Modelling Math: Modelling Problems Algebraically Page 1 Getting Started: Frequency Ranges, Review of Prerequisite Skills Page 2 1.1. Reviewing the Exponent Laws Page 4 1.3. Rational Exponents Page 11 1.3. Solving Exponential Equations Page 19 Technology Extension: Solving Exponential Equations With a Graphing Calculator Page 27 1.4. Review: Adding, Subtracting, and Multiplying Polynomials Page 28 1.5. Simplifying Rational Expressions Page 35 1.6. Multiplying and Dividing Rational Expressions Page 44 1.7. Adding and Subtracting Rational Expressions, I Page 53 1.8. Adding and Subtracting Rational Expressions, II Page 62 Technology Extension: Rational Expressions and the Graphing Calculator Page 70 1.9. Solving First-Degree Inequalities Page 72 Technology Extension: Solving Inequalities With a Graphing Calculator Page 82 Investigate & Apply: Modelling Restrictions Graphically Page 83 Review of Key Concepts Page 85 Chapter Test Page 90 Challenge Problems Page 92 Problem Solving Strategy: Model and Communicate Solutions Page 93 Problem Solving: Using the Strategies Page 95 Specific Expectations Page 96 Modelling Math: Measurements of Lengths and Areas Page 97 Getting Started: Store Profits, Review of Prerequisite Skills Page 98 2.1. The Complex Number System Page 100 2.2. Maximum or Minimum of a Quadratic Function by Completing the Square Page 110 2.3. Solving Quadratic Equations Page 120 Technology Extension: Solving Quadratic Equations Page 134 2.4. Tools for Operating With Complex Numbers Page 135 Technology Extension: Radical Expressions and Graphing Calculators Page 143 2.5. Operations With Complex Numbers in Rectangular Form Page 144 Investigate & Apply: Interpreting a Mathematical Model Page 153 Review of Key Concepts Page 154 Chapter Test Page 158 Challenge Problems Page 160 Problem Solving Strategy: Look for a Pattern Page 161 Problem Solving: Using the Strategies Page 164 Cumulative Review: Chapters 1 and 2 Page 165 Specific Expectations Page 166 Modelling Math: Falling Objects Page 167 Getting Started: Human Physiology, Review of Prerequisite Skills Page 168 3.1. Functions Page 170 3.2. Investigation: Properties of Functions Defined by $f(x) = \sqrt{x}$ and $f(x) = \frac{1}{x}$ Page 182 3.3. Horizontal and Vertical Translations of Functions Page 184 3.4. Reflections of Functions Page 194 3.5. Inverse Functions Page 208 3.6. Stretches of Functions Page 221 3.7. Combinations of Transformations Page 233 Investigate & Apply: Frieze Patterns Page 244 Review of Key Concepts Page 246 Chapter Test Page 254 Challenge Problems Page 257 Problem Solving Strategy: Solve Rich Estimation Problems Page 258 Problem Solving: Using the Strategies Page 261 Specific Expectations Page 262 Modelling Math: Ship Navigation Page 263 Getting Started: Parallactic Displacement, Review of Prerequisite Skills Page 264 4.1. Reviewing the Trigonometry of Right Triangles Page 266 4.2. The Sine and the Cosine of Angles Greater Than 90° Page 276 4.3. The Sine Law and the Cosine Law Page 283 Technology Extension: Using The Geometer's Sketchpad to Explore the SSA Case Page 296 4.4. The Sine Law: The Ambiguous Case Page 300 Investigate & Apply: The Cosine Law and the Ambiguous Case Page 312 Review of Key Concepts Page 313 Chapter Test Page 316 Challenge Problems Page 318 Problem Solving Strategy: Use a Diagram Page 319 Problem Solving: Using the Strategies Page 322 Cumulative Review: Chapters 3 and 4 Page 323 Specific Expectations Page 324 Modelling Math: Ocean Cycles Page 325 Getting Started: Daylight Hours, Review of Prerequisite Skills Page 326 5.1. Radians and Angle Measure Page 328 5.2. Trigonometric Ratios of Any Angle Page 341 Extension: Positive and Negative Angles of Rotation Page 351 5.3. Modelling Periodic Behaviour Page 355 5.4. Investigation: Sketching the Graphs of f(x) = sin x, f(x) = cos x, and f(x) = tan x Page 363 5.5. Stretches of Periodic Functions Page 367 5.6. Translations and Combinations of Transformations Page 378 Technology Extension: Sinusoidal Regression Page 392 5.7. Trigonometric Identities Page 393 5.8. Trigonometric Equations Page 402 Investigate & Apply: Modelling Double Helixes Page 411 Review of Key Concepts Page 412 Chapter Test Page 418 Challenge Problems Page 420 Problem Solving Strategy: Solve a Simpler Problem Page 421 Problem Solving: Using the Strategies Page 423 Specific Expectations Page 424 Modelling Math: The Motion of a Pendulum Page 425 Getting Started: Exploring Sequences, Review of Prerequisite Skills Page 426 6.1. Sequences Page 428 6.2. Arithmetic Sequences Page 436 6.3. Geometric Sequences Page 447 6.4. Recursion Formulas Page 457 6.5. Arithmetic Series Page 465 6.6. Geometric Series Page 472 Investigate & Apply: Relating Sequences and Systems of Equations Page 479 Review of Key Concepts Page 480 Chapter Test Page 486 Challenge Problems Page 488 Problem Solving Strategy: Guess and Check Page 489 Problem Solving: Using the Strategies Page 492 Cumulative Review: Chapters 5 and 6 Page 493 Specific Expectations Page 494 Modelling Math: Making Financial Decisions Page 495 Getting Started: Comparing Costs, Review of Prerequisite Skills Page 496 7.1. Investigation: Simple Interest, Arithmetic Sequences, and Linear Growth Page 498 7.2. Compound Interest Page 501 7.3. Investigation: Compound Interest, Geometric Sequences, and Exponential Growth Page 512 7.4. Present Value Page 516 7.5. Amount of an Ordinary Annuity Page 526 7.6. Present Value of an Ordinary Annuity Page 534 7.7. Technology: Amortization Tables and Spreadsheets Page 544 7.8. Mortgages Page 559 Investigate & Apply: The Cost of Car Ownership Page 571 Review of Key Concepts Page 572 Chapter Test Page 577 Challenge Problems Page 579 Problem Solving Strategy: Use Logic Page 580 Problem Solving: Using the Strategies Page 583 Specific Expectations Page 584 Modelling Math: Motion in Space Page 585 Getting Started: Communications Satellites, Review of Prerequisite Skills Page 586 8.1. Technology: Constructing Loci Using The Geometer's Sketchpad Page 588 8.2. Equations of Loci Page 594 8.3. Technology: Loci and Conics Page 601 8.4. The Circle Page 608 8.5. The Ellipse Page 619 8.6. The Hyperbola Page 637 8.7. The Parabola Page 653 8.8. Conic Sections With Equations in the Form $ax^2 + by^2 + 2gx + 2fy + c = 0$ Page 665 8.9. Intersections of Lines and Conics Page 675 Investigate & Apply: Confocal Conics Page 688 Review of Key Concepts Page 689 Chapter Test Page 694 Challenge Problems Page 696 Problem Solving Strategy: Use a Data Bank Page 697 Problem Solving: Using the Strategies Page 700 Cumulative Review: Chapters 7 and 8 Page 701 Appendix A. Review of Prerequisite Skills Page 702 Appendix B. Graphing Calculator Keystrokes Page 717 Appendix C. Computer Software Page 743 Answers Page 774 Glossary Page 812 Technology Index Page 822 Index Page 824 Credits Page 827