Intermediate algebra within reach

693 Pages·2014·52.584 MB·English

by  Larson, Ron

Geometry
Formulas for Area (A), Perimeter (P), Circumference (C), and Volume (V)
Square Rectangle
A = s2 A = lw w
s
P = 4s P = 2l + 2w
l
s
Triangle Circle
1 A = πr2
A = — bh a c
2 r
h C = 2πr
P = a + b + c
b
Trapezoid b Parallelogram
1
1 A = bh
A = — 2 h(b1 + b2) h h a
P = 2a + 2b
b
2 b
Cube Rectangular Solid
h
s
V = s3 V = lwh
l
s
w
s
Circular Cylinder r Sphere
V = πr2h 4
V = — π r3
h 3 r
Special Triangles Pythagorean Theorem
Equilateral Triangle Isosceles Triangle a2 + b2 = c2

a a c
a a
a
a
b
b
Right Triangle
Similar Triangles
Hypotenuse
a b c f
Legs —d = — e = — f c a d
b e
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Common Formulas Basic Rules of Algebra
Distance Commutative Property of Addition
d = distance traveled
d = rt a+ b = b + a
t = time
r = rate
Commutative Property of Multiplication
Temperature ab= ba
9 F = degrees Fahrenheit
F = — C + 32 Associative Property of Addition
5 C = degrees Celsius
(a + b) + c = a + (b + c)
Simple Interest
Associative Property of Multiplication
I = interest
I = Prt
P = principal (ab)c = a(bc)
r = annual interest rate
t = time in years Left Distributive Property
a(b + c) = ab + ac
Compound Interest
( r)nt A = balance Right Distributive Property
A = P 1 + — n P = principal
(a + b)c = ac + bc
r = annual interest rate
n = compoundings per year
Additive Identity Property
t = time in years
a+ 0 = 0 + a = a
Coordinate Plane: Midpoint Formula Multiplicative Identity Property
Midpoint of line segment ( x + x y + y ) a⋅ 1 = 1 ⋅ a = a
joining (x , y ) and (x , y ) —1 2 , —1 2
1 1 2 2 2 2
Additive Inverse Property
Coordinate Plane: Distance Formula a + (−a) = 0
d = distance between points (x , y ) and (x , y ) Multiplicative Inverse Property
1 1 2 2
d = √—(x2 − x1)2 +— (y2 − y1)2 a ⋅ —1a = 1, a ≠ 0
Quadratic Formula Properties of Equality
Solutions of ax2 + bx + c = 0 Addition Property of Equality
−b ± √—b2 − 4ac If a = b, then a + c = b + c.
x = — —
2a
Multiplication Property of Equality
Rules of Exponents If a = b, then ac = bc
(Assume a ≠ 0 and b ≠ 0.)
Cancellation Property of Addition
a0 = 1 am ⋅ an = am + n If a + c = b + c, then a = b.
(ab)m = am ⋅ bm (am)n = amn
Cancellation Property of Multiplication
am ( a)m am
— = am − n — = — If ac = bc, and c ≠ 0, then a = b.
an b bm
1 ( a)−n bn
a−n = — an —b = — an Zero Factor Property
If ab = 0, then a = 0 or b = 0.
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INTERMEDIATE
Algebra Within Reach
SIXTH EDITION
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INTERMEDIATE
Algebra Within Reach
SIXTH EDITION
Ron Larson
The Pennsylvania State University
The Behrend College
With the assistance of Kimberly Nolting
Hillsborough Community College
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
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Intermediate Algebra Within Reach, © 2014, 2010, 2005 Brooks/Cole, Cengage Learning
Sixth Edition
WCN: 02-200-203
Ron Larson
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Contents
1 FUNDAMENTALS OF ALGEBRA 1
1.1 The Real Number System 2
1.2 Operations with Real Numbers 10
1.3 Properties of Real Numbers 18
Mid-Chapter Quiz 26
1.4 Algebraic Expressions 28
1.5 Constructing Algebraic Expressions 36
Chapter Summary 44
Review Exercises 46
Chapter Test 48
2 LINEAR EQUATIONS AND INEQUALITIES 49
2.1 Linear Equations 50
2.2 Linear Equations and Problem Solving 58
2.3 Business and Scientific Problems 66
Mid-Chapter Quiz 76
2.4 Linear Inequalities 78
2.5 Absolute Value Equations and Inequalities 86
Chapter Summary 94
Review Exercises 96
Chapter Test 100
3 G RAPHS AND FUNCTIONS 101
3.1 The Rectangular Coordinate System 102
3.2 Graphs of Equations 110
3.3 Slope and Graphs of Linear Equations 118
3.4 Equations of Lines 126
Mid-Chapter Quiz 134
3.5 Graphs of Linear Inequalities 136
3.6 Relations and Functions 144
3.7 Graphs of Functions 152
Chapter Summary 160
Review Exercises 162
Chapter Test 166
4 S YSTEMS OF EQUATIONS
AND INEQUALITIES 167
4.1 Systems of Equations 168
4.2 Linear Systems in Two Variables 176
4.3 Linear Systems in Three Variables 184
Mid-Chapter Quiz 192
4.4 Matrices and Linear Systems 194
4.5 Determinants and Linear Systems 204
4.6 Systems of Linear Inequalities 214
Chapter Summary 222
Review Exercises 224
Chapter Test 227
Cumulative Test: Chapters 1−4 228
v
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vi Contents
5 POLYNOMIALS AND FACTORING 229
5.1 Integer Exponents and Scientific Notation 230
5.2 Adding and Subtracting Polynomials 238
5.3 Multiplying Polynomials 246
Mid-Chapter Quiz 254
5.4 Factoring by Grouping and Special Forms 256
5.5 Factoring Trinomials 264
5.6 Solving Polynomial Equations by Factoring 272
Chapter Summary 280
Review Exercises 282
Chapter Test 286
6 R ATIONAL EXPRESSIONS, EQUATIONS,
AND FUNCTIONS 287
6.1 Rational Expressions and Functions 288
6.2 Multiplying and Dividing Rational Expressions 296
6.3 Adding and Subtracting Rational Expressions 304
6.4 Complex Fractions 312
Mid-Chapter Quiz 320
6.5 Dividing Polynomials and Synthetic Division 322
6.6 Solving Rational Equations 330
6.7 Variation 338
Chapter Summary 346
Review Exercises 348
Chapter Test 352
7 R ADICALS AND COMPLEX NUMBERS 353
7.1 Radicals and Rational Exponents 354
7.2 Simplifying Radical Expressions 362
7.3 Adding and Subtracting Radical Expressions 370
Mid-Chapter Quiz 378
7.4 Multiplying and Dividing Radical Expressions 380
7.5 Radical Equations and Applications 388
7.6 Complex Numbers 396
Chapter Summary 404
Review Exercises 406
Chapter Test 410
Cumulative Test: Chapters 5−7 411
8 Q UADRATIC EQUATIONS, FUNCTIONS,
AND INEQUALITIES 413
8.1 Solving Quadratic Equations 414
8.2 Completing the Square 422
8.3 The Quadratic Formula 430
Mid-Chapter Quiz 438
8.4 Graphs of Quadratic Functions 440
8.5 Applications of Quadratic Equations 448
8.6 Quadratic and Rational Inequalities 456
Chapter Summary 464
Review Exercises 466
Chapter Test 470
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