<p><a href="http://edu.sina.com.cn/****i/2007/0613/115203050.html%5B/url%5D">http://edu.sina.com.cn/****i/2007/0613/115203050.html</a></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>

<ol>

<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)

MCs:</li>

<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>

</ol>

<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>