AP Calculus BC Diagnostic

Short topic-level assessments built around documented student misconceptions. Each diagnostic is ten items keyed to a specific wrong way of thinking; miss one and the result routes you straight to the drill that fixes it. All 10 units are here: units 1 through 8 are shared with AP Calculus AB, while units 9 and 10, and six topics inside units 6, 7, and 8, are BC only and carry a badge. Pick a topic to start.

Unit 1

Limits and Continuity

1.1 Introducing Calculus: Can Change Occur at an Instant? Start → 1.2 Defining Limits and Using Limit Notation Start → 1.3 Estimating Limit Values from Graphs Start → 1.4 Estimating Limit Values from Tables Start → 1.5 Determining Limits Using Algebraic Properties of Limits Start → 1.6 Determining Limits Using Algebraic Manipulation Start → 1.7 Selecting Procedures for Determining Limits Start → 1.8 Determining Limits Using the Squeeze Theorem Start → 1.9 Connecting Multiple Representations of Limits Start → 1.10 Exploring Types of Discontinuities Start → 1.11 Defining Continuity at a Point Start → 1.12 Confirming Continuity over an Interval Start → 1.13 Removing Discontinuities Start → 1.14 Connecting Infinite Limits and Vertical Asymptotes Start → 1.15 Connecting Limits at Infinity and Horizontal Asymptotes Start → 1.16 Working with the Intermediate Value Theorem (IVT) Start →

Unit 2

Differentiation: Definition and Fundamental Properties

2.1 Defining Average and Instantaneous Rates of Change at a Point Start → 2.2 Defining the Derivative of a Function and Using Derivative Notation Start → 2.3 Estimating Derivatives of a Function at a Point Start → 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist Start → 2.5 Applying the Power Rule Start → 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple Start → 2.7 Derivatives of cos x, sin x, e^x, and ln x Start → 2.8 The Product Rule Start → 2.9 The Quotient Rule Start → 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions Start →

Unit 3

Differentiation: Composite, Implicit, and Inverse Functions

3.1 The Chain Rule Start → 3.2 Implicit Differentiation Start → 3.3 Differentiating Inverse Functions Start → 3.4 Differentiating Inverse Trigonometric Functions Start → 3.5 Selecting Procedures for Calculating Derivatives Start → 3.6 Calculating Higher-Order Derivatives Start →

Unit 4

Contextual Applications of Differentiation

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

Unit 5

Analytical Applications of Differentiation

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

Unit 6

Integration and Accumulation of Change

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

Unit 7

Differential Equations

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

Unit 8

Applications of Integration

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

Unit 9

Parametric Equations, Polar Coordinates, and Vector-Valued FunctionsBC only

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

Unit 10

Infinite Sequences and SeriesBC only

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

Each diagnostic is about 10 questions and takes 8 to 12 minutes. Missed items map to named misconceptions; the result page links you straight to drills that target those specific failures.