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Pre-calculus · AP

AP-aligned materials for 1.7 (Polynomial and Rational Functions). This topic is assessed on the AP Exam.

What this standard means

  • Rational Functions and End Behavior Describe end behaviors of rational functions. If neither polynomial in a rational function dominates the other for input values of large magnitude, then the quotient of the leading terms is a constant, and that constant indicates the location of a horizontal asymptote of the graph of the original rational function. 1.7.A.5 If the polynomial in the denominator dominates the polynomial in the numerator for input values of large magnitude, then the quotient of the leading terms is a rational function with a constant in the numerator and nonconstant polynomial in the denominator, and the graph of the original rational function has a horizontal asymptote at y = 0. 1.7.A.6 When the graph of a rational function r has a horizontal asymptote at y = b, where b is a constant, the output values of the rational function get arbitrarily close to b and stay arbitrarily close to b as input values increase or decrease without bound. The corresponding mathematical notation is lim r x( ) = b or x lim r x( ) = b. x
  • 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 1.7.

  • [ ] 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

For your personal study only. Copying, printing, screenshotting, or sharing this material is not permitted and may result in loss of access.

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