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[Sc]oring [Ba]dly? 

12/24/2014

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SPECIAL NEW CUSTOMER OFFER: Free 30-minute diagnostic session. Limited spots. 415-623-4251.
Did you like the TV show “[Br]eaking [Ba]d?” So did I. Follow these tips, inspired by that show, and you won’t be [Sc]oring [Ba]dly on the SAT!

Better Call Saul! Know the “law” of the test and how to use it. Any good legal argument is based on authoritative sources, provable evidence, and logic. That means that definitions and authoritative sources are your friends. In the case of a criminal prosecution Saul is defending, the source is the criminal law of New Mexico.  In the case of the reading sections, the authoritative source is the passage itself. Read like a meathead literalist. Here’s where knowing something about the subject of a passage can hurt you; you may fall for an answer that is correct, but isn’t mentioned in the passage. The questions will always either ask you what is in the passage, or what can reasonably be inferred from the passage. So don’t pick any answer that isn’t directly stated in the passage, or isn’t an obvious conclusion you can reach by reading the passage. If you have to make too many inferences or assumptions, RUN AWAY! In other words, if you go too far “out on a limb” you will fall off the tree!

In the sentence correction questions, the rules of grammar and punctuation are the law; study them! Even if the sentence looks and “sounds” right in your head, is it grammatical? Study the rules in your SAT review book and English textbooks. In the sentence completion questions, use the dictionary definitions of the words, not common slang usages (look words up in the dictionary- you may be surprised as to what they really mean! They often have other meanings than the common one. Don’t believe me? Look up “pervert,” “unique,” “fulsome,” “spastic,” and other words people use, but don’t really understand). Study your Greek and Latin word roots, and you can figure out word meanings.

Similarly, on the essay, just remember, you don’t have to argue what you really feel, just what you can “prove” or support with evidence. Like any defense attorney, Saul doesn’t have to prove what he’s saying is true; the prosecutor has to prove it’s false in order to convict Jesse, Walter, or anyone else. Saul can’t help his client if his client talks to the cops, tells them one story, then tells another story on the stand that’s not consistent with the first story. While this isn’t sworn testimony, you want to argue convincingly with relevant and convincing examples.  If you can make a better case for the side you don’t agree with, just go with it. It’s not going to be used against you in court ;-) .

Rely on diagrams that aren’t marked “Note: Figure Not Drawn to Scale.” You can check the length of lines in diagrams using a “ruler” made of a piece of paper from your test booklet or the side of your answer sheet. Do NOT make unwarranted assumptions. Write out the math or use your calculator if you’re not good at math in your head. Check your work.

If you don’t know a common mathematical formula or fact, BETTER CALL SAUL! Look at the “Math Facts” at the beginning of the section. While you should memorize all those facts LONG before the test, if you forget something or are panicking, take a few seconds to go and look. The same goes for use of the calculator- if you know you’re not good at doing arithmetic in your head, or on paper, just use the calculator. Don’t worry about what anyone else is doing.

If you don’t know the meaning of a weird symbol (say, a smiley face, a funny-looking cross, or a triangle) used to define a function (mathematical operation), don’t panic! The problem HAS to define it for you. Just read the definition, and I guarantee you’ll know how to do it.

“Tread Lightly” – Be Careful and Avoid Drastic Moves. Remember Walter White’s advice to Hank Schrader : “Tread Lightly.” Be careful, but avoid panicking and making drastic moves on test day.

“Tread lightly” – don’t pick “sucker punch” answers that are tempting but wrong. (See my entry “Don’t Go to the SPA”). You can avoid that by looking at ALL the answer choices and understanding why the right one is right and the wrong one is wrong.

However, don’t worry TOO much about the right answer or the “best” answer. If you overthink your answers, you can end up changing a correct answer to a wrong one, or taking what would have been a great essay and making it a real piece of junk.  For example, don’t decide to change your essay completely in the middle of writing it. Take time to think, then set up a little outline in your answer book, which can literally be one or two words on each line. After that, start writing and don’t look back! Don’t contradict yourself by leaving some things in from your first draft, then adding some inconsistent information (unless you can explain the inconsistency). Don’t waste time by starting over again, or by panicking at the beginning. Just pick a position, go with it, write your best argument, and go with it.

Similarly, you can psych yourself out with subtle differences in word meanings, or “What do the SAT people *want* me to answer?” Don’t let yourself think “Well, this *could* be right under some circumstances.” The point is to pick the *best* answer, not every *possible* answer. Just read the question, figure out the answer, compare it to the the listed answers, and pick the answer that makes sense to you.   The answers will then work to your advantage if you know what the answer should be – just pick the right one. If your answer doesn’t match any of the answers (on a math problem), the SAT people just did you a favor- check your work, re-read the problem, and you’ll get the right answer!

Don’t get bogged down in the minute details, and again, don’t make assumptions. Walter White remembered his main purpose – getting money for his family after he was dead. He usually didn’t let extraneous factors get in the way, or make unwarranted assumptions. When he did, it got him in trouble (think about the Los Pollos Hermanos security head). The same applies to you – don’t make assumptions, or you will lose points!


On the essay, as stated above, you don’t have to argue your real opinion on a subject, If you can’t figure out how to solve a question within about one minute, pick an answer that seems reasonable and move on. If you can’t see that any of the answers are unreasonable (e.g., it’s a negative number when only a positive one will do), then just SKIP IT, and move on.



Even Heisenberg can be certain about this: If you follow this advice, you won’t be scoring badly, and you’ll avoid the blues!

​SPECIAL NEW CUSTOMER OFFER: Free 30-minute diagnostic session. Limited spots. 415-623-4251.
 


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Solid Geometry Formulas for the SAT

12/24/2014

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Solid Geometry

Rectangular Prisms

You will ABSOLUTELY need to know the formula for the volume of a rectangular prism (you know, a box-shaped thing), which is length X width X height. 

V = L * W * H.  

Surface Area of a Rectangular Prism: There are three different sets of two rectangular sides – two sides have area L*W; two have area W*H; the last two have area L*H.

So SA = 2LW + 2WH +2LH, or 2(LW+WH+LH).

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Cubes

A cube is simply a special case of a rectangular prism – since all the sides, or “edges” are the same length, width, and height, the volume is L * W * H , which is the same as L * L * L, since L=W=H in a cube.

So if a cube has edge length 2, the volume is 2 * 2 * 2, which is 2 to the third power (2^3), or “2 cubed.” That’s why the third power of any number is called that number “cubed,” get it? ;-) This information is likely to appear in a word problem where you’re given the volume of the cube and expected to find the edge length (and perhaps find the area of one of the cube’s sides or something else)

Surface Area of a Cube: Just take the edge length, square it to find the area of one side, and multiply it by six (a cube has six sides). The surface area is six times the edge length squared.

So, SA = e*e*6 or 6e^2. (or 6a^2,as in the figure below).


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Right Cylinders:

The SAT and other tests ask about the volume of a right cylinder (you know, something shaped like a soda can) ALL THE TIME. Count on seeing problems that require you to know the formula for the volume of a cylinder.  It’s pretty simple – just take the formula for the area of a circle (good ol’ pi-r-squared) and multiply it by the height. So V = πr^2h, where V is the volume, r is the radius, and h is the height.

The surface area of a cylinder is equal to 2(πr^2) + 2πrh.


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Note on All Solids:

Notice that the volume of any 3-dimensional shape (cylinder, prism, etc) is just the area of the end shape, multiplied by the other side (the height, length, or depth – you know, the part that doesn’t form the end shape). So a triangular prism would have a volume of V = 1/2bh*L, where L is the length of the prism, b is the base of the triangle on each end, and h is the height of the triangle. Not that I’ve seen it, but a good SAT problem would be to take a shape formed from two geometric figures, then make it into a prism, so the student has to calculate the area of the shape, then multiply by the length of the other side to get the volume. (Think of a crude version of a hotel or house piece from Monopoly™, where the sides are just squares topped with triangles.) See if you can figure out the formula for the surface are of a triangular prism.


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Spheres

While this is less likely to be on the SAT, it’s worth knowing the formula for the volume of a sphere.

The formula for the surface area of a sphere (really not likely to be on the SAT, but here it is):

V = (4/3)πr^3

The surface area of a sphere is SA= 4πr^3



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Cones

You probably won’t see any questions about cones on the SAT, but just in case:

The formula for the volume of a right circular cone is: πr^2(h/3)

The formula for the surface area of a right circular cone is: SA = πr(r^2 + √(H^2 + r^2))


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Math Facts You Should Know for Standardized Tests

12/19/2014

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Here are some things you should know for the SAT, ACT, GMAT, GRE, or any other standardized test that tests math.

Most standardized tests given for admission to grad schools (other than physical science, medical, or engineering school) test math at a high school level.   That’s good news, in that the highest-level math you’ll be expected to know is geometry, or, in the case of the ACT, some basic trigonometry.  It’s also bad news, in that it’s still a lot of information to remember, especially if it’s been a while since you’ve taken high school math.

The SAT, and possibly some other tests, do give you a “Math Facts” section with many of these facts listed for you, but you really don’t want to have to flip back from a problem on which you are working just to look up a formula, thus breaking your train of thought and wasting a few seconds, when it’s really not that hard to memorize these formulas. The best way to memorize the facts is to work enough practice problems that you remember how you solved similar problems, including what formula you used.

So, without further ado, here are some basic math facts you should memorize before going into a standardized test.

Geometry:

Pythagorean Theorem:  

The length of the hypotenuse (longest side) of a right triangle (a triangle in which one of the angles is a right angle, or 90-degree angle) relates to the lengths of the other two sides in the following way: h2 = a2 + b2, where h is the length of the hypotenuse, and a and b are the lengths of the other two sides. You can also derive the formula for the distance between two points on a Cartesian coordinate grid using the Pythagorean Theorem – just use the points to make a right triangle, using the line between the points as the hypotenuse.

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Notice that the sides of a triangle can also be the sides of squares, which is something you’re likely to see in an SAT problem.

Special Right Triangles

30-60-90 triangle:  The ratio of the lengths of the sides opposite the angles are 1,√3, and 2, respectively. That is, the shortest side is 1, the second longest side is √3  hypotenuse is 2.

45-45-90 triangle:  The ratio of the lengths of the sides opposite the angles  is 1-1-√2.


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Powers To Remember  

Knowing various powers of the numbers 0 through 20, will “exponentially” increase your chances of getting a high score on a standardized test. All right, now that you’re done wincing and groaning at that awful pun, here are some powers you’ll need to know.

For Pythagorean Theorem purposes, know the squares of all numbers from 0 to 20. It’s not likely you’ll be required to know the square of any number larger than 20, unless it’s an easy one to calculate such as the square 30, 40, 50, or so on, and in the rare instances where you do, you can rely on your calculator.


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You should know the powers of 2 from 0 to 10, since powers of 2 are useful for so many SAT problems (e.g., a bacterial culture that doubles the number of cells every period of time).

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Higher Powers:

You really only need to know a few powers higher than 3 on the SAT. You should probably know 1 through 6 to up to the fourth power, and 7 through 9 up to the third power. (To get any power of 10, just add that number of zeroes behind it; 101 = 10, 102 =100, and so on.)

Distance Formula:

Distance = Rate X Time , so Rate = Distance/Time, Time = Distance

For example, 100 miles = 100 miles per hour (miles/hour) * 1 hour.

100 miles/hr = 100 miles/1 hr, and

1 hr = (100 miles)/ (100 miles/ 1hr) = 1 hr.

Coordinate Distance formula:

As discussed in the Pythagorean Theorem section above, the distance between two points on a Cartesian coordinate (x-y) grid, can be determined using the Pythagorean Theorem and the coordinates. The formula for the distance between points A = (x1, y1) and B = (x2, y2), which we can call AB, is:

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This formula will help you with coordinate geometry (Cartesian coordinate) problems.

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College Application Essays

12/8/2014

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If you are applying to practically any college or university, you will have to write an essay, either in response to a specific question or topic (or “prompt,” as the SAT people call their essay question topics), or just as a general statement. While this may frighten you at first, the task of writing these essays will not seem quite so daunting if you keep a few simple ideas in mind.

 

First, a few general details:

 

(1)        Write using sophisticated, but not pretentious, language. You don't want to sound like a kid, but you don't want to sound like you are trying to impress the admissions officers with your huge vocabulary. Don't use slang terms if you don't have to, and if you have to (meaning your writing is more effective using the slang terms), make sure you define the terms.

 

(2)        Set up a structure – you can use the SAT essay format, which copies the Toastmasters method – “tell ‘em what you’re gonna tell ‘em; then tell ‘em; then tell ‘em what you just told ‘em,” which I discuss in detail in my blog entry on essays for the SSAT. You can also make your essay a narrative (you know, a story, with a beginning, middle, and an end). Any structure that makes your essay make sense and easy to read is a good thing. Now is not the time to try some avant-garde, postmodern narrative style. Just tell a story that answers the question.

 

(3)        It should go without saying that you should not make references to any legally protected class. By “protected class,” I mean race, sex, gender identity, sexual orientation, etc. Basically, I suggest you follow the old advice about conversational topics in mixed company- "Never discuss sex, politics, or religion." The only exceptions that come into my mind are: 1) if you were the first member of a protected class to achieve something, or be admitted to an organization (for example, you were the first girl on your high school's wrestling team) or 2) you made some impressive contributions to a political organization, then, by all means, mention those topics.

 

(4)        Last, but not least, keep in mind the real reason you’re writing the essay. The admissions officers want to know about YOU. A general essay about why education is important, or some current event, or a book you read, isn’t going to do much to improve your chance of admission if you don’t let the admissions people know why you’re any more interesting than the hundreds, if not thousands, of other applicants.

 

Now a few more specific details:

 

If there’s a topic, answer the question.  No one will want to let you into college if you show them on the application, that you cannot follow directions.

 

If there is no set topic or prompt, try to be fresh, engaging, and sincere. Imagine being an admissions officer at a selective college and having to read the same essay about "excellence" for the hundredth time.  You’re going to read the essay and think “Yeah, yeah, you’re a 17-year-old hotshot who’s ‘committed to excellence.’ You and the Oakland Raiders. Wonderful. Hey, I wonder if anyone else has a more interesting essay here?” I know people who’ve gotten into selective colleges with exactly such essays, but I can only imagine their grades and other factors carried them through. All things being equal, the candidate with the fresher, more interesting, essay is going to be admitted ahead of the applicant with the cookie-cutter “Excellent things are excellent; that’s why I work really hard to be excellent!” essay.

 

Any college, university, or educational institution is not just trying to sell you (or your parents) an education. It’s also selling its graduates to employers and government agencies in order to get job placements to make it look better, and for research grants to fund the institution.  That means students aren’t just the institution’s customers; they’re its products.

 

Since you are the potential raw material for the institution’s most valuable, if not only, product, anything you write should let the institution know why you’re a worthwhile candidate for admission. In other words, what can you do for them? “Diversity” is the watchword of all college admissions committees.  What will you bring to their institution to make it a more interesting place? How likely are you to succeed in life once you graduate from there? Are you likely to help other students succeed? Showing ambition, drive, and willingness to help others is the key to a successful college admissions essay.

 

Let someone else edit your essay.  What is important to you, may not be important to someone else. You may be focusing on just one aspect of yourself, or why you want to attend the institution, or the question they asked you on the application.  You may have misspellings, grammatical errors, an inappropriate tone, or other problems with your essay.  It’s always easier to see problems in someone else’s writing, just as it’s always easy to see any problem or fault another person has, even if we have the exact same fault. Use someone you trust, and whose writing ability you respect, as a resource, and really listen to what they have to say.

 

Finally, “be yourself.” It’s a cliché because it’s true. I’d rather read an honest essay that makes a point I with which I do not agree, than read something I think is insincere or, even worse, dishonest.  If you write an essay about how your life’s passion is service to others (subtext: “Hey, I’m a good person! You want me at your school, where I can help others!”), but there’s no volunteer (or paid) work experience on your application to support that statement, the admissions officers will seriously discount it. They’d be happier to see that you’re working hard to advance yourself, and that you’ve written that in your essay, even if they’re die-hard liberals.  Obviously, you shouldn’t write that you did things you didn’t – count on getting caught.

 

I hope this helps; your application essays are the only things that can set you apart from very similar applicants for the same colleges, and, along with your SAT or ACT scores, the only things you can improve during your senior year of high school. Good luck with your applications.  Feel free to contact me if you have any questions, and happy holidays!

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    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.

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