<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>wait till you see the HUGE trig proves!</p>
<p>Chinese math doesn't cover a lot (example. no calculus etc.) but it goes SUPER DEEP, i mean what else are you gonna do for math in the high school years if you are not gonna learn calculus?
my dad took the test about 30 years ago >.< he got perfect on physics, really well on math and failed the Chinese part</p>
<p>sigh. both of my parents went to this really top school in China (3rd ranked in China as of 2007 and 2005) too bad i don't get any legacy, and the 3rd in China would probably be pretty bad compare to the universities in the world. since they got pretty high education, college i am applying to probably expect me to be very good too because of them, but they really can't help me in school because English is too confusing for them</p>
<p>and hey
China doesn't get # 1 at IMO for nothing!
=)
when i was in China, we got finals since FIRST GRADE!
i remember the part of the first semester final for first grade math was doing 100 , two-digit addition and subtraction problem in 10 minutes.(if you run out of time... sucks for you. and most of the people get above 95 on that part and lots of perfects)
algebra I was taught in about 6th grade
but i remember focusing a lot on quick calculations like
99*43 = 43 *(100-1) = 4300-43 (3rd grade? ish)
decimals and fractions were learned earlier on than comparing to the US
everything is just like a big math boot camp till the college exam</p>
<p>What a silly article! I found the juxtaposition of Chinese and British test questions particularly repulsive. You can conjure an enormous gulf in "difficulty" between any two tests by picking the easiest question on one and perhaps the hardest on another.</p>
<p>Now, I don't doubt that tests probably require more effort in China than in Britain, but this article is just vapid and sensationalist. And who are these idiot chemists that find big, pointless geometry problems to be good examples of curricular rigor?</p>
<p>True. I have done quite many GCSE problems before and they are nothing like the one in the article.</p>
<p>Sometimes, to make a point you have to exaggerate, which the news media always does. That said, the point is the same. The "gulf of difficulty", as you say, is hardly vapid. I remember my <em>fourth grade</em> class learning the <em>times tables</em> - 9x9!....the standards of rigor are totally different. And of course you could say there are drawbacks to each system...but it's not like the differences don't exist, or are small...(I mean, I <em>bet</em> that triangle question is not typical of British exams..although it seems like an SAT problem, sort of)</p>
<p>What question are they offering 500pounds for??</p>
<p>I am far too lazy to do that proof in the traditional sense, so I think I'll do it this way.</p>
<p>The test asks you to prove that BD is perpendicular to A(sub1)C, therefore it must be have been proven by some method by the testmakers, so it must be true.
QED.</p>
<p>:-)</p>
<p>The problem appeared really intimidating to me when I first saw it, but it doesn't seem that hard now. For now, I only proved part 1 because it's so late. I refreshed my math mind for the time being. Good prep for going to college next year.</p>
<p>Some Paper 2 IB HL math problems on the exam are much harder than this one. I agree with the above posters that this isn't necessarily a good representation. The Chinese problem should be compared to an AP Free Response, IB HL Paper 2, or A-level problem (not familiar with the exam), not a 3-4-5 triangle. The difficulty is about the same, given similar time constraints.</p>
<p>Spoiler Warning:</p>
<ol>
<li>Set D to coordinate (0,0,0). Let AD be the x axis and CD be the y axis. Thus, we can find the points A, C, and D since they gave the magnitudes. We know the z coordinate for B is 0, so we need to find the x and y coordinates for B, which we define as Bx and By. We have two givens: 1. Magnitude of AB is 2, so we can use Pythagorean theorem to write one equation with 2 unknowns. 2. Line AC is perpendicular to Line BD. Since D is the origin, BD is the same as B. We can write another equation with the scalar product of AC and BD. Two equations, two unknowns, and we can find Bx, By, and the coordinate B.</li>
</ol>
<p>We use the scalar product again to find the proof for the perpendicular BD and A1C. We already found BD, and A1 is just A except with a Z coordinate of Sqrt(3) instead of 0. Find the vector A1C, and then scalar product the two vectors (BD and A1C). The scalar product is 0, proving that it's perpendicular.</p>
<ol>
<li><p>We know the coordinates for A1, B, and D. We also know C1 is just C with a z coordinate of Sqrt(3) instead of 0. Find position vectors from B to A1 and B to D, and take the cross product. Find vector from BC1 and BD and take the cross product. Use the scalar product formula (a*b = [a]**cosn), where [a] is the magnitude of a. Thus find n, the angle.</p></li>
<li><p>We know A, we know D, we know B, we know C1. Find vectors AD and BC1. Use the scalar product formula to find the angle.</p></li>
</ol>
<p>Sorry, I got too excited when doing this problem. I should have entered the contest :(</p>
<p>yeah its all just easy vector stuff, but much harder than what you see on the SAT.
just find the coordinates for points that you need (use the fact that this is a square prism, etc.) then find the representative vectors of certain line segments to show that they are parallel or perpendicular, and look at the normal vectors of plans (which can be found using cross products) to find the angle between planes, etc.</p>
<p>oh and i agree that its kind of bad that the dude found one of the easier problems on the british exam just to make the difference more dramatic.</p>
<p>
[quote]
What a silly article! I found the juxtaposition of Chinese and British test questions particularly repulsive. You can conjure an enormous gulf in "difficulty" between any two tests by picking the easiest question on one and perhaps the hardest on another.
[/quote]
</p>
<p>Had they picked the hardest question on any UK (or US) college entrance exam it still would have been much easier than the Chinese problem. That was the point.</p>
<p>i dunno about a comparison between chinese and british tests, but i know that in china the average student is about two years ahead of the average american student in math. my cousin who was going into 7th grade last summer was doing 9th and 10th grade american math (trig and complicated geometry)</p>
<p>well, in China they don't get to calculus, so once they do like complicated trig and geo, they learn more complicated algebra, trig and geo every year.
American hs is mainly about breath, try everything kinda. Chinese hs is like ..."learn this! and you better learn it WELL!" ( you don't get to pick your classes in china either)</p>
<p>
[quote]
i dunno about a comparison between chinese and british tests, but i know that in china the average student is about two years ahead of the average american student in math. my cousin who was going into 7th grade last summer was doing 9th and 10th grade american math (trig and complicated geometry)
[/quote]
</p>
<p>With a lot more rigor than 9th/10th grade math here, mind you.</p>
<p>
[quote]
I have done quite many GCSE problems before and they are nothing like the one in the article.
[/quote]
</p>
<p>But are they anything like the Chinese problem in their scope or difficulty?</p>