Study Guide

Pre-calculus · AP

AP-aligned materials for 1.12 (Polynomial and Rational Functions). This topic is assessed on the AP Exam.

What this standard means

• Transformations of Functions Linear functions model data sets or aspects of contextual scenarios that demonstrate roughly constant rates of change. 1.13.A.2 Quadratic functions model data sets or aspects of contextual scenarios that demonstrate roughly linear rates of change, or data sets that are roughly symmetric with a unique maximum or minimum value. 1.13.A.3 Geometric contexts involving area or two dimensions can often be modeled by quadratic functions. Geometric contexts involving volume or three dimensions can often be modeled by cubic functions. 1.13.A.4 Polynomial functions model data sets or contextual scenarios with multiple real zeros or multiple maxima or minima. 1.13.A.5 A polynomial function of degree n models data sets or contextual scenarios that demonstrate roughly constant nonzero nth differences. 1.13.A.6 A polynomial function of degree n or less can be used to model a graph of n + 1 points with distinct input values.
• 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 1.12.

• [ ] 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