link to IIT joint entrance exam (JEE) http://www.wiziq.com/tutorial/98820-IIT-JEE-Mathematics-Pape...
Some questions have more than one answers right and all answers have to be marked to get credit =)
MIT Entrance exam (1869)
21–30 of 74 posts
Re: MIT Entrance exam (1869)
#22the geometry section is much harder: http://libraries.mit.edu/archives/exhibits/exam/geometry.htm...
Not really
1. Construct a triangle ABC. Construct a line parellel to AB through C. Alternate angles and angle sum of triangle shows it is 180 degrees
2. Use congruent triangles
3. A number of ways doing this. I would cut it into two triangles
4. 360/6 = 60 degrees. Thus each sector is a equilateral triangle.
5. 100 pi
6. Basic algebra, let x be the length of the perpendicular. x = 12, solve for sides using Pythagoras. 20 and 15
7. x : x^2
Would expect to be year 7 or year 8 level.
Re: MIT Entrance exam (1869)
#23Re: MIT Entrance exam (1869)
#24the geometry section is much harder: http://libraries.mit.edu/archives/exhibits/exam/geometry.htm...
Not really 1. Construct a triangle ABC. Construct a line parellel to AB through C. Alternate angles and angle sum of triangle shows it is 180 degrees 2. Use congruent triangles 3. A number of ways doing this. I would cut it into two triangles 4. 360/6 = 60 degrees. Thus each sector is a equilateral triangle. 5. 100 pi 6. Basic algebra, let x be the length of the perpendicular. x = 12, solve for sides using Pythagoras…
Yep, the algebra was frankly also elementary school level IMO.
Re: MIT Entrance exam (1869)
#25Isn't that kind of high school level algebra? I thought we were all supposed to have been dumbed down compared to our illustrious forefathers?
Depends on how far back you go. For a Roman, mental multiplication was exceedingly difficult. Clearly this implies that there was a period of upward trend. If we believe that we're dumber than some of our forefathers, then there must have been a peak at some point in the past (or perhaps even multiple peaks, but we don't have enough evidence to suspect more than one, so let's assume it's an approximately parabolic tr…
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Re: MIT Entrance exam (1869)
#26Earlier quoted context omitted.
Not really 1. Construct a triangle ABC. Construct a line parellel to AB through C. Alternate angles and angle sum of triangle shows it is 180 degrees 2. Use congruent triangles 3. A number of ways doing this. I would cut it into two triangles 4. 360/6 = 60 degrees. Thus each sector is a equilateral triangle. 5. 100 pi 6. Basic algebra, let x be the length of the perpendicular. x = 12, solve for sides using Pythagoras…
Yep, the algebra was frankly also elementary school level IMO.
Algebra isn't normally taught at the elementary school level. Now, I'd argue that it SHOULD be, so students can choose to study some interesting fields of mathematics after grade 5, but that's a different argument entirely.
If I remember correctly, my school district didn't offer true algebra until 8th grade, for honors students only, in a class that started an hour before any regular class. Hardly elementary.
Re: MIT Entrance exam (1869)
#27Earlier quoted context omitted.
Depends on how far back you go. For a Roman, mental multiplication was exceedingly difficult. Clearly this implies that there was a period of upward trend. If we believe that we're dumber than some of our forefathers, then there must have been a peak at some point in the past (or perhaps even multiple peaks, but we don't have enough evidence to suspect more than one, so let's assume it's an approximately parabolic tr…
I'm sorry, but being able to perform arithmetic does not equate to higher intelligence or mental capacity. As society begins to perform more calculations via computer, it will allow us to begin address more abstract and higher level mathematics, problems which would be near impossible to address had we been required to do the math with grease pencils. Conrad Wolfram recently gave a wonder TED talk on the subject. htt…
If you can't do arithmetic in your head, the other problems are considerably more involved. I can't see a time where the ability to do mental multiplication is not a prerequisite for higher maths.
Re: MIT Entrance exam (1869)
#28link to IIT joint entrance exam (JEE) http://www.wiziq.com/tutorial/98820-IIT-JEE-Mathematics-Pape...
what's considered a good score on the iit?
Re: MIT Entrance exam (1869)
#29Earlier quoted context omitted.
Yep, the algebra was frankly also elementary school level IMO.
Algebra isn't normally taught at the elementary school level. Now, I'd argue that it SHOULD be, so students can choose to study some interesting fields of mathematics after grade 5, but that's a different argument entirely. If I remember correctly, my school district didn't offer true algebra until 8th grade, for honors students only, in a class that started an hour before any regular class. Hardly elementary.
When I was in middle school (5 years ago), algebra was standard 8th grade math. Honor students got 2 years of algebra from 7th to 8th grade.
At least, my year was given two years of algebra.
Re: MIT Entrance exam (1869)
#30link to IIT joint entrance exam (JEE) http://www.wiziq.com/tutorial/98820-IIT-JEE-Mathematics-Pape...
what's considered a good score on the iit?
in 1998, we used to aim for 50-60% on all 3 (P,C,M) to get in top 500 out of total ~2500 seats - all india topper that year scored himself at 85% (they just tell you the rank you have to score yourself later).