Algebra

Link of the Day

Many of you have been following the news about Hurricane Sandy, and our thoughts and prayers are with those affected by the storm.  For others, it may be easy to hear things like “school is out” and “the power is out” and wish you were in the same situation.  You may think of enjoyable times spent wrapped in blankets and telling stories as a candle or flashlight flickers.  Think for a moment about how important power is for a hospital.  Here is an article about how one hospital responded to the storm.  Think about broad themes such as courage, the fight for life, and the response to danger as you read about this current event.

10/30 Algebra

Read the following SAT test question and then select the correct answer. 

If you approach all math problems the same way, you are less likely to make a careless mistake.  Start by reading the problem carefully and identifying the bottom line.  Assess your options for solving the problem so that you do not do more work than you need to.  Then attack the problem and solve it.  Loop back after you have finished to make sure that you found the bottom line.

If  , for which of the following values of x is y NOT defined?

Bottom line:  Although the problem includes an equation for y, you need an x value.  Your answer will be an x value that does something specific to this equation to produce a y that is not defined.  So make a note: x = ?

Assess your options:  You could work backwards and plug in answer choices to find a value that produces a y that is not defined.  This might require you to work the problem numerous times.  Instead, think about your knowledge of number properties.

Attack the problem: Any time a number is divided by zero, it is not defined.  If y is not defined, then it must be equal to something over zero.   Take the bottom part of your fraction and set it equal to zero: (x + 3)(x – 4) = 0.  For which values is this true?  Well, anytime zero is multiplied by a number, the answer is zero.  If either of these binomials is equal to zero, then there will be a zero on the bottom.  So set each binomial equal to zero: x + 3 = 0 and x – 4 = 0.  When you solve both of these equations, you will get two answers: x = -3 and 4.  Both answers will create a zero in the bottom of your fraction.

Loop back:  You found two answers for x that will create a zero on the bottom of your fraction.  Look down at your answer choices to see which one is present.

(A) -4

(B) -3

(C) -1

(D) 2

(E) 3

The correct answer is (B).

On sat.collegeboard.org, 55% of the responses were correct.

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