AP Pre-Calculus Prerequisite Review Series

Introduction

• Presenter: Judy from the AP program.
• Goal: Prepare students with necessary skills and content knowledge for success in AP Pre-Calculus.
• Prerequisites: Completion of Algebra 1, Geometry, and Algebra 2.

Structure of the Series

• Components:
  • Instructional video for each topic.
  • Practice problem sets.
  • Annotated solutions.
  • Solution video explanations.
• Evaluation: Self-assessment to determine need for additional help.
• Outcome: Build confidence and readiness for AP Pre-Calculus.

Key Mathematical Skills for AP Pre-Calculus

• Focus: Build on existing skills from Algebra 1, Geometry, and Algebra 2.

Linear Functions

Forms of Linear Equations

1. Slope-Intercept Form:
   • Equation: ( f(x) = mx + b )
   • Use: Graphing lines easily.
2. Point-Slope Form:
   • Equation: ( y - y_1 = m(x - x_1) )
   • Use: When a line passes through a known point.
3. Standard Form:
   • Equation: ( Ax + By = C )
   • Use: Solving systems of equations.

Characteristics of Linear Equations

• Rate of Change: Constant.
• Domain: All real numbers (unless contextually restricted).
• Range: All real numbers (unless contextually restricted).

Examples and Problem Solving

Example 1: Finding Equations of a Line

• Given Points: (-2, -4) and (-5, 5)
• **Steps: **
  1. Calculate slope.
  2. Use point-slope form.
  3. Convert to slope-intercept and standard forms.

Example 2: Sketching Graphs

• Equation: ( y = -2x + 5 )
• Form: Slope-intercept.
• Graphing: Start at y-intercept, use slope to find additional points.

Example 3: Graphing with Standard Form

• Equation: ( 3x + 2y = 12 )
• Steps:
  • Find x and y intercepts.
  • Sketch the line.

Example 4: Word Problem - Car Rental

• Scenario: Calculate costs based on distance driven.
• Tasks:
  1. Find per mile fee.
  2. Calculate base fee.
  3. Write linear equation.
• Solution:( y = 0.6x + 120 )

Example 5: Draining a Bathtub

• Graph Interpretation: Time vs. Liters of water.
• Tasks:
  1. Determine time to drain.
  2. Calculate initial water amount.
  3. Write linear equation.
• Solution:( y = -72x + 360 )

Conclusion

• Review: Emphasize mastery of linear equations as foundational for AP Pre-Calculus.
• Encouragement: Confidence in pre-calculus skills.
• Next Steps: Continue with future lessons.