Here’s some last minute advice on math problems and the SAT essay, just in time for tomorrow’s SAT.
First, let’s consider rate problems:
Remember, Distance = Rate * Time
Also, Work = Rate * Time
Simple enough, right? The “distance” and “work” formulas are incredibly simple, but can lead to some incredibly difficult problems. For example, you may be asked to find how long it would take two workers or two machines working together to complete a job if you know how long it takes each person or machine to perform the job alone.
For example : Bill can fix the time-traveling phone booth’s flux capacitor in 1 hour. Ted can fix the flux capacitor in 2 hours. How long would it take Bill & Ted, working together, to finish the job so they could have an excellent adventure?
Okay, so we have two equations given to us:
1 job (flux capacitor repair) = (Ted’s Rate) * t or 1 = TR * t
Since Ted takes 2 hours to do the job, 1 job = TR * 2 hours, so TR = ½ jobs/hour
1 job (flux capacitor repair) = (Bill’’s Rate) * t or 1 = BR * t
Since Bill takes 1 hour to do the job, 1 job = BR * 1 hour, so BR = 1 job/hour
For Bill and Ted working together, the equation would be 1 job = (TR + BR) * t
So the time, t, for Bill and Ted to complete the job would be t = 1 job / (TR jobs/hr + BR job/hr)
Substituting in the values we have for BR and TR, we get t = 1 job/( ½ +1 ) hours = 1 job /(3/2) hours = 2/3 hour/job. So 1 job would take 2/3 of an hour if Bill and Ted work together. “History is about to be rewritten by two guys who can’t spell.” ;-)
A trickier variation on that problem would be to let you know how long it takes one worker to do the job, how long it takes both of them working together to do the job, then asking you to figure out how long it would take the other worker to do the same job without help.
We could have the same problem, except where we are told Bill and Ted can do the job in 2/3 of an hour, and Ted can do it himself in two hours.
So then we have the time, t, for Bill and Ted to complete the job would be
2/3 hr = 1 job / (TR job/hr + BR job/hr), which is 2/3 hr = 1 job / (1/2 job/hr + BR job/hr) when we substitute in Ted’s rate of ½ job/hr for TR. Doing the algebra, we see 2/3 hr * (1/2 job/hr + BR) = 1 job
So 2/6 job + 2/3 BR job = 1 job = 1/3 job + BR job, so 2/3 job = 2/3 BR job, which means, when we divide by “2/3 job” on both sides, we get 1 = BR. So Bill’s rate is 1 job/hour.
Another seemingly easy question that can trip you up is the percentage problem. Take the following problem:
Brenda buys a guinea pig at the local pet store, the Eeporium. While the normal price of a guinea pig is $5.00, the pet store is running a sale , and all rodents are 10% off. The local sales tax is , coincidentally, 10%. How much did Brenda pay, including tax?
Opening paragraph for essay:
While you can’t prepare a “one size fits all” general opening or closing paragraph for the essay, you can have “essay bites” ready for the SAT essay. The first sentence should be something like
“The author of the passage presents a convincing case that [state the author’s thesis - the main idea] through the apt use of logic, appeals to emotion, humor, and powerful, evocative language. “
The author’s argument is compelling and extremely difficult to counter – most readers would be convinced by this piece.
“While the passage fails to address some obvious counterarguments, it is generally a solid argument for the author’s point.”
“The author’s argument is fundamentally deficient because the author fails to support the main assertions with convincing evidence, [AND/OR] “is written using unclear language that is hard to understand [AND/OR] does not address several obvious counterarguments. This writing fails to achieve its objective.”
Obviously, your choice of one of these opening sentences, or your choice to write a different sentence depends on how you analyze the piece. Be able to see what’s right and what’s wrong about the piece, write the body paragraphs about that, and THEN write the introduction and the conclusion. That means you should leave a about 4 or 5 lines for your introduction, then write the body paragraphs, then finish by writing the introduction and the conclusion, using the “introduction bites” above, preferably using at ;least a few different words from the ones I’ve used.
The second sentence should be something like
“In the presented passage, the author supports his/her case with:”
As far as the body paragraphs are concerned, just analyze each paragraph as you go detailing the devices used in each paragraph of the passage in a paragraph of your essay, or organize the paragraphs by discussing one rhetorical device (writing/argument strategy) per paragraph. Either approach is fine, as long as you don’t leave anything out. This is why I prefer to analyze the passages paragraph by paragraph. It’s like mowing a lawn – as long as you mow one row after another, with your inner wheels on the edge of the row you just mowed, you’ll never miss a spot.
Also, you’re unlikely to “miss a spot” in the argument if you use transitional phrases that link one part of the essay to another – for example, “In contrast to the focus of the first paragraph on a narrow aspect, the second paragraph focuses on ‘the big picture.’” Even if a transition just states something “The second paragraph continues the argument that … by [discussing whatever],”it provides enough flow from one topic to another to guide the reader, lets the grader know you read the whole piece, and forces you to actually look at the passage and see how the pieces fit together.
Hopefully, this piece will help you “fit your pieces together” in time for tomorrow’s SAT. In any event, if you’re taking the SAT in June, you almost certainly can take it again the fall before college application time if you need to do so, so DON’T PANIC! Just relax and do your best, and call me if you need some tutoring for the next time you take the SAT and ACT… Good luck! And don’t forget to go have a donut. It’s National Donut Day. Donuts are the perfect SAT study food. ;-)
 Brief digression - You probably won’t be able to, but you will be officially awesome in my book if you can cite to Bill and Ted’s Excellent Adventure; The Simpsons Movie, The LEGO Movie, Animal House, or The Blues Brothers in your SAT essay… I suggest working in the following Animal House quotes – “What we need now is a really stupid, futile gesture! And we’re just the guys to do it!” “Face it – you f**ked up – you trusted us!” Or you could try to work in “They can’t stop us; we’re on a mission from God!” or “I HATE ILLINOIS NAZIS!” from The Blues Brothers. But enough joking around for now.
Author: John Linneball Who did you think? ;-)
I'm the proprietor and only tutor for this business; that's why I named it after me.