How an undergraduate math exam in the US looks like?

Huan Dao

Huan Dao

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6/29/10
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I'm just curious how do a final exam (math, cs paper) in a good state school in US like? I'm from Singapore, and I always feel that our papers create too much stress, each paper is usually 2 hours long, and you have to literally think and write at a lightning speed. For example, this is an 2 hours long paper of an one semester calculus course(I only manage to upload 4 over 8 questions here), if you're interested, see the pdf file.
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Wait, are you saying this exam is really hard? If so, you probably shouldn't be a quant... this is an easy exam.
 
Some of the questions are difficult, some routine. I hope in Singapore they're not using the same grading scheme of A = 90+, B= 80+, etc. This calc exam is assuming familiarity with Fourier analysis and vector analysis.
 
bigbadwolf said:
Some of the questions are difficult, some routine. I hope in Singapore they're not using the same grading scheme of A = 90+, B= 80+, etc. This calc exam is assuming familiarity with Fourier analysis and vector analysis.
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Alright, I just skimmed through it, and I didn't notice the fourier analysis. The vector analysis should still be fairly easy though.
 
euroazn said:
Wait, are you saying this exam is really hard? If so, you probably shouldn't be a quant... this is an easy exam.
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Did you notice that I only post half of the exam here? see the pdf file, there's another . I just say that's a bit too long.
 
bigbadwolf said:
Some of the questions are difficult, some routine. I hope in Singapore they're not using the same grading scheme of A = 90+, B= 80+, etc. This calc exam is assuming familiarity with Fourier analysis and vector analysis.
Click to expand...
It seems like you did see the pdf file there, there's line integral, surface integral, Stoke's theorem, etc...
 
Jacksc said:
Did you notice that I only post half of the exam here? see the pdf file, there's another . I just say that's a bit too long.
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I don't think it's too long. Of 8 questions, 2 are complete jokes, so you have about 20 minutes a question. The timing is fine.
@darth might be too "optimistic" though ;)
 
I'd say this were fairly lengthy for a 75 minute class, in 2 hours, I would say it's doable.

What class is this for? Is it an upper level class? If it's an upper level class, I wouldn't say its difficult at all, but at a lower level, I would say it was fair.
 
OK so you have around 8 questions, some of which have subsections. That is about the same as the LSE exam papers I have here - also a two hour time frame.
They cover slightly different areas though (Matrices, Integration by parts, Lagrange multiplier, Profit functions, geometric series, curve sketching, differentiation and optimisation to name a few)

So it doesn't seem too dissimilar in many ways with regards to time to complete the exam and number of questions
 
Looks about right for a final exam. Maybe slightly lengthy given its only a 2hr long exam, but still fair. I only skimmed through though.
 
Well strictly speaking the exam isn't difficult. But for a typical first calculus course, the emphasis is usually on the mechanics of calculus, and it's probably not easy to come up with a difficult problem that isn't contrived.

Note that the course is titled Mathematics I. Judging from the breadth of material asked, it seems appropriate to venture whether any state universities, or rather any U.S. universities, teach single variable calc including basic fourier analysis and multivariable calculus in one semester.
 
Here is a copy of the syllabus of Mathematics 1 module I've been taking (it is only a half module mind), I'd be interested to hear how this compares to the intro course anyone else is taking at undergrad?

This half unit develops basic mathematical
methods and will emphasis their applications
to problems in economics, management and
related areas.

Basics: Basic algebra; Sets, functions and
graphs; Factorisation (including cubics);
Inverse and composite functions; Exponential
and logarithm functions; Trigonometrical
functions.

Differentiation: The meaning of the
derivative; Standard derivatives; Product rule,
quotient rule and chain rule; Optimisation;
Curve sketching; Economic applications of the
derivative: marginals and profit maximisation.

Integration: Indefinite integrals; Definite
integrals; Standard integrals; Substitution
method; Integration by parts; Partial fractions;

Economic applications of integration:
determination of total cost from marginal cost,
and cumulative changes.

Functions of several variables: Partial
differentiation; Implicit partial differentiation;
Critical points and their natures; Optimisation;
Economic applications of optimisation;
Constrained optimisation and the Lagrange
multiplier method; The meaning of the
Lagrange multiplier; Economic applications of
constrained optimisation.

Matrices and linear equations: Vectors and
matrices, and their algebra; Systems of linear
equations and their expression in matrix form;
Solving systems of linear equations using row
operations (in the case where there is a unique
solution); Some economic/managerial
applications of linear equations.

Sequences and series: Arithmetic and
Geometric Progressions; Some Financial
application of sequences and series.
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NewHavenCT said:
OK so you have around 8 questions, some of which have subsections. That is about the same as the LSE exam papers I have here - also a two hour time frame.
They cover slightly different areas though (Matrices, Integration by parts, Lagrange multiplier, Profit functions, geometric series, curve sketching, differentiation and optimisation to name a few)

So it doesn't seem too dissimilar in many ways with regards to time to complete the exam and number of questions
Click to expand...

My exams at King's (and Birkbeck) were also 2 hours, with six questions, each with two parts. But you only had to answer any four to get full marks, and just getting three completely correct got 75% of the marks, which was an A grade (As starting at 70%). For each question, the first part would be easy and the second one tricky. That's why I'm asking about the grading scheme.
 
bigbadwolf - Just checked the paper I have here. Section A consists of 6 questions at 10 points each, and section B of two questions at 20 points each, all of which are compulsory.
 
NewHavenCT said:
Here is a copy of the syllabus of Mathematics 1 module I've been taking (it is only a half module mind), I'd be interested to hear how this compares to the intro course anyone else is taking at undergrad?
Click to expand...

The issue isn't the topics; it's the difficulty of the questions that get asked at exam time. For each of the topics mentioned it's possible to ask fairly straightforward questions that are "plug-and-chug." If -- as seems to be the case -- this course is meant for finance and economics types -- the problems will usually be plug-and-chug. Not the kind of thing that might occur in a math olympiad, which require strong computational mastery of the material coupled with flashes of insight.
 
NewHavenCT said:
bigbadwolf - Just checked the paper I have here. Section A consists of 6 questions at 10 points each, and section B of two questions at 20 points each, all of which are compulsory.
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Section A questions will be to allow duffers like myself to get a passing grade (plug-and-chug problems that demonstrate basic understanding), while section B will be designed to separate the goats from the sheep.
 
BBW - Yep that sounds about right on the plug and chug in section A (incidentally where I am hoping to gain most of my marks ;) ).
 
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