| Introduction |
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2 | (1) |
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PART 1 SETTING THE FOUNDATION: THE NUTS AND BOLTS OF PRE-CALCULUS |
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5 | (108) |
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Chapter 1 Preparing for Pre-Calculus |
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7 | (18) |
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Reviewing Order of Operations: The Fun in Fundamentals |
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8 | (2) |
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Keeping Your Balance While Solving Equalities |
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10 | (2) |
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When Your Image Really Counts: Graphing Equalities and Inequalities |
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12 | (3) |
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12 | (1) |
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Graphing by using the slope-intercept form |
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13 | (1) |
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14 | (1) |
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Using Graphs to Find Distance, Midpoint, and Slope |
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15 | (4) |
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15 | (1) |
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16 | (1) |
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16 | (3) |
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Answers to Problems on Fundamentals |
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19 | (6) |
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Chapter 2 Real Numbers Come Clean |
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25 | (14) |
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25 | (3) |
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Expressing Inequality Solutions in Interval Notation |
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28 | (2) |
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Radicals and Exponents --- Just Simplify! |
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30 | (3) |
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Getting Out of a Sticky Situation, or Rationalizing |
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33 | (2) |
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Answers to Problems on Real Numbers |
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35 | (4) |
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Chapter 3 Controlling Functions by Knowing Their Function |
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39 | (36) |
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Using Both Faces of the Coin: Even and Odd |
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40 | (2) |
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Leaving the Nest: Transforming Parent Graphs |
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42 | (7) |
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42 | (1) |
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42 | (1) |
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43 | (1) |
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43 | (1) |
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44 | (1) |
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44 | (2) |
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46 | (1) |
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46 | (1) |
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Combinations of transformations |
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46 | (3) |
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Graphing Rational Functions |
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49 | (3) |
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Piecing Together Piecewise Functions |
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52 | (2) |
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54 | (1) |
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Evaluating Composition of Functions |
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55 | (2) |
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Working Together: Domain and Range |
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57 | (2) |
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Unlocking the Inverse of a Function: Turning It Inside Out |
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59 | (2) |
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Answers to Problems on Functions |
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61 | (14) |
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Chapter 4 Searching for Roots |
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75 | (20) |
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Factoring a Factorable Quadratic |
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75 | (3) |
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Solving a Quadratic Polynomial Equation |
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78 | (2) |
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78 | (1) |
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79 | (1) |
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Solving High-Order Polynomials |
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80 | (4) |
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80 | (1) |
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Determining positive and negative roots: Descartes' Rule of Signs |
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81 | (1) |
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Counting on imaginary roots |
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81 | (1) |
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Getting the rational roots |
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81 | (1) |
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Finding roots through synthetic division |
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82 | (2) |
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Using Roots to Create an Equation |
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84 | (1) |
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85 | (4) |
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Answers to Problems on Roots and Degrees |
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89 | (6) |
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Chapter 5 Exponential and Logarithmic Functions |
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95 | (18) |
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Working with Exponential Functions |
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95 | (3) |
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Eagerly Engaging Edgy Logarithmic Solutions |
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98 | (3) |
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Making Exponents and Logs Work Together |
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101 | (2) |
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Using Exponents and Logs in Practical Applications |
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103 | (3) |
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Answers to Problems on Exponential and Logarithmic Functions |
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106 | (7) |
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PART 2 TRIG IS THE KEY: BASIC REVIEW, THE UNIT CIRCLE, AND GRAPHS |
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113 | (42) |
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Chapter 6 Basic Trigonometry and the Unit Circle |
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115 | (22) |
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Finding the Six Trigonometric Ratios |
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115 | (3) |
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Solving Word Problems with Right Triangles |
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118 | (3) |
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Unit Circle and the Coordinate Plane: Finding Points and Angles |
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121 | (3) |
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Finding Ratios from Angles on the Unit Circle |
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124 | (3) |
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127 | (2) |
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Making and Measuring Arcs |
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129 | (2) |
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Answers to Problems on Basic Trig and the Unit Circle |
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131 | (6) |
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Chapter 7 Graphing and Transforming Trig Functions |
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137 | (18) |
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Getting a Grip on Periodic Graphs |
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137 | (1) |
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Parent Graphs and Transformations: Sine and Cosine |
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138 | (3) |
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Tangent and Cotangent: More Family Members |
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141 | (2) |
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Generations: Secant and Cosecant |
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143 | (4) |
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Answers to Problems on Graphing and Transforming Trig Functions |
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147 | (8) |
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PART 3 DIGGING INTO ADVANCED TRIG: IDENTITIES, THEOREMS, AND APPLICATIONS |
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155 | (54) |
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Chapter 8 Basic Trig Identities |
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157 | (18) |
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Using Reciprocal Identities to Simplify Trig Expressions |
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157 | (2) |
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Simplifying with Pythagorean Identities |
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159 | (1) |
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Discovering Even-Odd Identities |
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160 | (2) |
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Simplifying with Co-Function Identities |
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162 | (1) |
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Moving with Periodicity Identities |
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163 | (2) |
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Tackling Trig Proofs (Identities) |
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165 | (2) |
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Answers to Problems on Basic Trig Identities |
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167 | (8) |
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Chapter 9 Advanced Trig Identities |
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175 | (18) |
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Simplifying with Sum and Difference Identities |
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175 | (3) |
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Using Double-Angle Identities |
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178 | (2) |
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Reducing with Half-Angle Identities |
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180 | (1) |
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Changing Products to Sums |
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181 | (1) |
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Expressing Sums as Products |
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182 | (2) |
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Powering Down: Power-Reducing Formulas |
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184 | (2) |
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Answers to Problems on Advanced Trig Identities |
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186 | (7) |
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Chapter 10 Solving Oblique Triangles |
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193 | (16) |
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Solving a Triangle with the Law of Sines: ASA and AAS |
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194 | (1) |
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Tackling Triangles in the Ambiguous Case: SSA |
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195 | (2) |
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Conquering a Triangle with the Law of Cosines: SAS and SSS |
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197 | (1) |
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Using Oblique Triangles to Solve Practical Applications |
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198 | (3) |
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201 | (1) |
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Answers to Problems on Solving Triangles |
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202 | (7) |
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PART 4 POLAR COORDINATES, CONES, SOLUTIONS, SEQUENCES, AND FINDING YOUR LIMITS |
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209 | (120) |
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Chapter 11 Exploring Complex Numbers and Polar Coordinates |
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211 | (18) |
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Performing Operations with and Graphing Complex Numbers |
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212 | (3) |
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Round a Pole: Graphing Polar Coordinates |
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215 | (2) |
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Changing to and from Polar |
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217 | (3) |
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220 | (3) |
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220 | (1) |
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220 | (1) |
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220 | (1) |
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220 | (1) |
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220 | (1) |
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221 | (2) |
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Answers to Problems on Complex Numbers and Polar Coordinates |
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223 | (6) |
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Chapter 12 Conquering Conic Sections |
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229 | (36) |
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230 | (1) |
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Going Round and Round with Circles |
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230 | (2) |
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The Ups and Downs: Graphing Parabolas |
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232 | (5) |
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Standing tall: Vertical parabolas |
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233 | (2) |
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Lying down on the job: Horizontal parabolas |
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235 | (2) |
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The Fat and the Skinny: Graphing Ellipses |
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237 | (4) |
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Short and fat: The horizontal ellipse |
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237 | (2) |
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Tall and skinny: The vertical ellipse |
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239 | (2) |
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No Caffeine Required: Graphing Hyperbolas |
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241 | (5) |
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241 | (3) |
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244 | (2) |
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Identifying Conic Sections |
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246 | (2) |
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Conic Sections in Parametric Form and Polar Coordinates |
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248 | (5) |
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Parametric form for conic sections |
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248 | (2) |
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Changing from parametric form to rectangular form |
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250 | (1) |
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Conic sections on the polar coordinate plane |
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251 | (2) |
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Answers to Problems on Conic Sections |
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253 | (12) |
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Chapter 13 Finding Solutions for Systems of Equations |
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265 | (36) |
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A Quick-and-Dirty Technique Overview |
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266 | (1) |
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Solving Two Linear Equations with Two Variables |
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266 | (3) |
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267 | (1) |
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268 | (1) |
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Not-So-Straight: Solving Nonlinear Systems |
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269 | (3) |
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One equation that's linear and one that isn't |
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269 | (1) |
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270 | (1) |
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Systems of rational equations |
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271 | (1) |
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Systems of More Than Two Equations |
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272 | (2) |
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Graphing Systems of Inequalities |
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274 | (2) |
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Breaking Down Decomposing Partial Fractions |
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276 | (2) |
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278 | (3) |
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Getting It in the Right Form: Simplifying Matrices |
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281 | (2) |
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Solving Systems of Equations Using Matrices |
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283 | (6) |
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283 | (2) |
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285 | (2) |
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287 | (2) |
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Answers to Problems on Systems of Equations |
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289 | (12) |
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Chapter 14 Spotting Patterns in Sequences and Series |
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301 | (14) |
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General Sequences and Series: Determining Terms |
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301 | (2) |
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Working Out the Common Difference: Arithmetic Sequences and Series |
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303 | (2) |
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Simplifying Geometric Sequences and Series |
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305 | (3) |
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Expanding Polynomials Using the Binomial Theorem |
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308 | (2) |
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Answers to Problems on Sequences, Series, and Binomials |
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310 | (5) |
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Chapter 15 Previewing Calculus |
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315 | (14) |
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Finding Limits: Graphically, Analytically, and Algebraically |
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316 | (5) |
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316 | (2) |
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318 | (1) |
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319 | (2) |
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321 | (1) |
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Calculating the Average Rate of Change |
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322 | (1) |
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323 | (3) |
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Answers to Problems on Calculus |
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326 | (3) |
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329 | (16) |
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Chapter 16 Ten Plus Parent Graphs |
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331 | (10) |
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Squaring Up with Quadratics |
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331 | (1) |
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332 | (1) |
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Rooting for Square Roots and Cube Roots |
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333 | (1) |
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Graphing Absolutely Fabulous Absolute Value Functions |
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334 | (1) |
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Flipping over Rational Functions |
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334 | (1) |
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Exploring Exponential Graphs and Logarithmic Graphs |
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335 | (1) |
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Seeing the Sine and Cosine |
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336 | (1) |
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Covering Cosecant and Secant |
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337 | (1) |
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Tripping over Tangent and Cotangent |
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338 | (1) |
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Lining Up and Going Straight with Lines |
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339 | (2) |
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Chapter 17 Ten Missteps to Avoid |
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341 | (4) |
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Going Out of Order (of Operations) |
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341 | (1) |
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FOILing Binomials Incorrectly |
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342 | (1) |
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Breaking Up Fractions Badly |
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342 | (1) |
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Combining Terms That Can't Be Combined |
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342 | (1) |
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Forgetting to Flip the Fraction |
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342 | (1) |
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Losing the Negative (Sign) |
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343 | (1) |
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343 | (1) |
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Executing Exponent Errors |
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343 | (1) |
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344 | (1) |
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Misinterpreting Trig Notation |
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344 | (1) |
| Index |
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345 | |
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