<p>The 1876 MIT entrance exam did not have science either - just math and English. Perhaps science was not a high school subject and the expectation was that it would be covered in college.</p>
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<p>The SAT doesn’t have science today but it’s still taught in high schools.</p>
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<p>Good for you. I wish that the HS grads could pass the geometry part.</p>
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<p>Obvious. I was responding to collegealum’s post, and comparing the nineteenth century Harvard and MIT entrance exams, not present day exams. Harvard’s included Greek, Latin, and geography, while MIT only covered math and English. Although MIT was founded to as a institution dedicated to science and technology, and as an alternative to schools like Harvard which focused on a classical education, it is worth noting that there was not a science requirement for admission.</p>
<p>In MIT’s mission statement:</p>
<p>The Institute admitted its first students in 1865, four years after the approval of its founding charter. The opening marked the culmination of an extended effort by William Barton Rogers, a distinguished natural scientist, to establish a new kind of independent educational institution relevant to an increasingly industrialized America.</p>
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<p>I can’t guarantee that all HS grads could do the geometry (not all even apply to any college), but ANYONE applying to a top tier university certainly should. Open any freshman Geometry book–it’s all there, pretty black and white. It’s not like they were asking for any advanced reasoning skills!</p>
<p>The relative depths of the Harvard and MIT math sections left me puzzled. Wouldn’t the geeky vocational guy know the algorithm for doing square roots rather than the preppy Harvard applicant, not because it is complicated, but you’d think that wouldn’t be a priority. The Harvard algebra section looked very similar to the one I took in my college entrance exam, and while we learned things like vulgar fractions in HS, I don’t think arithmetic was big in our college entrance exam. </p>
<p>Interesting that there were so many proofs in geometry versus “find this angle”; I guess it avoids having to draw diagrams on the question paper, but qn 2 left me scratching my head. Loved the terminology in geom 5, “…are drawn from a point without a circle.” The only time I had encountered this usage was in Shakespeare.</p>
<p>I love the proof centric Harvard geometry as opposed to the ACT and SAT preference of having you spit out a load of angle and line measurements. Proofs show you can actually UNDERSTAND and APPLY as opposed to being a math sausage maker. Put in the numbers, give back the sausage. Harvard instead asks you to tell them how and why the sausage is made. Very superior.</p>
<p>^^ reminds me so much about my D and a couple of kids I tried to help out with math. They loved to plug values into the formula of the day and say, “Is that right?” I recall trying to get them interested in why something is b squared minus 4ac etc. or why the derivative of uv is such and such, or come up with a couple of strategies for calculating pi, etc. and completely struck out.<br>
DS, fortunately, I kept him going a full four months while he was trying to figure out a general formula on integer solutions to a squared + b squared = c squared and had several partial solutions before he accidentally blundered into a book that spilled out the answer, much to our disappointment. I don’t think any of his classmates or his middle school math teacher cared much about his discoveries though.</p>
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<p>I googled it because I didn’t know such an algorithm existed. It doesn’t. Binary search exists, which is apparently the method used here.</p>
<p>I have relatives in Boston dating back to the 17th century - I believe quite a few of them attended Harvard. My Mother’s mother was one of the first women to graduate from MIT (in architecture). My Dad’s Mom was a DAR though I don’t actually know where her family came from originally. My Dad’s Dad emigrated from Germany at the turn of the century, never graduated from high school himself, but sent all three sons to Harvard.</p>
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<p>I’m afraid you didn’t look very hard. See, for example, [url=<a href=“http://xlinux.nist.gov/dads//HTML/squareRoot.html]here[/url”>square root]here[/url</a>]. A similar algorithm can calculate cube roots. I assume this is what the Harvard exam expected the student to know.</p>
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<p>Could it be that you are talking about a different test. I really doubt that every student applying to a top tier school would do very well the MIT test, let alone ace the geometry section. I believe that most would have serious problems, especially without the typical crutch of a graphic calculator.</p>
<p>[MIT</a> Entrance Examination, 1869-70: Exhibits: : Institute Archives & Special Collections: MIT](<a href=“http://libraries.mit.edu/archives/exhibits/exam/geometry.html]MIT”>http://libraries.mit.edu/archives/exhibits/exam/geometry.html)</p>
<p>I think it would be an eye-opener to reproduce the question number 6 in the SAT forum. My guess is that almost everyone would claim there is information missing and a great number of students would simply be unable to visualize the problem correctly. Expecting many students to know the laws of proportional mean might be illusory.</p>
<p>PS The problem is “The perpendicular dropped from the vertex of the right triangle upon the hypothenuse divides it into two segments of 9 and 16 feet respectively. Find the lengths of the perpendicular and the two legs of the triangle.”</p>
<p>I gave the Harvard test to my son, who said, “Is this calculator-free?” He was kidding, but for some reason he thought the whole idea of having a TI-84 back then was hilarious. He’s always loved the idea of time travel, so I guess it is fun to think about.</p>
<p>I have to agree with xiggi. I maintain that the majority or more of high school college applicants would be squashed by the math portion of these tests. Proofs are not nearly as emphasized as they used to be, and in many HS curricula (like the one in use here in NJ) the calculator is heavily used. The problem that xiggi mentions above would easily be a level 5 problem on the SAT, if it were to appear at all.</p>
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Are the sides 20 and 15 and the altitude 12? </p>
<p>I suspect most kids don’t remember the mean altitude proportionality because they learn it as freshmen or sophmores in high school now, and don’t have much ocassion to use it. I suspect that it was learned later in those days. If smart kids studying for entrance exams today knew this was something likely to be on the test, many could easily memorize geometrical formulae, even proofs and identities to some extent. I’d bet they do know the 3-4-5 rule pretty much off the top of their heads though.</p>
<p>Also, question 5 is a little ridiculous, don’t you think? Given a circle of radius 10 what’s the area?</p>
<p>I agree that geonetry proofs can be difficult. I hated them. I don’t know if kids do those step by step proofs these days.</p>
<p>THe main thing that makes these exams difficult, AFAIC, is that they are not multiple choice. I believe that there are some people for whom multiple choice exams are just easier - and I am one of those people.</p>
<p>Now that we’re discussing the tests - on one of those exams there is a question - “name one work fromm Irving, one from Tennyson, and one from Pope”. I couldn’t name anything by Pope - I barely know who he is.
But I was able to drag up from the recesses of my brain “THe Legend of Sleepy Hollow” (Irving) and “The Charge of the Light Brigade” (Tennyson). But that’s pretty much the extent of my knowledge on either of these authors. Just the names of those works. So I’m not sure what that proves exactly.</p>
<p>But thanks to the posters of these tests, it is really fun and interesting.</p>
<p>^Yes, that’s right. 12 is called the “geometric mean” of 9 and 16 (as opposed to the usual arithmetic mean). On that MIT geometry section, most SAT test takers would get question 5 but none of the others correct, I would guess.</p>
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<p>One would think so, Bovertine, but things that might appear crystal clear to you (and to someone such as Fignewton) seem to frustrate many students. Fwiw, while the 3-4-5 rules are well-known, the ability of recognize the patterns when NOT given is much rarer. In this case, please note that students are only given the two segments 9 and 16. </p>
<p>The altitude 12 is obviously found through 9/x = x/16 or x^2 = 144.</p>
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<p>Come on, is there really a parent who visits this site who would not immediately recognize Loren Pope and CTCL.</p>
<p>[About</a> Loren Pope | Colleges That Change Lives](<a href=“http://www.ctcl.org/about/loren-pope]About”>http://www.ctcl.org/about/loren-pope)</p>
<p>I think he wrote his first edition in 1856.
:)</p>
<p>I know Alexander Pope mostly as the guy who wrote the poem “Eloisa to Abelard” from which came a line that became the title of a 2004 movie starring Jim Carrey and Kate Winslet:</p>
<p>How happy is the blameless vestal’s lot!
The world forgetting, by the world forgot.
Eternal sunshine of the spotless mind!
Each prayer accepted, and each wish resigned;</p>
<pre><code>Alexander Pope, “Eloisa to Abelard”
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<p>Whoever commented about calculator reliance:</p>
<p>I believe this is becoming a SERIOUS issue. Many kids in my IB Mathematics class consistently consult their calculators for arithmetic that would have been easily mentally solved in the days of yor, because it had to! We have become enormously lazy. This is also one of the reasons I loved my Geometry and Algebra II teacher, she allowed NO shortcuts on proofs, and when it came time to solve systems of equations anyone who used their graphing calculator for a quick solve received zero points. A calculator is FINE if you know the theory and method behind it, but a crutch for ignorance when you do not.</p>
<p>That is another reason I dislike timed math contests and the math sections on SATs and ACTs: true mathematical skill does not require speed. It should only require concisely and well solved solutions. Putting a time gun to students’ heads encourages sloppy technique and ultimately degrades the experience.</p>