Marlbridge guide to AP® Calculus BC

Unit roadmap

Units and topics exactly as numbered in the 2026–27 Course and Exam Description. Weightings are the official multiple-choice ranges. Marlbridge has written resources for 111 of 111 topics so far; the rest are planned and marked as such. 30 topics are BC only.

1. Unit 1: Limits and Continuity 5–10% of multiple choice · 16 topics

   • 1.1 Introducing Calculus: Can Change Occur at an Instant? Study guideRevision notesPractice questionsTopic checklist
   • 1.2 Defining Limits and Using Limit Notation Study guideRevision notesPractice questionsTopic checklist
   • 1.3 Estimating Limit Values from Graphs Study guideRevision notesPractice questionsTopic checklist
   • 1.4 Estimating Limit Values from Tables Study guideRevision notesPractice questionsTopic checklist
   • 1.5 Determining Limits Using Algebraic Properties of Limits Study guideRevision notesPractice questionsTopic checklist
   • 1.6 Determining Limits Using Algebraic Manipulation Study guideRevision notesPractice questionsTopic checklist
   • 1.7 Selecting Procedures for Determining Limits Study guideRevision notesPractice questionsTopic checklist
   • 1.8 Determining Limits Using the Squeeze Theorem Study guideRevision notesPractice questionsTopic checklist
   • 1.9 Connecting Multiple Representations of Limits Study guideRevision notesPractice questionsTopic checklist
   • 1.10 Exploring Types of Discontinuities Study guideRevision notesPractice questionsTopic checklist
   • 1.11 Defining Continuity at a Point Study guideRevision notesPractice questionsTopic checklist
   • 1.12 Confirming Continuity over an Interval Study guideRevision notesPractice questionsTopic checklist
   • 1.13 Removing Discontinuities Study guideRevision notesPractice questionsTopic checklist
   • 1.14 Connecting Infinite Limits and Vertical Asymptotes Study guideRevision notesPractice questionsTopic checklist
   • 1.15 Connecting Limits at Infinity and Horizontal Asymptotes Study guideRevision notesPractice questionsTopic checklist
   • 1.16 Working with the Intermediate Value Theorem (IVT) Study guideRevision notesPractice questionsTopic checklist
   • Limits and Continuity: Unit Diagnostic (Calculus AB Unit 1)
   • Limits and Continuity: Mixed Unit Review (Calculus AB Unit 1)
2. Unit 2: Differentiation: Definition and Fundamental Properties 5–10% of multiple choice · 10 topics

   • 2.1 Defining Average and Instantaneous Rates of Change at a Point Study guideRevision notesPractice questionsTopic checklist
   • 2.2 Defining the Derivative of a Function and Using Derivative Notation Study guideRevision notesPractice questionsTopic checklist
   • 2.3 Estimating Derivatives of a Function at a Point Study guideRevision notesPractice questionsTopic checklist
   • 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist Study guideRevision notesPractice questionsTopic checklist
   • 2.5 Applying the Power Rule Study guideRevision notesPractice questionsTopic checklist
   • 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple Study guideRevision notesPractice questionsTopic checklist
   • 2.7 Derivatives of cos x, sin x, eˣ, and ln x Study guideRevision notesPractice questionsTopic checklist
   • 2.8 The Product Rule Study guideRevision notesPractice questionsTopic checklist
   • 2.9 The Quotient Rule Study guideRevision notesPractice questionsTopic checklist
   • 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions Study guideRevision notesPractice questionsTopic checklist
   • Differentiation: Definition and Fundamental Properties: Unit Diagnostic (Calculus AB Unit 2)
   • Differentiation: Definition and Fundamental Properties: Mixed Unit Review (Calculus AB Unit 2)
3. Unit 3: Differentiation: Composite, Implicit, and Inverse Functions 5–10% of multiple choice · 6 topics

   • 3.1 The Chain Rule Study guideRevision notesPractice questionsTopic checklist
   • 3.2 Implicit Differentiation Study guideRevision notesPractice questionsTopic checklist
   • 3.3 Differentiating Inverse Functions Study guideRevision notesPractice questionsTopic checklist
   • 3.4 Differentiating Inverse Trigonometric Functions Study guideRevision notesPractice questionsTopic checklist
   • 3.5 Selecting Procedures for Calculating Derivatives Study guideRevision notesPractice questionsTopic checklist
   • 3.6 Calculating Higher-Order Derivatives Study guideRevision notesPractice questionsTopic checklist
   • Differentiation: Composite, Implicit, and Inverse Functions: Unit Diagnostic (Calculus AB Unit 3)
   • Differentiation: Composite, Implicit, and Inverse Functions: Mixed Unit Review (Calculus AB Unit 3)
4. Unit 4: Contextual Applications of Differentiation 5–10% of multiple choice · 7 topics

   • 4.1 Interpreting the Meaning of the Derivative in Context Study guideRevision notesPractice questionsTopic checklist
   • 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration Study guideRevision notesPractice questionsTopic checklist
   • 4.3 Rates of Change in Applied Contexts Other Than Motion Study guideRevision notesPractice questionsTopic checklist
   • 4.4 Introduction to Related Rates Study guideRevision notesPractice questionsTopic checklist
   • 4.5 Solving Related Rates Problems Study guideRevision notesPractice questionsTopic checklist
   • 4.6 Approximating Values of a Function Using Local Linearity and Linearization Study guideRevision notesPractice questionsTopic checklist
   • 4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms Study guideRevision notesPractice questionsTopic checklist
   • Contextual Applications of Differentiation: Unit Diagnostic (Calculus AB Unit 4)
   • Contextual Applications of Differentiation: Mixed Unit Review (Calculus AB Unit 4)
5. Unit 5: Analytical Applications of Differentiation 10–15% of multiple choice · 12 topics

   • 5.1 Using the Mean Value Theorem Study guideRevision notesPractice questionsTopic checklist
   • 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points Study guideRevision notesPractice questionsTopic checklist
   • 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing Study guideRevision notesPractice questionsTopic checklist
   • 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema Study guideRevision notesPractice questionsTopic checklist
   • 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema Study guideRevision notesPractice questionsTopic checklist
   • 5.6 Determining Concavity of Functions over Their Domains Study guideRevision notesPractice questionsTopic checklist
   • 5.7 Using the Second Derivative Test to Determine Extrema Study guideRevision notesPractice questionsTopic checklist
   • 5.8 Sketching Graphs of Functions and Their Derivatives Study guideRevision notesPractice questionsTopic checklist
   • 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative Study guideRevision notesPractice questionsTopic checklist
   • 5.10 Introduction to Optimization Problems Study guideRevision notesPractice questionsTopic checklist
   • 5.11 Solving Optimization Problems Study guideRevision notesPractice questionsTopic checklist
   • 5.12 Exploring Behaviors of Implicit Relations Study guideRevision notesPractice questionsTopic checklist
   • Analytical Applications of Differentiation: Unit Diagnostic (Calculus AB Unit 5)
   • Analytical Applications of Differentiation: Mixed Unit Review (Calculus AB Unit 5)
6. Unit 6: Integration and Accumulation of Change 15–20% of multiple choice · 14 topics

   • 6.1 Exploring Accumulations of Change Study guideRevision notesPractice questionsTopic checklist
   • 6.2 Approximating Areas with Riemann Sums Study guideRevision notesPractice questionsTopic checklist
   • 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation Study guideRevision notesPractice questionsTopic checklist
   • 6.4 The Fundamental Theorem of Calculus and Accumulation Functions Study guideRevision notesPractice questionsTopic checklist
   • 6.5 Interpreting the Behavior of Accumulation Functions Involving Area Study guideRevision notesPractice questionsTopic checklist
   • 6.6 Applying Properties of Definite Integrals Study guideRevision notesPractice questionsTopic checklist
   • 6.7 The Fundamental Theorem of Calculus and Definite Integrals Study guideRevision notesPractice questionsTopic checklist
   • 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation Study guideRevision notesPractice questionsTopic checklist
   • 6.9 Integrating Using Substitution Study guideRevision notesPractice questionsTopic checklist
   • 6.10 Integrating Functions Using Long Division and Completing the Square Study guideRevision notesPractice questionsTopic checklist
   • 6.11 Integrating Using Integration by PartsBC only Study guideRevision notesPractice questionsTopic checklist
   • 6.12 Integrating Using Linear Partial FractionsBC only Study guideRevision notesPractice questionsTopic checklist
   • 6.13 Evaluating Improper IntegralsBC only Study guideRevision notesPractice questionsTopic checklist
   • 6.14 Selecting Techniques for Antidifferentiation Study guideRevision notesPractice questionsTopic checklist
   • Integration and Accumulation of Change: Unit Diagnostic (Calculus AB Unit 6)
   • Integration and Accumulation of Change: Mixed Unit Review (Calculus AB Unit 6)
7. Unit 7: Differential Equations 5–10% of multiple choice · 9 topics

   • 7.1 Modeling Situations with Differential Equations Study guideRevision notesPractice questionsTopic checklist
   • 7.2 Verifying Solutions for Differential Equations Study guideRevision notesPractice questionsTopic checklist
   • 7.3 Sketching Slope Fields Study guideRevision notesPractice questionsTopic checklist
   • 7.4 Reasoning Using Slope Fields Study guideRevision notesPractice questionsTopic checklist
   • 7.5 Approximating Solutions Using Euler’s MethodBC only Study guideRevision notesPractice questionsTopic checklist
   • 7.6 Finding General Solutions Using Separation of Variables Study guideRevision notesPractice questionsTopic checklist
   • 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables Study guideRevision notesPractice questionsTopic checklist
   • 7.8 Exponential Models with Differential Equations Study guideRevision notesPractice questionsTopic checklist
   • 7.9 Logistic Models with Differential EquationsBC only Study guideRevision notesPractice questionsTopic checklist
   • Differential Equations: Unit Diagnostic (Calculus AB Unit 7)
   • Differential Equations: Mixed Unit Review (Calculus AB Unit 7)
8. Unit 8: Applications of Integration 5–10% of multiple choice · 13 topics

   • 8.1 Finding the Average Value of a Function on an Interval Study guideRevision notesPractice questionsTopic checklist
   • 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals Study guideRevision notesPractice questionsTopic checklist
   • 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts Study guideRevision notesPractice questionsTopic checklist
   • 8.4 Finding the Area Between Curves Expressed as Functions of x Study guideRevision notesPractice questionsTopic checklist
   • 8.5 Finding the Area Between Curves Expressed as Functions of y Study guideRevision notesPractice questionsTopic checklist
   • 8.6 Finding the Area Between Curves That Intersect at More Than Two Points Study guideRevision notesPractice questionsTopic checklist
   • 8.7 Volumes with Cross Sections: Squares and Rectangles Study guideRevision notesPractice questionsTopic checklist
   • 8.8 Volumes with Cross Sections: Triangles and Semicircles Study guideRevision notesPractice questionsTopic checklist
   • 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis Study guideRevision notesPractice questionsTopic checklist
   • 8.10 Volume with Disc Method: Revolving Around Other Axes Study guideRevision notesPractice questionsTopic checklist
   • 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis Study guideRevision notesPractice questionsTopic checklist
   • 8.12 Volume with Washer Method: Revolving Around Other Axes Study guideRevision notesPractice questionsTopic checklist
   • 8.13 The Arc Length of a Smooth, Planar Curve and Distance TraveledBC only Study guideRevision notesPractice questionsTopic checklist
   • Applications of Integration: Unit Diagnostic (Calculus AB Unit 8)
   • Applications of Integration: Mixed Unit Review (Calculus AB Unit 8)
9. Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued FunctionsBC only 10–15% of multiple choice · 9 topics

   • 9.1 Defining and Differentiating Parametric EquationsBC only Study guideRevision notesPractice questionsTopic checklist
   • 9.2 Second Derivatives of Parametric EquationsBC only Study guideRevision notesPractice questionsTopic checklist
   • 9.3 Finding Arc Lengths of Curves Given by Parametric EquationsBC only Study guideRevision notesPractice questionsTopic checklist
   • 9.4 Defining and Differentiating Vector-Valued FunctionsBC only Study guideRevision notesPractice questionsTopic checklist
   • 9.5 Integrating Vector-Valued FunctionsBC only Study guideRevision notesPractice questionsTopic checklist
   • 9.6 Solving Motion Problems Using Parametric and Vector-Valued FunctionsBC only Study guideRevision notesPractice questionsTopic checklist
   • 9.7 Defining Polar Coordinates and Differentiating in Polar FormBC only Study guideRevision notesPractice questionsTopic checklist
   • 9.8 Finding the Area of a Polar Region or the Area Bounded by a Single Polar CurveBC only Study guideRevision notesPractice questionsTopic checklist
   • 9.9 Finding the Area of the Region Bounded by Two Polar CurvesBC only Study guideRevision notesPractice questionsTopic checklist
   • Parametric Equations, Polar Coordinates and Vector-Valued Functions: Unit Diagnostic (Calculus BC Unit 9)
   • Parametric Equations, Polar Coordinates and Vector-Valued Functions: Mixed Unit Review (Calculus BC Unit 9)
10. Unit 10: Infinite Sequences and SeriesBC only 15–20% of multiple choice · 15 topics

    • 10.1 Defining Convergent and Divergent Infinite SeriesBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.2 Working with Geometric SeriesBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.3 The nth Term Test for DivergenceBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.4 Integral Test for ConvergenceBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.5 Harmonic Series and p-SeriesBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.6 Comparison Tests for ConvergenceBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.7 Alternating Series Test for ConvergenceBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.8 Ratio Test for ConvergenceBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.9 Determining Absolute or Conditional ConvergenceBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.10 Alternating Series Error BoundBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.11 Finding Taylor Polynomial Approximations of FunctionsBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.12 Lagrange Error BoundBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.13 Radius and Interval of Convergence of Power SeriesBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.14 Finding Taylor or Maclaurin Series for a FunctionBC only Study guideRevision notesPractice questionsTopic checklist
    • 10.15 Representing Functions as Power SeriesBC only Study guideRevision notesPractice questionsTopic checklist
    • Infinite Sequences and Series: Unit Diagnostic (Calculus BC Unit 10)
    • Infinite Sequences and Series: Mixed Unit Review (Calculus BC Unit 10)

Exam skills

Guides that apply across every unit: what each task verb asks you to do, and how to set out answers so every step of your reasoning is visible.

• Notation, Justification and Communication: Exam Skills Guide (Calculus AB and BC)

  How to write calculus answers that earn credit: clear notation, theorem conditions, sign-chart justifications, units in context, and calculator set-ups.

• Task Verbs and Free-Response Technique: Exam Skills Guide (Calculus AB and BC)

  What each free-response task verb asks you to do, how much to write, how to plan your time and show work, and what earns or loses credit, with original worked examples.

Mathematical practices

1. Implementing Mathematical Processes

Determine expressions and values using mathematical procedures and rules.

2. Connecting Representations

Translate mathematical information from a single representation or across multiple representations.

3. Justification

Justify reasoning and solutions.

4. Communication and Notation

Use correct notation, language and mathematical conventions to communicate results or solutions. (Free response only.)