Notes on AP Pre-Calculus Exam and FRQ1

Introduction

• The speaker has experience with the AP pre-calculus exam.
• Focus is on the Free Response Questions (FRQ), particularly FRQ1.
• The exam sometimes provides specific topics and even potential questions.

Structure of FRQ1

• Requires a graphing calculator.
• Starts with a graph, table, or equation.
• Three parts to solve based on the given information.
• Six potential topics for questions:
  • Function composition
  • Inverse functions
  • Input/output values
  • Zeros
  • Behavior and predicting function models
• Video channel has resources on these topics.

Example from 2024 AP Exam

Given:

• A graph with domain -3.5 to 3.5.
• Points on graph: (-3, 1), (0, 1), (3, 1).
• Function g: g(x) = 2.916 * 0.7^x

Part A: Calculate h(3)

• Function h defined as: h(x) = g(f(x)).
• Find f(3) from the graph, which is 1.
• Calculate g(1) using the g function.
• Result: h(3) ≈ 2.041.

Part B: Values of x for f(x) = 1

• Occurs at x = -3, 0, 3 based on graph observations.

Part C: Values of x for g(x) = 2

• Method 1: Use calculator to find intersection.
• Method 2: Algebraically solve:
  • Set y = 2, solve for x.
  • x ≈ 1.057.

Part D: Determine end behavior of g

• Exponential decay function (b = 0.7).
• Use limit notation for behavior as x increases.

Part E: Does f have an inverse function?

• Test with horizontal line rule; f fails the test.
• Provide explanation: Output 1 maps to multiple inputs (-3, 0, 3).

Exam Strategy

• Show all work for partial credit.
• Partial credit can impact final scores.
• College Board requires work shown even if the answer is correct.

Conclusion

• Importance of studying and understanding the exam format.
• Engaging with video resources for further clarification.
• Encouragement to follow the channel and related social media platforms.