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Pre-calculus · AP

AP-aligned materials for 1.1 (Polynomial and Rational Functions). This topic is assessed on the AP Exam.

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 is mapped to exactly one output value. The set of input values is called the domain of the function, and the set of output values is called the range of the function. The variable representing input values is called the independent variable, and the variable representing output values is called the dependent variable. 1.1.A.2 The input and output values of a function vary in tandem according to the function rule, which can be expressed graphically, numerically, analytically, or verbally. 1.1.A.3 A function is increasing over an interval of its domain if, as the input values increase, the output values always increase. That is, for all a and b in the interval, if a < b, then f a( ) < f b( ). 1.1.A.4 A function is decreasing over an interval of its domain if, as the input values increase, the output values always decrease. That is, for all a and b in the interval, if a < b, then f a( ) > f b( ).
  • 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 1.1.

  • [ ] 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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