By: Victor Hui Introduction Leonhard Euler was a ground-breaking Swiss mathematician and physicist from the 1700’s. He made many revolutionary discoveries. However‚ the one that caught my eye was his solution to the Basel Problem in the year 1734. The Basel problem was initially posed by an Italian mathematician by the name of Pietro Mengoli in the early 1640’s. This problem baffled the even the greatest minds at the time. Branching from mathematical analysis‚ the Basel problem involved knowledge
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|equations and inequalities‚ graphing linear equations in two variables‚ solving systems of linear | | |equations in two variables‚ operations with exponential expressions and polynomials‚ factoring | |
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Graded Assignment Unit Test‚ Part 2: Polynomials and Power Functions Answer the questions and show your work. When you are finished‚ submit this assignment to your teacher through the appropriate dropbox basket. (3 pts) 1.) Factor 100x^2 – 49 to factor‚ use the difference of squares formula‚ because both the terms are perfect squares the difference of squares formula is a^2 – b^2 = (a-b)(a+b) therefore 100x^2 – 49 = (10x)^2 – 7^2 = (10x – 7)(10x +7) (5 pts) 2.) Solve x^2 –
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ACCUPLACER Arithmetic & Elementary Algebra Study Guide Acknowledgments We would like to thank Aims Community College for allowing us to use their ACCUPLACER Study Guides as well as Aims Community College English Faculty for creating the Sentence Skills Study Guide. Table of Contents Assessment Rules and Regulations …………………………………... . 1-2 Arithmetic ……………………………………………...….……………. .. 3-11 Elementary Algebra …………………………………………………….. 12-26 Math Sequence …………………………………………………… back page
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for example: √5’ (for clarification purposes ’ marks the end of the root) • √a’ x √b’ = √a x b’ = √ab’ • √a’ / √b’ = √a/b’ • √a+b’ ≠ √a’+√b’ It is often more useful when denominator of a fraction is rationalised. This is done by multiplying the top and bottom by the conjugate‚ as the product of two conjugates is always rationalised because (a+b)(a-b)=(a^2)-(b^2) and a surd^2 is always rational. (^2 means squared) Quadratic Graphs and
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CHAPTER 1 – THE REAL NUMBER SYSTEM 1 .1 – THE CONCEPT OF OPPOSITES Any movement from an initial point on the number line going to the right is represented by a positive sign (+) ‚while a movement to the left is represented by a negative sign (-).These numbers are sometimes called directed numbers or signed numbers. e.g. 1.2 - FUNDAMENTAL OPERATIONS ON INTEGERS 1.2.1 – ADDITION OF INTEGERS To add integers with the same sign ‚add without regard to the signs.Then affix the common sign of
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Higher Level Mathematics Internal Assessment Type I Shadow Functions Contents Introduction: Functions/Polynomials 3 Part A: Quadratic Polynomials 4 Part B: Cubic Polynomials 12 Introduction: In mathematics‚ function is defined as a relationship‚ or more of a correspondence between the set of input values and the set of output values. Also‚ a rule is involved‚ or as it may be referred to‚ a ‘set of ordered pairs’ that assigns a unique output for each of the input. The
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Chinese remainder theorem The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. It was first published in the 3rd to 5th centuries by Chinese mathematician Sun Tzu. In its basic form‚ the Chinese remainder theorem will determine a number n that when divided by some given divisors leaves given remainders. For example‚ what is the lowest number n that when divided by 3 leaves a remainder of 2‚ when divided by 5 leaves a remainder
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Philadelphia‚ PA‚ USA April 27‚ 1997 ii Contents Foreword vii A Quick Start . . . ix I 1 Background 1 Proof Machines 1.1 Evolution of the province of human thought 1.2 Canonical and normal forms . . . . . . . . . 1.3 Polynomial identities . . . . . . . . . . . . . 1.4 Proofs by example? . . . . . . . . . . . . . . 1.5 Trigonometric identities . . . . . . . . . . . 1.6 Fibonacci identities . . . . . . . . . . . . . . 1.7 Symmetric function identities . . . . . . .
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References: Dugopolski‚ M. (2012). Elementary and intermediate algebra (4th ed.). New York‚ NY: McGraw-Hill Publishing Polynomials. (2013). Retrieved from http://www.mathsisfun.com/algebra/polynomials.html The Pythagorean Theorem. (1991-2012). Retrieved August 4‚ 2013‚ from the Pythagorean Theorem website: http://www.purplemath.com/index.htm
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