MATH 112 Guided Workbook
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1 MATH 112 Guided Workbook Department of Mathematics The University of Arizona Academic Year Table of Contents Table of Contents... 1 Syllabus Highlights... 3 Quick Reference Guide... 4 Strategies for Checking Answers... 5 Quadratic Formula Program for Graphing Calculators... 6 Quadratic Formula - TI Quadratic Formula - TI 83, TI 83 Plus, and TI 84 Plus... 7 Quadratic Formula - TI 85, TI Quadratic Formula Casio models... 9 CHAPTER 1 Equations, Inequalities, and Applications Section 1.1 Linear Equations Section 1.2 Applications of Linear Equations Section 1.4 Quadratic Equations Section 1.5 Applications of Quadratic Equations CHAPTER 2 The Rectangular Coordinate System, Lines, and Circles Section 2.3 Lines Section 2.4 Parallel and Perpendicular Lines CHAPTER 3 Functions Section 3.1 Relations and Functions Section 3.2 Properties of a Function s Graph Section 3.3 Graphs of Basic Functions; Piecewise Functions Section 3.4 Transformations of Functions Section 3.5 The Algebra of Functions; Composite Functions Section 3.6 One-to-One Functions; Inverse Functions Page 1
2 CHAPTER 4 Polynomial and Rational Functions Section 4.1 Quadratic Functions Section 4.2 Applications and Modeling of Quadratic Functions Section 4.3 The Graphs of Polynomial Functions Section 4.4 Synthetic Division; The Remainder and Factor Theorems Section 4.6 Rational Functions and Their Graphs CHAPTER 5 Exponential and Logarithmic Functions and Equations Section 5.1 Exponential Functions Section 5.2 The Natural Exponential Function Section 5.3 Logarithmic Functions Section 5.4 Properties of Logarithms Section 5.5 Exponential and Logarithmic Equations Section 5.6 Applications of Exponential and Logarithmic Functions Answers to End-of-Section Self-Assessments Page 2
3 Syllabus Highlights Welcome to Math 112! The following highlights some of the most important parts of the full syllabus. Students are still expected to know the contents of the full syllabus, which is posted in D2L. Required Materials MyMathLab access Math 112 Guided Workbook Graphing Calculator In-Person Class Meetings An important and mandatory part of the course, the in-person class meetings allow students time to interact with their instructor and classmates. Written assignments will be collected at class and constitute a significant portion of the course grade. Online Work The book, homework, and online quizzes are all hosted on (MML). Enrollment in the mymathlab.com course must be completed by the end of the first day of classes. Failure to enroll by the third day of classes will result in administrative drop. Exams There will be two midterm exams and a cumulative final exam. Course Grade Break Down Homework: 100 points MML Tests: 100 points (25 points each) Midterms: 400 points (200 points each) Final Exam 200 points Getting Help Office hours and appointments by Tutoring at ThinkTank Actions That May Result in an Administrative Drop Failing to sign up for MML Failing to come to class the first day Missing more than 3 classes Missing more than 5 assignments Page 3
4 Quick Reference Guide Math Department Information Math Dept Home Math Dept Tutoring Math 112 Homepage Math Common Final Exam Schedule University Information U of A Home Final Exam schedule Important Dates and Deadlines U of A Computing Homepage 24/7 Computing Support UAccess D2L Important University Policies Code of Academic Integrity Student Code of Conduct Manual/5-308-Student Code of Conduct.pdf Services for Students University Tutoring Services Disability Resource Center Campus Health Page 4
5 Strategies for Checking Answers One of the components of the written work in the course involves checking your answers. There are many ways to check your answer to a problem. These are some strategies you can try: 1. Use the answer you found and substitute it back into the original equation. When you are asked to solve an equation, this is the simplest and most straight-forward way to check your results. 2. When you are solving a word problem, check to see whether your solution yields the desired outcome. For example, if you are solving for the dimensions of a rectangle that give a certain area, use the length and width you found in your solution to calculate the area, and see if you get what you expect. 3. Solve the problem using a different technique or algorithm. For example, if you solved a quadratic equation by factoring, you could check it by using the quadratic formula. 4. Use a different approach to solve the problem. For example, if you solved a problem strictly algebraically, you can try graphing on your calculator to check your solution. (This can work the other way around as well!) 5. Check to see whether your answer makes sense. For example, if you are solving a problem to find the speed of a car driving on the highway, 350 mph is not a reasonable solution. 6. To take the previous strategy one step farther, you can refine what kind of answer is reasonable. For example, if the problem states that a person is given one 100 mg dosage of a drug, and you need to calculate the amount of the drug left in the person s system after a certain amount of time, then your answer must be greater than or equal to 0 mg, and less than or equal to 100 mg. So if you get an answer of 120 mg or -5 mg, you know you ve done something incorrectly. 7. Build a concrete example of the more abstract question. For example, if you are asked how the graph of y = 2f(x) is transformed from the graph of y = f(x), you can pick a specific function, say y = x, and take a look at the graph of y = x compared to the graph of y = 2 x. Note: Sometimes students try to check by re-doing the problem in the same way they approached it the first time. If you made a mistake the first time, it is very likely to make the same mistake the second time. This is not recommended as a way to check your work (though it may help in a pinch on an exam). Page 5
6 Quadratic Formula Program for Graphing Calculators Quadratic Formula - TI 82 Introduction This program solves equations of the form Ax 2 + Bx + C = 0 by using the quadratic formula. The Program :Prompt A,B,C {Prompt is in PRGM under I/O} :(B 2-4*A*C) D {The arrow is STO} :If D<0 {If is in PRGM under CTL} {< is in TEST } :Then {Then is in PRGM under CTL} :Disp "NO REAL SOLUTIONS" {Disp is in PRGM under I/O} {Words within "" are :Goto 1 {Goto is in PRGM under CTL} :Else {Else is in PRGM under CTL} :((-B+ (D))/(2A)) E {The is square root} {The - is the negative sign} :((-B- (D))/(2A)) F {The second - is the subtraction sign} :Disp "SOLUTIONS",E,F {Disp is in PRGM under I/O} {Words within "" are :Lbl 1 {Lbl is in PRGM under CTL} Running the program You will be asked to enter values for A, B, and C according to the quadratic formula. To test your program, try the following: A=2, B=3, C=4. Your answer should be NO REAL SOLUTIONS. A=5, B=4, C=-2. Your answer should be , Page 6
7 Quadratic Formula - TI 83, TI 83 Plus, and TI 84 Plus Introduction This program solves equations of the form Ax 2 + Bx + C = 0 by using the quadratic formula. The Program :Prompt A,B,C {Prompt is in PRGM under I/O} :(B 2-4*A*C) D {The arrow is STO} :If D<0 {If is in PRGM under CTL} {< is in TEST } :Then {Then is in PRGM under CTL} :Disp "NO REAL SOLUTIONS" {Disp is in PRGM under I/O} {Words within "" are :Goto 1 {Goto is in PRGM under CTL} :Else {Else is in PRGM under CTL} :((-B+ (D))/(2A)) E {The is square root} {The - is the negative sign} :((-B- (D))/(2A)) F {The second - is the subtraction sign} :Disp "SOLUTIONS",E,F {Disp is in PRGM under I/O} {Words within "" are :Lbl 1 {Lbl is in PRGM under CTL} Running the program You will be asked to enter values for A, B, and C according to the quadratic formula. To test your program, try the following: A=2, B=3, C=4. Your answer should be NO REAL SOLUTIONS. A=5, B=4, C=-2. Your answer should be , Page 7
8 Quadratic Formula - TI 85, TI 86 Introduction This program solves equations of the form Ax 2 + Bx + C = 0 by using the quadratic formula. The Program :Prompt A,B,C {Prompt is in PRGM under I/O} :(B 2-4*A*C) D {The arrow is STO} :If D<0 {If is in PRGM under CTL} {< is in TEST} :Then {Then is in PRGM under CTL} :Disp "NO REAL SOLUTIONS" {Disp is in PRGM under I/O} {Words within "" are :Goto P {Goto is in PRGM under CTL} :Else {Else is in PRGM under CTL} :((-B+ (D))/(2A)) E {The is square root} {The - is the negative sign} :((-B- (D))/(2A)) F {The second - is the subtraction sign} :Disp "SOLUTIONS",E,F {Disp is in PRGM under I/O} {Words within "" are :Lbl P {Lbl is in PRGM under CTL} Running the program You will be asked to enter values for A, B, and C according to the quadratic formula. To test your program, try the following: A=2, B=3, C=4. Your answer should be NO REAL SOLUTIONS. A=5, B=4, C=-2. Your answer should be , Page 8
9 Quadratic Formula Casio models Introduction This program solves equations of the form Ax 2 + Bx + C = 0 by using the quadratic formula. The Program 'QUADRATIC' {This will be the name of the program} "A"? A {" is in ALPHA} {? is in PRGM} { is on the, button} "B"? B "C"? C (B^2-4 A C) D { is the times sign} D<0 Goto 1 {, Goto are in PRGM under JMP} {< is in PRGM under REL} {0 is a zero} ((-B+ D) (2A)) E {The is the square root symbol} {The - is the negative sign} ((-B- D) (2A)) F {The second - is a subtraction sign} "SOLUTIONS" E { is in PRGM, do not hit EXE} F Goto 2 Lbl 1 {Lbl is in PRGM under JMP} "NO REAL SOLUTIONS" Lbl 2 Running the program You will be asked to enter values for A, B, and C according to the quadratic formula. To test your program, try the following: A=2, B=3, C=4. Your answer should be NO REAL SOLUTIONS. A=5, B=4, C=-2. Your answer should be , Page 9
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