Learn the Language of the SAT

Every standardized test has its own rules, its own language. The SAT is no different. To understand the language of a test, is to know how to attack each question type. To understand the language of the SAT is to be prepared and avoid the trick answer. In my next series of posts, I will address the language of the SAT for each topic: Math, Critical Reading and Writing........

Eliminate Before You Calculate!

In this fast paced, video game, text messaged world, the desire for instant gratification has never been greater. I have witnessed many students fall into this speed trap, especially when it comes to answering the Math SAT questions. The need for speed often leads to misread questions, sloppy set ups and silly mistakes.
Before coming up with the answer read the question until it is fully understood. Eliminate the obvious incorrect answers. For example--if the answer calls for a positive slope, eliminate the answers with negative slopes; if the answer must be less than 90 degrees, get rid of all those answers greater than 90 degrees. This method allows you to enjoy more accurate calculations while avoiding the "sucker answers" which are designed to catch the careless speed demons!

Important Math Formula

To find the sum of the interior angles of any polygon use: (n-2) X 180 where n represents the number of sides. Using this formula to find the sum of the interior angles of 5 sided figure (a pentagon) (5-2) X 180=540 degrees. Assuming all the angles are equal, to find the value of each angle use (n-2) X 180/n so (5-2) X 180/5=108.

Understanding Compound Percent Problems

Most of my student's parents were sold a bill of goods from their financial advisors who were either ignorant or stupid. I will give them the benefit of the doubt and call them ignorant. After suffering losses of 80% on a stock market investment in 2008, they were told not to sell because their stocks will eventually come back. Everyone with massive losses dreams that their investments will someday come back. Let's fantasize that the same stock which declined by 80% in 2008 increases in value by 100% in 2009. You would then be ahead 20% right? Wrong!!!! Never ever add or subtract percent increases or decreases on the SAT or in life.

The correct way to deal with the above compound percent problem is as follows:

1. Assign a theoretical value for our stock--I like to use $100 when dealing with percent.
2. At the end of 2008 our stock is now worth $20 (an 80% decline)
3. At the end of 2009 our stock is now worth $40 (a 100% increase)

Therefore our two year return is minus 60% not a gain of 20%---So the Rule here is when dealing with compound percent problems start with 100 and work your way up or down step by step. For additional practice try p. 491 problem #13 from the Official SAT Study Guide.

Your Calculator, The SAT and The ACT

Maybe I am old school, but I look at the calculator on the SAT and the ACT as a hindrance rather than as a useful tool. When I was a kid (many moons ago) there were no stinking calculators allowed in the testing rooms! Finally, when the test makers decided to allow calculators, did you really think that they were doing so for the students' benefit? Think about it! You can solve every math problem on the entire exam without a calculator. Remember the math is easy, its the set up that will get you every time. Never, ever, ever, use a calculator for a division problem when you are asked to solve for the remainder. Don't use a calculator when the answer choices are in fractions. When practicing math, try to solve every math problem without the use of your calculator. Use the calculator only to check for silly mathematical errors and for adding subtracting, multiplying and dividing complex numbers or numbers with decimals. That's my only exception to the NO CALCULATOR RULE!

Inverse Proportion

In the previous post we basically defined direct proportion as what we do to x, we must also do to y. Specifically we said that if you double x, then we must double y to maintain the relationship as directly proportional. With inverse proportion when we double y we must halve x. The equation xy=k where k is the constant. For example suppose when x=3 y=20. If x is doubled to equal 6, y must be cut in half to 10 to maintain an inverse relationship. Using our equation xy=k we first solve for k--(3)20=60 so k=60; if we double x from 3 to 6 then we have 6y=60; y=10. So when x is doubled from 3 to 6, y is halved from 20 to 10. Simple as that.

Direct and Inverse Proportion

There is usually at least one question on the math section which requires the student to know either direct proportion or inverse proportion. Quite simply with direct proportion if x goes up y goes up in proportion. If x decreases, y decreases in proportion. Here is a helpful rule for Direct proportion using variables x and y can be thought of as y=xk where k is a constant. Cross multiply and you get a variation of this equation: y/x=k. For example if x=2 when y=4, then when x=4 then y=8. The constant k=2 so y will always be twice x. Simple enough? If x were to be reduced from 2 to 1 then y would still be twice x but in this case it would be reduced to 2. In our next entry the more difficult concept of inverse proportion will be tackled.

Do The Easy Questions First

Today's Question of the Day involved a series of mathematical combinations and permutations. While the mathematical calculations were simple (as they always are) understanding and setting up the problem would have taken a lot of time (as most difficult math questions take). SAT scoring does not reward more points for these difficult questions. The SAT is not like Olympic diving or figure skating or even AP classes, ie. there is no extra credit for degree of difficulty. So don't be a hero, get as many easy points as possible, then go on to the medium questions then after checking for careless mistakes, use any extra time to tackle the more difficult questions. A math question which takes 5 minutes to solve is clearly not worth the time and effort and omitting such a question will not adversely impact your score.

Learn From Your Mistakes

When reviewing practice exams, you will learn more from the questions you get wrong than the ones you answer correctly for several reasons. First, if you answer a question correctly, presumably you already know how to do it, so there is no reason to focus on something you already know. Or worse, if you got the question right because it was a lucky guess you may think you know something you don't. Wrong answers represent with certainty, questions and concepts that must be studied. Ask yourself, "Was this a careless error? Do I understand why it is wrong? Is there a better method to get the correct answer?" For sentence completions, study all the vocabulary word answer choices you don't understand. Re-read a passage and try and find the answer. Learn a new rule of grammar from an incorrect short answer writing question. Look for patterns. Do you find that the same type of questions always give you the most difficulty? For example, a student of mine had trouble answering the critical reading main idea questions. So I directed the student to some study aids and quizzes designed specifically for that type of question. This is what I call efficient study time. Use your time wisely by zeroing in on those questions that pose the most difficulty.

The Math Is Easy...................

Its setting up the question that is the hard task on the Math section of the SAT. Read the question, if you don't understand it, read it again! I cannot tell you how many of my students make silly mistakes on math questions because of poor reading comprehension. Focus only on what is being asked. Focus only on what is being given. Do not invent things that simply are not there. Today's question of the day was a classic--Two sets of two lines were drawn. Only two of those lines labeled (l and m) were specifically given as parallel. The other two lines looked parallel but YOU CANNOT ASSUME THAT THEY ARE PARALLEL! If you assumed they were parallel your answer would be totally different and wrong. Remember there is always a wrong answer waiting for you if you are careless and misread the question.