Pre-Calculus AP Exam Practice Review

Introduction

• Full practice AP pre-calculus exam review.
• The exam consists of multiple choice questions with and without calculator.

Section 1: Multiple Choice (No Calculator)

Question 1: Graph Behavior

• Concepts:
  • Decreasing at an increasing rate.
  • Concave up means graph is smiling; slope increases as x increases.
• Strategy: Avoid overthinking. Recognize decreasing graph with increasing slope.

Question 2: Polynomial Concavity

• Concepts:
  • Concave down: rate of change is decreasing.
  • Second order differences: indicator of concavity.
• Strategy: Analyze patterns in differences for concavity assessment.

Question 3: Function Transformation

• Graph H as a transformation of G.
• Inverse function analysis: swap x and y in the function.

Question 4: Logarithmic Properties

• Combine logs using log properties before solving equations.
• Strategies for manipulating and solving logarithmic equations.

Question 5: Volume vs. Depth

• Understand filling rate dynamics in a cone.
• Differentiate between linear and non-linear volume growth.

Question 6: Binomial Theorem

• Expand using Pascal's Triangle.
• Identify terms and coefficients in binomial expansions.

Question 7: Rational Function Analysis

• Finding intervals where the function is non-negative.
• Use sign charts and key numbers for analysis.

Question 8: Exponential Decay

• Understand behavior of exponential functions (1/3 base).
• End behavior analysis through limits.

Question 9: Trigonometric Solutions

• Solving basic trigonometric equations for specific intervals.

Question 10: Logarithmic Simplification

• Use properties to simplify logarithmic expressions.

Question 11: Vertical Asymptotes

• Rational functions involve identifying vertical asymptotes.
• Use unit circle and cosine analysis for tangent vertical asymptotes.

Question 12: Polynomial End Behavior

• Determine polynomial degree and leading coefficient sign from behavior.

Question 13: Rational Function Limits

• One-sided limits as x approaches a specific value.

Question 14: Graph Holes and Limits

• Determine holes and limit behavior for rational functions.

Question 15: Minimum Polynomial Degree

• Analyze roots and multiplicities for minimum degree.

Question 16: Polar Graphs

• Evaluate polar graph behavior at specific points.

Question 17: Odd Functions

• Recognize odd function properties and solve given characteristics.

Question 18: Trigonometric Function Analysis

• Evaluate periodic functions for amplitude, period, and phase shift.

Question 19: Exponential Function Manipulation

• Use exponent properties for transforming expressions.

Question 20: Slant Asymptotes

• Apply long division or synthetic division to find equations.

Question 21: Cosine Values

• Determine cosine value from point on unit circle.

Question 22: Exponent Properties

• Simplify expressions using power of a power rule.

Question 23: Logarithmic Evaluation

• Understanding base conversions and negative exponents.

Question 24: Logarithmic Properties

• Combine logs and solve for x using properties.

Question 25: Function Intersection

• Solve for x where two functions intersect or are equal.

Question 26: Data Analysis with Exponentials

• Regression analysis for predicting future values.

Section 2: Multiple Choice (Calculator Allowed)

Question 27: Graph Motion Analysis

• Average rate of change and its calculation.

Question 28: Regression Analysis

• Use calculator for regression to predict future population values.

Question 29: Function Compositions and Transformations

• Analyze effects of transformations on functions.

Question 30: Rate Graphs

• Analyze rate changes, inflection points, and second derivative concepts.

Question 31: Logarithmic Growth

• Understand inverse and exponential relationships.

Question 32: Trigonometric Analysis

• Use unit circle for triangle and angle analysis.

Question 33: Statistical Predictions

• Use regression for predicting population based on past data.

Section 3: Free Response (Calculator Allowed)

Question 1: Function Composition

• Find specific values and solve compositions using graphs and tables.

Question 2: Modeling Non-Periodic Contexts

• Develop equations from data, analyze rate of change, and interpret results.

Section 4: Free Response (No Calculator)

Question 3: Trigonometric Function Analysis

• Analyze periodic function movements and changes over time.

Question 4: Rational and Trigonometric Expression Simplification

• Solve equations by simplifying complex expressions using trigonometric identities.

General Exam Strategies

• Understand and apply foundational concepts (exponent rules, trigonometric identities, etc.).
• Use calculator effectively for regression and solving complex equations.
• Practice interpreting problems to identify underlying mathematical concepts.