...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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...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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...displacement d in pounds, C is determined by the function. a).Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet. b). Solve the equation for d. 2.104. Sailboat speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a 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...
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...Distributive Property Kimberly Smith MAT 221 Introductions to Algebra Instructor: Andrew Halverson February 15,2014 I will be using distributive property to solve how properties of real numbers are used while I simplified the three given expression. To solve these three math problem I will use the distributive property to remove the parentheses in the problem. I will also combine like terms by adding coefficients and add or subtract when needed. Finally I would have my answer and then decide if the answer is simplified, if not I will simplify. The solving of properties of real number the properties of real numbers are important to know in all subjects, even complex numbers, because many of the properties are shared. Additionally the argument to any equation in algebra is real; therefore, algebraic expressions only manipulate reals (that is, if you have integer coefficients and no radicals). 1. 2a(a-5)+4(a-5) = The given expression 2a^2-10a+4a-20 = I will use the distributive property to remove parentheses so I can combine like terms by adding coefficient. 2a^2-6a-20 = Is simplified no combine like terms by adding coefficients 2a^2-6a-20 = Answer 2. 2w – 3 + 3(w – 4) – 5(w – 6)= The given expression 2w - 3 + 3(w - 4) - 5(w - 6) = Distributive property removes parentheses 2w - 3 + 3w - 12 - 5w + 30 = Combine like terms 2w + 3w - 5w - 3 -12 + 30 = Combine like terms by adding coefficients and add and subtract to get sum. Use the commutative...
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...Higher Order Thinking and Diverse Learners Grand Canyon University: Secondary Methods and Data-Driven Pedagogy April Smith GCU: SED-444 August 25, 2013 Higher Order Thinking and Diverse Learners Grand Canyon University: Secondary Methods and Data-Driven Pedagogy April Smith GCU: SED-444 August 25, 2013 Higher Order Thinking and Diverse Learners This unit is designed for students in beginning Algebra classes. It is an introduction to the basic functions of algebra including the definition of an equation, using basic mathematical skills to solve equations, and applying equations to problem solving. South Carolina Standard 8-3: Through the process standards students will demonstrate an understanding of equations, inequalities, and linear functions (South Carolina Department of Education, 2007). Specific Indicators as outlined by the South Carolina Department of Education 8-3.1 Translate among verbal, graphical, tabular and algebraic representations of linear functions. 8-3.2 Represent algebraic relationships with equations and inequalities. 8-3.3 Use properties to examine equivalence of a variety of algebraic expressions. 8-3.4 Apply procedures to solve multi-step equations. 8-3.5 Classify relationships between two variables as linear or non-linear. Objectives Day 1 Objective: Students will learn the definition of an algebraic equation and the parts of an equation. Day 2 Objective: Students will apply their knowledge of addition and...
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...Annotated Bibliography Brain Pop. (1999–2013). Algebra symbols, patterns, changes, variables, and quantitative relationships. Retrieved from http://www.brainpop.com/math/algebra.com Brain Pop is an educational website that entails many short animated movies for students to use as a learning tool. Brain Pop has two main animated characters their names are Tim and Moby they are the narrators on the website. They introduce the math concepts and their experience with using the math to the audience. This website could be used to support individual, teams, and whole class learning skills. Teachers can use Brain Pop as a supplement to cultivate the student’s curiosity in math. Gamequarium. (2000-2009). The site that swims with learning fun! Retrieved from http: //www.gamequarium.com The Gameaquarium have abundances of bright colorful, interactiviting, engaging games for students to play. The Gameaquarium is divided into three areas, which may perhaps work for every student’s needs. The teachers could use the interactive games to work out any issues that the students are having or they could use the game to advance the students to the next level. The website is free, which makes it splendid for the students. They can use the website at home as extra practice. Math Fact Café. (2000-2013). The fact sheet factory. Retrieved from http://www.mathfactcafe...
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...called like terms because they contain the same letter. Like terms can be added together – this is called collecting like terms. Instead of writing 2m ϩ 3m ϩ b ϩ 2b, we can write 5m ϩ 3b or 3b ϩ 5m. We cannot combine 5m and 3b in any simpler way than this because m and b are not like terms – they stand in for different unknown numbers. We can multiply two or more unknowns together. a ϫ b is written as ab. b ϫ a is the same as a ϫ b and is also written as ab. Instead of writing 2a ϩ 3b ϩ 3ab ϩ ba, we can write 2a ϩ 3b ϩ 4ab. We can add 3ab to ba to make 4ab because ab and ba are like terms. Example Simplify the following by collecting like terms: a) 3m ϩ 4m ϩ m ϩ n ϩ 2n b) 4mv ϩ 2z Ϫ 3mv ϩ z ϩ 3m There are eight lots of m and three lots of n. a) 3m ϩ 4m ϩ m ϩ n ϩ 2n ϭ 8m ؉ 3n b) 4mv ϩ 2z Ϫ 3mv ϩ z ϩ 3m ϭ mv ϩ 3z ϩ 3m First look at the mv terms: 4mv Ϫ 3mv ϭ 1mv (which we usually write as mv) Now look at the z terms: 2z ϩ z ϭ 3z Now look at the m terms: you have 3m Exercise 6.1 .......................................................................................... ᕡ Simplify the following expressions by collecting like terms: a) b) c) d) e) yϩyϩyϩyϩy m+m+m+b+m zϩaϩaϩa pϩrϩpϩpϩpϩrϩrϩpϩrϩpϩpϩrϩpϩpϩrϩp tϩtϪqϩtϪqϪq ᕢ Simplify the following expressions by collecting like terms: a) 9p ϩ 3r Ϫ 2p ϩ r ϩ 2r Ϫ p c) b Ϫ t ϩ 3t Ϫ t e) x ϩ y Ϫ x Ϫ y 58 Maths Connect 1R b) 5x ϩ 2y ϩ y Ϫ x Ϫ y ϩ 7x ϩ 3y...
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...Simplifying Expressions Christy Bailey MATT 221: Introduction to Algebra Instructor: Stacie Williams October 13, 2013 Simplifying Expression Include in this paper I have demonstrated the following solutions for the three problems listed below. Using th given vocabulary words I have broken down each problem using the proper steps in solving the algebraic expressions. Also shown will be what is important about real numbers and in what way they are useful in using real numbers in solving algebraic expressions. By breaking down the equation you can simplify the equation down to lowest terms. Gathering the like terms in the equation is a step in breaking down the expression correctly. Take the coefficient and multiply it by the variable. The distributive property in the expression is the letters in the expression. When solving a algebraic expression you always remove the parenthesis first. A.)2a(-5 + a) + 4(a + -5) Simplify the terms (-5 * 2a + a * 2a) + 4(a + -5) (-10a + 2a2) + 4(a + -5) -10a + 2a2 + 4(-5 + a) Reorder the terms -10a + 2a2 + (-5 * 4 + a * 4) -10a + 2a2 + (-20 + 4a) -10a + 4a = -6a -20 + -6a + 2a2 Combine the like terms : -20 + -6a + 2a2 a = 5 This is...
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...Jennifer Dominguez MAT221: Introduction to Algebra (ACP1424E) Instructor: Calandra Bean Assignment week 1 June 16,2014 P.1 · 2a(a – 5) + 4(a – 5) First I would start by simplifying the equation with multiplying 2a to the numbers within the parenthesis. So it would be 2a times, a which would be 2a squared because you would put a one in front of the a in the parenthesis. Then you would multiply 2a times five, which would be -10a. Then you would multiply four times (a) which would be 4a then you would multiply four times negative five which would be negative twenty. So the new equation without the parenthesis would be 2a^2-10a+4a-20 which would then be 2a ^2-6a-20 because you would subtract -10a from 4a. 2a^2-6a-20 this is the simplified form. · 2w – 3 + 3(w – 4) – 5(w – 6) First you would need to simplify the equation by multiply three times w then to the -4, which would be 3w-4, then you would multiply -5 by the w in the parenthesis then by -6 so you would have -5w+30. So when you have the equation it would be 2w-3+3w-12-5w+30 then you would start left to right with like terms. 2w +3w, which would be 5w-5w, which would be w then you, would do -3-12, which equals -15+30 which equals 15. Then the simplified equation would be w+15 P.2 · 0.05(0.3m + 35n) – 0.8(-0.09n – 22m) First you would multiply 0.05 by 0.3m which would be 0.015m, then you would multiply 0.05 by 35n which equals 1.75n. Then you would multiply -0.8 times...
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...MYKA E. AUTRIZ BSBM 101 B CHAPTER II SET OF NUMBERS Although the concepts of set is very general, important sets, which we meet in elementary mathematics, are set of numbers. Of particular importance is the set of real numbers, its operations and properties. NATURAL NUMBERS are represented by the set of counting numbers or real numbers. EXAMPLES: 6, 7.8.9.10.11.12.13.14.15.16.17, 18, 19, 20…………………. WHOLE NUMBERS are represented by natural numbers including zero. EXAMPLES: 1, 2, 3, 50, 178, 2, 856, and 1,000,000 INTEGERS are negative and positive numbers including zero. EXAMPLES: -4, -3, -2, -1, 0, 1, 2, 3, 4…………………….. RATIONAL NUMBERS are exact quotient of two numbers, which are set of integers, terminating decimals, non-terminating but repeating decimals, and mixed numbers. EXAMPLES: 4/5, -5/2, 8, 0.75, 0.3 IRRATIONAL NUMBERS EXAMPLES: 3, 11/4, -7, 5/8, 2.8 ABSOLUTE VALUE of number is positive (or zero). The absolute value of a real numbers x is the undirected distance between the graph of x and the origin. EXAMPLES: /7/-/3/ solution /7/-/3/=7-3=4 and /-8/-/-6/=8-6=2 OPERATIONS ON INTEGERS ADDITION SUBTRACTION MULTIPLICATION DIVISON 9+5=14 9 - -5=14 -45x8=-360 -108÷9=-12 -15+5=10 23 - -4=27 -8+-5=-13 -89 -136=-225 -13+20=7 ...
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...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% | 43-53 | 4 | 5% | B) http://nces.ed.gov/nceskids/createagraph/graphwrite.asp?ID=b8877424c4834801b7d9e181d80b9102&file=png C) I believe this graph would be bimodal. It has two high points very close together and has the same cause throughout. It is easy to tell that...
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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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...The Influence of Mathematics on Daily Social Activities MTH/110 March 2, 2015 The Influence of Mathematics Society is an important concept in which stands the intellectual development of mathematics and science. Today, in society, mathematics makes extraordinary demands and so to the world of mathematicians and scientists. The purpose of the report is to identify the influence and effects of mathematics in society. It includes some history of math and its major demands and capabilities that come with the material and mathematicians. Math Background People have believed in mathematics and the discipline that comes with it since centuries ago, some may like, and some may not. Some people used to worship mathematics and believe in it for living like Aryabatta and Bhaskara. Back to the 4th century, Aristotle and Plato had already an idea of the existence of mathematics in their mind and the external world; also he argued about a positive effect on individuals (Dossey). In the middle ages, mathematicians were coming out and at one point competing without knowing in discovering new techniques. Archimedes had one of the greatest impacts on its work in mathematics but he was known later in the 16th century when Federico Commandino in 1558 translation into Latin most of his printing texts and spread it out with other mathematicians and physics of the time, that includes Johannes Kepler and Galileo Galilei (Toomer, 2014). Many other mathematicians...
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...is equivalent to the OR logic function, as well as parallel switch contacts. • Boolean multiplication is equivalent to the AND logic function, as well as series switch contacts. • Boolean complementation is equivalent to the NOT logic function, as well as normallyclosed relay contacts. 1 Boolean algebraic identities The algebraic identity of x + 0 = x tells us that anything (x) added to zero equals the original ”anything,” no matter what value that ”anything” (x) may be. Like ordinary algebra, Boolean algebra has its own unique identities based on the bivalent states of Boolean variables. The first Boolean identity is that the sum of anything and zero is the same as the original ”anything.” This identity is no different from its real-number algebraic equivalent: No matter what the value of A, the output will always be the same: when A=1, the output will also be 1; when A=0, the output will also be 0. The next identity is most definitely different from any seen in normal algebra. Here we discover that the sum of anything and one is one: Next, we examine the effect of adding A and A together, which is the same as connecting both inputs of an OR gate to each other and activating them with the same signal: Introducing the uniquely Boolean concept of complementation into an additive identity, we find an interesting effect. Since there must be one ”1” value between any variable and its complement, and since the sum of any Boolean quantity and 1 is 1, the sum of a variable...
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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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