...1.1 EXERCISE SET In Exercises 1–14, write each English phrase as an algebraic expression. Let x represent the number. 1. Five more than a number X+5 3. Four less than a number X-4 5. Four times a number 4X 7. Ten more than twice a number 2X+10 9. The difference of six and half of a number 6 – ½X 11. Two less than the quotient of four and a number 4/X -2 13. The quotient of three and the difference of five and a number = 3/5-X In Exercises 15–26, evaluate each algebraic expression for the given value or values of the variable(s). 15. 7 + 5x, for x = 10 7+5.10 7+50 = 57 17. 6x − y, for x = 3 and y = 8 6.3-8 18-8=10 19. x2 + 3x, for = 1 10/9 21. x2 − 6x + 3, for x = 7 49-42+3 = 10 23. 4 + 5(x − 7)3, for x = 9 4+5 (9.-7 ) ³ 4+5 (2)³ 4+5.8 4+40 = 44 25. x2 − 3(x − y), for x = 8 and y = 2 X²-3X+3Y 8²-3 (8)+3(2) 64-24+6 = 46 expresses the relationship between Fahrenheit temperature, F, and Celsius temperature, C. In Exercises 95–96, use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. 95. 50°F = 10 C = ( 50-32) = 5/9 C = (12 ) 5/9 C+ 10 A football was kicked vertically upward from a height of 4 feet with an initial speed of 60 feet per second. The formula H= 4+60t -16t² describes the ball’s height above the ground, h, in feet, t seconds after it was kicked. Use this formula to solve Exercises 97–98. 97. What was the ball’s height 2 seconds...
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...My topic is a topic I am sure runs through the head of at least ninety percent of all college students. Why should all college majors require you to take college algebra? The requirements for your basic college classes include college algebra. Without the proper ACT score you will be taking remedial algebra before you reach college algebra. For those who don’t know college algebra is a very difficult class. About fifty eight percent of all students who take it fail it at least once. It is especially difficult for the people who fall under the same class as me that struggle with math even before college algebra. The reason I chose this topic is because I know how extremely challenging this class is and I believe it is unfair for colleges to...
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...you confronted with the help of mathematics First, let me say math classes are what my nightmares have been made out of since before I even enrolled in college. I had not stepped foot in a classroom in nearly 30 years and my last classroom was untraditional. My last formal math class was when I was in 8th grade in 1981, and because of my untraditional schooling, I had never had to take algebra. This was a problem because I had understanding of it and it did not make sense to me at all. I spent 10 years trying to learn algebra so I could test out of the remedial classes. I had books, videos, friends, and even my children try to teach me algebra. All to no avail, they would give me a rule and I would ask why? And they would say because that is how it is done,...
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...COMALGE FINAL EXAM (SET B) September 5, 2013 I. MULTIPLE CHOICE Write the letter corresponding to the correct answer. Write your answers on the first page of your test booklet. (2 points each) 1. The multiplicative inverse of the additive inverse of −a is b−c a b−c A. C. c−b a a c−b B. D. b−c a 2. Which of the following is TRUE? 8. Factor x2 − 2xy + y 2 − xw + yw completely. A. (x − y − w)(x − y) C. xy(x − 2)(y + w) B. (x − y + w)(x − y) D. w(x − y)2 9. Each of the following is a factor of u6 − 64w6 EXCEPT A. u − 2w A. Rational numbers are integers. B. u + 2w B. Integers are whole numbers. C. u2 − 2uw + 4w2 C. Whole numbers are rational numbers. D. (u + 2w)2 D. There is a number that is both rational and irra- 10. Find the quotient: (x3 + 2x2 − 1) ÷ (x + 1) tional. A. x2 − x + 1 3. Which of the following is NOT TRUE? B. x2 + x − 1 A. a2 (a3 ) = a5 2 3 6 B. (3a )(2a ) = 6a 4. 3x−1 y −1 5x0 y 3 6 A. 10x2 y 8 9 B. 25x2 y 16 C. 2a(a2 ) = 2a3 1 D. − 4a2 = −2a 2 2 is equal to 9 25x2 y 8 9 D. 25y 8 C. 5. Which of the following is TRUE? I. Every integer has a multiplicative inverse. II. The sum of two rational numbers is rational. A. I only C. Both I and II B. II only D. Neither I not II 6. 2(x + y)−1 is equal to 1 2x + 2y 2 B. x+y A. C. x2 + 3x + 3 D. x2 − 3x − 3 s−1 2 is equal to − 2 s + 2 s + 2s s−1 s2 + 5s + 2 C. 2 A. 2 + 2s) s + 2s ...
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...W6 Assignment 1. Determine the domain of the function 2. Determine the domains of f and g 3. State the domain of the following function 4. Find the domain of the function and identify any vertical and horizontal asymptotes. 5. Find the domain of the function and identify any vertical and horizontal asymptotes. 6. Find the domain of 7. Determine the domain of 8. Find the domain of the function and identify any vertical and horizontal asymptotes. 9. Determine the equations of the vertical and horizontal asymptotes of the graph of the function 10. Determine the equations of any horizontal and vertical asymptotes of 11. Identify any vertical and slant asymptotes of the following function. 12. Determine the equations of any horizontal and vertical asymptotes of 13. Determine the value that the function f approaches as the magnitude of x increases. 14. Find the domain of the function and identify any vertical and horizontal asymptotes. 15. Given , determine the equations of any slant and vertical asymptote. 16. Identify all intercepts of the following function. 17. Use the graph to determine any x-intercepts of the graph of the rational function. 18. Sketch the graph of the rational function. 19. Which of the following is the graph of the given equation? 20. The game commission introduces 100 deer into newly acquired state game lands. The population N of the herd is modeled by where t is the time in years. Find the populations when t = 40. (Round your answer...
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...Detailed Lesson Plan in Algebra Feb. 11, 2015 I. Objectives a. Define polynomials b. Classify polynomials according to number c. Perform operation involving polynomials, addition and subtraction. II. Subject Matter Topic: Polynomials Materials: visuals, chalk and board Reference/s: College Algebra, pages 1-4 III. Presentation A. Preliminaries 1. Opening prayer 2. Checking of Attendance 3. Checking of Assignments 4. Motivation (Video clip) B. Lesson Proper Teacher’s Activity In the video that you’ve watched, what will be our lesson for today? Yes, George? Yes it has. Anyone can tell what it is? Yes, Fred. Very good. Can someone tell what is a polynomial is? Yes Claire. Yes, very well said, any additional information? Ok, so let’s proceed. So terms that different only in their constant coefficients are called “like terms”. Polynomials and algebraic expressions can be classified(according to the number of term) as; Monomial – having one term Binomial – having two terms Trinomials – having three termsMultinomials – having more than three terms. The degree of a polyomial is determined by the hiegst exponent of its variable. Someone give me an examples of polynomials. (called several students). Thank you for your answers. Is there any question? Oko next is adding and subtracting polynomials: Rule:Add/subtract the constant coefficients...
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...The Cartesian Plane Before the end of the European Renaissance, math was cleanly divided into the two separate subjects of geometry and algebra. You didn't use algebraic equations in geometry, and you didn't draw any pictures in algebra. Then, around 1637, a French guy named René Descartes (pronounced "ray-NAY day-CART") came up with a way to put these two subjects together. Rene Descartes was born on March 31, 1596, in Touraine, France. He was entered into Jesuit College at the age of eight, where he studied for about eight years. Although he studied the classics, logic and philosophy, Descartes only found mathematics to be satisfactory in reaching the truth of the science of nature. He then received a law degree in 1616. Thereafter, Descartes chose to join the army and served from 1617-1621. Descartes resigned from the army and traveled extensively for five years. During this period, he continued studying pure mathematics. Finally, in 1628, he devoted his life to seeking the truth about the science of nature. At that point, he moved to Holland and remained there for twenty years, dedicating his time to philosophy and mathematics. During this time, Descartes had his work "Meditations on First Philosophy" published. It was in this work that he introduced the famous phrase "I think, therefore I am." Descartes hoped to use this statement to find truth by the use of reason. He sought to take complex ideas and break them down into simpler ones that were clear...
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...displacement of d pounds and a sail area of A square feet S is determined by the function a)Find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds. b) Write d in terms of A and S. Mathematics - Algebra Real World Radical Formulas . Read the following instructions in order to complete this assignment: a. Solve parts a and b of problem 103 on page 605 and problem 104 on page 606 of Elementary and Intermediate Algebra . b. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include: § An explanation of what the parts of the formula mean before using it to get your answers. Study the Instructor Guidance examples to learn how to solve the formula for another variable. § Your solution to the above problems, making sure to include all mathematical work. § A discussion of how and why these concepts are important in the “real world.” Describe another situation that could be evaluated using these concepts. A great tip if you're just starting out in college...
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...this year has been teaching most of the 2012 class algebra 2. The way he handles things may seem harsh at times but inevitably will only lead to our success in life. My first year having Dr. Beach was my sophomore year geometry class. I was so use to flying by all my classes with hardly looking into my notes and homework when Dr. Beaches class started to demand more from us. It started with more homework, a lot of random projects and of course our financial/intelligent conversations. There are many good sides to his class. Some things would be the lessons you learn. He teaches us that we are responsible for our actions and he doesn’t fail us, we only fail ourselves. We basically write out our own grades by deciding to do the homework, extra credit, study for quizzes/tests and taking good notes. Taking responsibility is a HUGE theme in our algebra 2 class this year especially. I feel like everything in Dr. Beach’s class has had a separate meaning then just algebra 2 or geometry. All the home work we receive is just to prepare us for the amount of work in college and our future jobs. The quizzes and tests are preparing us for the responsibilities of using our skills and abilities then turning them into something greater. The lessons are to help us comprehend and understand complex and even basic things. Some negative sides to Dr. Beach’s methods would be the feeling that algebra 2 is our only class and keeping up with homework, projects...
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...LONDON'S GLOBAL UNIVERSITY Mathematics with Management Studies BSc UCAS code: G1N2 www.ucl.ac.uk/prospectus/maths MATHEMATICS WITH MANAGEMENT STUDIES BSc This BSc combines a broad-based training in mathematics with highly practical courses from UCL’s Department of Management Science and Innovation, which will be of direct use to those seeking a career in management. No previous knowledge of management studies is required. Degree summary • • • • Gain transferable skills such as numeracy, problem-solving and logical thinking, which can lead to a large variety of interesting, diverse and well-paid careers. All of the courses given by UCL's Department of Management Science are validated by external experts from the private, public and charitable sectors. Many of our graduates choose to build their management knowledge and experience by following a further management qualification, such as the MBA (Masters in Business Administration). UCL's internationally renowned Mathematics Department is home to world-leading researchers in a wide range of fields, especially geometry, spectral theory, number theory, fluid dynamics and mathematical modelling. Peer Assisted Learning has been pioneered in the department, with second-year students offering support and advice to first years. Your career We aim to develop your skills in mathematical reasoning, problem-solving and accurate mathematical manipulation. You will also learn to handle abstract concepts and to think critically...
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...Math and Me Vanessa Bashore MM212: College Algebra “We both just did out fives yesterday, how can she be doing her sixes already today?” I can remember thinking this like it was yesterday instead of 29 years ago. I was in first grade, and we were doing our times tables. I had been the first one to do all of my numbers so far in the class, and now Sara was up there doing her sixes before I knew them. That would just not do for me, so that night I went home and learned the rest of my numbers, six through nine, to be able to do them for the teacher the very next day. I guess you can say that this is where my love for math started. I am not saying that I never had to study or that I have never struggled with any math in my life, but for the most part, most of the math classes I have taken in my life have come pretty easily to me. I love when you are struggling with something in math and all of a sudden you have that a-ha moment where everything suddenly makes sense. In the past I have taken all the basics in math including Algebra and Geometry. However, these courses were also taken almost 20 years ago, and I have to admit that I am a bit rusty when it comes to all of the formulas and properties. Even though I may not remember all of the formulas, I still consider my previous courses a success. I may not remember the exact formula, but I do remember that the formulas exist and it is just a matter of looking the formula up and plugging in the right numbers to get the correct...
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...Ch.1. Review Amber Hennrich May 26, 2014 12. Explain and give an example for each of the following types of variables: (a) equal-interval, (b) rank-order, (c) nominal, (d) ratio scale, (e) continuous. A) An equal-interval is a variable in which numbers stand for approximately equals amounts of what is being measured. Example: Grade Point Average B) A rank-order variable is numeric and the numbers stand only for the relative ranking. Example: A graduate standing in their class. Their GPA makes a big difference for instance if they stand first or second in the class. C) A nominal variable is not numeric and values are names or categories. Example: A nominal variable for gender would be female and male. D) A ratio scale is measured by equal-interval variable. An equal-interval variable has an absolute zero point on the ratio scale. An absolute zero point means there is an absence of the variable. Example: A number of cats an individual has. If one person has three and the other has six, you can say that they have three times the amount of that person. E) A continuous variable is a theory that you can have an infinite number between 2 variables. Example: An example of this would big age. You can say you are 12.5 years old. 15. Make (a) a frequency table and (b) a histogram. Then (c) describe the general shape of the distribution. A) Speeds | Frequency | Percent | 15-21 | 2 | 5% | 22-28 | 4 | 10% | 29-35 | 17 | 42.50% | 36-42 | 13 | 32.50% | ...
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...DETAILED SOLUTIONS AND CONCEPTS - FORMULAS AND WORD PROBLEMS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! PLEASE NOTE THAT YOU CANNOT USE A CALCULATOR ON THE ACCUPLACER ELEMENTARY ALGEBRA TEST! YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR! Formula rearrangement refers to isolating a letter term other than the one already isolated in the formula. Solving formulas in the manner often shortens our work when doing repeated formula evaluations. After we solve the formula for the desired variable, we rewrite the formula with the variable on the left side for convenience and for use in electronic spreadsheets. Problem 1: Solve the "mark up" formula M = S - C for S. To solve the equation above, we will use the Addition Axiom to isolate the variable S by "moving" all terms associated with S by addition away from the variable. The variable associated with S by addition is C. Therefore, we must add C to both sides of the equation. M+C=S-C+C and M + C = S Finally, we rewrite the formula with S on the left S=M+C Problem 2: Solve the interest formula I = PRT for R. It stands for Interest = Principal Time. Rate To solve the equation above, we will use the Multiplication Axiom to isolate the variable R by "moving" all terms associated with R by addition away from the variable. The variables associated by multiplication with R are P T or PT. Therefore...
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...BACOLOD CITY COLLEGE BSOA/BSIS/ACT DEPARTMENT Course Syllabus Course Code : MATH_01 Course Title : College Algebra Course Description : This course covers algebraic expressions and equations; solution sets of algebraic in one variable: linear, quadratic, polynomial of degree n, fractional, radical equations, radical in form, exponential and logarithmic equations; decomposition of fractions into partial fractions; solution sets of systems of linear equation involving up to three variables. Pre-requisite Subject : None Credit Units : 3 units (3 hrs. lecture) General Objectives : At the end of the term, the students should be able to: 1. Operate and simplify algebraic expressions; 2. Determine the solution sets of all types of algebraic equations and logarithmic equations; and inequalities. 3. Use the manipulative and analytical skills acquired in Objectives 1 to 2 to solve word problems; and 4. Identify the domain and range of a given relation/function. Topic/Coverage |Specific Objectives (Cognitive, Affective, Psychomotor) |NCBTS Domain |Teaching Strategies/ Learning Activities |Values Statement/ Value Indicators | Instructional Materials/ References |Evaluation | |MIDTERM: I. Set of Real Numbers A. Integer Exponents B. Polynomials, Operations, Sepcial Products C. Binomial Expansion (Binomial Theorem) D. Factoring...
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...A Brief Look at the Origin of Algebra Connie Beach Professor Clifton E. Collins, Sr. Math 105: Introduction to College Mathematics May 22, 2010 Abstract In this paper we look at the history of algebra and some of its different writers. Algebra originated in ancient Egypt and Babylon around 1650 B.C. Diophantus of Alexandria, a Greek mathematician, and Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī, a Persian mathematician from Baghdad, astronomer and geographer, shared the credit of being the founders of algebra. Diophantus, who is known as the “father of algebra”, carried on the work of the ancient Egyptians and Babylonians, but the word Algebra actually came from the word al-jabr, which is from al-Khwārizmī’s work, Kitab al-Jabr wa-l-Muqabala. The algebraic notation had gone through 3 stages: rhetorical (or verbal), stage, syncopated (use of abbreviated words) stage, and symbolism (the use of letters for the unknown) stage. As a matter of fact, the algebra that we know of today began during the 16th century, even though its history shows that it began almost 4000 years ago. A Brief Look at the Origin of Algebra I have always had a love for math. My favorite math class was Algebra; in fact, I had taken Algebra I, II, III, and IV all through high school, and aced every class. I can just look at a problem and know the answer. Then, I returned to college after 30 years, and took an Intro to College Math class. I wasn’t sure if I still remembered what I had learned...
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