SCHAUM’S Easy OUTLINES - sman78-jkt.sch.id

1 schaum 'S easy OUTLINES . PRECALCULUS. Other Books in schaum 's easy OUTLINES Series Include: schaum 's easy OUTLINES : College Mathematics schaum 's easy OUTLINES : College Algebra schaum 's easy OUTLINES : Calculus schaum 's easy OUTLINES : Elementary Algebra schaum 's easy OUTLINES : Mathematical Handbook of Formulas and Tables schaum 's easy OUTLINES : Geometry schaum 's easy OUTLINES : Trigonometry schaum 's easy OUTLINES : Probability and Statistics schaum 's easy OUTLINES : Statistics schaum 's easy OUTLINES : Principles of Accounting schaum 's easy OUTLINES : Biology schaum 's easy OUTLINES : College Chemistry schaum 's easy OUTLINES : Genetics schaum 's easy OUTLINES : Human Anatomy and Physiology schaum 's easy OUTLINES : Organic Chemistry schaum 's easy OUTLINES .

2 Physics schaum 's easy OUTLINES : Basic Electricity schaum 's easy OUTLINES : Programming with C++. schaum 's easy OUTLINES : Programming with Java schaum 's easy OUTLINES : French schaum 's easy OUTLINES : German schaum 's easy OUTLINES : Spanish schaum 's easy OUTLINES : Writing and Grammar schaum 'S easy OUTLINES . PRECALCULUS. Ba s e d o n S c h a u m ' s outline of P re c a l c u l u s by Fred Safier Abridgement Editor: K i m b e r ly S . K i r k p at r i c k S C H AU M ' S O U T L I N E S E R I E S. M c G R AW - H I L L. New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America.

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7 Contents Chapter 1 Number Systems, Polynomials, and Exponents 1. Chapter 2 Equations and Inequalities 13. Chapter 3 Systems of Equations and Partial Fractions 27. Chapter 4 Analytic Geometry and Functions 39. Chapter 5 Algebraic Functions and Their Graphs 54. Chapter 6 Exponential and Logarithmic Functions 71. Chapter 7 Conic Sections 78. Chapter 8 Trigonometric Functions 87. Chapter 9 Trigonometric Identities and Trigonometric Inverses 104. Chapter 10 Sequences and Series 116. Index 121. v Copyright 2002 by the Mcgraw-Hill Companies, Inc. Click Here for Terms of Use. This page intentionally left blank. Chapter 1. Number Systems, Polynomials, and Exponents In This Chapter: Sets of Numbers Axioms for the Real Number System Properties of Inequalities Absolute Value Complex Numbers Order of Operations Polynomials Factoring Exponents Rational and Radical Expressions Sets of Numbers The sets of numbers used in algebra are, in general, subsets of R, the set of real numbers.

8 Natural numbers N: The counting numbers, , 1, 2, 3, . Integers Z: The counting numbers, together with their opposites and 0, , 0, 1, 2, 3, , 1, 2, 3 . 1. Copyright 2002 by the Mcgraw-Hill Companies, Inc. Click Here for Terms of Use. 2 PRECALCULUS. Rational Numbers Q: The set of all numbers that can be written as quotients a/b, b 0, a and b integers, , 3/17, 5/13, . Irrational Numbers H: All real numbers that are not rational 3. numbers, , , 2 , 5 , /3, . Example : The number 5 is a member of the sets Z, Q, R. The number is a member of the sets Q, R. The number 5 is a member of the sets H, R. Axioms for the Real Number System There are two fundamental operations, addition and multiplication, which have the following properties (a, b, c arbitrary real numbers): Commutative Laws : a + b = b + a: order does not matter in addition.

9 Ab = ba: order does not matter in multiplication. Associative Laws: a + (b + c) = (a + b) + c: grouping does not matter in repeated addition. a(bc) = (ab)c: grouping does not matter in repeated multi- plication. Distributive Laws: a(b + c) = ab + ac; also (a + b)c = ac + bc: multiplication is distributive over addition. Zero Factor Laws: For every real number a, a 0 = 0. If ab = 0, then either a = 0 or b = 0. Laws for Negatives: ( a) = a ( a)( b) = ab ab = ( a)b = a( b) = ( a)( b) = (ab). ( 1)a = a Laws for Quotients: a a a a = = = . b b b b a a =. b b a c = if and only if ad = bc. b d CHAPTER 1: Number Systems, Polynomials, and Exponents 3. a ka = , for k any nonzero real number. b kb Properties of Inequalities The number a is less than b, written a < b, if b a is positive.

10 If a < b then b is greater than a, written b > a. If a is either less than or equal to b, this is written a b. If a b then b is greater than or equal to a, written b a. The following properties may be deduced from these definitions: If a < b, then a + c < b + c. ac < bc if c > 0. If a < b, then . ac > bc if c < 0 . If a < b and b < c, then a < c. Absolute Value The absolute value of a real number a, written a , is defined as follows: a if a 0. a = . a if a < 0 . Complex Numbers Not all numbers are real numbers. The set of complex numbers, C, con- tains all numbers of the standard form a + bi, where a and b are real and i 2 = 1. Since every real number x can be written as x + 0i, it follows that every real number is also a complex number.