# Final Exam Review Part 2 #4

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1 Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + = 8. Solve for, where is a real number. 9 1 = 3. Solve for, where is a real number. = Solve for u, where u is a real number. 3u + 7 = u 3 ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 1 / 19

2 5. Solve for v, where v is a real number. v =. Solve for v, where v is a real number. v = v 8v Solve for v, where v is a real number. v 1 = 8. Solve for u, where u is a real number. 3u = 8 9. Solve 50 = 0, where is a real number. Simplif our answer as much as possible. ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. / 19

3 10. Solve = 0 where is a real number. Write our answer in simplified radical form Solve z + = 5 where z is a real number. Simplif our answer as much as possible. 1. Solve = 10 where is a real number. Simplif our answer as much as possible. 13. Write in terms of i. Simplif our answer as much as possible Simplif the epressions below as much as possible. Leave no negative numbers under radicals and no radicals in denominators = = ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 3 / 19

4 15. Subtract. 3 3i 5 i Write our answer as a comple number in standard form. 1. Multipl. + i + 5i Write our answer as a comple number in standard form. 17. Divide. 3 + i 5i Write our answer as a comple number in standard form. 18. Simplif the comple number i 51 as much as possible. 19. Solve for u, where u is a real number. u 5 = 9 8u 0. Solve v = 5, where v is a real number. Simplif our answer as much as possible. 1. Solve u 3 = 0, where u is a real number. Simplif our answer as much as possible. ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. / 19

5 . Fill in the blank to make the epression a perfect square Solve the quadratic equation b completing the square = 0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas. Form: + = = Solution: =. Use the quadratic formula to solve for. + 7 = 0 5. Use the quadratic formula to solve for. 5 3 = 3 Round our answer to the nearest hundredth.. Find all comple solutions of = 0. ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 5 / 19

6 7. Compute the value of the discriminant and give the number of real solutions of the quadratic equation = 0 Discriminant: Number of real solutions: 8. A model rocket is launched with an initial upward velocit of 01 ft/ s. The rocket's height h (in feet) after t seconds is given b the following. h = 01t 1t Find all values of t for which the rocket's height is 93 feet. Round our answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.) h ground 9. Write the quadratic equation whose roots are 1 and 5, and whose leading coefficient is. ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. / 19

7 30. Solve. 13 = 3 If there is more than one solution, separate them with commas. 31. Find all real number solutions. 3 1 = 0 3. The graph of a function is given below. Give all -intercepts and -intercepts shown If there is more than one answer, separate them with commas. -intercept(s): -intercept(s): ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 7 / 19

8 33. Graph the parabola. = Graph the function g = ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 8 / 19

9 35. Graph the parabola. = Graph the parabola. = ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 9 / 19

10 37. Find the -intercept(s) and the coordinates of the verte for the parabola = 1. If there is more than one -intercept, separate them with commas. 38. Find the -intercept(s) and the coordinates of the verte for the parabola = If there is more than one -intercept, separate them with commas. 39. Use the graph of the parabola to fill in the table below (a) Does the parabola open upward or downward? { upward, downward } (b) Find the -intercept(s). -intercept(s): (c) Find the equation of the ais of smmetr. equation of ais of smmetr: (d) Find the coordinates of the verte. verte:, ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 10 / 19

11 0. Answer the questions below about the quadratic function. f = Does the function have a minimum or maimum value? What is the function's minimum or maimum value? Where does the minimum or maimum value occur? = 1. A medical equipment industr manufactures X-ra machines. The unit cost C (the cost in dollars to make each X-ra machine) depends on the number of machines made. If machines are made, then the unit cost is given b the function C = ,13. What is the minimum unit cost? Do not round our answer. ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 11 / 19

12 . Look at the graphs and their equations below. Then fill in the information about the leading coefficients A, B, C, and D = A = B = C = D A B C D (a) For each coefficient, choose whether it is positive or negative - Positive - Negative - Positive - Negative - Positive - Negative - Positive - Negative (b) Choose the coefficient closest to 0 (c) Choose the coefficient with the greatest value ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 1 / 19

13 3. Graph the solution to the following inequalit on the number line Graph the solution to the following inequalit on the number line. + > Solve the following inequalit. + > 0 Write our answer using interval notation.. Solve the following inequalit < Write our answer as an interval or union of intervals. ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 13 / 19

14 Final Eam Review Part # Answers for class Intermediate Algebra / MAT 135 Fall 01 Master 1. = 58. = 3. = 9,. u = 5. v = 1. v =, 7. v = 1 8. u = 9. = + 5, = z = 1. = i = = 50 ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 1 / 19

15 i 1. 3i i 18. i 19. u = 0. v = 5, 5 1. u = +, Form: + = 8 = 7 Solution: + = 8 7, , = 1.13, = 3 7 +, i 3 7 i 7. Discriminant = 7 Number of real solutions = 0 8. t = 0.8 seconds or t = 1.08 seconds ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 15 / 19

16 = =,, 3, = intercept(s): 1 -intercept(s): 1, ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 1 / 19

17 intercept(s): 3, 7 verte:, intercept(s): 1, 7 verte:, 9 ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 17 / 19

18 39. (a) Does the parabola open upward or downward? upward (b) Find the -intercept(s). -intercept(s):, (c) Find the equation of the ais of smmetr. equation of ais of smmetr: (d) Find the coordinates of the verte. verte:, = 0. Does the function have a minimum or maimum value? minimum What is the function's minimum or maimum value? Where does the minimum or maimum value occur? = 1. Unit cost: \$18,38. A B C D (a) For each coefficient, choose whether it is positive or negative - Positive - Negative - Positive - Negative - Positive - Negative - Positive - Negative (b) Choose the coefficient closest to 0 (c) Choose the coefficient with the greatest value ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 18 / 19

19 ,. 5, 7 1 ALEKS Final Eam Review Part # - 05/5/01 09:07 AM EDT - Copright 01 UC Regents and ALEKS Corporation. P. 19 / 19

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