Study Guide — Polynomial and Rational Functions
Pre-calculus · AP
AP-aligned study guide for Polynomial and Rational Functions.
What this standard means
- Change in Tandem A function is a mathematical relation that maps a set of input values to a set of output values such that each input value
- Rates of Change
- Rates of Change in Linear and Quadratic Functions For a linear function, the average rate of change over any length input-value interval is
- Polynomial Functions and Rates of Change Identify key characteristics of polynomial functions related to rates of change.
- Polynomial Functions and Complex Zeros The degree of a polynomial function can be found by examining the successive differences of the outpu
- Polynomial Functions and End Behavior Describe end behaviors of rational functions. A rational function is analytically represented as a quo
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Label unit circle coordinates for key angles 2. Connect radians and degrees 3. Graph sine and cosine with amplitude and period
_See printable PDF for diagram._
Common mistakes
- Wrong quadrant signs
- Period or amplitude errors in graphs
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for Polynomial and Rational Functions.
- [ ] Evaluates trig functions at standard angles
- [ ] Uses unit circle reasoning
- [ ] Graphs basic trig functions with transformations
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors