1314-MJ1E3 -V1 Level J Algebra First Two Weeks Sample Questions Exam 1. Solve‚ x ( x + 9 ) = 0. Reference: Algebra 1‚ Part 2‚ Chapter 8.7‚ Activity (1a)‚ Page 78 Solution: x = 0 or x = −9 2. Factor‚ x 2 + 5 x + 2 xy + 10 y. . Reference: Algebra 1‚ Part 2‚ Chapter 8.6.1 Activity 1 #(d)‚ Page 73 Solution: x 2 + 5 x + 2 xy + 10 y = x( x + 5) + 2 y ( x + 5) = ( x + 5)( x + 2 y ) 3. Factor‚ a 2 + 4 a − 32. Reference: Algebra 1 Part 2‚ Chapter 8.4.3‚ Activity (a)‚ Page 61
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Quadratic Equations ax2 + bx + c = 0 Examples of Quadratic equations 1. x2 +2x – 8 = 0 2. x2 – 10x + 25 = 0 3. 3x2 + x - 2 = 0 Quadratic Formula If [pic] a x2 + b x + c = 0‚ then [pic] Finding the zeros of the quadratic functions - The zeros of a function are the input values which result in an output value of zero. One way of solving quadratic equations is using factoring Examples are the following: 1) x2 + 5x + 6 = 0 Set this equal to zero:
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following relational database: employee(employee-name‚ street‚ city) works(employee-name‚ company-name‚ salary) company(company-name‚ city) manages(employee-name‚ manager-name) For each of the following queries‚ give an expression in relational algebra‚ tuple relational calculus‚ and domain relational calculus: a. Find the names of all employees who work for First Bank Corporation. b. Find the names and cities of residence of all employees who work for First Bank Corporation. c. Find
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STUDY GUIDE LINEAR ALGEBRA AND ITS APPLICATIONS THIRD EDITION UPDATE David C. Lay University of Maryland – College Park Copyright © 2006 Pearson Addison-Wesley. All rights reserved. Reproduced by Pearson Addison-Wesley from electronic files supplied by the author. Copyright © 2006 Pearson Education‚ Inc. Publishing as Pearson Addison-Wesley‚ 75 Arlington Street‚ Boston‚ MA 02116. All rights reserved. No part of this publication may be reproduced‚ stored in a retrieval system‚ or transmitted
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Quadratic equation In elementary algebra‚ a quadratic equation (from the Latin quadratus for "square") is any equation having the form where x represents an unknown‚ and a‚ b‚ and c represent known numbers such that a is not equal to 0. If a = 0‚ then the equation is linear‚ not quadratic. The numbers a‚ b‚ and c are the coefficients of the equation‚ and may be distinguished by calling them‚ the quadratic coefficient‚ the linear coefficient and the constant or free
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Summer 2010-3 CLASS NOTES CHAPTER 1 Section 1.1: Linear Equations Learning Objectives: 1. Solve a linear equation 2. Solve equations that lead to linear equations 3. Solve applied problems involving linear equations Examples: 1. [pic] [pic] 3. A total of $51‚000 is to be invested‚ some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3‚000‚ how much will be invested in each type
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CBSE TEST PAPER-01 MATHEMATICS (Class-10) Chapter 3 : Pair Linear Equations in Two Variables 1. 2. 3. 4. For which values of p does the pair of equations given below have unique solution? (2 marks) 4x + py + 8 = 0‚ 2x + 2y + 2 = 0 Solve graphically: 3x + 2y = 14x‚ x – 4y = 7 (3 marks) Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y -12 = 0. Represent this situation geometrically. (3 marks) a b c On comparing the ratio 1 ‚ 1 and 1 find out whether the lines representing the
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7 x2 = 11 x1 + 2 x2 = −2 1 5 1 0 1 0 1 0 2 7 2 −3 2 1 0 1 −2 11 −2 21 −2 −7 12 −7 −3x2 = 21 x1 + 2 x2 = −2 x2 = −7 x1 = 12 x2 = −7 1 2 CHAPTER 1 • Linear Equations in Linear Algebra 3. The point of intersection satisfies the system of two linear equations: x1 + 5 x2 = 7 x1 − 2 x2 = −2 1 1 5 −2 7 −2 x1 + 5 x2 = 7 Replace R2 by R2 + (–1)R1 and obtain: Scale R2 by –1/7: Replace R1 by R1 + (–5)R2: The point
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Algebra in the Real World and Everyday Life Hal Hagood u07a2 Table of Contents Page Number Table of Contents …………………………………………………………………… 2 Introduction ………………………………………………………………………… 3 Ways That Algebra Affects Business or Science ………………………………….. 5 How Algebraic Concepts Can Solve Everyday Problems in Life …………………. 6 Ways Algebra Can Solve Everyday Problems in Business or Science ……………. 9 A Surprising Finding About How Algebra Affects
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Elluminate Live! - LIVE LESSON 7.09 Jan 9‚ 2013 7:48:40 PM Welcome to Lesson 7.09 Page 1. Elluminate Live! - LIVE LESSON 7.09 Jan 9‚ 2013 7:48:40 PM 7.09 Room 1 - Attendance Page 2. Elluminate Live! - LIVE LESSON 7.09 Jan 9‚ 2013 7:48:40 PM 7.09 Room 1 - 7.09 Polynomials Activity Page 3. Elluminate Live! - LIVE LESSON 7.09 Jan 9‚ 2013 7:48:40 PM 7.09 Room 1 - Common Core Standards Covered in this Lesson: Page 4. Elluminate Live! - LIVE LESSON 7
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