Math 009 Midterm Exam Fall 2016 Professor: Dr. Kate Bauer Name________________________________ Instructions: The exam is worth 60 points. There are 12 problems, 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 allows 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 should show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit. 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 the exam. 1) Simplify the following expression: 18 6 5 7 3 5 14 Math 009 Midterm Exam 2) Evaluate the following expression if Page 2 3 x 4 and 1 y 3 . Write your answer in simplest form. 24x3 y 2 3) Simplify the following expression: 8 4 x 5 14 2 x 3 4) Solve the equation. Show all work and show the complete check of your answer: 4 x 19 87 Math 009 Midterm Exam Page 3 5) Solve the equation. Show all work and show the complete check of your answer: 5 2 7 x 6x 4 5 6x 6) Solve the equation. Show all work and show the complete check of your answer: 1.6 3.8x 4.7 4.5x 7) Solve the equation. Show all work and show the complete check of your answer. Start by multiplying both sides of the equation by the least common denominator to clear all fractions: 1 x 5 5 x 1 2 3 2 Math 009 Midterm Exam Page 4 8) In a sample of 4500 new iPhones, 21 were found to be defective. At this rate, how many defective iPhones would be expected in a sample of 360,000 new iPhones? Use a proportion to set up and solve this problem. Write a complete answer including units. 9) Mark borrows $27,000 to buy a new car. If the simple interest rate on the car loan is 8.35% and he pays off the loan in 5 years, how much interest does he pay? Write a complete answer including units. 10) Sally paid $24,180 as a down payment for her new home. If the down payment was 12.4% of the total price of the house, what was the total price of the house? Start by defining the unknown in terms of a variable; then write an equation based on the information given and show all work as you solve the equation. Write a complete answer including units. Math 009 Midterm Exam Page 5 11) Michael's annual salary is $94,800. He has been promised a 5.2% merit raise in the year ahead. Find the amount of the raise and the new salary. Show all work and write a complete answer including units. 12) Anna inherits $70,000 and decides to invest part of it in an education account for her daughter and the rest in a 5-year CD. If the amount she puts in the education account is $10,000 more than three times the amount she puts in the CD, how much money does Anna invest in each account? Start by defining the unknown quantities in terms of a variable; then write an equation based on the information given and show all work as you solve the equation. Write a complete answer including units. End of exam: please do not forget to write and sign (or type) the required statement explained in the box on Page 1 of the exam. Math 012 Midterm Exam Fall 2016 Professor: Tara Wells Name________________________________ Instructions: The exam is worth 75 points. There are 15 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 (tara.wells@faculty.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 using the methods discussed in Chapter 1 of our text. If the equation has a unique solution, please show the complete check of your answer. 4 7 8x 5 5 5 x 1 Math 012 Midterm Exam Page 2 2) Solve the equation using the methods discussed in Chapter 1 of our text. If the equation has a unique solution, please show the complete check of your answer. 6 x 5 x 7 x 6 12 3) Solve the equation using the methods discussed in Chapter 1 of our text. Clear fractions from the equation in the first step. If the equation has a unique solution, please show the complete check of your answer. 2a 1 5a 7 15 3 6 30 4) Solve the inequality using the methods discussed in Chapter 3 of our text. Write your answer in interval notation and graph the solution set on a number line. 3 4m 3 2 1 m 3 Math 012 Midterm Exam Page 3 5) Solve the inequality using the methods discussed in Chapter 3 of our text. Clear fractions from the inequality in the first step. Write your answer in interval notation and graph the solution set on a number line. 4 1 11 x x 3 6 3 6) Solve the inequality using the methods discussed in Chapter 3 of our text. Write your answer in interval notation and graph the solution set on a number line. 14 3x 7 49 7) Solve the inequality using the methods discussed in Chapter 3 of our text. Write your answer in interval notation and graph the solution set on a number line. 12 5 x 16 Math 012 Midterm Exam Page 4 8) The amount of pollution varies directly with the population of a city. City A has a population of 442,000 people and produces 260,000 tons of pollution. How much pollution should we expect City B to produce if its population is 344,000 people? Round your answer to the nearest whole ton. 9) Jeff wins $600,000 (after taxes) in the lottery and decides to invest half of it in a 10-year CD that pays 7.25% interest compounded monthly. He invests the other half in a money market fund that unfortunately turns out to average only 3.2% 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 10) The average annual tuition and fees at all 4-year institutions in the US in 1982 was $10,385 and in 2012 was $ 23,872. Let y be the average tuition and fees in the year x, where x = 0 represents the year 1982. 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 2030. c) Explain what the slope of this line means in the context of the problem. Math 012 Midterm Exam Page 6 11) Given the linear equation 5 x 2 y 10 : a) Convert the equation to slope-intercept form. State the slope of the line and the y-intercept as an ordered pair. b) Use the slope and the y-intercept to graph the line represented by the equation. You may use the axes provided, or create your own graph. 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 Math 012 Midterm Exam Page 7 12) Given the following two linear equations, determine whether the lines are parallel, perpendicular, or neither. Show all work and explain your conclusion clearly. 6 x 7 y 42 7 x 16 6 y 13) Write an equation of a line through the point (-5, -2) that is perpendicular to the x-axis. Graph the line on the grid below or create your own graph. State the slope of the line. 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 Math 012 Midterm Exam Page 8 14) Find an equation of the line through (-6, 10), parallel to the line with equation 3x - 7y = 14. Write the new equation in point-slope form. 15) Convert the equation of the new line found in problem #14 to standard form, Ax + By = C, where A, B, and C are integers. End of exam: please do not forget to write and sign (or type) the required statement explained on Page 1 of the exam