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f(x) = 0, where f(x) = -8x2 + 8x + 7.

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2 Answers

This is a multiple-choice question - the type you find on standardized tests like the SAT. Your approach should be to answer the question as quickly as possible without worrying about understanding details.

Rule #1: On a multiple-choice question, your first step is not to work the problem.

The first step is to eliminate as many answers as possible, and in this case it's sufficient.

The answer is (a) for the following reasons:

1.56 squared is about 2.5, so the expression is close to zero..  1.56 definitely a candidate 
-8 , -1 and -1.14 don't come close to making the expression zero. - do a rough estimate in your head.

So the only possible answer is a because for the other choices one solution definitely fails.

Remember, on a standardised test (or any multiple-choice question like this) your goal is to select the right answer, and not to prove you can work the problem! Just select the right answer, then go on to the next problem!

Never take any problem personally on a standardized test - for example, if you feel shaky about your ability to work a problem - don't let that enter into the equation. Just use what you know.

This approach works really well on multiple-choice tests because most test-writers are lazy and don't take time or don't know how to make up credible alternative answers.

Comments

"most test-writers are lazy and don't take time or don't know how to make up credible alternative answers."
 
It's not that they're lazy or don't want to take the time; it's that they don't have the time.
 
When I started teaching I made my own tests and I spent hours creating multiple choice answers based on the mistakes students make. I quickly ran out of time to prepare lessons, coach, and tutor.
 
As a side note, many of my students pleaded with me to give them open response questions, not multiple choice questions because the multiple choice questions were too hard!
I apologize for hurting your feelings.  
 
However, this answer-elimination strategy is what I teach my students for the SAT and other exams. Students who want to do as well as possible on those exams will, I believe, use this strategy.  And I think that, if you check, you will find that all the classes in standardized exams teach this same strategy.  And I believe the reason why it works is obvious.
 
 
 
 
 
 
I have NO problem teaching test taking techniques as you have described, Kenneth.
 
I DO take umbrage with your characterization that "test-writers are lazy". 99.99% of the teachers I knew put on brave faces, were kind to their students, tried to help them succeed, knew their subject very well, but were flat out time wise. It's the major reason why large percentages of new teachers leave teaching within 5 years.
"I spent hours creating multiple choice answers based on the mistakes students make"
 
This is one problem with multiple-choice questions.  They don't really show you very well what a student is doing right or wrong.   If you include common student mistakes, you are in danger of reinforcing student misunderstanding because a student who might not have made that mistake on his or her own may see that answer and think it must be right.  This is the thin line between tricky and fair for these questions.
 
In my classes I always prefer to see a student's work - to see what the student does right and wrong - so that I can be more helpful.
 
 
Wonderful philosophy but hard to keep up when you have 150 students. Impossible to correct tests with only open response questions and make grade posting deadlines imposed by administration.
 
Did I mention that most new teachers leave within their first 5 years?
When I was in College, tuition was less than my apartment rent for one month and classes were rarely over 30 students each.  When I started teaching tuition had risen to being equal with my rent for three months and classes were rarely over 60 students.  
 
Today, classes over 150 students are common, tuition is three times my rent for a year, and no one has time to teach. 
 
I think we should start over.
f(x) = -8x^2 + 8x + 7 = 0
 
8x^2 - 8x - 7 = 0
 
(ax + b)^2 = (ax)^2 + 2abx + b^2
 
(x√(8))^2+2(√(8))(-√(8)/2)x+(-√(8)/2)^2-(-√(8)/2)^2-7=0
 
(x√(8)-√(8)/2)^2 - (-√(8)/2)^2 - 7 = 0
 
8(x-1/2)^2 - (8/4) - 7 = 0
 
8(x-1/2)^2 = 9
 
(x-1/2)^2 = 9/8 = 3*3*2/2*2*2*2
 
|x-1/2| = 3√(2)/4
 
x = 1/2 ± 3√(2)/4
 
The only answer with pairs whose average is 1/2 is A.

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