Projects for Precalculus

Table of Contents

1. Crickets - Nature's Thermometer -- Linear functions that relate the rate of crickets' chirps and temperature are analyzed.

2. A Taxing Problem -- Piecewise functions are studied by analyzing the federal income tax function

3. Newton - A Real Swinger -- The square root function for the period of a pendulum is examined.

4. Rolling Along -- An interesting square root function is determined that relates the length of a roll of toilet paper to its radius.

5. The Amazing Golf-O-Meter -- A device that measures distance to a flag stick on a golf course is developed using an application of a rational function.

6. Crossroads -- The length of time that a traffic light must remain yellow is determined by using a sum of functions

7. More than Meets the Eye -- Can the formula for a polynomial function be determined by just using the graph

8. Rational Behavior of Rational Functions -- The long term behavior of rational functions is explored as the concept of a limit is introduced.

9. Setting the Tone -- Exponential equations are used to examine the frequencies of the notes of the musical scale.

10. The Population Problem -- Exponential growth is explored using the world's human population.

11. Risky Business -- Some of life's risks are analyzed using a logarithmic scale.

12. A Stitch in Time -- Right triangle trigonometry is used to determine the size of triangular shaped quilting pieces.

13. Moving Right Along -- Right triangle trigonometry is used to analyze a conveyer belt system that sorts pieces of wood.

14. Looking Out to Sea -- Trigonometry is used to determine the distance one can see when looking out to sea from various heights.

15. As Easy as Pi -- Using trigonometry along with inscribed and circumscribed regular polygons about a circle, an approximation for pi is determined.

16. Days of our Lives -- The amplitude, period, and phase shift of a trigonometric function which models the amount of daylight throughout the year are determined by using a table and its graph.

17. Identity Crisis -- The identities for cosine and sine of a sum are proved.

18. Split the Uprights -- Trigonometry is used to compare the difficulty of kicking a field goal in the NFL, the CFL, and the NCAA.

19. Winging It -- Using the Law of Sines (and Cosines), the correct flight plan for an airplane flying with a cross wind is determined.

20. Life in the Fast Lane -- Police officers need to know the law (the law of cosines that is) to stop speeders.

21. Elliptipool -- An interesting property of an elliptical shaped pool table is explored.

22. Remote Possibilities -- The probability of one neighbor accidently opening another neighbor's garage door is explored.

23. Buy Now, Pay Later -- One can see that time does equal money after the formula for monthly payments on a loan is derived using a geometric series.

24. The Point Les Trip -- A point named Les takes an interesting journey whose length can be determined using an infinite geometric series involving trigonometry.

25. Zero to Sixty -- Distance traveled and velocity of an automobile are determined as the concept of a limit is introduced

26. How Cold is It? or Feeling the Chill in Frostbite Falls -- The multivariable wind chill function is analyzed by fixing each variable and examining the resulting behavior.