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