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📈AP Precalculus
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📈AP Precalculus

FRQ 3 – Modeling a Periodic Context (No Calculator)
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Unit 3: Trigonometric and Polar Functions
AP Precalculus FRQ Types & Units

Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

FRQFocusUnitsWhy
FRQ 1Function Concepts (Calculator)1-2Tests function analysis with graphing calculator - Units 1-2 polynomial/rational functions
FRQ 2Modeling a Non-Periodic Context1-2Tests modeling with polynomial, rational, exponential, or logarithmic functions
FRQ 3Modeling a Periodic Context3 onlyTests modeling with trigonometric functions - all Unit 3 content
FRQ 4Symbolic Manipulations2-3Tests exponential, logarithmic, and trigonometric equation solving and rewriting

This mapping reflects College Board's exam structure - each FRQ type tests specific skills that are taught in particular units.

Practice FRQ 1 of 201/20
No Calculator

3. The following functions are defined for this question: h(t)=−15cos⁡(π30t)+17h(t) = -15\cos\left(\frac{\pi}{30}t\right) + 17h(t)=−15cos(30π​t)+17 t(y)=30πarccos⁡(17−y15)t(y) = \frac{30}{\pi}\arccos\left(\frac{17-y}{15}\right)t(y)=π30​arccos(1517−y​)

A Ferris wheel at an amusement park rotates at a constant speed. Passengers board the Ferris wheel at its lowest point, which is 2 meters above the ground. The wheel has a radius of 15 meters, and its center is 17 meters above the ground. A passenger boards the Ferris wheel at time t=0t = 0t=0 seconds. The Ferris wheel completes one full rotation every 60 seconds. The height of the passenger above the ground, in meters, can be modeled by a sinusoidal function HHH of time ttt, in seconds.

  • h(t)=−15cos⁡(π30t)+17h(t) = -15\cos\left(\frac{\pi}{30}t\right) + 17h(t)=−15cos(30π​t)+17

  • t(y)=30πarccos⁡(17−y15)t(y) = \frac{30}{\pi}\arccos\left(\frac{17-y}{15}\right)t(y)=π30​arccos(1517−y​)

Figure 1. Graph of passenger height H versus time t for one full Ferris wheel rotation (period 60 s)

Figure 1
A.

Using the information given, find the coordinates of the four labeled points A, B, C, and D on the graph of HHH.

B.

The function HHH can be written in the form H(t)=acos⁡(b(t+c))+dH(t) = a\cos(b(t + c)) + dH(t)=acos(b(t+c))+d. Find the values of constants aaa, bbb, ccc, and ddd.

C.

Find all values of ttt in the interval 0≤t≤600 ≤ t ≤ 600≤t≤60 for which H(t)=26H(t) = 26H(t)=26.

Timed

00:00

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Free Response Question Practice

This practice environment simulates the AP AP Precalculus Free Response Questions section. Here are some guidelines:

  • Read each question carefully before responding. Pay attention to command verbs like "identify," "explain," "analyze," or "evaluate."
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Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.