Introduction to College Algebra November 9‚ 2009 2 Chapter 1 Sets Definition 1.1. A set is a well-defined collection of distinct objects. Each object in a set is called an element of the set. By “well-defined”‚ we mean that the rule of membership to the set is clear. Example 1.2. The following are examples of sets. 1. The set of counting number less than 5. 2. The set of vowels in the word “mathematics”. 3. The set of cities in the Philippines. 4. The set of positive integers from −2 to
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MIDTERM NOTES Solve Linear Equations 0. Cancel all denominators by multiplying every term by the LCD. 1. Simplify LHS and RHS. 2. Eliminate variable term on RHS. 3. Eliminate variable term on LHS. 4. Eliminate the coefficient of the variable. Solve Rational Equations 1. Find LCD. 2. Cancel all denominators by multiplying every term by the LCD. 3. Solve. 4. Omit those solutions that make LCD=0. Complex Numbers: a + bi Powers of i: i0 = 1‚ i1 = i‚ i2 = −1‚ i3 = −i in = ir where r is the
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Even though college algebra is considered to be an obstacle for many students in terms of degree completion‚ as teachers we must teach useful strategies to motivate our students to find interest in mathematics. Recently‚ there is a psychological problem that we as teachers will face in the future‚ which is that some students believe they were born incompetent in math. However‚ “effort is key to their success and failure is a result of a lack of effort” (Cortes-Suarez‚ 2004). As teachers‚ we must
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Tutorial 1: Review of Basic Concepts 1. Let[pic]. List the elements of A that belong to the given set. i. Nature numbers ii. Integers iii. Rational numbers 2. Let set M =[pic]. List the elements of M that belong to the given set. i. Whole numbers ii. Integers iii. Rational numbers 3. Multiply out the brackets: a) 7(x + 2y) – 2(3y – 5x) (b) 2x2 + y – z2 – 2(3x2 + 2y – z) (c) (2x – 5)(5 + 2x) (d) (9y - 8)(3y - 3) 4. Evaluate the following without
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At first‚ it seems that the Video Text Interactive Algebra Course is expensive compared to other programs‚ however since this curriculum includes Pre-Algebra‚ Algebra 1‚ and Algebra 2 it is less expensive than other curriculum that sells each course individually. Each Algebra Program Module includes Course Notes‚ Student Work Text‚ Solutions Manual‚ Instructor’s Guide & Progress Tests‚ and DVDs. The video lessons are around 5 to 10 minutes long. This version is still available‚ but an online version
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Bibliography: Published on U.S. 2007 Flanders‚ Harley and Price‚ Justin J.‚ Algebra Published on U.S. 2007 Hackworth‚ Robert‚ Focus on Elementary Algebra Published on U.S. 2008 Rowe‚ David E
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On the side of his house‚ a man is going to build two enclosures. One enclosure for a garden and another enclosure to keep his dogs in so the dogs aren’t roaming around. It is illegal to have any dogs roaming around. He bought 180ft of fence to use and one side is already existing. Refer to the picture on the next page. Since there are three short sides and one long side‚ to set up the perimeter‚ the short sides will be x and the long side will be y. So the equation is 3x + y = 180. The 180 comes
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Student Answer Form Unit 5 IP_2 April 22‚ 2011 (1.) a. e^(0.05t)=1600 Answer: t=147.556 Show your work: ln(e^(0.05t))=ln(1600) 0.05t=ln(1600) (0.05t)/(0.05)=(ln(1600))/(0.05) t=(ln(1600))/(0.05) t=20ln(1600) t=147.556 b. ln(4x)=3 Answer: x= 5.0214 Show your work: 4x = e^3/4 c. log2(8-6x) = 5 Answer: x= -4 Show work: 8 – 6x = 2^5 6x = 8 – 32 X = - 24/6 d. 4 + 5e – x = 0 Answer: no solution found Show work: e ^ - x = - 4/5 (2.)
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Student Answer form Unit 2 1. a. x-4x=-6 A) 1 B) -10 C) -6 X^2-10x-24=0 (X-4) (x+6) X-4=0 x=4 X+6=0 x+-6 b. x=7+4=5.5 x=7-4=1.5 x=-b±b2-4ac2a x= (-7) ± (-7)2-4(3) (20)2a x=7±64-802a x=7±-16 x=7+4/2=5.5 x=7-4/2=1.5 c. 10x^2+x-3=0 x=-b±b2-4ac2a x=-1± (1)2-4(10) (-3)2(10) x=1±1-12020 x=1±10 x=1+320 = 5 x=1-320= 10 2. a. (-2.3‚ 0)‚ (0‚ 6.3) b. This is a maximum function.
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titled “Basic Algebra Skills-Real numbers & Algebraic Equations‚ Exponents & Scientific Notation‚ Radicals & Radical Exponents‚ and Polynomials”. I chose this presentation because I felt I needed to remember algebraic equations‚ exponents and polynomials. I have not had algebra for many years so this presentation was a very good refresher. It reminded me about real numbers and algebraic expressions and square roots. It was good to be reminded about the steps you take in algebra to solve an equation
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