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AP Precalculus — Unit 1: Polynomial and Rational Functions: 211 practice questions

211 original AP Precalculus questions on Unit 1: Polynomial and Rational Functions, each with an explanation and its source. Topics: Rates of Change, Rates of Change in Linear and Quadratic Functions, Polynomial Functions and Complex Zeros, Polynomial Functions and End Behavior, Rational Functions and Vertical Asymptotes, Rational Functions and Holes, Polynomial Functions and Rates of Change, Rational Functions and End Behavior, Rational Functions and Zeros, Equivalent Representations of Polynomial and Rational Expressions, Transformations of Functions, Function Model Selection and Assumption Articulation, Change in Tandem, Function Model Construction and Application, 1.5 Polynomial Functions and Complex Zeros, 1.6 Polynomial Functions and End Behavior, 1.12 Transformations of Functions, 1.7 Rational Functions and End Behavior, 1.8 Rational Functions and Zeros, 1.13 Function Model Selection and Assumption Articulation, 1.1 Change in Tandem, 1.2 Rates of Change, 1.3 Rates of Change in Linear and Quadratic Functions, 1.4 Polynomial Functions and Rates of Change, 1.9 Rational Functions and Vertical Asymptotes, 1.10 Rational Functions and Holes, 1.11 Equivalent Representations of Polynomial and Rational Expressions, 1.13 Function Model Selection, 1.14 Function Model Construction. Two free samples are below. Try 5 more free, no sign-up.

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Two Unit 1: Polynomial and Rational Functions questions with explanations

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Q1 Rates of Change

For f(x)=x², what is the average rate of change on [1, 3]?

  1. 2
  2. 4
  3. 6
  4. 8
Show the answer and explanation

Answer: B. The average rate is [f(3)−f(1)]/(3−1)=(9−1)/2=4. It measures the average output change per unit of input over the interval.

Sources: College Board, AP Precalculus Course and Exam Description · College Board AP Central, AP Precalculus

Q2 Rates of Change in Linear and Quadratic Functions

For f(x)=x², the average rates of change over [0,1], [1,2], and [2,3] are 1, 3, and 5. Which conclusion is supported?

  1. The rates increase by a constant amount, consistent with a quadratic function concave up.
  2. The function is linear because every interval has a rate.
  3. The function is decreasing on all three intervals.
  4. The output is constant.
Show the answer and explanation

Answer: A. For equal-width intervals, the rates 1, 3, 5 have constant first differences of 2. This is characteristic of a quadratic function; increasing rates indicate concavity up.

Sources: College Board, AP Precalculus Course and Exam Description · College Board AP Central, AP Precalculus

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