1. Functions 1.1 Functions...............................................................12 1.2 Rate of change.......................................................24 1.3 Analyzing Functions................................................33 1.4 Piecewise Functions................................................47 1.5 Transforming Function............................................54 1.6 Composing Functions..............................................70 1.7 Inverse Function.....................................................76 1.8 Limit.......................................................................90 2. Polynomial and Rational Functions 2.1 Polynomial Functions..............................................100 2.2 Diving Polynomials..................................................113 2.3 Real Zeros of Poly...................................................122 2.4 Fundamental Theorem of Algebra............................126 2.5 Rational Function....................................................134 2.6 Polynomial and Rational Inequalities........................151 2.7 Binomial Expansion.................................................162 Free Response Questions (from ch1-ch2)......................165 3. Exponential and Logarithmic Functions 3.1 Exponential Function..............................................168 3.2 Compound Interest..................................................182 3.3 Logarithmic Function..............................................189 3.4 Properties of Logarithm..........................................203 3.5 Exp and Log Equations and Inequalities...................212 3.6 Exponential Growth and Modeling............................226 3.7 Sequences..............................................................235 3.8 Regression..............................................................249 3.9 Semilog plots..........................................................256 Free Response Questions (from ch3).............................263 4. Trigonometry Definition and Graphs 4.1 Angles in Radian..................................................... 266 4.2 Trigonometry of Right Triangles............................... 276 4.3 Trigonometry of Any Angles.................................... 284 4.4 Trigonometry in Unit Circle...................................... 293 4.5 Trigonometric Graphs for Sin, Cos............................ 302 4.6 Modeling using Sin, Cos functions ........................... 315 4.7 Trigonometric Graphs for Others............................. 322 5. Trigonometry Identities 5.1 Inverse Trigonometry Function................................ 334 5.2 Basic Trigonometric Identities.................................. 347 5.3 Verifying Trigonometric Identities............................ 355 5.4 Sum and difference Identities.................................. 361 5.5 Double-Angle Identity............................................. 369 6. Trig Equations and Inequalities 6.1 Basic Trigonometric Equations................................. 380 6.2 More Trigonometric Equations................................. 388 6.3 Trigonometric Inequalities....................................... 396 7. Polar Curve 7.1 Polar Coordinates.................................................... 402 7.2 Graphs of Polar Equations....................................... 412 7.3 Complex Numbers .................................................. 428 Free Response Questions (from ch4-ch7)...................... 434 (※Ch8-Ch11 is NOT assessed on the AP Exam) 8. Parametric Equation 8.1 Parametric Equations.............................................. 440 8.2 Motions and Parametric Equations........................... 447 8.3 Lines and Circles in Parametric Form........................ 454 9. Conic Section 9.1 Conic Sections and Parabolas.................................. 460 9.2 Ellipses................................................................... 466 9.3 Hyperbolas............................................................. 473 9.4 Transformation of Conics........................................ 479 9.5 Conic Sections in Parametric Form........................... 488 10. Vector 10.1 Vectors in Two Dimensions.................................... 496 10.2 Finding Resultant Vector using Trig........................ 508 10.3 The Dot Product.................................................... 512 10.4 Motions in Vectors................................................. 517 11. Matrices 11.1 Algebra of Matrices............................................... 522 11.2 Determinant and Inverse Matrix............................. 529 11.3 Linear Transformation........................................... 533 11.4 Matrices modeling Context.................................... 541 Calculator Skills (for Ti 84, Ti nspire CAS) ..................... 546 Multiple Choice Practice Test......................................... 567 Answer Key................................................................... 581