Exam_3_f2011_KEYpost[1] - KEY AAA&BBB(and comments MATH 125...

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KEY (and comments) AAA & BBB MATH 125 EXAM 3 FALL 2011 There are more ways of doing something wrong than doing it correctly, so, In no necessary order: 1. make sure you use the correct mode when you use your calculator 2. if the question asks for EXACT VALUE, don’t use your calculator 3. make sure you know the exact values of functions of key angles 4. know the difference between concepts and the notation of a function and the value of the function, and use the proper notation. 5. read questions carefully, and follow directions (also, hints may actually be useful); that is, do or give what the questions say to do or give 5.1 this includes rounding to specified number of digits 5.2 this means knowing what rounding means 6. if there are multiple parts to a question, answer all of them 7. if pictures are called for, draw them (for your benefit), and then check to make sure that your drawing corresponds to the verbal description 8. for trig functions, remember that their signs vary from quadrant to quadrant 9. because the functions are overdetermined, all values can be obtained if you know only one; know how this is done 10. know how to solve different kinds of equations; not all functions are polynomials (they may be log, trig, inverse etc.) and not all “unknowns” are “x” (they may be “sin x,” or angles , or values of functions). 11. while the identities will be given, it will help if you “sort of” know them so you can recognize what’s right 12. you will have to know certain laws (sines, cosines, interest, …) and when and how to use them (This applies to future tests) 13. know the different “definitions” of the trig functions and how they are related to each other Math 125 Sections 008 & 087 Fall 2011 Exam 3 KEY AAA&BBB 11/4 Page 1 of 11
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1 For the function h ( x ) = (1/3) x a) (3 points) Make a table including AT LEAST 5 specific points that you will want to plot. b) (4 points) On the set of axes to the right, plot the function Make sure that you label the axes. 3.1 16 FOLLOW DIRECTIONS It says plot, plot . It says label axes, label axes . It says include 5 points, make a table that does that. And, since this is an exponential function, use points that play to that. Have the x values include 0, 1 and -1 because you can evaluate those without trouble, and then include 2 & -2 because they are easy as well. YOU DON’T HAVE TO USE YOUR CALCULATOR FOR THIS (OR FOR MANY OF THE OTHER PROBLEMS – USE YOUR MIND INSTEAD). x | -2 | -1 | 0 | 1 | 2 | y = f (x) | 9 | 3 | 1 | 1/3 | 1/9 | Check the properties of exponential functions in the text. Source: 3.1 14 (I was fairly lenient in giving credit for this. Some of you just used positive values for x, and ended up with very small positive fractions that you clearly couldn’t plot. If your tables were ok, I let it pass. But if the direction says “plot,” it strikes me that you should have selected points that you could plot.) 2 What is the formula for the accumulated (total) value, A , of an investment of P dollars compounded n times per year FOR t years at an annual interest rate of r%? (2 points) 3.1 54 modified This subject was covered twice in the text.
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