NationStates Jolt Archive

Mathematicians set Chinese test
Maths enthusiasts are being challenged to answer a sample question from Chinese university entrance tests.

The tests are set for prospective science undergraduates.

The UK's Royal Society of Chemistry is offering a £500 prize to one lucky but bright person who answers the question below correctly.

It has also published a test used in a "well known and respected" English university - the society is not naming it - to assess the strength of incoming science undergraduates' maths skills.


A glance at the two questions reveals how much more advanced is the maths teaching in China, where children learn the subject up to the age of 18, the society says.

Science undergraduates in England are likely not to have studied maths beyond GCSE level at the age of 16, it says.

It has sounded a warning about Britain's future economic prospects which it claims are threatened by competition from scientists in China.

RSC chief executive Richard Pike says mathematics is seen as integral to the sciences in China and its economy.

"There, the concept of remedial courses at university would be inconceivable.

"UK chemistry departments are often world-renowned for their creativity; however, mathematics tests set in England by many universities for undergraduate chemistry students in their first term to diagnose remedial requirements are disconcertingly simple.

"They encapsulate the challenge facing this country," says Dr Pike.
http://news.bbc.co.uk/2/hi/uk_news/education/6589301.stm

For those of you who can't be bothered clicking the link, here's the Chinese pre-entry test:
http://newsimg.bbc.co.uk/media/images/42842000/gif/_42842559_maths_diagram_416.gif

And here's the English University first-year test:
http://newsimg.bbc.co.uk/media/images/42843000/gif/_42843291_maths_diagram02_416.gif

ah...yeah. There does appear to be a slight difference in levels there.
So how would you fare? Think you could handle it?

I haven't had any kind of university entrance exam, but that looks like something I'd expect in the fifth or sixth year of high school here.

I might be able to do it.... but I don't wanna

Thank god I don't live in China.

I shudder to think how simplistic the test in this country must be.

Yeah. You can't speak or understand any Chinese, for a start. :p

That might pose a bit of a problem.

Thank god I don't live in China.
Yeah. You can't speak or understand any Chinese, for a start. :p

hmm. I've seen that question before. In a GCSE Maths Paper.

Maybe it has to do with the sheer number of applicants for a Chinese university. They can afford to only pick the very best.

That being said, I used to do similar problems in advanced maths class in high school, though I'm completely out of the loop today and would probably spend the whole day on it.

The English one seems a bit silly though. They must be desperate.

i wouldn't even be able to do the second one, nor would i ever need to. got to love being an arts student :D

Buh... I thought the very definition of a prism is that BD is perpendicular to AC... am I missing something here?

i wouldn't even be able to do the second one, nor would i ever need to. got to love being an arts student :DThat really is quite shameful if you can't remember Pythagoras' theorem.

That really is quite shameful if you can't remember Pythagoras' theorem.

i remember it's got As and Bs and Cs in it and it has some squared's, but i can't remember if it there's adding or multiplying or whatever to do. i haven't had to do that sort of thing since i was 15, last maths i had to do was a bit of statistics for A level geography and we were given the equations in the question anyway.

That really is quite shameful if you can't remember Pythagoras' theorem.
That's not even the worst thing. That triangle is pretty much the most obvious Pythagorean triple there is.

i remember it's got As and Bs and Cs in it and it has some squared's, but i can't remember if it there's adding or multiplying or whatever to do. i haven't had to do that sort of thing since i was 15, last maths i had to do was a bit of statistics for A level geography and we were given the equations in the question anyway....

Geography - the subject those who like colouring.

Wow, the first question is something I had in my last years of secondary school. The second question is something from first/second grade of my secondary school (highest level). The english universities must be really desperate... And over here they already claim that the math level is very low :(

That's not even the worst thing. That triangle is pretty much the most obvious Pythagorean triple there is.

...

Geography - the subject those who like colouring.

yeah well, i'm the guy who had to get his little sister to help him with his GCSE maths homework back in the day, i'm shit at maths and i've avoided it as much as i can.

it always strikes me as odd that no-one who doesn't do geography has any idea what geography is. i blame secondary school geography syllabuses (syllabi? whatever), they're a joke.

yeah well, i'm the guy who had to get his little sister to help him with his GCSE maths homework back in the day, i'm shit at maths and i've avoided it as much as i can.

it always strikes me as odd that no-one who doesn't do geography has any idea what geography is. i blame secondary school geography syllabuses (syllabi? whatever), they're a joke.I have a friend who came to the student union bar and whipped about some paper and started colouring in some drawings. They looked like comic-book-type planets or something. So I was curious and asked what she was drawing. Turned out she was finishing off some lab work where they'd been looking through microscopes as mineral structures.

It really is colouring in. :P Especially with the damned multiple choice exams they get. :mad:

Hooray for going to art school!

In mother Russia we say "harder than Chinese grammar."
Says something about the level of Soviet math instruction I think:p

That's a kite prism. The Chinese examiners can't draw straight. :p

I noticed that too

That's a kite prism. The Chinese examiners can't draw straight. :p

I have a friend who came to the student union bar and whipped about some paper and started colouring in some drawings. They looked like comic-book-type planets or something. So I was curious and asked what she was drawing. Turned out she was finishing off some lab work where they'd been looking through microscopes as mineral structures.

It really is colouring in. :P Especially with the damned multiple choice exams they get. :mad:

ah well, that's physical geographers for you :p. i did a bit of that in first year but it was such a piss-take i used to turn up to the labs stoned and leave halfway through as soon as the lecture part finished.

human geography on the other hand involves writing essay after essay after essay about how 'space' relates to just about anything you can think of.

but, truly i am an archaeologist. i like digging and then making shit up about what i uncover.

The difference in difficulty between the two examples is ridiculous. I'm a first year Scottish Undergraduate by the way.

The Chinese question I could not do, because I haven't really encountered anything like that before, in all my High School years.

The English equivalent I could have done in my 3rd or 4th year of High School.

ah well, that's physical geographers for you :p. i did a bit of that in first year but it was such a piss-take i used to turn up to the labs stoned and leave halfway through as soon as the lecture part finished.

human geography on the other hand involves writing essay after essay after essay about how 'space' relates to just about anything you can think of.
Physical geography's better than human geography. It means you can go on field trips and stand in rivers and stuff. :)

Plus I have fond memories of A Level physical geography. My teacher hated me, I hated him, I never did any work (and once managed to get 7% on a mock exam), then proceeded to ace the real exam and get a very high A. Happy days.

The Chinese question I could not do, because I haven't really encountered anything like that before, in all my High School years.

We learnt the equations to do all that (in) last year... but I don't remember them

I could probably do it, but looking at it makes me sad.

That's not even the worst thing. That triangle is pretty much the most obvious Pythagorean triple there is.

Obvious perhaps. But beautiful.

I was lucky enough to have a "mad professor" maths teacher in HS. I remember the day he took a double period (80 minutes) and proved Euler's Formula for us. There was lots of arm-waving and chalk dust, and while it wasn't proven in the sense that we all followed all of it, we were dead impressed that you could take two fundamental constants and an imaginary number and make a simple equation of them.

That I pursued mathematics beyond my natural ability and almost went insane from staring into the eyes of god isn't really his fault. I did learn that very few girls really appreciate a square root. Ah well.

Euler's Formula:
http://upload.wikimedia.org/math/8/7/f/87fb1b28005b72b5f2d3734e98cbc13e.png

Euler's Formula:
http://upload.wikimedia.org/math/8/7/f/87fb1b28005b72b5f2d3734e98cbc13e.png

I only just realised.... e^ipi.... is i^2... oh god.... oh dear god no... *head explodes*

I thought I'd edit in... that's the third time today I've posted my implosion or explosion

Physical geography's better than human geography. It means you can go on field trips and stand in rivers and stuff. :)

Plus I have fond memories of A Level physical geography. My teacher hated me, I hated him, I never did any work (and once managed to get 7% on a mock exam), then proceeded to ace the real exam and get a very high A. Happy days.

oh yeah, the fieldtrips are fun, if you can afford them, but the rest is just mind-numbing boredom to me. whereas with human geography you get to be all philosophical and stuff which i like cuz you can do that with the minimum amount of effort :p

"They encapsulate the challenge facing this country," says Dr Pike.
http://news.bbc.co.uk/2/hi/uk_news/education/6589301.stm

For those of you who can't be bothered clicking the link, here's the Chinese pre-entry test:
http://newsimg.bbc.co.uk/media/images/42842000/gif/_42842559_maths_diagram_416.gif

And here's the English University first-year test:
http://newsimg.bbc.co.uk/media/images/42843000/gif/_42843291_maths_diagram02_416.gif

ah...yeah. There does appear to be a slight difference in levels there.
So how would you fare? Think you could handle it?

The English test is ridiculously easy and I can't believe it to be a first year test at English universities. They must've twisted it somehow. Maybe that was one of the first questions on the test which everyone would be able to answer because I really don't believe that it's that bad quality at universities in England.

Yeah. I learned how to do that in the 8th grade. And we're talking about the American public school system here:eek:
EDIT: I'm talking about the English one of course.

Think you could handle it?

no. I learned all my math stuff long enough to take the test and then I smoked a lot of pot and forgot it. I can remember pieces now.... I did get to the level of the first question, but I remember making a B in that portion of that class, which is a low grade for me.

the second question is stuff my kid is doing now.....so, I can totally do that.

I have a friend who came to the student union bar and whipped about some paper and started colouring in some drawings. They looked like comic-book-type planets or something. So I was curious and asked what she was drawing. Turned out she was finishing off some lab work where they'd been looking through microscopes as mineral structures.

It really is colouring in. :P Especially with the damned multiple choice exams they get. :mad:

That sounds suspiciously like geology. *kicks geographers off our turf*

... but then how much math does a History major have to know before being admitted to University? These are the minimal requirements for all students, right? In this context the English standard is far more appropriate then the ridiculously exclusive Chinese one. All this may mean is that a larger percentage of the British population has a chance of attending a university, which is a good thing.

The second one is ridiculously easy. I did it in my head as I read it. Until I realised I forgot what tan is (sin/cos?), but other than that...

The chinese one I could have done right after high school, when geo/trig was still fresh in my head, but it's been a long time since then. Mind you, I could easily model it in 3D and then ask the computer for the information I need.

And for me, the phrase ' harder than chinese algebra' is used primarily to describe erections, isn't it? i.e. she got me harder than chinese algebra...

Answer to part i of the Chinese puzzle:

(i) Prove BD⊥A¹C

In Soviet Russia, BD⊥A¹C proves you

"Human geography" sounds like fun. Good clean dirty fun. :p

There are hard tests and easy tests, though. The "English test" is too easy, an above average student would get 100%, making it impossible to distinguish a good student from an outstanding one ... by that one question. It may have been the easiest question in the test.
The "Chinese test" is very hard, but I suspect an honest effort at all three sections and a partial proof of the perpendicular planes thing would get you marks. It may have been the hardest question in the test.

Normalize the results to get the number of passes you have places for, Mao's your uncle.

The diagram still sucks. At least three right angles are not marked, and I can't see E(1) there at all. Right angles in two perpendicular planes makes (i) pretty simple. I think (ii) is 90 degrees, and for (iii), lines in different planes do not "form an angle."

... but then how much math does a History major have to know before being admitted to University? These are the minimal requirements for all students, right? In this context the English standard is far more appropriate then the ridiculously exclusive Chinese one. All this may mean is that a larger percentage of the British population has a chance of attending a university, which is a good thing.
The British one is a chemistry maths paper with the intention of determining which students might need help with maths. The question they chose for the BBC article is likely to be one of the easier ones in that paper. Similarly, it wouldn't surprise me if the question from the Chinese maths paper is one of the hardest from that exam. It's not really a fair comparison.

Maybe it has to do with the sheer number of applicants for a Chinese university. They can afford to only pick the very best.
There is that - for all we know, the Chinese math question could be from one of their most prestigious university. I would imagine first year questions in, say, Oxbridge or Harvard would be a tad more difficult that the pythag question.

That said, I once helped a 11 yr-old student do his maths homework here (in HK). He had to solve some algebra equations using quadratic formula.
Quadratic formula at age 11!
In NZ we don't teach it until year 12 - youngest student by then would be 16.

So, has anyone actually done the Chinese one yet?

In mother Russia we say "harder than Chinese grammar."
Says something about the level of Soviet math instruction I think:p
Russian maths is a different kettle of fish altogether.
Anything that produces people like this guy:
http://www.newscientist.com/article.ns?id=dn9775
is way beyond what we should consider normal maths.

funnily enough, Chinese grammar's actually pretty simple. (Almost) no tenses, no plurals, no pronouns, no gerunds...

to Gift-of-god: I'm fully aware of what the phrase 'Harder than Chinese Algebra' means. Why do you think I chose it!;)

The British one is a chemistry maths paper with the intention of determining which students might need help with maths. The question they chose for the BBC article is likely to be one of the easier ones in that paper. Similarly, it wouldn't surprise me if the question from the Chinese maths paper is one of the hardest from that exam. It's not really a fair comparison.

But it wouldn't make that big news if it was a fair comparison. You can make a comparison like that from the same test if you want. Just compare the hardest question with the easiest.

funnily enough, Chinese grammar's actually pretty simple. (Almost) no tenses, no plurals, no pronouns, no gerunds...

To be honest, the Russian phrase about Chinese grammar isn't so much about difficulty as it is about incomprehensibility (i.e. "it's Greek to me") and I believe that it refers to the writing more then the grammar. So yes, what I said earlier was a complete non sequitur :p

So, has anyone actually done the Chinese one yet?

Yes. With lots of hand-waving and "y'know" but I've got it. Part 3 is a trick question.

Typesetting the shit, now that's another kettle of fish.

(i)A(1)C is in the plane of A(1)AC, which is a perpendicular plane to the line BD. Therefore (i).

(ii)When you draw it right, it looks like 90 degrees. The angle between planes A(1)BD and BC(1)D is the angle between A(1)EE(1) and EE(1)C(1), which you can get from the triangles A(1)EB and BEC(1), which you get from trig of AA(1), AB, AD, and DC. I call 90 degrees because I can't be fucked.

(iii) Trick question. English test.

The second one is ridiculously easy. I did it in my head as I read it. Until I realised I forgot what tan is (sin/cos?), but other than that...

Easier to find than that. The tan(A) = o/a

Just the length of the opposite side of the triangle divided by the length of the adjacent side...tan(theta) = 3/4

Yes. With lots of hand-waving and "y'know" but I've got it. Part 3 is a trick question.

I was kinda looking at that one going "huh"?

The Chinese question looks similar to the things I saw in Grade 12 geometry (Students age 17-18). It doesn't look as though the math behind it is particularly high level, the diagram is just complicated. Personally, I think that making problems ugly and complicated doesn't test your understanding of the material better than a simple problem, it just makes it easier to mess up.

The first 2 parts of the English one could probably be done by a Grade 6 student, and the trigonometry part I learned in Grade 10.

Remember this is for studying chemistry at an English university, not maths.

Geometry seems to be studied a lot more in other countries than in our own. I have a maths degree, and yet I've pretty much never studied it once. Well, apart from the very basics.

Having said that, I should still be able to do the chinese questions, but can't remember a thing about vector geometry.

Wow. The Chinese test made my brain itch but even as a high school freshman I can still do the English exam...

Sad much?

Mathematics is abstract thinking.
You can think abstractly without necessarily being good at maths, but you can't go far in maths without thinking abstractly. Hence, there are good abstract thinkers who are not mathematicians, but no mathematicians who cannot do good abstract thinking.

Mathematicians are the scientists of scientists. Philosophers may be good abstract thinkers, they may even be scientists, but they are crippled in abstract thinking by a need to also make common sense.

IF you had autocratic power over an education system, a huge pool of teenage talent in the fastest growing economy on earth, in a command economy going up against the presumptive imperial power of your age, a power that slapped you down effortlessly when you thought your were doing fine ... wouldn't you? Try to pick the Einsteins, the Bohrs, the Fords of your times, and give them a little encouragement? Give them a scholarship, and their families a big-screen TV?

It may well be maths that is the key to revolutionary knowledge, to the knowledge that is power enough to rule this century. It may also be philosophy. Or it may be some human talent as irrelevant, as disdained now as physics and maths were at the beginning of the last century. EDIT: Or as philosophy is now.

I'd prefer to see a comparison of the final year exam questions (although they might hurt my head too much)

Having said that, I should still be able to do the chinese questions, but can't remember a thing about vector geometry.

Plot it on a 3D vector diagram. Do the triangle thing two dimensions at a time.
You know, the triangle thing. Tri ... er, something. Use a calculator.

Oh, fuck it. I for one welcome our new Chinese overlords.

I'd prefer to see a comparison of the final year exam questions (although they might hurt my head too much)

Yeah, go get them and your second post will be more welcome and valuable than my 2,000th.

NSG is a wide open field to talent. :)

(iii) Trick question. English test.How is that a trick question?

How is that a trick question?

Two lines must share a common point to form an angle. Even in the distorted diagram, you can see that those two lines (or rays or whatever) do not share a common point (intersect.)

Correct answer is "AD and BC(1) do not form an angle."

Two lines must share a common point to form an angle. Even in the distorted diagram, you can see that those two lines (or rays or whatever) do not share a common point (intersect.)

Correct answer is "AD and BC(1) do not form an angle."two lines do not have to intersect to form an angle. what the heck are you talking about. for the angle t between any two vectors a and b the following applies: cos(t) = (a*b) / (|a|*|b|), in this case that would be t = arccos((D-A * C1-B) / |D-A| * |C1-B|))

two lines do not have to intersect to form an angle. what the heck are you talking about. for the angle t between any two vectors a and b the following applies: cos(t) = (a*b) / (|a|*|b|), in this case that would be t = arccos((D-A * C1-B) / |D-A| * |C1-B|))

Heh, not only would you get no marks, but you'd get a visit from the state police to ask you about how you messed with Google.

"In Soviet Earth, GOOGLE SEARCHES YOU!"

"which are not in the same plane" ... take the hint, give the right answer, or fail. Your revisionist definitions of "line" as "vector" are not welcome here.

Heh, not only would you get no marks, but you'd get a visit from the state police to ask you about how you messed with Google.

"In Soviet Earth, GOOGLE SEARCHES YOU!"

"which are not in the same plane" ... take the hint, give the right answer, or fail. Your revisionist definitions of "line" as "vector" are not welcome here.so these lines are not in any way positioned relative to one another? and a line does not have a vector?and what does google have to do with that? do you have the official solution to problem iii ?
i wonder how i ever wrote a ray-tracer program... or how i could ever work with CATIA...

The English test is ridiculously easy and I can't believe it to be a first year test at English universities. They must've twisted it somehow. Maybe that was one of the first questions on the test which everyone would be able to answer because I really don't believe that it's that bad quality at universities in England.

As I understand it, the English one is to find out if non-maths students require remedial maths tuition to support their chosen area of study (specifically chemistry). i.e. not a first year maths test. It is still worrying though - i went to just about the worst quality school ever and even I learned how to answer that test in about 3rd year.

Edit: 3rd year = 3rd year at secondary school, age 13/14

so these lines are not in any way positioned relative to one another? and a line does not have a vector?and what does google have to do with that? do you have the official solution to problem iii ?
i wonder how i ever wrote a ray-tracer program... or how i could ever work with CATIA...

If lines do not intersect, they do not form an angle.

The official solution is: The angle is undefined.

You will encounter many math problems that attempt to make sure you understand the subject matter, by giving you a problem that cannot be solved, because there is no solution.

As a first year engineering student (so, infact precicely the group they are talking about) I think i can say with fair certainty BULLSHIT.
That is not a question you would find on a first year maths paper. I dont know what arsehole made up this crap but it makes a mockery of british education.

so these lines are not in any way positioned relative to one another? and a line does not have a vector?and what does google have to do with that? do you have the official solution to problem iii ?
i wonder how i ever wrote a ray-tracer program... or how i could ever work with CATIA...The solid is described as a prism. A prism is defined 'as a solid having bases or ends that are parallel, congruent polygons and sides that are parallelograms'. The questions asks what the angle is between two lines, one on each base. Angles are normally expressed in terms such as <AOB. If you can find the angle, you can find O. Where is O?

If lines do not intersect, they do not form an angle.

The official solution is: The angle is undefined.

You will encounter many math problems that attempt to make sure you understand the subject matter, by giving you a problem that cannot be solved, because there is no solution.I maintain the position that any two non-zero-length lines do form an angle, no matter how far apart they are translated. And there is alway just one value for the angle. the angle between any two lines is the angle between their direction vectors. However, since the hint at the different planes in the text, they might want to hear that the problem is unsolvable. But then what defines the parallelity of lines? and what defines the parallelity of two squares that are positioned anywhere?

btw if iii has no solution what is the solution of i again?

http://newsimg.bbc.co.uk/media/images/42842000/gif/_42842559_maths_diagram_416.gif

Two lines must share a common point to form an angle. Even in the distorted diagram, you can see that those two lines (or rays or whatever) do not share a common point (intersect.)

Correct answer is "AD and BC(1) do not form an angle."When taking exams in Maths, one of the major things they tell you in the UK is never assume a diagram is visually accurate unless it says 'to scale'.

I maintain the position that any two non-zero-length lines do form an angle, no matter how far apart they are translated. And there is alway just one value for the angle. However, since the hint at the different planes in the text, they might want to hear that the problem is unsolvable. But then what defines the parallelity of lines? and what defines the parallelity of two squares that are positioned anywhere?That a line perpendicular to one of the lines is perpendicular to the other as well?

Besides, like I said, it's not a hint, the two planes the lines are in have been defined as parallel.

... I suppose if you figure out the angle that the lines would form if you super imposed them. Because they must both cross the same perpendicular line. Unless of course their are other planes in which they are parallel.

As I understand it, the English one is to find out if non-maths students require remedial maths tuition to support their chosen area of study (specifically chemistry). i.e. not a first year maths test. It is still worrying though - i went to just about the worst quality school ever and even I learned how to answer that test in about 3rd year.

Edit: 3rd year = 3rd year at secondary school, age 13/14

If you can't solve that problem you need more than extra help to pass as a chemistry student since chemistry is full of math. If that was in fact a problem from a test, it must've been one of the easiest that everyone would solve.

Besides, like I said, it's not a hint, the two planes the lines are in have been defined as parallel.the planes that AD and BC are in respectively are not parallel.

Answer to part i of the Chinese puzzle:

(i) Prove BD⊥A¹C

In Soviet Russia, BD⊥A¹C proves you

In Soviet Russia... what the hell man? That's my schtick!

the planes that AD and BC are in respectively are not parallel.Bah, too many subscripts are confusing me.

AD and BC would be in the same plane. I thought it was asking for AD and B(1)C(1) which are in paralell planes, or that the 1 was a comma or something. But it is asking for the angle between AD and BC(1).

...

ahhahaha, AD is the plane of the flat polygon ABCD, BC(1) only runs through that plane at one point (at which it does not intersect AD). Therefore the angle for which AD and BC(1) is undefined... but I worked out that the angle which AD and BC form is 60 degrees - do I get a cookie?)

snip

ah...yeah. There does appear to be a slight difference in levels there.
So how would you fare? Think you could handle it?

This is a completely false comparison.



But the society has been accused by a maths professor of a "cheap and uninformed" attack on UK teaching.

William Shaw, professor of financial mathematics at King's College, London, said he had taught students from many countries and their training differed.

Within the Uk the emphasis had shifted over the years. Where once there was "a huge amount of geometry and algebra", students these days spent more time on statistics, probability and data interpretation.

"I recall admitting and then teaching some very bright and well-taught Chinese students while a tutor in Oxford," he said.

"At school these students had done lots of geometry, algebra and all kinds of puzzle-solving.

"But I found myself having to teach introductory calculus to some of them. Some had just not done it."

Similarly, in the United States, many good students might not learn calculus until they got to college.

"So I could set a test for university entrants in China (or the US) which many British sixth form maths students could do, based on some calculus, which could make a similarly unbalanced media story in the Chinese papers," he said.


link (http://news.bbc.co.uk/1/hi/education/6588695.stm)



So just a story being created out of something.

I am in no way trying to insult anyone here; but here goes.

The English First Year test looks like something I did in 7th grade, and my youngest brother who is in 7th grade was doing that about 2 months ago.
The chinese one looks like what my sister was doing last night...

Here in the US, at least in my state of Pennsylvania the english one is required to pass from 7th to 8th grade and the other is from an elective course for Juniors and Seniors.

i remember it's got As and Bs and Cs in it and it has some squared's, but i can't remember if it there's adding or multiplying or whatever to do. i haven't had to do that sort of thing since i was 15, last maths i had to do was a bit of statistics for A level geography and we were given the equations in the question anyway.

Pythagoras' theorem: A^2 + B^2 = C^2

I am in no way trying to insult anyone here; but here goes.

The English First Year test looks like something I did in 7th grade, and my youngest brother who is in 7th grade was doing that about 2 months ago.
The chinese one looks like what my sister was doing last night...

Here in the US, at least in my state of Pennsylvania the english one is required to pass from 7th to 8th grade and the other is from an elective course for Juniors and Seniors.

It's because we do other stuff the Chinese and US don't do until University. So we have less time to devote to this stuff and hence aren't as advanced in it, but are more advanced in other areas.

It's because we do other stuff the Chinese and US don't do until University. So we have less time to devote to this stuff and hence aren't as advanced in it, but are more advanced in other areas.

Like integration. Bet they can integrate half as well as i can.

I am in no way trying to insult anyone here; but here goes.

The English First Year test looks like something I did in 7th grade, and my youngest brother who is in 7th grade was doing that about 2 months ago.
The chinese one looks like what my sister was doing last night...

Here in the US, at least in my state of Pennsylvania the english one is required to pass from 7th to 8th grade and the other is from an elective course for Juniors and Seniors.

There is no reason why that test should be hard, all it shows is that you can do basic maths to make the sciences a little easier. It's retarded to not let someone study science simply because he can't do advanced mechanical maths. Being advanced in mathematics shouldn't be a requirement to study at University unless you are doing certain subjects that require maths.

Solution to chinese problem:
rt(x) means square root of x

Given:
AB=AD=2
CD=2rt(3)
AA1=rt(3)
The crossbeams AC and BD are perpendicular
AD and DC are perpendicular.

As previously mentioned, it's a kite. It's symmetrical, so BC=CD=2rt(3)


Just looking at the base, you can use pythagorean to find AC=4 from AB and BC, or from AD and CD. (2^2+ 2r(3)^2=16)

Set AE to 4-x. You can use pythagorean to find that BE=rt(12-x^2). Use pathogrean again with triangle BCE. you'll find that 16-8x+x^2+12-x^2=4. Simplify to 8x=24. x=3.

So far:
AB=AD=2
BC=CD=2rt(3)
AE=1
CE=3
BE=ED=rt(3)

The top is the same as the bottom, and the height of the prism is rt(3).

Question 1 and question 3 ask similar things. I'm surprised with Nobel Hobos' answer. BD and A1C are skew, just like AD and BC1. I don't know exactly how they expect a student to prove something that isn't true.

I'm going to approach question 2 first because it's easier.
Nobel Hobos was on the right track on this one. The angle between the twoo planes is going to be the angle A1EC1. I think the easiest way to find this out is going to be to find the angles AEA1, and CEC1.

The angle A1EC1 = 180 - (AEA1 + CEC1).
AEA1 is the angle formed by AE and EA1. We know AA1, and we know AE. That's the opposite, and the adjacent. The angle is arctan(rt(3)/1)) = arctan(rt(3))=60.
Same with CEC1. The angle is arctan(rt(3)/3)=arctan(1/rt(3))=30.
It's a right angle. Nobel Hobos had the right answer.

Back to 1 and 3, if we want to treat the lines as vectors...
1: BD and A1C. Let a line which encompasses BD be the positive y axis. Let a line which encompasses AC be the postive x axis.
BD=<0,rt(3),0>
A1C=<4,0,rt(3)>
BD dot product A1C = 0*4 + rt(3)*0 + 0*rt(3) = 0. They are perpendicular.

3: AD and BC1. Use the same coordinates from question 1.
AD=<1,rt(3),0>
BC1=<3,rt(3),rt(3)>
AD dot product BC1 = 3+3+0 = 6
|AD|=rt(1+3)=2
|BC1|=rt(9+3+3)=3rt(2)
6=2*3rt2*sin(theta)
sin(theta)=1/rt(2)
theta=45

To summarize:

1: Use dot product of vectors. If it equals 0, it's perpendicular.
2: The two planes make a line. Use the projection of a line perpendicular to that one onto the two planes. (A perpendicular line is given in the question set-up). Find the angle that the projection on each plane makes... to summarize further, find the angle between A1E, and EC1. It's 90.
3: A dot B = |A| |B| sin (theta). Use that to find the angle. It's 45.

*gives a round of applause*
Now can you do the english problem? ;)

To summarize:

1: Use dot product of vectors. If it equals 0, it's perpendicular.
2: The two planes make a line. Use the projection of a line perpendicular to that one onto the two planes. (A perpendicular line is given in the question set-up). Find the angle that the projection on each plane makes... to summarize further, find the angle between A1E, and EC1. It's 90.
3: A dot B = |A| |B| sin (theta). Use that to find the angle. It's 45.

Russian Reversal wins the thread!

*gives a round of applause*
Now can you do the english problem? ;)

:)

I could have done the English problem at 8 years old. My dad showed me the pythagorean thereom around then. I thought it was soooo cool.
The Chinese one... I probably could have done part 2 at 12. Parts 1 and 3, I think require trigonometry... so 15.

Part 1 of the chinese problem can sort of intuitively done. If you set it up with those coordinates, you can see that one line only has components in the x direction, and the other only has components in the y and z directions.

Part 3... I don't know how to do that without trig.

The Chinese version shouldn't hard for math majors. Hell I could solve most of it and I haven't taken a math course in over two years.

The Chinese version shouldn't hard for math majors. Hell I could solve most of it and I haven't taken a math course in over two years.

Tho the problem would look an awful lot easier if they could just work out that E came after D, not A1.
But then, thats examiners for you. THey enjoy confusing people :D

Pythagoras' theorem: A^2 + B^2 = C^2

i definitely don't remember those pointy things from when i did it. what do they mean?

Tho the problem would look an awful lot easier if they could just work out that E came after D, not A1.
But then, thats examiners for you. THey enjoy confusing people :D

I don't think so. ABCD is exactly the same shape as A1B1C1D1. I think that's easier to grasp than using EFGH.

There's not some sort of unspoken rule about when you 'win the thread' you're not supposed to contribute to it anymore, is there?

Remember this is for studying chemistry at an English university, not maths.

Not that this has much to do with the topic, but getting a chemistry major requires a lot of difficult math.

Not that this has much to do with the topic, but getting a chemistry major requires a lot of difficult math.

Yeah but not mechanical maths (which is what the question is).

Yeah but not mechanical maths (which is what the question is).

What's mechanical math? I've never heard this terminology before, sorry.

What's mechanical math? I've never heard this terminology before, sorry.

Maths involving things like trigonometry and shapes etc... Rather then just plain old algebra which is what you would get in chemistry.

What's mechanical math? I've never heard this terminology before, sorry.

Applied Mathematics. Borderline Physics, mainly deals with forces and similar.

Applied Mathematics. Borderline Physics, mainly deals with forces and similar.

Applied mathematics refers to any math used for "non math" purposes.... such as chemistry. This particular geometric problem could have applications in chemistry (chemical bonding in particular).

Maths involving things like trigonometry and shapes etc... Rather then just plain old algebra which is what you would get in chemistry.

I don't know if that's entirely true. I'm a biochemistry major... it requires Calc 1 and 2... derivatives and integrals.

To really get into understanding atomic orbitals etc. you need differential equations.

I guess high school chemistry requires high school algebra... but things like enzyme rate mechanics I think require a bit more complex math.

I don't know if that's entirely true. I'm a biochemistry major... it requires Calc 1 and 2... derivatives and integrals.

To really get into understanding atomic orbitals etc. you need differential equations.


I wouldn't call that maths mechanics though. I'm doing calculus and thats taught in a pure maths/cor maths class not the mechanics class.

Maths involving things like trigonometry and shapes etc... Rather then just plain old algebra which is what you would get in chemistry.

There's a lot more to chemistry. Studying enzymatics at the molecular level requires an insane amount of tedious geometry work. Though a lot of it these days can be handled by computers, but still, chemistry is built on math, all branches of it including algebra, calculus, geometry etc.

I think "mechanics math" might a terminology used only in England because it is generally not come across here in the US.

If you can't solve that problem you need more than extra help to pass as a chemistry student since chemistry is full of math. If that was in fact a problem from a test, it must've been one of the easiest that everyone would solve.

Maybe - I suppose that people who have got into university to study chemistry have got A level chemistry and are not stupid, meaning they are capable of making up any maths shortfall. If they're serious about getting their degree, they'll put the extra time and effort into maths. On the other hand, rumour has it that some students prefer partying to studying... :p

i definitely don't remember those pointy things from when i did it. what do they mean?

A squared + B squared = C squared.

Bah, too many subscripts are confusing me.

AD and BC would be in the same plane. I thought it was asking for AD and B(1)C(1) which are in paralell planes, or that the 1 was a comma or something. But it is asking for the angle between AD and BC(1).

...

ahhahaha, AD is the plane of the flat polygon ABCD, BC(1) only runs through that plane at one point (at which it does not intersect AD). Therefore the angle for which AD and BC(1) is undefined... but I worked out that the angle which AD and BC form is 60 degrees - do I get a cookie?)Not from a Jedi....

Not from a Jedi....Quit your jibber jabber, fool.