# Content Update: AP Statistics and Multivariable Calculus

We’re thrilled to let you know about the addition of new content to two math courses!

## AP Statistics

- Mosaic plots
- Influential points, outliers, and high-leverage points in scatterplots
- Systematic random sampling
- Prospective and retrospective studies
- Mean and standard deviation of geometric distributions
- Sampling distributions for differences between two means or proportions

**New Articles:**

- Differences of sample proportions — Probability examples
- Differences of sample means — Probability examples

**New Exercises:**

- Types of studies
- Sampling method considerations
- Mosaic plots
- Identify influential points
- Geometric distributions
- Mean and standard deviation of difference of sample proportions
- Mean and standard deviation of difference of sample means
- Shape of sampling distributions for differences in sample proportions
- Shape of sampling distributions for differences in sample mean

## Multivariable Calculus

The course is now mastery-enabled with 50 new exercises containing over 600 unique problems, each with detailed hints and step-by-step solutions. Many exercises focus on visual understanding to help students gain an intuition for concepts.

**New Articles:**

- Prerequisites overview
- Vectors and notation
- Dot products
- Cross products
- Matrices, intro
- Visualizing matrices
- Determinants
- Gradient descent

**New Exercises:**

- Basic partial derivatives
- Finding partial derivatives
- Higher order partial derivatives
- Finding gradients
- Visual gradient
- Finding directional derivatives
- Vector-valued functions differentiation
- Parametric velocity and speed
- Multivariable chain rule intro
- Multivariable chain rule
- Visual parametric surfaces
- Partial derivatives of vector valued functions
- Visual divergence
- Finding divergence
- Visual curl
- Finding curl in 2D
- Finding curl in 3D
- Symbols practice: The gradient
- Finding the Laplacian
- Finding the Jacobian
- Jacobian determinant
- Finding tangent planes
- The Hessian matrix
- Find critical points of multivariable functions
- Visual zero gradient
- Classifying critical points
- Line integrals of scalar functions
- Line integrals in vector fields
- Line integrals in conservative vector fields
- Distinguishing conservative vector fields
- Potential functions
- Iterated integrals
- Double integrals with variable bounds
- Finding bounds of regions
- Switching bounds on double integrals
- Triple integrals
- Change of variables: Bound
- Change of variables: Factor
- Double integrals in polar
- Integrals in spherical and cylindrical coordinates
- Find area elements
- Surface integrals to find surface area
- Simple, closed, connected, piecewise-smooth practice
- Circulation form of Green's theorem
- Normal form of Green's theorem
- Orientations and boundaries
- Stokes' theorem
- The divergence theorem

**Removed Exercises:**

- Thinking about multivariable functions review practice
- Derivatives of multivariable functions review practice

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