AP®MathsCollege BoardPrecalculusExam QuestionsPolynomial & Rational FunctionsModeling with Polynomial & Rational Functions

Modeling with Polynomial & Rational Functions (College Board AP® Precalculus): Exam Questions

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Modeling with Polynomial & Rational Functions

1
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1 mark

The variable space y is inversely proportional to x. If space y equals 18 when x equals 2, what is the value of space y when x equals 6?

  • 2

  • 6

  • 9

  • 54

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2
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1 mark

The table gives values of space f open parentheses x close parentheses at selected values of x.

space x

0

1

2

3

4

space f open parentheses x close parentheses

2

5

14

35

74

Based on this data, which type of polynomial function is most appropriate to model space f?

  • Linear

  • Quadratic

  • Cubic

  • Quartic

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3
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1 mark

The piecewise-defined function f is given by

space f open parentheses x close parentheses equals open curly brackets table row cell x squared plus 1 comma space space space space space space x less than 1 end cell row cell 4 minus x comma space space space space space space space space x greater or equal than 1 end cell end table close

What is the value of space f open parentheses 0 close parentheses plus f open parentheses 1 close parentheses plus f open parentheses 3 close parentheses ?

  • 4

  • 5

  • 8

  • 13

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4
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1 mark

A car is traveling on a highway. The total distance, D open parentheses t close parentheses (in miles), the car has traveled t hours after entering the highway is modeled by the linear function D open parentheses t close parentheses equals 65 t plus 5. Which of the following best describes an underlying assumption of this model?

  • The car's distance from the starting point doubles every hour.

  • The car has traveled 5 miles per hour since entering the highway.

  • The car's speed is constant at 65 miles per hour.

  • The car's speed increases by 65 miles per hour each hour.

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5
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1 mark

The quadratic function space f, given by space f open parentheses x close parentheses equals a x squared plus b x plus c, models a set of data. The graph of space f passes through the points open parentheses 0 comma 5 close parentheses, open parentheses 2 comma 9 close parentheses, and open parentheses 4 comma 21 close parentheses. What is the value of a?

  • 0

  • 1

  • 2

  • 5

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6
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1 mark

The profit (in thousands of dollars) earned by a small business t months after launch is modeled by P open parentheses t close parentheses equals negative 0.4 t cubed plus 4.8 t squared minus 12 t plus 15 for 0 less or equal than t less or equal than 8. What is the maximum value of P open parentheses t close parentheses on this interval?

  • 6.442

  • 15.000

  • 21.400

  • 29.958

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7
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1 mark

A parking garage charges a flat fee of $5 for parking up to 1 hour. Beyond 1 hour, an additional $3 per hour is charged at a continuous rate. Let C open parentheses t close parentheses represent the total parking charge, in dollars, for parking t hours, where t greater than 0. Which of the following piecewise functions correctly models C open parentheses t close parentheses ?

  • C open parentheses t close parentheses equals open curly brackets table row cell 5 comma space space space space space 0 less than t less or equal than 1 end cell row cell 3 t comma space space space space t greater than 1 end cell end table close

  • C open parentheses t close parentheses equals open curly brackets table row cell 5 comma space space space space space space space space space space space space 0 less than t less or equal than 1 end cell row cell 3 t plus 2 comma space space space space t greater than 1 end cell end table close

  • C open parentheses t close parentheses equals open curly brackets table row cell 5 comma space space space space space space space space space space space space 0 less than t less or equal than 1 end cell row cell 3 t plus 5 comma space space space space t greater than 1 end cell end table close

  • C open parentheses t close parentheses equals open curly brackets table row cell 5 t comma space space space space space space space space space space 0 less than t less or equal than 1 end cell row cell 3 t plus 2 comma space space space space t greater than 1 end cell end table close

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8
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1 mark

The intensity I (in watts per square meter) of light from a particular source is inversely proportional to the square of the distance d (in meters) from the source. When d equals 1.5 meters, the intensity is 240 watts per square meter. To 3 decimal places, what is the intensity when d equals 4.7 meters?

  • 24 . 445

  • 76 . 596

  • 114 . 894

  • 2 comma 356.267

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9
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1 mark

A model for the squirrel population (in hundreds) in a small park is given by N open parentheses t close parentheses equals negative 0.3 t squared plus 6 t plus 5 for 0 less or equal than t less or equal than 10, where t is the number of years since the park opened. What is the value of t, to 3 decimal places, at which N open parentheses t close parentheses equals 25?

  • 4 . 226

  • 5 . 556

  • 10 . 000

  • 15 . 774

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10
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1 mark

Let S open parentheses t close parentheses represent the total amount of snow, in inches, that has fallen during a snowstorm, where t is the number of hours since the start of the storm. The total snowfall is modeled by the function S open parentheses t close parentheses equals negative 1 fourth t squared plus 3 t for 0 less or equal than t less or equal than T, where T is the latest time at which the model is appropriate. What is the largest value of T for which the model is appropriate in this context?

  • T = 3

  • T = 6

  • T = 9

  • T = 12

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