Math 012 Midterm Exam Fall 2016 Professor: Dr. Kate Bauer Name________________________________ Instructions: The exam is worth 60 points. There are 12 questions, each worth 5 points. Your score on the exam will be converted to a percentage and posted in your assignment folder with comments. This exam is open book and open notes, and you may take as long as you like on it provided that you submit the exam no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer. Please type your work in your copy of the exam, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your exam in the Exams Module. If you have any questions, please contact me by e-mail (kate.bauer@umuc.edu). At the end of your exam you must include the following dated statement with your name typed in lieu of a signature. Without this signed statement you will receive a zero. I have completed this exam myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this exam. Name: Date: Please remember to show all work on every problem. 1) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer. 6 x 1 7 7 8 x 7 Math 012 Midterm Exam Page 2 2) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer. 6 1 x 8x 2 x 6 3) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer. 4 n 11 n 29 2 n 3 3 30 5 Math 012 Midterm Exam Page 3 4) Solve the inequality below. Show all work following the methods discussed in class; if an inequality includes fractions, clear the fractions in the first step. Write your answer in interval notation and graph the solution set on a number line. 2 7 x 6 5 x 5) Solve the inequality below. Show all work following the methods discussed in class; if an inequality includes fractions, clear the fractions in the first step. Write your answer in interval notation and graph the solution set on a number line. 14 9 x 5 31 Math 012 Midterm Exam Page 4 6) Michael wins $800,000 (after taxes) in the lottery and decides to invest half of it in a 10-year CD that pays 5.35% interest compounded monthly. He invests the other half in a money market fund that unfortunately turns out to average only 4.3% interest compounded annually over the 10-year period. How much money will he have altogether in the two accounts at the end of the 10-year period? Math 012 Midterm Exam Page 5 7) The average annual tuition and fees at all 4-year institutions in the US in 1992 was $14,216 and in 2010 was $ 23,118. Let y be the average tuition and fees in the year x, where x = 0 represents the year 1992. a) Write a linear equation, in slope-intercept form, that models the growth in average tuition and fees at all 4-year institutions in the US in terms of the year x. b) Use this equation to predict the average tuition and fees at 4-year institutions in the US in the year 2020. c) Explain what the slope of this line means in the context of the problem. Math 012 Midterm Exam 8) Given the equation Page 6 4 x 3 y 15 : a) Convert the equation to slope-intercept form. State the slope of the line and state the yintercept as an ordered pair. b) Write an equation in point-slope form of the line through the point (3, -2) perpendicular to the line with the equation given above. c) Convert the equation found in part (b) to slope-intercept form. d) Convert the equation found in part (c) to standard form, Ax + By = C, where A, B, and C are integers. e) Graph both lines on one coordinate system. You may use the grid below or create your own. Math 012 Midterm Exam Page 7 8 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 y x 1 2 3 4 5 6 7 8 9) Show all work as you perform the indicated operations and simplify the result: 5 x3 y4 2x y 2 9 3 10) Show all work as you perform the indicated operations and simplify the result. Write the answer with positive exponents only. 48x5 y 17 60 x 2 y Math 012 Midterm Exam Page 8 11) Show all work as you perform the indicated operations and simplify the result. Start by clearing all parentheses. 7 x 5x 3 2 2x 4x 15x 9x 2 3x 11 3 2 19 Math 012 Midterm Exam Page 9 12) Show all work as you multiply the polynomials and simplify the result: 5 x 2 4 x 2 3x 9 End of exam: please do not forget to write and sign (or type) the required statement explained on Page 1 of the exam