AP Calculus BC – MCQs and Free response -Exam Style Practice question and Answer

Multiple Choice Questions

MCQs

  • Time: 90 minutes 
  • 60 multiple – choice questions (core)
  • No marks deducted from incorrect answers
  • A four-function, scientific, or graphing calculator is allowed 
  • 50% weight

Free-Response Questions

  • Time: 105 minutes 
  • 4 Questions
  • No marks deducted from incorrect answers
  • A four-function, scientific, or graphing calculator is allowed 
  • 50% weight

Free-Response Questions(FRQs)

MCQs

  • Time: 90 minutes 
  • 60 multiple – choice questions (core)
  • No marks deducted from incorrect answers
  • A four-function, scientific, or graphing calculator is allowed 
  • 50% weight

Free-Response Questions

  • Time: 105 minutes 
  • 4 Questions
  • No marks deducted from incorrect answers
  • A four-function, scientific, or graphing calculator is allowed 
  • 50% weight

Unit 4: Contextual Applications of Differentiation

  • 4.1 Interpreting the Meaning of the  Derivative in Context
  • 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
  • 4.3 Rates of Change in Applied Contexts Other  Than Motion
  • 4.4 Introduction to Related Rates
  • 4.5 Solving Related Rates Problems
  • 4.6 Approximating Values of a Function Using Local Linearity and Linearization
  • 4.7 Using L’Hospital’s Rule for Determining Limits  of Indeterminate Forms

Unit 5: Analytical Applications of Differentiation

  • 5.1 Using the Mean Value Theorem
  • 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
  • 5.3 Determining Intervals on Which a Function Is  Increasing or Decreasing
  • 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
  • 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
  • 5.6 Determining Concavity of Functions over Their  Domains
  • 5.7 Using the Second Derivative Test to  Determine Extrema
  • 5.8 Sketching Graphs of Functions and Their  Derivatives
  • 5.9 Connecting a Function, Its First Derivative, and  Its Second Derivative
  • 5.10 Introduction to Optimization Problems
  • 5.11 Solving Optimization Problems
  • 5.12 Exploring Behaviors of Implicit Relations

Unit 6: Integration and Accumulation of Change

  • 6.1 Exploring Accumulations of  Change
  • 6.2 Approximating Areas  with Riemann Sums
  • 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
  • 6.4 The Fundamental Theorem of Calculus and Accumulation Functions
  • 6.5 Interpreting the Behavior of Accumulation Functions Involving Area
  • 6.6 Applying Properties of  Definite Integrals
  • 6.7 The Fundamental Theorem of Calculus and Definite Integrals
  • 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
  • 6.9 Integrating Using  Substitution
  • 6.10 Integrating Functions Using Long Division and Completing the Square
  • 6.11 Integrating Using Integration by Parts bc only
  • 6.12 Using Linear Partial  Fractions bc only
  • 6.13 Evaluating Improper  Integrals bc only
  • 6.14 Selecting Techniques  for Antidifferentiation 

Unit 7: Differential Equations

  • 7.1 Modeling Situations with Differential  Equations
  • 7.2 Verifying Solutions for  Differential Equations
  • 7.3 Sketching Slope Fields
  • 7.4 Reasoning Using Slope Fields
  • 7.5 Approximating Solutions Using Euler’s Method bc only
  • 7.6 Finding General Solutions Using Separation of Variables
  • 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
  • 7.8 Exponential Models with Differential  Equations
  • 7.9 Logistic Models with Differential Equations bc only

Unit 8: Applications of Integration

  • 8.1 Finding the Average Value of a Function on  an Interval
  • 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
  • 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
  • 8.4 Finding the Area Between Curves Expressed as Functions of x
  • 8.5 Finding the Area Between Curves Expressed as Functions of y
  • 8.6 Finding the Area Between Curves That Intersect at More Than Two Points
  • 8.7 Volumes with Cross Sections: Squares and  Rectangles
  • 8.8 Volumes with Cross Sections: Triangles and  Semicircles
  • 8.9 Volume with Disc Method: Revolving  Around the x- or y-Axis
  • 8.10 Volume with Disc Method: Revolving  Around Other Axes
  • 8.11 Volume with Washer Method: Revolving  Around the x- or y-Axis
  • 8.12 Volume with Washer Method: Revolving  Around Other Axes
  • 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled bc only

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions bc only

  • 9.1 Defining and Differentiating Parametric Equations
  • 9.2 Second Derivatives of Parametric Equations
  • 9.3 Finding Arc Lengths of Curves Given by Parametric Equations
  • 9.4 Defining and Differentiating Vector-  Valued Functions
  • 9.5 Integrating Vector- Valued Functions
  • 9.6 Solving Motion Problems Using Parametric and Vector- Valued Functions
  • 9.7 Defining Polar Coordinates and Differentiating in Polar Form
  • 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
  • 9.9 Finding the Area of the Region Bounded by Two Polar Curves

Unit 10 : Infinite Sequences and Series bc only

  • 10.1 Defining Convergent and Divergent Infinite  Series
  • 10.2 Working with  Geometric Series
  • 10.3 The nth Term Test for Divergence
  • 10.4 Integral Test for  Convergence
  • 10.5 Harmonic Series and  p-Series
  • 10.6 Comparison Tests for  Convergence
  • 10.7 Alternating Series Test  for Convergence
  • 10.8 Ratio Test for  Convergence
  • 10.9 Determining Absolute or Conditional  Convergence
  • 10.10 Alternating Series  Error Bound
  • 10.11 Finding Taylor Polynomial Approximations of Functions
  • 10.12 Lagrange Error Bound
  • 10.13 Radius and Interval of Convergence of  Power Series
  • 10.14 Finding Taylor or Maclaurin Series for  a Function
  • 10.15 Representing Functions as  Power Series

Course Content

The AP Chemistry Exam assesses student understanding of the science practices and learning objectives outlined in the course framework. The exam is 3 hours and 15 minutes long and includes 60 multiple-choice questions and 7 free-response questions. Starting with the 2022–23 school year (spring 2023 exam), a scientific or graphing calculator is recommended for use on both sections of the exam. Students are provided with the periodic table and a formula sheet that lists specific and relevant formulas for use on the exam