Instructional Video
Sophia Learning

Sophia: Using Concavity to Optimize: Lesson 4

9th - 10th
This lesson practices isolating extremes using concavity of a function. It is 4 of 6 in the series titled "Using Concavity to Optimize."
Instructional Video
Sophia Learning

Sophia: Simplifying Exponential Equations: Lesson 2

9th - 10th
This lesson practices using the fact that e is a constant to simplify equations. It is 2 of 6 in the series titled "Simplifying Exponential Equations."
Instructional Video
Sophia Learning

Sophia: Simplifying Exponential Equations: Lesson 5

9th - 10th Standards
This lesson practices using the fact that e is a constant to simplify equations. It is 5 of 6 in the series titled "Simplifying Exponential Equations."
Instructional Video
Sophia Learning

Sophia: Units and Integration: Lesson 2

9th - 10th
Given an integral with specific parameters, this lesson shows how to properly adjust those parameters when evaluating the integral. It is 2 of 4 in the series titled "Units and Integration."
Instructional Video
Sophia Learning

Sophia: Using Concavity to Optimize: Lesson 1

9th - 10th
This lesson practices isolating extremes using concavity of a function. It is 1 of 6 in the series titled "Using Concavity to Optimize."
Instructional Video
Sophia Learning

Sophia: Using Concavity to Optimize: Lesson 6

9th - 10th
This lesson practices isolating extremes using concavity of a function. It is 6 of 6 in the series titled "Using Concavity to Optimize."
Instructional Video
Sophia Learning

Sophia: Using Implicit Differentiation: Lesson 2

9th - 10th
This lesson explains how to carry out implicit as opposed to explicit differentiation. It is 2 of 5 in the series titled "Using Implicit Differentiation."
Instructional Video
Sophia Learning

Sophia: Using Static Rates of Change: Lesson 3

9th - 10th Standards
This lesson practices using the derivative to find a ratio of one parameter to another, which is not time. It is 3 of 6 in the series titled "Using Static Rates of Change."
Instructional Video
Sophia Learning

Sophia: Ways to Simplify Exponential Equations: Lesson 2

9th - 10th
Using the fact that e is a constant to simplify any equation is shown here. This lesson is 2 of 5 in the series titled "Ways to Simplify Exponential Equations."
Instructional Video
Sophia Learning

Sophia: Using Static Rates of Change: Lesson 6

9th - 10th Standards
This lesson practices using the derivative to find a ratio of one parameter to another, which is not time. It is 6 of 6 in the series titled "Using Static Rates of Change."