Mar 31 2010
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Mathematics > Standard Multiple Choice
Read the following SAT test question, then click on a button to select your answer.
My tutoring note: If you take out the figures, the question reads this way:
If the function is defined by , and if , what is the value of ?
Answer Choices (A) (B) (C) (D) (E) The answer choices are all one number. The numbers start with A.4 and go up in amount, and they are all whole numbers and positive. The answer will be whole and positive.
As usual, I do want you to go to the SAT site and to look at the problem, attempt to solve the problem, use your strategies, and look at the hint--even if you know how to do the problem.
Today's answer is explained on the SAT in a comprehensive way if you put the hint together with the final answer.
I want a test-taker (and student) to understand how to do this problem, and I want you to understand that if you can look at a problem you do not understand completely and reword it for yourself, you may be able to answer it correctly without immediately remembering how to do each traditional step.
The reason this is true more often on an SAT question than on some standardized tests is that the SAT questions are designed to test your aptitude.
Therefore, with the information given, you will always know more than you realize immediately. Part of your assistance in answering the question will be enclosed in the question and the format PLUS the fact that the calculations are not usually the point of the question, so they work out better than in 'normal' life.
Strategy One: Use your calculator if you do not do fast arithmetic and multiplication while figuring out how to do a problem. The numbers will often be the most manageable part of the problem when the question is about how to do a problem. For example, in this problem, the numbers are all low, whole, and positive.
The question here is:
If the function of f is defined by f(x)=2x+3, and if f(a)=11, what is the value of a?
Look at the explanation of how to do this to see the way to use the pattern to solve more complicated problems.
For this problem, I wrote it in the format to find the value: f(a)=2a+3 and merely plugged in the first answer, 4, because it was easy to do. f(a)=2(4)+3=11.
So I knew immediately that '4' is the answer. Also, all the other numbers are too big. The only way I would be able to do this in this way is if the answers are given, as they are on a multiple choice test.
If you study the answer on the SAT, you will learn how to answer even more mathematics questions that are written in this way.
If you study my strategy, you will learn one of the better mathematics strategies I learned from the Princeton Review. That is, when you are trying to visualize a mathematics solution, plug in some numbers that are easy for you to manage. In this case, one of the answers filled the bill for this strategy.
In some cases, the answers do NOT provide an easy way to 'plug in' numbers so you can see how the math problem is going.
Next time, I will show you how this strategy really helps in learning mathematics--as well as answering correctly on a standardized test.
When you 'teach' yourself, rather than just learn the steps, you reach a different area of your brain capacity. The results are an increased level of performance that reveals what you know to yourself as well as to others.
judiethcarol&rocketcatMarch2010
