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Math Review Autumn 2013

EXPONENT LAWS:

xa+xb=xa+xb (xa)b= xab

xa*xb=xa+b xaxb=xa-b DERIVATIVE NOTATION: Single variable: ddxfx=dfdx=f'(x)= “Taking the derivative of the function f with respect to x” Multiple variables: ∂∂xfx,y=∂f∂x=fx= “Taking the partial derivative of the function f with respect to x” ∂∂yfx,y=∂f∂y=fy = “Taking the partial derivative of the function f with respect to y” DERIVATIVE RULES: Product Rule: ddxfx*gx=f'x*gx+fx*g'(x) Quotient Rule: ddxfxgx=f'x*gx-fx*g'(x)gx2 Chain Rule: ddxfgx=f'x*g'(x) USEFL DERIVATIVES: ddxxn=nxn-1 ddxlnx=1x OTHER USEFUL THINGS: MUx=∂Ux,y∂x=∂U∂x= “Marginal utility with respect to x”: How much more utility you get from obtaining one more unit of x MUy=∂Ux,y∂y=∂U∂y= “Marginal utility with respect to y”: How much more utility you get from obtaining one more unit of y Endogenous Variables: Dependent variable explained by the model Exogenous Variables: Independent variables outside of the model and affect a model without being affected by it; given parameters

Practice Problems →

DERIVATIVES

Single variable:

e.g., given fx=2x0.2+x0.4+ x-0.3 , find f'x

Exercises: for each of the following function, find f'x

(i) fx=3x

(ii) fx=6x19

(iii) fx=x2-2xx7+3

(iv) fx= 2ln(x2)

Multiple variables (partial derivatives) :

e.g., given fx,y=2x+3y+1 , find fx and fy

e.g., given fx,y=6x2y2-7xy-x , find fx and fy

Exercises: for each of the following function, find fx , fy

(i) fx,y=10xy2

(ii) fx,y=5x2-6y+1

(iii) fx,y=20x1/2y1/4

(iv) fx,y=2xlny3-5xy ln(x2) Answers (Single Variable): (i) 13x- 23 (ii) 23x- 89 (iii) x9-2x8+3x2-6x (iv) 4x

Answers (Multiple Variable): (i) fx=10y2, fy=20xy (ii) ) fx=10x2, fy=-6y (iii) fx=10x-12y14 ,…...

...Math Review for the Quantitative Reasoning Measure of the GRE® revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important to understand in order to solve problems and to reason quantitatively on the Quantitative Reasoning measure of the GRE revised General Test. The following material includes many definitions, properties, and examples, as well as a set of exercises (with answers) at the end of each review section. Note, however, that this review is not intended to be allinclusive—there may be some concepts on the test that are not explicitly presented in this review. Also, if any topics in this review seem especially unfamiliar or are covered too briefly, we encourage you to consult appropriate mathematics texts for a more detailed treatment. Copyright © 2012 by Educational Testing Service. All rights reserved. ETS, the ETS logo, LISTENING. LEARNING. LEADING. and GRE are registered trademarks of Educational Testing Service (ETS). Table of Contents ARITHMETIC .............................................................................................................................. 1 1.1 Integers.................................................................................................................................. 1 1.2 Fractions ................................................................................................................................ 3 1.3......

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...MATH 3330 INFORMATION SHEET FOR FINAL EXAM FALL 2011 FINAL EXAM will be in PKH 103 at 2:00-4:30 pm on Tues Dec 13 • See above for date, time and location of FINAL EXAM. Recall from the ﬁrst-day handout that any student not obtaining a positive score on the FINAL EXAM will not pass this class. • The material covered will be the same as that covered on the homework from the start of the semester through Dec 6 (but not §6.3) inclusive. (Homework is listed at my website: www.uta.edu/math/vancliﬀ/T/F11 .) • My remaining oﬃce hours are: 3:30-4:20 pm on Thurs Dec 8 and 3:30-5:30 pm on Mon Dec 12. • This test will be, in part, multiple choice, but you do NOT need to bring a scantron form. There will be several choices of answer per multiple-choice question and, for each, only one answer will be the correct one. You should do rough work on the test or on paper provided by me. No calculator is allowed. No notes or cards are allowed. BRING YOUR MYMAV ID CARD WITH YOU. • When I write a test, I look over the lecture notes and homework which have already been assigned, and use them to model about 85% of the test problems (and most of them are fair game). You should expect between 30 and 40 questions in total. • A good way to review is to go over the homework problems you have not already done & make sure you understand all the homework well by 48 hours prior to the test. You should also look over the past tests/midterms and understand those fully. In addition,......

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...say whether I was able to learn how to be a better teacher and what the teacher did that I could possibly use in the future. While analyzing and going through the process of this assignment it is helping realize how to become a better teacher as well. I would also like to get more comfortable and experience on using this template of the paper. Memories Of A Teacher My teacher, Mr. G, used many different instructional techniques and approaches to his lessons. Mr. G had taught me math for three years in a row, so I think that I have a good grasp on his approaches to the lessons that he would teach. He would assign many homework assignments, as well as in-class assignments, which helped me and other students understand and get practice with the lesson that we were learning. I think that with math having a lot of homework is a good thing. In my mind, the only way to learn how to do math is plenty of practice. The more you practice, the easier it will be. Mr. G would also have the students do some math problems on the chalk board or smart board to show the class and go over the corrections with the whole class so that everyone would understand the problem. Playing “racing” games also helped and added fun to the class. With the “racing” games, the students would get into groups and have to take turns doing problems on the chalk board and see who could get the correct answer first. It added fun and a little friendly competition to the class. It also helped the students want to......

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...Diana Garza 1-16-12 Reflection The ideas Stein presents on problem saving and just math in general are that everyone has a different way of saving their own math problems. For explains when you’re doing a math problem you submit all kinds of different numbers into a data or formula till something works or maybe it’s impossible to come up with a solution. For math in general he talks about how math is so big and its due in large measure to the wide variety of situations how it can sit for a long time without being unexamined. Waiting for someone comes along to find a totally unexpected use for it. Just like has work he couldn’t figure it out and someone else found a use for it and now everyone uses it for their banking account. For myself this made me think about how math isn’t always going to have a solution. To any math problem I come across have to come with a clear mind and ready to understand it carefully. If I don’t understand or having hard time taking a small break will help a lot. The guidelines for problem solving will help me a lot to take it step by step instead of trying to do it all at once. Just like the introduction said the impossible takes forever. The things that surprised me are that I didn’t realize how much math can be used in music and how someone who was trying to find something else came to the discovery that he find toe. What may people were trying to find before Feynmsn....

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...vary. This class introduces a lot of new topics, which can be challenging, and take lots of practice outside of school if you do not pay attention or do your math homework. I strongly advise you to do your math homework everyday, not for just a grade, but it also helps you when it comes time for quizzes and tests. She rarely checks homework, but when she does, she will not tell you. It is also a great review for tests and quizzes. Ms.Hull’s tests and quizzes are not the easiest things you will take. The quizzes take new concepts and apply to the quiz. Also, her tests are usually always hard. It is a good idea to practice new concepts and review old ones from previous units, so you can get a good grade on the tests. I also advise you to be organized throughout the year. Organization is the key to success especially in math class. Tool kits are an extremely helpful resource to use. There are going to be a lot of conjectures and theorems that will be new, and it would be hard to just memorize them. My overall geometry year was not exactly the way I hoped it would turn out. It was extremely had, and it moves at a very quick pace, so keeping up was hard for me personally. If I could have done something differently, it would have been practicing math more often. Each concept was hard, and I did not have anytime to review it, because I have a lot of honors classes which require a lot of work too. The key to being successful in this course is to pay attention, practice a......

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...digits to encourage ease of understanding | |Three students with ADD- Give students with attention disorder fewer problems to solve | |One student with visual difficulty- Incorporation of visual enhancements such as pictures | |Materials/Equipment: | |Paper and pencils for students | |Math handbook | |Chart | |Flash Cards | |Computer with internet connection | |Interesting Short Story: The Lion’s Share ......

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...Intermediate Algebra With Applications and Visualization. Read the University of Phoenix Material: MyMathLab Study Plan. Participate in class discussion. Respond to weekly discussion questions. Resource: University of Phoenix Material: Using MyMathLab ® Log on to MyMathLab on the student website. ® Complete the MyMathLab Orientation exercise. ® ® 4/15/13 4/15/13 4/15/13 2 2 Watch this week’s videos located on your student website. Follow the Math Help Community in PhoenixConnect. The focus of the community is to help students succeed in their math courses. Post questions and receive answers from other students, faculty, and staff from the Center for Mathematics Excellence. Resource: Learning Team Toolkit Complete the Learning Team Charter. Complete the Week One assignment in MyMathLab . ® 4/15/13 6 Review your Study Plan in MyMathLab after completing the homework assignment for the week. Select each topic from Ch. 5 in your study plan that has been highlighted with a pushpin • for further review. ® 4/15/13 1 First, complete some Practice problems until you feel ready for a Syllabus 3 MTH/209 Version 6 quiz. o Click the green Practice button within Objectives to Practice and Master. o Complete Practice problems until you feel ready for a quiz. o Click the Close button and return to the main page for the Study Plan. • When you are ready to prove mastery of a concept, click Quiz Me. o Click the Quiz Me button within Objectives......

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...Game Theory Math Review 1 1.1 Function Deﬁnition If we write down the relation of x and y as follows, y = f (x) this means y is related to x under the rule f . Also we say that the value of y depends on the value of x. This relation y = f (x) is called as a function if 1) the rule f assigns a single x value to single y value or 2) assigns multiple x values to single y value. 2 2.1 Shape of function When f (x) = ax + b Suppose that the function is given as follows. y = f (x) = ax + b ´ 1) Slope: f (x) = a and Y −intercept: b Y − axis is b.. b −a 2) Intersection with Y − axis: This is the case when x = 0. So from f (0) = b, the Intersection with 3) Intersection with X − axis: This is the case when y = 0. So the intersection with X − axis is from ax + b = 0. Example Suppose y = f (x) = ax + b. Draw this function in following each case. 1) When a > 0, b > 0 2) When a > 0, b < 0 3) When a < 0, b > 0 4) When a < 0, b < 0 Now suppose you want to ﬁnd the linear function that passes through following two points,. x = (a, b) and y = (c, d). Then the linear function is deﬁned as follows. ¶ µ b−d (x − a) + b f (x) = a−c µ ¶ b−d = (x − c) + d a−c ´ ³ ´ ³ b−d b−d So from f (x) = a−c (x − a) + b or f (x) = a−c (x − c) + d, ¶ (bc − ad) b−d x+ f (x) = a−c (c − a) | {z } | {z } µ 1 Here, the ﬁrst term is the slope and the second term is Y-intercept. Example Find the linear function that passes through following two points. A = (2, 4) and B = (−4, −2) 2...

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...Jasmine Petersen Dr. Abdeljabbar MAT 1111 April 23, 2014 Algebra is one of the most important subjects someone can learn. It is a subject that transfers into daily life. A lot of people do not realize that they are using algebra. Algebra can be anything from calculating the amount of money you’ve spent on your grocery shopping, designing structural plans for a building, and keeping track of the calories you have in your diet. Our professor told us that in every subject, we use math. My major is chemistry and mathematics is used widely in chemistry as well as all other sciences. Mathematical calculations are absolutely necessary to explore important concepts in chemistry. You’ll need to convert things from one unit to another. For example, you need to convert 12 inches to feet. Also, we use simple arithmetic to balance equations. A lot of things I’ve had learned from this course and one of them was that we use Math for everyday life. I’ve also learned many ways how to solve equations such as linear, quadratic, exponential, and logarithmic equations. All the material that we did learn was all easy to learn and understand. I believe that the instructor did a good job explaining on how to solve problems. If my friend was asking me how to determine the differences between the equation of the ellipse and the equation of the hyperbola, I would first give he or she the definition of the two words ellipse and hyperbola. An ellipse is a set of all points in a plane such that the......

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...separate file. * You must clearly state your position with well-structured paragraphs using proper grammar, spelling, and sentence structure. * This is not an “opinion” question – you must offer evidence to support your position, using properly-cited sources. * Your answer must be between ¾-1 page in length. * You must cite and reference at least one source (book, website, periodical) using APA format. The required website counts as one source. You may submit your Assignments to the Math Center for review. Tutors will not grade or correct the Assignment, but they will provide guidance for improvement. Tutors will not, however, help you find web sites for the Assignment. Be sure to submit Assignments early enough to receive feedback and make corrections before the Assignment due date (24 hour turn-around times Monday-Thursday and 48 hour turn-around times on weekends are typical). Email Assignments to: kumc@kaplan.edu. Please put “MM255 Assignment Review” in the subject line of the message. There are many advantages and disadvantages of higher interest rates on investments. The advantages are during the high interest rate times the investment income can extend their maturities into the future. Incentiven to save, high risk reward, and stronger currency are also advantages. The disadvantages of higher interest rates on investments is a slow economy. If there is a slow economy that an high interst rate can actually hurt your investment because the......

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...This article is about the study of topics, such as quantity and structure. For other uses, see Mathematics (disambiguation). "Math" redirects here. For other uses, see Math (disambiguation). Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[1] Mathematics is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8] Mathematicians seek out patterns[9][10] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become......

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...5: Review of Formulas and Integration Techniques7.1: Integration by Parts | | 2 | Sept 21 - Sept 25 | 7.2: Trigonometric Integrals7.3: Trigonometric Substitution | | 3 | Sept 28 – Oct 2 | 7.4: Integration of Rational Functions by Partial Fractions 7.5: Strategy for Integration | | | Oct 5– Oct 9 | Holiday (Eid Al Adha) | | 4 | Oct 12– Oct 16 | 7.8: Improper Integrals | | 5 | Oct 19 – Oct 23 | 8.1: Arc Length8.2: Area of a Surface of Revolution | | 6 | Oct 26 – Oct 30 | 10.1: Parametric Equations10.2: Calculus with Parametric Curves | | 7 | Nov 2 – Nov 6 | Review for Midterm Exam 1Midterm Exam 1 | Exam 1 : Wed, Nov 5, 5:30-7:00pm Sections: 7.1-7.5, 7.8, 8.1-8.2 | 8 | Nov 9-Nov 13Nov 9 – Nov 13 | 10.3: Polar Coordinates10.4 Area and Length in Polar Coordinates | | 9 | Nov 16 – Nov 20 | 11.1 Sequences11.2 Infinite Series | | 10 | Nov 23– Nov 27 | 11.3: Integral Test and Estimates of Sums11.4: Comparison Tests | | 11 | Nov 30– Dec 4 | 11.5: Alternating Series | | 12 | Dec 7 – Dec 11 | 11.6: Absolute Convergence and the Ratio and Root Tests Review for Midterm Exam 2Midterm Exam 2 | Exam 2 : Wed, Dec 10, 5:30-7:00pm Sections: 10.1-10.4, 11.1-11.5 | 13 | Dec 14 – Dec 18 | 11.8: Power Series11.9: Representation of Functions as Power Series | | 14 | Jan 4 – Jan 8 | 11.10: Taylor and Maclaurin Series 11.11: Applications of Taylor PolynomialsComplex Numbers | | 15 | Jan 11 – Jan 15 | Review for Final Exam | Final Exam (comprehensive) | Math......

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...can see how to split up the original equation into its factor pair, this is the quickest and allows you to solve the problem in one step. Week 9 capstone part 1 Has the content in this course allowed you to think of math as a useful tool? If so, how? What concepts investigated in this course can apply to your personal and professional life? In the course, I have learned about polynomials, rational expressions, radical equations, and quadratic equations. Quadratic equations seem to have the most real life applications -- in things such as ticket sales, bike repairs, and modeling. Rational expressions are also important, if I know how long it takes me to clean my sons room, and know how long it takes him to clean his own room. I can use rational expressions to determine how long it will take the two of us working together to clean his room. The Math lab site was useful in some ways, since it allowed me to check my answers to the problems immediately. However, especially in math 117, it was too sensitive to formatting of the equations and answers. I sometimes put an answer into the math lab that I knew was right, but it marked it wrong because of the math lab expecting slightly different formatting Week 9 capstone part 2 I really didn't use center for math excellence because i found that MML was more convenient for me. I think that MML reassures you that you’re doing the problem correctly. MML is extra support because it carefully walks you through the problem visually......

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...Review the list of elements of QL. Identify and discuss the one in which you are weakest AND the one in which you are strongest. For my strongest ability I would say that is “Making decisions”. According to the “The Case for Quantitative Literacy handout”, “making decisions is the ability to use mathematics, make decisions and solve problems in everyday life”. In my everyday life I have to keep the balance in my check book, pay bills, take care of kids, run my house, cook, clean etc. With cooking I am using math, measuring how much food to make for four people (I still haven’t mastered that one). With bills I am using math, how much each company gets, to how much money I have to spare (which these days is not much). In my everyday life I do use some form of a math. It might not be how I was taught, but I have learned to adapt to my surroundings and do math how I know it be used, the basic ways, none of that fancy stuff. For my weakest ability I would say I fall into “Confidence with Mathematics”. Math has never been one of my favorite subjects to learn. It is like my brain knows I have to learn it, but it puts up a wall and doesn’t allow the information to stay in there. The handout “The Case for Quantitative Literacy” states I should be at ease with applying quantitative methods, and comfortable with quantitative ideas. To be honest this class scares the crap out of me, and I am worried I won’t do well in this class. The handout also says confidence is the opposite......

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... | | |Location | | |on-line | | | | | |Times | | |on-line, or in Maier Hall , Math Lab, Peninsula College | | | | | |Start Date | | |Sept. 21, 2015 End Date Dec. 9, 2015 | | | | | |Course Credits ...

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