>Don't understand some of the terms in 8, 9, and 10. </p>

<li>Given x^2 + (y-1)^2 =1 and P can be any point but the origin on the circle. Line OP has an inclined angle of theta, and lOPl = d; sketch d = f(theta)
<li>Given 2+ai, b+i are two roots of x^2+px+q=0; the value of p and q are:</li>
<li>Given a, b are non-zero real numbers and a<b; then which one of the following is true?</li>
<li>in cartesian coordinate xOy, unit vector i,j are parallel to x-axis and y-axis, respectively; if in a right triangle, vector AB = 2i + j and vector AC = 3i + kj, how many possible values does k have?</li>
<li>given the domain of f(x) is all positive integers and k is any value within the domain; if f(k) >= k^2 is true, then f(k+1) >= (k+1)^2 is also true; which of the following is true:
A. if f(3) >=9 is true, then for any given k >= 1, f(k) >= k^2 is also true.
B, C, and D can be similarly translated. </li>

<p>While some don't look so bad (the first few are the easiest), keep in mind the time limit is 2 hours. The goal is probably to finish the first 15 FBs and MCs within the first hour (or less) do the 6essay questions within the remaining time. That leaves an average of about 10 mins to do each of those 6 long problems. It's definitely not an easy public exam.</p>