...Algebra 1 Pacing Plan 2012-2013 1st Quarter Tools of Algebra 1.1 Using Variables 1.2 Exponents and Order of Operations 1.3 Exploring Real Numbers 1.4 Adding Real Numbers 1.5 Subtracting Real Numbers 1.6 Multiplying and Dividing Real Numbers (1.3 – 1.6 mini lessons based on need) 1.7 The Distributive Property 1.8 Properties of Numbers Solving Equations and Inequalities 2.1 Solving One-Step and Two-Step Equations 3.1 Inequalities and Their Graphs 3.2 Solving Inequalities using Addition and Subtraction 3.3 Solving Inequalities using Multiplication and Division 2.2 Solving Multi-Step Equations 3.4 Solving Multi-Step Inequalities 2.4 Ratios & Proportions (mini lessons) 3.5 Compound Inequalities 3.6 Absolute Value Equations and Inequalities 2.5 Equations and Problem Solving 2.6 Mixture Problems and Work Problems California Content Standards 1.0, 1.1, 2.0, 4.0, 10.0, 24.1, 24.3, 25.0, 25.1, 25.2 2.0, 3.0, 4.0, 5.0, 24.2, 24.3, 25.0, 25.2, 25.3 2nd Quarter Linear Equations and Their Graphs 4.1 Graphing on the Coordinate Plane 5.1 Rate of Change and Slope 5.1.1 Graphing Using Input-Output Table (Supplemented) 5.1.2 Graphing Using Slope-Intercept Form (Supplemented) 5.1.3 Graphing Using...
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...Considering there are multiple ways of solving a quadratic equation, there might be a method that you prefer over the others. You also need to take into consideration that some methods are not the best route to take depending on the equation. For example, if you have (x+5)2 you cannot use the quadratic formula with this equation without squaring the binomial. In my opinion, and through the Intellipath of my last math course I found the quadratic formula, factoring a quadratic equation, and factoring by grouping the simplest. Whereas, completing the square of a quadratic equation was very difficult for me to get through. I do not mind using the quadratic formula, because it is as simple as plugging in your values and solving the equation. So if you have y= x2+5x+4, we can use our quadratic equation format of y=ax2+bx+c, where a, b, and c are the coefficients and plug in our values to the formula to solve for x. Here is the quadratic formula, x=-b±b2-4ac2a . So now we just need to set our a, b, and c values. A=1 (Since there is no coefficient on the x2 it is a one), B=5, and C=4. So now we just plug in the values and solve.x=-(5)±(5)2-4(1)(4)2(1) → x=-(5)±25-162 → x=-5±92 → x=-5±32 →x=-5+32 =-1 x=-5-32 =-4 so x equals (– 4) or (– 1). Now if we were going solve this same equation by factoring, we need to ask ourselves what factors of 4 are the product of 5. Since 4 factors in to 4 and 1 and 2 and 2 this problem is fairly simple. We know that 2+2 doesn’t equal 5, but...
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...college-level algebra and its applications. Emphasis is placed upon the solution and the application of linear and quadratic equations, word problems, polynomials, and rational and radical equations. Students perform operations on real numbers and polynomials and simplify algebraic, rational, and radical expressions. Arithmetic and geometric sequences are examined, and linear equations and inequalities are discussed. Students learn to graph linear, quadratic, absolute value, and piecewise-defined functions and solve and graph exponential and logarithmic equations. Other topics include solving applications using linear systems as well as evaluating and finding partial sums of a series. Course Objectives After completing this course, students will be able to: ● Identify and then calculate perimeter, area, surface area, and volume for standard geometric figures ● Perform operations on real numbers and polynomials. ● Simplify algebraic, rational, and radical expressions. ● Solve both linear and quadratic equations and inequalities. ● Solve word problems involving linear and quadratic equations and inequalities. ● Solve polynomial, rational, and radical equations and applications. ● Solve and graph linear, quadratic, absolute value, and piecewise-defined functions. ● Perform operations with functions as well as find composition and inverse functions. ● Graph quadratic, square root, cubic, and cube root functions. ● Graph and find zeroes of polynomial...
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...Real World Quadratic Functions Christine Sandoval MAT222: Intermediate Algebra (ACR1438C) Instructor: Yvette Gonzalez-Smith October 10, 2014 Real World Quadratic Functions In some types of business being able to solve real world quadratic functions are very important. When we think about the quadratic curves I would point to curves known as the circle, ellipse, hyperbola and parabola (Dugopolski, 2012). I at first thought this was something that came about during my time but these actual quadratic curves came about during the ancient Greek times but they now have more real world applicability than one would think. Quadratic equations described the orbits where the planets moved round the Sun but also furthered advances in astronomy (Budd & Sangwin, 2004). A long time ago Galileo found some type of link between quadratic equations and acceleration (2004). I would believe that being able to solve real world quadratic problems are important in business because we should be able to show a return on investment or profit. We need to be able to analyze the accounts payable and receivable to determine how the business looks. Quadratic functions are not only used in business they are used in science and engineering just to name a couple of areas. Our task today is not only to show how important it is to understand quadratic functions but also to explain how important they are in business. When we think about quadratic functions we may think about the u-shape of the parabola...
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...set-builder notation | | FEB | 5 | T | 12.1 The Algebra of Functions | | | 7 | R | Review for Test 1 Advise Lab Quiz 3 | | | 12 | T | Test 1 (sections 3.4, 3.5, 3.6, 8.1, 8.2, 9.1, and 12.1) | LABS 2 and 3—FEB. 12 | | 14 | R | 4.1 Solving Systems of Linear Equations by Graphing; Appendix D on graphing window9.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities | | | 19 | T | 4.2 Solving Systems of Linear Equations by Substitution 4.3 Solving Systems of Linear Equations by Addition | | | 21 | R | 4.5 Systems of Linear Equations and Problem-Solving Advise Lab Quiz 4 | | | 26 | T | Integrated Review: Choosing a Factoring...
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...15 9 + 6 = 15 15 =15 This is the original quadratic equation. In order to solve it, we will set it equal to zero. Subtract 15 from both sides of the equal sign Now that our trinomial is equal to zero we can start factoring the equation. In order to do that we have to factor the trinomial into two binomials because we cannot use the completing the square method. The reason why I picked -5 and 3 is because when we multiply both numbers we get -15 and when we add them they equal -2. Now we will find the value of the variables by isolating them. Solution Let’s check our first solution (5) by plugging it in to our original quadratic equation. Our second solution also equals to 15. Problem #82 3v2 + 4v -1 = 0 x= -b±b2-4ac2a a = 3 b =4 c =-1 v = -4±42-4(3)(-1)2(3) The second quadratic equation will be solved using the quadratic formula. Quadratic Formula These three variables will be plugged into our formula. Now we will multiply the given values v = -4±286 v = -4±(4)(7)6 27 v = -4±276 Divide by 2 (numerator and denominator) v = --2±73 v = {.215 , -1.549} After simplifying the equation we can see that our discriminant b2 – 4ac is equal to 16 + 12 or 28. This means that our quadratic equation will have two solutions. Our next step will be simplify our radical. Our next step will be to simplify our equation and divide the rest of the quadratic formula by 2 in order to simplify it one more time....
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...of solutions a quadratic equation has is to graph the equation. The number of times the equation crosses the x-axis is the number of real solutions the equation will have. If you are given the solutions (roots) p and q of a quadratic equation then you can find the equation by plugging p and q into the formula (x-p)(x-q) = 0. It is possible for two quadratic equations to have the same solutions. An example of that would be -x^2 + 4 and x^2 - 4. Each of these equations have roots at x = -2 and 2 Example: x^6-3 Example: -x^6+3 Week 7 DQ Quadratic formula: In my opinion, this is likely the best overall. It will always work, and if you memorize the formula, there is no guessing about how to apply it. The formula allows you to find real and complex solutions. Graphing: graphing the equation will only give valid results if the equation has real solutions. The solutions are located where the graph crosses the x axis. If the solutions are irrational or fractions with large denominators, this method will only be able to approximate the solutions. If you have a graphing calculator, this method is the quickest. If you don't have a calculator, it can be difficult to graph the equation. Completing the square: This is probably the most difficult method. I find it hardest to remember how to apply this method. Since the quadratic formula was derived from this method, I don't think there is a good reason to use completing the square when you have the formula Factoring: this is probably...
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...Factoring The sport of skydiving was born in the 1930s soon after the military began using parachutes as a means of deploying troops. Today, skydiving is a popular sport around the world. With as little as 8 hours of ground instruction, first-time jumpers can be ready to make a solo jump. Without the assistance of oxygen, skydivers can jump from as high as 14,000 feet and reach speeds of more than 100 miles per hour as they fall toward the earth. Jumpers usually open their parachutes between 2000 and 3000 feet and then gradually glide down to their landing area. If the jump and the parachute are handled correctly, the landing can be as gentle as jumping off two steps. Making a jump and floating to earth are only part of the sport of skydiving. For 5 5.1 Factoring Out Common Factors Special Products and Grouping Factoring the Trinomial ax2 bx c with a 1 Factoring the Trinomial ax2 bx c with a 1 Difference and Sum of Cubes and a Strategy Solving Quadratic Equations by Factoring 5.2 Chapter 5.3 5.4 5.5 5.6 example, in an activity called “relative work skydiving,” a team of as many as 920 free-falling skydivers join together to make geometrically shaped formations. In a related exercise called “canopy relative work,” the team members form geometric patterns after their parachutes or canopies have opened. This kind of skydiving takes skill and practice, and teams are not always successful in their attempts. The amount of time a skydiver has for a free fall depends...
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... | | |Axia College | | |MAT/117 Version 7 | | |Algebra 1B | Copyright © 2010, 2009, 2007 by University of Phoenix. All rights reserved. Course Description This course explores advanced algebra concepts and assists in building the algebraic and problem-solving skills developed in Algebra 1A. Students solve polynomials, quadratic equations, rational equations, and radical equations. These concepts and skills serve as a foundation for subsequent business coursework. Applications to real-world problems are also explored throughout the course. This course is the second half of the college algebra sequence, which began with MAT/116, Algebra 1A. Policies Faculty and students/learners will be held responsible for understanding and adhering to all policies contained within the following two documents: • University policies: You must be logged into the student website to view this document. • Instructor policies: This document is posted in the Course Materials forum. University policies are subject to change. Be sure to read the policies at the beginning...
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...Essential Mathematics 1: Algebra and Trigonometry Assignment One Question 1a) Solve 2+x=3x+2x-3. Leave solutions in simplest rational form. The linear equation which is in the form ax+b=0 or can be transformed into an equivalent equation into this form. 2+x=3x+2x-3 Expand 2x-3. 2+x=3x+2x-6 Add 3x+2x together. 2+x=5x-6 Subtract 5x from both sides. 2-4x=-6 Subract 2 from both sides -4x=-8 Divide both sides by-4 x=2 Check Solution x=2 2+x=3x+2x-3 Change x to 2 2+2=3×2+22-3 Add 2+2 together, multiply 3 and 2, expand 22-3 4=6+4-6 Subtract 6 from 6+4 4=4 Thus, the solution for 2+x=3x+2x-3 is x=2 . Question 1b) Solve 2xx-1+3x=x-9xx-1 This equation is rational, it can be written as the quotient of two polynomials. In addiction of expressions with unequal denominators, the result is written in lowest terms and expressions are built to higher terms using the lowest common denominator. 2xx-1+3x=x-9xx-1 multiply x-1 from 3x 2+3x-1=x-9 Expand 3x-1 2+3x-3=x-9 Subtract 3 from 2 3x-1=x-9 Subtract x from both sides 2x-1=-9 Add 1 from both sides 2x=-8 Divide 2 from both sides ...
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...the east. If they share their information then they can find x and save a lot of digging. What is x? The key to solving this equation is to use the Pythagorean Theorem which has a right angle in the equation with a & b equaling side c. Based on the example we know that we will have to use the formula A^2 + B^2 = C^2. What we know is that Ahmed’s half of the map is 2x + 6 = treasure, which would be how far he would need to walk, (A^2). Vanessa’s map needs to show her how to get to the North of Castle Rock, which is 2x + 4, (C^2). We are trying to solve for X (side B). Vanessa is forming a 90 degree angle from point B and walk (2x + 4) until she made it to C. The formula we would use to solve for X is the following: (2x + 6)^2 = x^2 + (2x + 4)^2 4x^2 + 24x + 36 = x^2 +4x^2 + 16x + 16 The next step would be to combine like terms, multiplying, adding, and subtracting. 24x + 36 = x^2 + 16x + 16 -24x -24x 36 = x^2 – 8x + 16 -36 -36 Now we have a quadratic equation. Treasure = x^2 – 8x – 20. We have simplified the equation, now we can solve for X. Inside the quadratic equation, x^2 – 8x – 20 = 0, we can solve by factoring and using the zero factor. This is called the compound equation, because we know that the two factors we have are 10 and -2, so we can solve for each binomial. The equation is (x-a)(x+b)=0 or (x – 10)(x + 2). The answer...
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...MAT 117 Week 8 CONCEPT APPLICATION Answer the following questions. Use Equation Editor or MathType when writing mathematical expressions or equations. Points will be deducted if a math editor is not used to properly format your work. First, download and save this file to your hard drive by selecting Save As from the File menu. Save with the filename: yourLastnameFirstnameMat117Week8CA. Click the 3rd column to enter your work, the rows will automatically expand as you enter text. Attach your completed document and post to the Assignments Section. |# | |Show your work and final answer in this column. |- Pts |+ Pts | | | |Include units when applicable. | | | |1 |A plasma TV company determines that its total profit on the production and sale of x TVs is given by: [pic] | |0 |0 | |a |Will the graph of this function open up or down? | | |2 | | |How can you tell by looking at the equation? | | | | |b |As the number of TV’s produced increases, what | | |2 | | |happens with the profit? | ...
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...Running head: Pythagorean Quadratic Pythagorean Quadratic Sharlee M. Walker MAT 221 Instructor Xiaolong Yao December 2, 2013 Pythagorean Quadratic Ahmed’s half of the map doesn’t indicate which direction the 2x + 6 paces should go, we can assume that his and Vanessa’s paces should end up in the same place. I did this out on scratch piece of paper and I saw that it forms a right triangle with 2x + 6 being the length of the hypotenuse, and x and 2x + 4 being the legs of the triangle. Now I know how I can use the Pythagorean Theorem to solve for x. The Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse c, these lengths have the formula of a2 + b2 = c2. Let a = x, and b = 2x + 4, so that c = 2x + 6. Then, by putting these measurements into the Theorem equation we have x2 + (2x + 4)2 = (2x + 6)2. The binomials into the Pythagorean Thermo x2 + 4x2 + 16x + 16 = 4x2 + 24x + 36 are the binomials squared. Then 4x2 on both sides of the equation which can be (-4x2 -4x2) subtracted out first leaving the equation to be x2 + 16x + 16 = 24x + 36. Next we should subtract 16x from both sides of equation, which then leaves us with: x2 +16 = 8x + 36. The next step would then be to subtract 36 from both sides to get a result of. x2 -20= 8x. Finally we need to subtract 8x from both sides to get x2 – 8x...
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...MAPÚA INSTITUTE OF TECHNOLOGY Department of Mathematics COURSE SYLLABUS 1. Course Code: Math 10-3 2. Course Title: Algebra 3. Pre-requisite: none 4. Co-requisite: none 5. Credit: 3 units 6. Course Description: This course covers discussions on a wide range of topics necessary to meet the demands of college mathematics. The course discussion starts with an introductory set theories then progresses to cover the following topics: the real number system, algebraic expressions, rational expressions, rational exponents and radicals, linear and quadratic equations and their applications, inequalities, and ratio, proportion and variations. 7. Student Outcomes and Relationship to Program Educational Objectives Student Outcomes Program Educational Objectives 1 2 (a) an ability to apply knowledge of mathematics, science, and engineering √ (b) an ability to design and conduct experiments, as well as to analyze and interpret from data √ (c) an ability to design a system, component, or process to meet desired needs √ (d) an ability to function on multidisciplinary teams √ √ (e) an ability to identify, formulate, and solve engineering problems √ (f) an understanding of professional and ethical responsibility √ (g) an ability to communicate effectively √ √ (h) the broad education necessary to understand the impact of engineering solutions in the global and societal context √ √ (i) a recognition of the need for, and an ability to engage...
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...Republic of the Philippines EDUARDO L. JOSON MEMORIAL COLLEGE Palayan City S Y L L A B U S COURSE NO. : Math 18 PROGRAM: B.S. in Business Administration DESCRIPTIVE TITLE : Quantitative Techniques YEAR AND SECTION: 3A, 3B, 3C, 3D CREDIT : 3 Units SCHOOL YEAR: 1ST SEMESTER 2013-2014 COURSE DESCRIPTION: This course is designed for Commerce and Accountancy students which deals with the basic algebraic expressions, linear equations and inequalities, solving problems in a linear programming involving graphical method, simplex method, transportation method and assignment method, the break even analysis, the decision theory, business forecasting and inventory. GRADING SYSTEM: To obtain a passing mark, students should at least master 75% of the lesson. Computations of grades are shown below: For Prelim, Midterm and Final: |Class Standing (70%) |Examination (30%) | |Quizzes (20%) |Assignment (10%) |Project(20%) |Participation(20%) | | |Tentative Grade = Class standing + Examination | |Final Grade = Prelim (30%) + Midterm (30%) + Final (40%) ...
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