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Make sure you know the day and time of the final exam for this section of Math 110: Day: ______ Date:______ Time: ______ to _______ • All Math 110 finals will be given in your regular classroom. • Final exam schedules for all sections are posted on the bulletin board and in your course syllabus. Math 110 Final Exam: • Comprehensive – covers the whole semester • Worth 200 points (20% of course grade) • 47 questions • Test period is one hour and 50 minutes • Practice Final is worth 10 points and also has 47 questions and unlimited tries. • Your best score on the practice final will also earn up to 20 extra credit points on the final. • The practice final is due at the scheduled start time of this section’s final exam. • IMPORTANT NOTE!!! To get access to the practice final, you must have submitted all four final exam review homework assignments and have scored at least 80% on each one. Final Exam Review Materials: 1. Four review homework assignments: These are each worth 10 points, vs. the usual homework assignment of 6 points. • Unit 1 review homework (Chapters 1, 2, 3). • Unit 2 review homework (Chapters 4, 5, 8): Due today. • Unit 3 review homework (Chapter 6): NOTE: You must get at least 80% on the Unit 2 Review before you can start the Unit 3 review. Check with your teacher for due date & time. •Unit 4 review homework (Chapter 7): NOTE: You must get at least 80% on the Unit 3 Review before you can start the Unit 4 review. Check with your teacher for due date and time. Comprehensive Practice Final: Once you finish the Unit 4 Final Review homework with at least an 80% score, you will have access to the practice final, with as many attempts as you want. The practice final is worth 10 points, plus a possible bonus of up to 20 extra credit points on the final exam. Your best percentage score on the practice final will earn that percent of 10 points toward your course grade, plus that best score percent times 20 extra credit points will be added on to your final exam point score before partial credit points are added. This makes it extremely important for you to make sure you work to get at least 80% on each of the four final exam review homework assignments so that you can get access to the practice final. Math TLC Open Lab Hours: Room 203 Jarvis Hall Science Wing Regular hours through last day of classes (8:00 AM – 7:30 PM) Finals week open lab hours: Check bulletin boards in JHSW 214 and 203 Now please CLOSE YOUR LAPTOPS and turn off and put away your cell phones. Any questions on the Unit 2 Review Homework? Final Exam Review, Units 3 & 4 Units 3 & 4 Cover: Chapter 6 (Rational expressions) Chapter 7 (Radicals, rational exponents, rationalizing radical denominators) Unit 3:Chapter 6 (Rational Expressions) Don’t forget to review the application problems from section 6.6 homework and your work on the offline worksheet. (Remember those fun problems about planes and cars, and three people doing a job at different rates?) These were a common source of trouble for many students in previous semesters, so make sure you study the application problems on the Practice Test, and then review the section 6.6 homework if you need more work on those problems. IMPORTANT: Almost all problems in Chapter 6 on rational expressions require you to use one or more techniques for factoring polynomials. DON’T FORGET TO REVIEW THESE FACTORING METHODS AND KNOW HOW AND WHEN TO USE EACH ONE! Two methods that students often have trouble with are factoring by grouping and sums/differences of cubes, so make sure you review problems using these methods. Domain example: Find the domain of the expression x 2 3x 4 x 2 x 20 Solution: Set the denominator equal to zero and solve for x. (Notice that this boils down to a factoring problem.) x2 – x – 20 = 0 (x – 5)(x + 4) = 0 (x – 5) = 0 gives x = 5, and (x + 4) = 0 gives x = -4 Therefore the domain is {x | x ≠ 5 and x ≠ -4} Example Multiply the following rational expressions. a a bab 3 2 6a 2 3 a a 3 2a 2b 3 Solution: Factor each polynomial completely, then cancel all factors that appear on both the top and the bottom. NOTE: This problem uses factoring by grouping, factoring 3a out a GCF (twice!), and the ANSWER : 2 a ab b 2 sum of cubes formula. Whew! Example Add the following rational expressions. 4 x , 2 x x 6 x 5x 6 2 4 x 4 x 2 x x 6 x 5 x 6 ( x 3)( x 2) ( x 3)( x 2) 2 4( x 3) x( x 3) ( x 3)( x 2)( x 3) ( x 3)( x 2)( x 3) 4 x 12 x 2 3 x x 2 x 12 ( x 2)( x 3)( x 3) ( x 2)( x 3)( x 3) Dividing a polynomial by a monomial: Divide each term of the polynomial separately by the monomial. Example 12 a 3 36 a 15 12 a 3 36 a 15 3a 3a 3a 3a 5 4a 12 2 a Example Dividing a trinomial by a binomial: 4x 5 Divide 7x into 28x2. Multiply 4x times 7x+3. 7 x 3 28 x 23 x 15 2 Subtract 28x2 + 12x from 28x2 – 23x. 28x 12x 2 Bring down -15. Divide 7x into –35x. 35 x 15 Multiply -5 times 7x+3. Subtract –35x–15 from –35x–15. 35x 15 Nothing to bring down. So our answer is 4x – 5. HOW WOULD YOU CHECK THIS ANSWER??? Example of a complex fraction: 10 3x . 5 6x Solution: view as a division problem: 10 ÷ 5 = 10 · 6x = 4 3x 6x 3x 5 Example: Solving a rational equation: Solve 2x + 1 = 1 . 2x – 1 x 2x – 1 Solution: 1. Multiply both sides by the LCD x(2x – 1). This gives 2x(x) + 1(2x – 1) = 1(x) 2. Now simplify this equation: 2x2 + 2x – 1 = x 2x2 + x – 1 = 0 3. Solve either by factoring or by using the quadratic formula. Answers: x = -1, x = 1/2 Example (continued): NOW CHECK BOTH ANSWERS in original equation: Note that when you plug in x = 1, everything checks out OK ( you get -1/3 = -1/3) BUT when you plug in x = 1/2, you get zeroes in some denominators, so this number is NOT a solution. (it gives 1 + 1 = 1 0 ½ 0 So the final answer is just x = -1 (if you write x = -1, 1/2, you’ll get ZERO credit.) To Review Unit 4 (Ch. 7) Make sure you look over your graded Test 4 worksheet and go over the problems you missed with a teacher or TA to make sure you understand how to do them. Since we just reviewed this material for Test 4, we won’t be doing a formal review of this material in class today. REMINDER: Comprehensive Practice Final: Once you finish the Unit 3 and 4 Final Review homework assignments with at least an 80% score, you will have access to the practice final, with as many attempts as you want. The practice final is worth 10 points, plus a possible bonus of up to 20 extra credit points on the final exam. Your best percentage score on the practice final will earn that percent of 10 points toward your course grade, plus that best score percent times 20 extra credit points will be added on to your final exam point score before partial credit points are added. This makes it extremely important for you to make sure you work to get at least 80% on each of the four final exam review homework assignments so that you can get access to the practice final. Math TLC Open Lab Hours: Room 203 Jarvis Hall Science Wing Regular hours through last day of classes (8:00 AM – 7:30 PM) Finals week open lab hours: Check bulletin boards in JHSW 214 and 203

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final exam, solution set, interval notation, equation of the line, real number, indicated operations, multiple choice questions, United States, system of equations, graphing calculator

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posted: | 3/13/2011 |

language: | English |

pages: | 22 |

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