# Content Updates - September 2020

Updated

We're always working to improve Khan Academy content! Here's what changed this month:

## AP Statistics

We’re thrilled to let you know about the addition of new content to our AP Statistics course, providing even more alignment to the updated Course and Exam Description from College Board. Here are some of the topics that we now cover:

- 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

We’ve also made smaller edits to some of our existing exercises to improve alignment based on changes in the Course and Exam Description.

**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 means

## 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