Unit 1: Polynomial & Rational Functions

1.1 Linear and quadratic patterns
1.2 Recursive vs explicit forms
1.3 Arithmetic sequences
1.4 Geometric sequences
1.5 Using functions to model patterns

1.6 End behavior of polynomials
1.7 Identifying polynomial functions
1.8 Adding, subtracting, and multiplying polynomials
1.9 Factoring polynomials
1.10 Zeros of polynomial functions
1.11 Multiplicity of roots
1.12 The Remainder Theorem
1.13 The Factor Theorem

1.14 Rational expressions and simplification
1.15 Adding and subtracting rational expressions
1.16 Multiplying and dividing rational expressions
1.17 Domain of rational functions
1.18 Vertical asymptotes and holes in rational functions
1.19 Horizontal & slant asymptotes in rational functions

1.20 Polynomial equations
1.21 Solving Rational equations
1.22 More practice with extraneous solutions
1.23 Solving polynomial inequalities
1.24 Solving rational inequalities
1.25 Modeling with polynomial & rational functions

Unit 2: Exponential & Logarithmic Functions

2.1 Structure of exponential functions
2.2 Exponential growth & decay

2.3 Growth factor & decay factor
2.4 Continuous growth (Euler’s number)
2.5 Applications of exponential modeling
2.6 Transformations of exponential functions
2.7 Exponential equations

2.8 Introduction to logarithms

2.9 Properties of logs (product, quotient, power)
2.10 Change of base formula
2.11 Logarithmic models
2.12 Logarithmic equations
2.13 Solving exponential models with logs
2.14 Extraneous solutions in log equations

2.15 Inverse relationships
2.16 Graphs of log vs exponential
2.17 Natural logarithms
2.18 Continuous growth models
2.19 Exponential regression (with TI84)

2.20 Half-life and doubling time
2.21 Real-world exponential comparisons
2.22 Logarithmic scales (pH, Richter, decibels)
2.23 Compound interest and finance models

Unit 3: Trigonometric & Polar Functions

3.1 Angle measurement (degrees vs radians)
3.2 Arc length

3.3 Unit circle structure
3.4 Definition of sine & cosine
3.5 Sine & cosine values on the unit circle
3.6 Symmetry & periodicity
3.7 Tangent and reciprocal trig functions

3.8 Graphing sine & cosine
3.9 Amplitude & midline
3.10 Period & frequency
3.11 Phase shift
3.12 Putting together all transformations
3.13 Graphing tangent & cotangent
3.14 Graphing secant & cosecant

3.15 Pythagorean identities
3.16 Reciprocal & quotient identities
3.17 Solving basic trig equations
3.18 Inverse trig functions
3.19 Solving advanced trig equations
3.20 Modeling with trig equations

3.21 Polar coordinates basics

3.22 Converting between polar & rectangular
3.23 Roses, limacons, cardioids
3.24 Parametric vs polar functions
3.25 Modeling with polar equations

Unit 4: Functions & Modeling

4.1 Function notation & structure
4.2 Average rate of change
4.3 Domain & range
4.4 Composition of functions
4.5 Inverse functions
4.6 Even & odd functions

4.7 Vertical & horizontal shifts
4.8 Reflections
4.9 Stretching & compressing
4.10 Combined transformations
4.11 Piecewise functions

4.12 Linear vs nonlinear models
4.13 Polynomial models
4.14 Rational models
4.15 Exponential models
4.16 Logarithmic models
4.17 Trigonometric models
4.18 Logistic models
4.19 Using TI84 for regression

4.20 Choosing the best model

AP® is a trademark registered by the College Board®, which is not affiliated with, and does not endorse, this product.