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Official Exam Structure (AB & BC Identical Format)
Official Exam Structure (AB & BC Identical Format)
Total Time: 3 hours 15 minutes
Total Score Weight: 50% Multiple Choice + 50% Free Response
Section 1: Multiple‑Choice Questions (105 minutes, 50%)
Section 1: Multiple‑Choice Questions (105 minutes, 50%)
Part A: No calculator allowed – 30 questions – 60 minutes
Part B: Graphing calculator allowed – 15 questions – 45 minutes
Section 2: Free‑Response Questions (90 minutes, 50%)
Section 2: Free‑Response Questions (90 minutes, 50%)
Part A: Graphing calculator allowed – 2 questions – 30 minutes
Part B: No calculator allowed – 4 questions – 60 minutes
Note: BC covers more advanced topics; the exam format is the same as AB.
Unit 1: Limits and Continuity
✅ Tested on AB
✅ Tested on BC
1.1 Introducing Limits
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limits from Graphs
1.4 Estimating Limits from Tables
1.5 Determining Limits Using Algebraic Properties
1.6 Limits Involving Trigonometric Functions
1.7 Selecting Procedures for Determining Limits
1.8 Squeeze Theorem
1.9 Connecting Multiple Representations of Limits
1.10 Defining Continuity at a Point
1.11 Removable Discontinuities
1.12 Intermediate Value Theorem
1.13 Asymptotes and Infinite Limits
1.14 Limits at Infinity and End Behavior
Unit 2: Differentiation – Definition and Basic Rules
✅ Tested on AB
✅ Tested on BC
2.1 Defining the Derivative and Derivative Notation
2.2 Average and Instantaneous Rate of Change
2.3 Estimating Derivatives from Graphs and Tables
2.4 Basic Differentiation Rules (Power, Constant, Sum, Difference)
2.5 Product Rule
2.6 Quotient Rule
2.7 Derivatives of Trigonometric Functions
2.8 The Chain Rule
2.9 Derivatives of Exponential Functions
2.10 Derivatives of Logarithmic Functions
2.11 Derivatives of Inverse Trigonometric Functions
2.12 Implicit Differentiation
2.13 Differentiating Inverse Functions
2.14 Related Rates
2.15 Local Linearity and Linear Approximation
Unit 3: Differentiation – Composite, Implicit and Inverse Functions
Unit 3: Differentiation – Composite, Implicit and Inverse Functions
✅ Tested on AB
✅ Tested on BC
3.1 The Chain Rule for Composite Functions
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Higher‑Order Derivatives
3.6 Calculating Derivatives of Parametric Equations (BC Only)
3.7 Calculating Derivatives of Vector‑Valued Functions (BC Only)
3.8 Derivatives of Polar Functions (BC Only)
Unit 4: Contextual Applications of Differentiation
Unit 4: Contextual Applications of Differentiation
✅ Tested on AB
✅ Tested on BC
4.1 Interpreting the Meaning of the Derivative in Context
4.2 Straight‑Line Motion: Position, Velocity, Acceleration
4.3 Rates of Change in Applied Contexts
4.4 Introduction to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values Using Linearization
4.7 L’Hospital’s Rule (BC Only)
Unit 5: Analytical Applications of Differentiation
Unit 5: Analytical Applications of Differentiation
✅ Tested on AB
✅ Tested on BC
5.1 Mean Value Theorem
5.2 Extreme Value Theorem
5.3 Determining Intervals of Increase and Decrease
5.4 First Derivative Test for Local Extrema
5.5 Using the Candidates Test for Absolute Extrema
5.6 Determining Concavity
5.7 Second Derivative Test
5.8 Sketching Graphs of Functions from Derivatives
5.9 Connecting a Function, Its First Derivative and Second Derivative
5.10 Optimization Problems
5.11 Solving Motion Problems Involving Velocity and Acceleration
Unit 6: Integration and Accumulation of Change
Unit 6: Integration and Accumulation of Change
✅ Tested on AB
✅ Tested on BC
6.1 Exploring Accumulations of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation and Definite Integrals
6.4 Fundamental Theorem of Calculus Part 1
6.5 Fundamental Theorem of Calculus Part 2
6.6 Properties of Definite Integrals
6.7 Integration by Substitution
6.8 Integrals of Exponential and Logarithmic Functions
6.9 Integrals of Trigonometric Functions
6.10 Integrating Inverse Trigonometric Functions
6.11 Integration by Parts (BC Only)
6.12 Partial Fraction Decomposition (BC Only)
6.13 Improper Integrals (BC Only)
Unit 7: Differential Equations
Unit 7: Differential Equations
✅ Tested on AB
✅ Tested on BC
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions to Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields
7.5 Separation of Variables
7.6 General and Particular Solutions
7.7 Exponential Growth and Decay Models
7.8 Logistic Differential Equations (BC Only)
Unit 8: Applications of Integration
Unit 8: Applications of Integration
✅ Tested on AB
✅ Tested on BC
8.1 Finding the Average Value of a Function
8.2 Connecting Position, Velocity and Acceleration with Integrals
8.3 Using Accumulation Functions in Applied Contexts
8.4 Area Between Curves (Cartesian)
8.5 Volumes of Solids with Known Cross‑Sections
8.6 Volumes Using the Disk Method
8.7 Volumes Using the Washer Method
8.8 Arc Length of Cartesian Curves (BC Only)
8.9 Area of Polar Curves (BC Only)
8.10 Arc Length of Parametric and Polar Curves (BC Only)
Unit 9: Parametric Equations, Polar Coordinates, and Vector‑Valued Functions
Unit 9: Parametric Equations, Polar Coordinates, and Vector‑Valued Functions
❌ Not tested on AB
✅ Tested on BC
9.1 Defining and Differentiating Parametric Equations
9.2 Second Derivatives of Parametric Equations
9.3 Finding Arc Lengths of Parametric Curves
9.4 Vector‑Valued Functions: Motion
9.5 Derivatives of Vector‑Valued Functions
9.6 Speed, Velocity and Acceleration for Vectors
9.7 Polar Coordinates and Polar Curves
9.8 Area Enclosed by Polar Curves
9.9 Tangent Lines to Polar Curves
Unit 10: Infinite Sequences and Series
Unit 10: Infinite Sequences and Series
❌ Not tested on AB
✅ Tested on BC
10.1 Convergence of Infinite Sequences
10.2 Series and the nth‑Term Test for Divergence
10.3 Geometric Series
10.4 Telescoping Series
10.5 Integral Test for Convergence
10.6 Comparison Tests
10.7 Alternating Series Test and Absolute / Conditional Convergence
10.8 Ratio Test and Root Test
10.9 Determining Error Bounds for Alternating Series
10.10 Taylor Polynomials and Approximations
10.11 Lagrange Error Bound
10.12 Maclaurin Series for Common Functions
10.13 Radius and Interval of Convergence for Power Series
Quick AB vs BC Summary
Quick AB vs BC Summary
AB = Units 1‑8 only
BC = All 10 Units (AB content + Units 9 & 10)
All BC exam questions build on AB knowledge; BC students still need full mastery of AB topics.
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