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Precalculus: A Concise Course
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Chapter 1 / Exercise 13
Precalculus: A Concise Course
Larson
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Unformatted text preview: MATH 105 Exam 1 Please be sure to save at least once every 15 minutes. If you leave this page without saving, or if your session times out, any answers you have not saved will be lost. The Submit for Grading button will become available once you've answered all questions. Exams are not timed; you do not have to finish an exam in one sitting as long as you have saved your answers. Q1. Evaluate (2xy + 35)/x given that x = 5 and y = 7. a. 7 b. 49 c. 9 d. 21 Q2. Evaluate 4|x| + 5|y| given that x = 8 and y = ­7. a. ­67 b. 3 c. ­3 d. 67 Q3. Write the expression √­64 and express your answer in the standard form a + bi. a. i√8 b. 8i c. ­8i d. ±8 Q4. Choose the graph of the number line that represents x > ­7. a. b. c. d. Q5. Find the real solutions of the equation 2x4 ­ 128x2 = 0 by factoring. a. {­8√2, 0, 8√2} b. {0} c. {­8, 0, 8} d. {­8, 8} Q6. The net income y (in millions of dollars) of Pet Products Unlimited from 1997 to 1999 is given by the equation y = 9x2 + 15x + 52, where x represents the number of years after 1997. Assume this trend continues and predict the year in which Pet Products Unlimited's net income will be $598 million. a. 2005 b. 2004 c. 2003 d. 2006 Q7. Find the real solutions of the equation √24x + 48 = x + 8. a. {­4} b. {6} c. {­3} d. {4} Q8. Fill in the blank with the correct inequality symbol. If x < 6, then ­3x ____ ­18. a. < b. ≥ c. ≤ d. > Q9. Find the real solutions of the equation (x + 3) 1/3 = ­2. a. {1} b. {­9} c. {­11} d. no real solution Q10. Solve (2x ­ 3) 2 = 49 by using the Square Root Method. a. {4, ­10} b. {5, ­2} c. {10, ­4} d. (2, ­5} Q11. Translate the following sentence into a mathematical equation. Be sure to identify the meaning of all symbols. The profit derived from the sale of x video cameras is $370 per unit less the sum of $2700 costs plus $160 per unit. a. If P is profit and x the units sold, then P = 370x ­ (2700 + 160x) or P = 210x ­ 2700. b. If P is profit and x the units sold, then P = 370x + 2700 ­ 160x or P = 210x + 2700. c. If P is profit and x the units sold, then P = 370x ­ (2700 ­ 160x) or P = 530x ­ 2700. d. If P is profit and x the units sold, then P = 370/x ­ (2700 + 160/x) or P = 210/x ­ 2700. Q12. Solve the rational equation (4x­1)/(2x+3)=(6x+8)/(3x­4) a. {28/15} b. {­28/53} c. {­20/53} d. {4/3} Q13. An inheritance of $210,000 is to be divided among Chris, Kelly, and Julie in the following manner: Kelly is to receive 3/5 of what Chris gets, while Julie gets 1/2 of what Chris gets. How much does Kelly receive? a. $20,000 b. $60,000 c. $100,000 d. $50,000 Q14. A bank loaned out $70,000, part of it at the rate of 12% per year and the rest at a rate of 6% per year. If the interest received was $5760, how much was loaned at 12%? a. $44,000 b. $26,000 c. $43,000 d. $27,000 Q15. Find the real solutions of the equation x + √x = 56. a. {8} b. {49} c. {7} d. {64} Q16. The manager of a candy shop sells chocolate covered peanuts for $6 per pound and chocolate covered cashews for $15 perpound. The manager wishes to mix 100 pounds of the cashews to get a cashew­ peanut mixture that will sell for $8 per pound. How many pounds of peanuts should be used? a. 225 lb b. 450 lb c. 175 lb d. 350 lb Q17. Solve the linear equation (x/3) ­ (1/3) = ­4 a. {­11} b. {­13} c. {11} d. {13} Q18. Write the inequality using interval notation, and illustrate the inequality using the real number line. ­4 ≤ x < 3 a. [­4, 3) b. (­4, 3] c. [­4, 3) d. (­∞, 3) Q19. Solve the rational equation x/(x­1)+6=1/(x­1) a. {­1} b. {1,­1} c. {1} d. no solution Q20. Solve the equation x2 + 144 = 0 in the complex number system. a. {­12, 12} b. {12} c. {12i} d. {­12i, 12i} Q21. Solve the inequality. Express your answer using interval notation. Graph the solution set. 4x + 1 > 3x ­ 4 a. (­∞, ­5] b. (­3, ∞) c. [­5, ∞) d. (­5, ∞) Q22. Solve the inequality. Express your answer using interval notation. Graph the solution set. 7 ≤ 2x + 3 ≤ 15 a. (­6, ­2) b. [­6, ­2] c. [2, 6] d. (2, 6) Q23. Find the center (h, k) and radius r of the circle with the given equation (x ­ 6) 2 + (y ­ 2) 2 = 16. a. (h, k) = (2, 6); r = 16 b. (h, k) = (6, 2); r = 4 c. (h, k) = (2, 6); r = 4 d. (h, k) = (6, 2); r = 16 Q24. Graph the following equation by plotting points: y = 1/x. a. b. c. d. Q25. Find the slope­intercept form of the equation of the line with the properties of a horizontal line containing the point (­2, 7). a. x = 7 b. y = 7 c. x = ­2 d. y = ­2 Q26. Find the general form of the equation for the line with slope = ­2/3 and containing the point (0, 4). a. 2x ­ 3y = 12 b. 3x + 2y = ­12 c. 2x + 3y = 12 d. 2x + 3y = ­12 Q27. Graph the follwing equation by plotting points: 5x + 2y = 10. a. b. c. d. Q28. Graph the equation (x + 2) 2 + (y + 3) 2 = 9. a. b. c. d. Q29. Graph the circle with radius r = 2 and center (h, k) = (­4, ­1). a. b. c. d. Q30. Write the standard form of the equation of the circle with radius r = 2 and center (h, k) = (0, 0). a. x2 + y2 = 4 b. x2 + y2 = 2 c. (x ­ 2)2 + (y ­ 2)2 = 2 d. (x ­ 2)2 + (y ­ 2)2 = 4 Q31. Find the slope and y­intercept of the line ­x + 10y = 70. a. slope = 10; y­intercept = ­70 b. slope = ­1; y­intercept = 70 c. slope = ­ 1/10; y­intercept = 7 d. slope = 1/10; y­intercept = 7 Q32. Graph the line containing the point P = (­2, ­8) and having slope m = 1/2. a. b. c. d. Q33. The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 8, 16, 20 a. right triangle; 8 b. right triangle; 16 c. right triangle; 20 d. not a right triangle Q34. Find an equation for the line with the properties of a vertical line containing the point (­6, ­4). a. y = ­6 b. x = ­6 c. y = ­4 d. x = ­4 Q35. Find the midpoint of the line segment joining the points P1 and P2. P1 = (­1, 6); P2 = (­5, 3) a. (­6, 9) b. (2, 3/2) c. (4, 3) d. (­3, 9/2) Q36. The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 15, 36, 39 a. right triangle; 39 b. right triangle; 15 c. right triangle; 36 d. not a right triangle Q37. Find the slope of the line containing the points (­7, 1) and (­8, ­5). a. ­1/6 b. ­6 c. 1/6 d. 6 Q38. Write 17x + 3y = 10 in slope­intercept form. a. y = 17x/3 + 10/3 b. y = 17x ­ 10 c. y = 17x/3 ­ 10/3 d. y = ­17x/3 + 10/3 Q39. List the intercepts and type(s) of symmetry, if any for y2 = ­x + 9. a. intercepts: (­9, 0), (0, 3), (0, ­3); symmetric with respect to x­axis b. intercepts: (0, ­9), (3, 0), (­3, 0); symmetric with respect to y­axis c. intercepts: (9, 0), (0, 3), (0, ­3); symmetric with respect to x­axis d. intercepts: (0, 9), (3, 0), (­3, 0); symmetric with respect to y­axis Q40. List the intercepts for the graph of the equation y = x3 ­ 27. a. (0, ­3), (­3, 0) b. (0, ­3), (0, 3) c. (­27, 0), (0, 3) d. (0, ­27), (3, 0) Privacy Policy | Contact Us | Copyright © 1998­2017 University of Management and Technology (UMT) | Consumer Information Disclosure ...
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