Open Box Problem Coursework Other Than A-G

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Posted by Paly Grad
a resident of Palo Alto High School
on May 29, 2012 at 10:03 pm

A few words from a Paly grad and current UC Berkeley student.

Blame it on the competitiveness of PAUSD. I can assure you that if this applicant came from any other school district, she would have gotten into at least one of those UCs.

The data show that the 25-75 SAT range for UC Santa Cruz is 1540-1980 and 22-27 for the ACT. The applicant's score of 32 (approx. 2130 on the SAT) is well above the 75%ile for admitted UC Santa Cruz students.

The problem lies in the fact that Palo Alto schools — Paly more so than Gunn for AP classes — have been rather successful in avoiding the astronomical grade inflation that has occurred at almost every school in the East Bay, the Central Velley, and Southern California.

At Berkeley, almost everyone I meet who did not attend a Palo Alto or Cupertino school (or East coast private/magnet school) has a ridiculously high HS GPA. High school GPAs as high as 4.78 or even 4.95 are more common than my "measly" 4.2-weighted Paly GPA. Most of the Berkeley students I've met, however, are not very bright by Paly standards. Consider that the average SAT at Berkeley is around 2030 (far far lower than the 75%ile at Paly of nearly 2175) and you can appreciate that most of the people I meet simply do not perform as well as those I worked/hung around with in HS. I can assure you that if any of my HS friends went to the schools most Berkeley students went to, he/she would have been valedictorian and gradated with a 4.7+.

To get into a good UC from Paly/Gunn (or a competitive East Coast school) therefore requires a very high SAT. Because GPAs at Paly/Gunn can only be so high — (Honors/AP classes involve much more work so fewer can be taken than at other schools; grading is harsher; Not every class is an "honors" class as it often is at other schools) — Paly/Gunn students need high SAT scores to compensate. From what I remember, the average SAT score of a Paly student admitted to UC Berkeley was in the mid-2200s my year (compared to 2030 overall). Every person I personally know attending Berkeley from Paly/Gunn had a SAT score in the 2300-2400 range.

This is a problem that I believe needs to be addressed by the School Board and our community. I am, however, not certain how/if it could be addressed. Palo Alto students, although disadvantaged in the admission process, learn far more than their peers do at other schools. Every Paly student I know of at Berkeley is doing extremely well. They read and write far better than other students, many of whom got through HS with straight As but 2s and 3s on their AP tests. Consider that my year I had to read over 20 books for AP English while my Berkeley friends had anywhere from 1-5. The same is true of almost any other class.

It is a shame that the lack of grade inflation in Palo Alto — although school profiles show that Gunn has succumbed to this phenomenon over the past few years — is preventing admission for many of our qualified students. At the same time, we should be careful to indulge in too much grade inflation for fear that it would erode the excellence of a Palo Alto HS education.

What I can say for this applicant is as follows: If he/she scored a 32/36 and received a 3.85 unweighted GPA from Paly/Gunn she will do great in college. I would recommend he/she immediately apply to SJSU or even a community college. I understand that this is might be far from desirable for the applicant and his/her family, but there is not much choice. I am confident she will perform at the top of her class at either SJSU or at a community college. If this is the case (which I am fairly certain it will be), she can easily transfer to any UC of her choice after two years, Berkeley and UCLA included. (She might want to retake the SAT and aim for a 2200 to solidify her chances).

The applicant could also consider taking a gap year and re-applying for freshman admission in the fall. If he/she chooses to do so, retakes the SAT, and applies herself to a certain job or extracurricular (and with good reason), she will have a far greater chance of gaining admission come Spring of 2013. She might not have to spend two years at a community college and could directly go to UC Berkeley or UCLA after spending a year doing what she enjoys. This might sound uncommon, but it really isn't. The Harvard College Admissions Office, for one, personally recommends this to its admitted students: Web Link.

You're told $L = 3 W$, so we'll make this substitution whenever we can.

The area of the base is $LW$, so the cost of the base is $5LW = 15 W^2$.

The sides have area $LH$ or $WH$, so the total cost of the sides is

$$4(2LH + 2WH) = 4(6WH + 2WH) = 32WH$$

and then the total cost of the box is $32WH + 15W^2$.

You know the total volume is $89$, so

$$LWH = 89,\\ 3W^2H = 89,\\ H = \dfrac{89}{3W^2}$$

and so total cost is

$$ C = 32W\left(\dfrac{89}{3W^2} \right) + 15W^2. $$

Now simplify this expression and find the minimum (i.e. the width that makes cost a minimum. Then work back to find $L$ and $H$ from the relationships above)

Explicitly, $C = \dfrac{2848}{3W} + 15W^2$ and so $$ \frac{dC}{dW} = -\dfrac{2848}{3W^2} + 30W. $$

Set this equal to $0$:

$$ 0 = -\dfrac{2848}{3W^2} + 30W $$

multiply by $W^2$: $$ 0 = -\dfrac{2848}{3} + 30W^3 \\ \dfrac{2848}{3} = 30W^3 \\ \dfrac{2848}{90} = W^3 \\ W = \sqrt[3]{\dfrac{2848}{90}} \simeq 3.16 $$

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