Study Guide

Pre-calculus · AP

AP-aligned materials for 1.14 (Polynomial and Rational Functions). This topic is assessed on the AP Exam.

What this standard means

• Function Model Construction and Application A model can be constructed based on restrictions identified in a mathematical or contextual scenario. 1.14.A.2 A model of a data set or a contextual scenario can be constructed using transformations of the parent function. 1.14.A.3 A model of a data set can be constructed using technology and regressions, including linear, quadratic, cubic, and quartic regressions. 1.14.A.4 A piecewise-defined function model can be constructed through a combination of modeling techniques. 1.14.B 1.14.B.1 Construct a rational function model based on a context.
• Demonstrate mastery on AP Exam-style questions for this topic.

_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 1.14.

• [ ] 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