Intermediate Algebra MTH 95

Transcription

1 Intermediate Algebra MTH 95 Self-Directed Course Materials (Do not purchase these materials if you are registered in a classroom-based Lecture class) Includes the Homework Assignments and Check Lists for the Self-Directed MTH 95 Course

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3 MTH 95 Intermediate Algebra Self-Directed Course Module 1 Checklist A. Learn the Material Use the combination of the textbook homework assignments and the computer homework assignments that works best for you. Either way, write up your notes and homework and keep them in a notebook. Section 3.1 Section 3. Section 3.3 Section 3.4 Section 3.5 Section 4.1 Section 4.3 Section 5.1 Section 5. Chapter 3 Integrated Review Chapter 4 Review Chapter 3 Review Chapter 5 Review B. Show you have learned the Material Do the Section Quizzes on the computer. Do all of the quizzes that begin with M1. Then do the comprehensive Module Quiz. You should get at least 80% on each section quiz, and 85% on the Module Quiz. M1 Sections 3.1, 3. Quiz M1 Sections 3.5 Quiz M1 Sections 5.1, 5. Quiz M1 Sections 3.3, 3.4 Quiz M1 Sections 4.1, 4.3 Quiz Module 1 Quiz Demonstrate you can apply what you have learned by doing the Module 1 Activity. It is included in this module packet after the Module 1 Homework Assignments Page. (Modules 1,, and 4 have activities.) Module 1 Activity C. Request Your Ticket, by ing your Instructor Take your ticket to your Testing Facility, along with your photo ID, calculator and pencil, and take your test. Then begin working on Module. SP1

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5 MTH 95 Calculator Review You are expected to know how to use a graphing calculator in MTH 95. Do the problems below on your calculator. If you find you need more instruction, there may be a free calculator workshop offered the first week of class that you could attend. Also we have videos to help you get started on TI 8, 83 and 86 calculators. The videos cover basics, graphing and advanced features on the calculator. CALCULATOR REVIEW Do the following problems on your calculator. Round to decimal places if needed. 1. 5( 6 + 3). 4 5 ( 7 ) π 3 + ( 7. 3) Graph each of the following (6 9) on your calculator. 6. y = x 3 7. y = x 8. y = x y = x + 6 x 4 For 9, use either Trace and Zoom or CALC and Value to find the value of y when x =. What is the value of x when y = 1.5? Answers 1) -47 ) 0 3) ) 365 5) ) 7) 8) 9) 1,.81 SP1

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7 Module 1 Book Homework Assignments (You may do these OR the online homework OR a combination of both.) Homework Page Section Problems Vocabulary and Readiness Check: None Exercise Set: 3, 5, 7, 8, 11, 13, 14, 15, 17, 19, 1, 5, 33, 35, 39, 69, 71, 73, 75, 77, 78, 79, 80, 81, 83, 89, 90, 91, 9, Vocabulary and Readiness Check: 1-6 Exercise Set: 1, 3, 5, 6, 11, 13, 17, 19, 1, 3, 5, 7, 9, 35, 37, 39, 55, 57, 63, 65, 69, 73, 75, 77, 95, 99, 117, Vocabulary and Readiness Check: 1-6 Exercise Set: 3, 7, 9-1, 13, 17, 7-30, 31, 35, 45, 47, 49, 51, 56, 73, 75, Vocabulary and Readiness Check: 1-8 Exercise Set: 1, 5, 9, 13, 17, 19-, 3, 5, 7, 9, 31, 33, 35, 37-40, 41, 45, 47, 49, 53, 59, 67, 69, 71, 73, 75, 80, 81, Vocabulary and Readiness Check: None Exercise Set: 7, 9, 11, 13, 15, 17, 19, 3, 7, 9, 31, 33, 35-40, 41, 43, 45, 49, 51, 53, 55, 59, 61, 63, 71, 7, 76, 78, Vocabulary and Readiness Check: 1-4 Exercise Set: 1, 3, 9, 11, 13, 15, 17, 19, 3, 5, 9, 31, 33, 37, 41, 43, 47, 49, 77, 83, Vocabulary and Readiness Check: None Exercise Set: 1, 5, 7, 11, 15, 17, 5, 9, 31, Vocabulary and Readiness Check: None Exercise Set: 1,, 3, 5, 9, 13, 15, 17, 3, 7, 33, 37, 43, 47, 51, 55, 59, 63, 67, 75, 77, 79, 83, 87, 135, Vocabulary and Readiness Check: 1, 3, 9 Exercise Set: 1, 3, 7, 9, 13, 17, 19, 1, 3, 5, 33, 35, 37, 39, 45, 47, 55, 89, 93 TEST PREP Chapter 3 Integrated Review (page 175):, 3, 5, 7, 8, 10, 1, 13, 14, 15, 19, 0, 3, 4 Chapter 3 Review (page 194): 1, 3, 5, 11, 13, 19, 1, 3, 5, 9, 41, 43, 50, 53, 57, 61, 65, 73, 78, 8, 88, 9 Chapter 4 Review (page 49): 1 6 all, 47, 49, 50 Chapter 5 Review (page 39): 3, 5, 9, 13, 3, 5, 9, 31, 33, 35 Study all homework problems, notes and textbook examples. Practice problems you have already done. Practice without looking at the solution first. F1

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9 Math 95 Activity Mod 1 Name Base Campus: Turn this sheet in with your activity at any Learning Center. Grading Completeness: all questions are answered; supporting work is shown Accuracy: answers are correct; explanations and graphs are accurate Details: complete sentences are used in explanations; units are included on answers; graphs are titled; scale on graph is labeled and reasonable; Neatness: work is legible and organized; Thoughtful: results are interpreted, opinions are explained and justified; answers are reasonable Bonus Points for exceptional work: Total score on Activity: / 5 SP1

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11 Job Activity Your Name: MTH 95 Self-Directed Module 1 Activity Base Campus: This activity is an opportunity to apply the concepts from this module to a real-life situation. Your grade on the activity will be based on accuracy, clarity of explanation, organization, and neatness of your final write-up. Use complete sentences and units in your answers to all questions that are not fill-in-the-blank. Skills Objectives: Writing Linear Equations, Solving Systems of Linear Equations You have received two job offers after interviewing at two different companies. The two jobs you ve been offered are essentially identical, with the exception of pay. Both jobs will pay you a base salary to perform your work. They both also pay a bonus for every specific task you complete. Company A s Offer Guaranteed base salary of $800 per month. Additional earnings of $30 per task Company B s offer Guaranteed base salary of $3000 per month. Additional earnings of $8 per task 1. Write as equation that describes your total monthly salary for each offer. Define your variable: Let t = Let S = Salary equation for the Company A: Salary equation for Company B: F1

12 . Graph both salary equations below. Use different colors to graph each equation and label the equations as A and B. Label the axes with the description of the variables, not just their letters. Think carefully and choose an appropriate scale before you begin to graph. Your graph should show the salary for completing up to 150 tasks. 3. Analyze the Graph. Before you decide which job to take, you re interested in knowing if it is possible to make the same amount of money at both jobs by completing the same number of tasks. How can use a graph to determine whether it is possible? Is it possible? Explain how your graph supports your answer.

13 4. Solve the System of Equations. Your two salary equations form a System of Equations. Use the Substitution Method or Elimination Method to solve the system. Show your work. 5. Explain the significance of your solution to the system of equations (from #4). What does it represent? Include the appropriate units in your explanation. F1

14 Analysis: For questions 6 and 7, you may want to use your graph to help you answer the questions. If you do, be sure to explain how your graph supports your answers. 6. With which company does your monthly income have the greatest potential? Explain why. 7. Describe the circumstances under which you d make more money working for Company A than Company B. Justify your answer and be specific as to the number of tasks.

15 MTH 95 Intermediate Algebra Self-Directed Course Module Checklist A. Learn the Material Use the combination of the textbook homework assignments and the computer homework assignments that works best for you. Either way, write up your notes and homework and keep them in a notebook. Section 7.1 Section 7. Section 7.3 Section 5.3 Section 5.4 Section 5.5 Section 5.6 Section 5.7 Chapter 7 Review Chapter 7 Test (Book Problems) Chapter 5 Vocabulary Chapter 5 Integrated Review Chapter 5 Review B. Show you have learned the Material Do the Section Quizzes on the computer. Do all of the quizzes that begin with M. Then do the comprehensive Module Quiz. You should get at least 80% on each section quiz, and 85% on the Module Quiz. M Sections 7.1, 7. Quiz M Sections 5.3 Quiz M Sections 5.6 Quiz Module Quiz M Sections 7.3 Quiz M Sections 5.4, 5.5 Quiz M Sections 5.7 Quiz Demonstrate you can apply what you have learned by doing the Module Activity. It is included in this module packet after the Module Homework Assignments Page. (Modules 1 and only have activities.) Module Activity C. Request Your Ticket, by ing your Instructor Take your ticket to your Testing Facility, along with your photo ID, calculator and pencil, and take your test. Then begin working on Module 3. F1

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17 Module Book Homework Assignments (You may do these OR the online homework OR a combination of both.) Homework Page Section Problems Vocabulary and Readiness Check: 1-8 Exercise Set: 1, 3, 7, 11, 15, 1, 5, 7, 31, 35, 39, 43, 45, 47, 53, 59, 63, 69, 75, 77, 81, 85, 87, 89, 95, 99, 107, Vocabulary and Readiness Check: 1-6 Exercise Set: 1, 5, 9, 11, 15, 19, 3, 7, 9, 31, 33, 37, 41, 45, 47, 49, 51, 53, 59, 73, 77, 81, 85, 87, 101, 105, 109, 111, Vocabulary and Readiness Check: None Exercise Set: 1, 5, 9, 13, 19, 5, 9, 31, 33, 37, 43, 47, 53, 57, 61, 65, 67, 69, 73, 101, 105, 115, 119, Vocabulary and Readiness Check: 1 8 Exercise Set: 1, 5, 9, 11, 13, 15, 19, 1, 5, 9, 31, 35, 37, 45, 47, 55, 59, 63, 67, 77, 81, 83, 85, 89-9, 95, 109, 111, 113, Vocabulary and Readiness Check: 1 5 Exercise Set: 1, 5, 7, 9, 11, 13, 1, 3, 7, 9, 31, 33, 47, 51, 53, 57, 61, 65, 69, 73, 83, 87, 89, 91, 93, 95, Vocabulary and Readiness Check: 1-7 Exercise Set: 1, 5, 9, 11, 13, 17, 19, 1, 7, 9, 31, 35, 39, 43, 49, 51, 53, 55, 59, 67, 71, 83, 89, 90, Set 1 Vocabulary and Readiness Check: None Exercise Set: 15, 17, 19, 1, 3, 5, 7, 9, 31, 33, 49, 51, 53, 55, Set 69, 73, 87, 99 Vocabulary and Readiness Check: None Exercise Set: 15, 17, 19, 1, 3, 5, 7, 9, 31, 33, 49, 51, 53, 55, 69, 73, 87, Vocabulary and Readiness Check: 1, 3 Exercise Set: 1, 3, 7, 9, 13, 15, 17, 19, 39, 41, 43, 45, 67, 69, 71, 75, 77, 79 TEST PREP: Chapter 7 Review (page 468): 1, 3, 5, 9, 13, 17, 19, 5, 9, 33, 35, 38, 40, 45, 47, 51, 55, 57, 61, 65, 67, 71, 145, 147, Chapter 7 Test (page 470 ): 1, 3, 5, 7, 9, 1 Chapter 5 Vocabulary Check (page 36): 1, 3, 4, 5, 7, 8, 10, 11, 1 Chapter 5 Integrated Review (p. 310):1, 5, 13, 15, 17, 1, 41 Chapter 5 Review (page 39): 41, 43, 45, 47, 55, 57, 61, 64, 67, 71, 79, 81, 83, 85, 87, 91, 93, 95, 97, 99, 105, 107, 109 Study all homework problems, notes and textbook examples. Practice problems you have already done. Practice without looking at the solution first. F1

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19 Math 95 Activity Mod Name Base Campus: Turn this sheet in with your activity at any Learning Center. Grading Completeness: all questions are answered; supporting work is shown Accuracy: answers are correct; explanations and graphs are accurate Details: complete sentences are used in explanations; units are included on answers; graphs are titled; scale on graph is labeled and reasonable; Neatness: work is legible and organized; Thoughtful: results are interpreted, opinions are explained and justified; answers are reasonable Bonus Points for exceptional work: Total score on Activity: / 5 SP1

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21 Module Your Name: Factoring Activity This activity is an opportunity to review all the factoring methods you have learned. Your grade on the activity will be based on accuracy, clarity of explanation, organization, and neatness of your final write-up. Use complete sentences and units in your answers to all questions that are not fill-in-theblank. Skills Objectives: Identifying when to use each polynomial factoring strategy. In Math 95 we have covered 5 main factoring strategies. The point of this activity is to help you identify when to use each of these strategies. 1. Factoring trinomials with leading coefficient of 1. Section 5.6 Three terms. Coefficient on x is a 1. Example: Factor x + 7x + 1 x + 7x + 1= ( x + 3)( x + 4). ( x 3)( x 4) x 4x 3x 1 x 7x = = + +. Factoring trinomials with a non-one leading coefficient. Section 5.6 Three terms. Coefficient on x is not a 1. Example: Factor x + 5x + 3. (x+3)(x+1)= x +x+3x+3=x +5x+3 SP1

22 3. Factor by grouping. Sect. 5.5 Four Terms. 3 Example: Factor x 3x + 5x x 3x + 5x 15 = x ( x 3) + 5( x 3). = ( x 3)( x + 5). 3 ( x 3)( x + 5) = x + 5x 3x 15 = 3 x x x Difference of squares. Section 5.7 Two terms. Always subtraction. Any polynomial of the form a b can be factored as ( a+ b)( a b). Example: Factor 4x 9y. In this example, So a = 4x so a= x and 4x 9 y = (x+ 3 y)(x 3 y). b = 9y so b= 3 y. (x + 3 y)(x 3 y) = 4x 6xy + 6xy 9y = 4x 9y 5. Removing common factors. Section 5.5 Use before trying other factoring techniques Often polynomials with more than one variable (eg. x and y s). 3 Example: Factor x 3x 4. x 3 Every term has a common factor of x. x 3x 4 x= xx ( 3x 4). The resulting quadratic factor, x 3x 4 can be factored in the usual way you factor trinomials. 3 x 3x 4 x= xx ( 3x 4) = xx ( 4)( x+ 1).

23 Practice Problems: Directions: First write which type of factoring problem it is from the above numbered examples 1-5. Some problems may require the use of more than one rule. After identifying the type of factoring, then go through and factor each problem. Factor: 1. x + 4x + 3 Rule Number(s). Rule Number(s) 3. Rule Number(s) x 8x x Rule Number(s) 5. (Hint: apply same rule twice!) Rule Number(s) SP1

24 6. Rule Number(s) 7. Rule Number(s) 8. x 9x + 14 Rule Number(s) 9. Rule Number(s) 10. x 3 7x 3x+ 1 Rule Number(s)

25 Short Answer Questions: Answer using complete sentences and correct spelling. 1. How can you check to see that you factored an expression correctly?. Explain why xy ( 6) + ( y 6) is not completely factored. 3. A student is trying to factor. They incorrectly get the following factorization:. a. Give the correct factorization of : b. Explain the mistake that the student made. 4. There is a mistake in the following attempted factorization: a. Give the correct factorization of : b. Explain the mistake that was made. 5. Which type of factoring do you tend to forget to use the most? Why? SP1

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27 MTH 95 Intermediate Algebra Self-Directed Course Module 3 Checklist A. Learn the Material Use the combination of the textbook homework assignments and the computer homework assignments that works best for you. Either way, write up your notes and homework and keep them in a notebook. Section 5.8 Section 6.1 Section 6. Section 6.5 Section 6.7 Section 7.7 Chapter 5 Review Chapter 6 Review Chapter 7 Review Chapter 6 Integrated Review Chapter 6 Optional Review B. Show you have learned the Material Do the Section Quizzes on the computer. Do all of the quizzes that begin with M3. Then do the comprehensive Module Quiz. You should get at least 80% on each section quiz, and 85% on the Module Quiz. M3 Sections 5.8 Quiz M3 Sections 6.5, 6.7 Quiz Module 3 Quiz M3 Sections 6.1, 6. Quiz M3 Sections 7.7 Quiz Module 3 does NOT have an activity. C. Request Your Ticket, by ing your Instructor Take your ticket to your Testing Facility, along with your photo ID, calculator and pencil, and take your test. Then begin working on Module 4. SP1

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29 Module 3 Book Homework Assignments (You may do these OR the online homework OR a combination of both.) Homework Page Section Problems Vocabulary and Readiness Check:1, 5 Exercise Set: 1, 3, 5, 7, 9, 11, 15, 19, 1, 5, 7, 31, 35, 39, 41, 47, 49, 53, 61, 71, 75, 79, Vocabulary and Readiness Check: 5, 6 Exercise Set: 3, 7, 9, 13, 19, 1, 35, 41, 43, 47, 55, Vocabulary and Readiness Check: 1-4 Exercise Set: 9, 31, 41, 45, 49, 55, Vocabulary and Readiness Check: 8-10 Exercise Set: 1, 5, 11, 13, 15, 19, 9, 31, 35, 41, 43, Vocabulary and Readiness Check: 5, 6, 8 Exercise Set: 7, 9, 11, 17, 1, 3, 5, 9, 39, Vocabulary and Readiness Check: 1-6 Exercise Set: 1, 3, 5, 9, 11, 13, 15, 17, 19, 1, 7, 9, 31, 33, 35, 37, 39, 49, 51, 53, 57, 61, 63, 67, 107, 109, Chapter 5 Review (page 331): 15, 17, 19, 131, 133, 135 Chapter 6 Integrated Review (p. 379):1, 3, 5, 7, 11, 15, 19, 1, 5 Optional review (pg. 380): 9-33 odd TEST PREP Chapter 6 Review (pg. 403): 3, 5, 9, 11, 15, 17, 19, 9, 31, 33, 63, 65, 67, 83, 84, 106 Chapter 7 Review (pg. 470): 18, 19, 130, 13, 135, 137 Study all homework problems, notes and textbook examples. Practice problems you have already done. Practice without looking at the solution first. SP1

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31 MTH 95 Intermediate Algebra Self-Directed Course Module 4 Checklist A. Learn the Material Use the combination of the textbook homework assignments and the computer homework assignments that works best for you. Either way, write up your notes and homework and keep them in a notebook. Section 8.1 Section 8. Section 8.5 Section 8.6 Chapter 8 Vocab Check Chapter 8 Review B. Show you have learned the Material Do the Section Quizzes on the computer. Do all of the quizzes that begin with M4. Then do the comprehensive Module Quiz. You should get at least 80% on each section quiz, and 85% on the Module Quiz. M4 Sections 8.1, 8. Quiz M4 Sections 8.5, 8.6 Quiz Module 4 does not have an activity. C. Mod 4 does NOT have its own test. The module 4 material will have extra emphasis on the Final Exam. What you should do now is the Final Exam Review in this packet. Then Request Your Final Exam Ticket, by ing your Instructor Take your ticket to your Testing Facility, along with your photo ID, calculator and pencil, and take your final exam.

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33 Module 4 Book Homework Assignments (You may do these OR the online homework OR a combination of both.) Homework Page Section Problems Vocabulary and Readiness Check: 1-6 Exercise Set: 5, 7, 11, 17, 19, 1, 5, 7, 31, 35, 37, 39, 45, 49, 65, 75, 77, 79, 81, 97, Vocabulary and Readiness Check: 1, 3, 4, 5, 6 Exercise Set: 3, 5, 9, 15, 1, 5, 7, 9, 33, 43, 45, 47, 51, 55, 63, Vocabulary and Readiness Check: 1-7, 9, 11, 13 Exercise Set: 1, 7, 13, 17, 19, 1, 3, 5, 7, 9, 31, 35, 39, 47, 55, 57, 61, 67, Vocabulary and Readiness Check: 1, Exercise Set: 1, 3, 5, 7, 9, 11, 19-, 3, 7, 31, 33, 35 Chapter 8 Vocabulary Check (pg 58): 1,, 3, 5, 6, 7, 8, 9, 10 TEST PREP Chapter 8 Review (pg 531): 1, 3, 5, 7, 9, 11, 1, 15, 17, 19, 0, 41, 43, 45, 47, 49, 54, 59, 61 Study all homework problems, notes and textbook examples. Practice problems you have already done. Practice without looking at the solution first.

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35 Review for Final Exam MTH (Sect 6.1/6.) Perform the indicated operation. Simplify. 3 4x y xy a xy 0x b. x x x x+ 3 x 4 4x 8 3x 6 c. x 3x+ x 1 d. e. x x x 3 3 x 16 8 x+ x + x + 4x x x x 3 x 4x+ 4 x 5x+ 6 f. +. (Sect 6.5) Solve for x. a. x 5 + = x+ 3 x x b. x 35 7 = + x 7 x 9x+ 14 x 3. (Sect 3.4/3.5) a. Find the slope of the line 3x+ 4y =. b. Write the equation of a line that passes through the point (3, ) that is parallel to the line in part a. c. What is the slope of a line perpendicular to the line in part a? 4. (Sect 4.3) A pizzeria baked five pepperoni pizzas and three vegetarian pizzas and charged $7. Another group ordered four pepperoni pizzas and six vegetarian pizzas and was charged $ What is the price of a pepperoni pizza?

36 5. (Sect 4.1) Solve by any algebraic method. a. x 5y = 9 3x y = 7 b. 6x 3y = 1 4x y = 7 6. (Sect 7.7) Perform the following operations. Leave answer in a + bi form. 3+ 6i 4 5i a. ( ) ( ) b. ( 3+ 6i) c. ( 3+ 5i)( 4+ i) 7. (Sect 5.3) Simplify the following. x 1 x + 3 a. ( ) ( ) b. ( x 3x+ 1) + ( 5x x+ ) 8. (Sect 5.4) Multiply and simplify. 5x 3x+ y 3 a. ( ) b. ( 4x+ 7)( x + 3x 1) c. ( 5x y)( x+ 3y) d. ( 6x 11y)( 6x+ 11y) 9. (Sect 5.5/5.6) Factor completely, if possible. a. b. c. d. e. 3x 5x+ 4x x 10 4x 9 x 3 6x 9x 4x+ 6 SP1

37 10. (Sect 8.5/8.6) Without graphing, match the graph with the equation. a. ( ) y = x b. ( ) y = x c. y = x + 3 d. ( ) y = x e. ( ) y = x+ + 1 g x 11. (Sect 8.5) Given the equation ( ) = ( x 3) + 1. Give the coordinates of the vertex, the equation of the axis of symmetry and the x-intercepts. Sketch the graph. vertex: equation of axis of symmetry: Compare the graph of g( x ) to the graph of f ( x) x =. State the shifts used. 1. (Sect 8.6) Given the equation ( ) g x = x + 6x+ 5, find the vertex and the zeros (xintercepts) and sketch the graph. Mark the axis of symmetry on the graph. vertex: x-intercepts:

38 3 13. a. (Sect 3.) Given g( x) = x 1 evaluate g(, ) g( 1, ) g( ) of g and graph g( x ) below. g ( ) = g ( 1) = g ( ) = Domain. State the domain b. (Sect 7.1) Given h( x) = 5 x evaluate h( 4, ) h( 1, ) h( 5) of h and graph h( x ) below. h( 4) = h ( 1) = h ( 5) = Domain. State the domain 14. (Sect 5.8) Solve for x by factoring. a. b. c. x x + x= x= 4 3x 75 = (Sect 8.) Solve for x using the quadratic formula. Give the answer for all real and non-real solutions. a. b. x x 6= 0 3x + x+ 4= 0 SP1

39 16. (Sect 8.1) Solve for x by completing the square. a. x 8x 11 = 0 b. c. x + 6x 5= 0 x = 10x (Sect 6.7) The radius r of a hailstone varies directly with the time t that the hailstone is in the high clouds before falling to earth. After a hailstone has been in the high clouds for 15 seconds, the radius is 0.8 inches. What would the radius be if it were in the high clouds for 0 seconds. Find the constant of variation and answer the question. Constant, k = Answer: 18. (Sect 5.3) Explain how to determine the degree of a polynomial. 19. (Sect 5.3) What is a monomial? A binomial? A trinomial? 0. (Sect 3.)Use the graph of f(x) shown below to answer the following questions. y a) Find f (1) : b) Find any values for which f( x ) = : c) State any x-intercepts of f( x ): d) State any y-intercepts of f( x ): e) State the domain of f( x ): f) State the range of f( x ): (-3, ) (1, -) (3, -) (6, 4) x g) Is f( x ) a function? Explain. Use complete sentences. 1. (Sect 4.3) How many gallons of 1% milk and 4% milk should be mixed to obtain 5 gallons of % milk?

40 . (Sect 5.1/5./7.) Simplify, using only positive exponents in the answer. 4xy 3 a. ( 3 x y ) 0 b. ( 4 pqr ) 3 15 c. ( ) 1 5 3x 3. (Sect 5.1/5./7.) Simplify using only positive exponents. a b. ( ) 5 mn c (Sect 3.) For the function f( x) = x + 4, find f( a ). 5. (Sect 7.) Fill in the table. Radical Form Rational Exponent Form 5 n ( ) 3 8xy 6. (Sect 6.1) Explain how to find the domain of a rational function, x 1 such as f( x) = x 8. SP1

41 Answers to Review for Final 1 1a. 5 5x y 1f. ( x + )( x + 1) 1b. 5x 1 ( x ) ( x 3) 1c. 4 3( x ) 1d. x( x + 4) x + 1e. x 3 x 4 a. 3, -1 b. no solution a. 3b. y = x c A pepperoni pizza costs $ a. (, -1) 5b. no solution 6a. 1+11i 6b i 6c i 7a. x + x 4 7b. 3x 5x a. 15x + 5x y 3 8b. 8x + 6x + 17x 7 8c. 10x + 13xy 3y 8d. 36x 11y 9a. ( 3x )( x 1) 9b. 4( x + 7) 9c. 5x ( x ) 9d. ( x 3)(x + 3) 9e. (3x )(x 3) 10a. 5 10b. 1 10c. 4 10d. 10e vertex (3, 1); equation of axis of symmetry: x = 3; shifts right 3 units and up 1 1. vertex (-3, -4); x-intercepts (-5,0) and (-1,0); shifts left 3 units and down 4 13a. -9, -, 7, (, ) 13b. 3,, 0, (,5] 14a. 0, - 14b. -4, -6 14c. 5, -5 15a. ± 8 ± i 44 1± i 11 or 1± 7 15b. or a. 4 ± 7 or 4 ± ± 19 16b. 16c. 5 ± 3i k =.053; The radius will be approximately 1.07 inches The degree of the polynomial is the degree of the term of highest degree. To find the degree of a term, you add up all the values of the exponents in the term. 19. A monomial is a polynomial with just one term; a binomial has terms; a trinomial has 3 terms. 0a. - 0b. x = -3 and 5 0c. (-1, 0) and (4, 0) 0d. (0, -1) 0e. [-3, 6] 0f. [-, 4] 0g. Yes, it is a function. It passes the vertical line test. 1. Let x = gallons of 1% milk. Then the equation is: 0.01x (5 x) = 0.0(5); 1 You need 3 gallons of 1% milk and 1 gallons of 4% milk x a. 5 y b. 64 r 6 3 p c. 3 x

42 3a b. m 5 n 10 3c f(a ) = a 4a n xy 5.,,, (8 ) 5 6. You need to find out what would make the denominator equal zero and then exclude that from the domain. For the example given, the domain would be: {x x is any real number except for and -}. SP1

43 Your Next Math Course after MTH 95 The next math course you should take depends on what you need for your degree. Be sure to read the options below carefully. You will take MTH 97 if you have had no geometry or if it has been some time since you have taken geometry and if you are continuing on to take MTH 111 and MTH 11 or MTH 11, 1 and 13. MTH 97 is an enforced pre-requisite for both MTH 11 and MTH 13. You will take MTH 111 if you are pursuing a degree that requires College Algebra as the final math course you need. You will take MTH 105 if you are pursuing a degree that does not require College Algebra. You will take MTH 11 if you are pursuing a degree in Elementary Education. MTH 13, the third term of the MTH sequence, has MTH 97 or a geometry course from some other institution as a pre-requisite.