AP Calculus Exam Study Guide

• Expect graphical questions involving finding values and derivatives at specific points.
• Tabular questions will be contextual, requiring derivative estimations or Riemann sums.
• Prior tests and homework should be reviewed for similar examples of tabular questions.
• Particle motion analysis includes determining when a particle accelerates or decelerates, and its directional movement.
• Velocity results from the derivative of position.
• Acceleration results from the derivative of velocity.
• Basic integration and U-substitution are essential for solving most AP test problems.
• Derivative rules to know include product, quotient, and chain rules.
• Questions may mix representations (graphs, tables, equations), focusing on both derivative and integral rules.

Graphical Problems

• Function values and derivatives can be determined at specific points from a graph.
• Example task: Find f(-5) and f'(-5).

Tabular Questions

• Data from tables can be interpreted to estimate derivatives.
• Concepts like the Intermediate Value Theorem (IVT) or Mean Value Theorem (MVT) may apply.
• Reviewing previous tabular questions provides valuable practice.

Particle Motion

• Position, velocity, and acceleration have interconnected relationships.
• Deriving the position function is possible when given a velocity function.

Integration Techniques

• Concentrate on mastering basic integration and U-substitution.
• Integration can involve finding areas under curves or extracting values from tables.

Derivative and Integral Rules

• Knowledge of all derivative rules is essential, including product, quotient, and chain rules.
• Be prepared to integrate functions represented as graphs, tables, or equations.