Khan Academy Exercises and Videos

Trust in the government

2026-07-22T12:59:39.156506

Learn about why and how trust in the government matters in a democracy.

How to spot misinformation

2026-07-22T12:59:39.156506

In this video, Sal discusses the importance of identifying and combatting false or skewed information to become a more informed participant in democracy.

State and local government

2026-07-22T12:59:39.156506

Learn about the state and local levels of government in the United States.

Relating height and volume of cylinders

2026-07-21T18:38:21.058934

Explore how height and volume relate as a linear function in the context of filling cylinders.

Estimating volume of hemispheres

2026-07-21T18:38:21.058934

Calculate the volumes of a cylinder and cone sharing the same radius and height, using them as upper and lower bounds for a hemisphere with that same radius. Use this reasoning to estimate the hemisphere's volume.

Finding the area of a tilted square

2026-07-21T18:38:21.058934

Find the area of a tilted square drawn on a grid, where its sides don't run along the gridlines. Practice using the grid to reason about area when the usual side-length approach doesn't directly apply.

Graphs of functions in context

2026-07-21T18:38:21.058934

Interpret points on graphs, including some that don't represent functions, and draw graphs to model real-world contexts. Explain which quantity depends on which, identifying which variable is a function of the other.

Determining solutions to 2-variable equations and graphs

2026-07-21T18:38:21.058934

Check whether ordered pairs are solutions to a two-variable linear equation by substituting and verifying. Connect this back to the graph: every point on the line is a solution, and any point off the line is not.

Relating side lengths and areas of squares

2026-07-21T18:38:21.058934

Introduce square roots as the side length of a square with a given area. Estimate a square's side length by comparing it to squares with known, nearby areas.

Comparing proportional and nonproportional linear relationships

2026-07-21T18:38:21.058934

Compare a proportional relationship to a nonproportional linear one using a cup-stacking scenario, testing whether stack height is proportional to the number of cups. Find the rate of change from a graph and interpret the vertical-axis intercept as a starting value rather than zero.

Small numbers on the number line

2026-07-21T18:38:21.058934

Use a number line to place very small numbers, coordinating their decimal forms with multiples of powers of 10, including negative exponents. Practice matching the two representations to build a sense of scale.

Solving aspect ratio problems with the Pythagorean theorem

2026-07-21T18:38:21.058934

Solve an aspect-ratio problem end to end with the Pythagorean theorem, setting up an equation from a given ratio and diagonal length. Solve for the unknown, find the actual side lengths, and finish by calculating the area.

Comparing scale in proportional relationship graphs

2026-07-21T18:38:21.058934

Practice graphing proportional relationships from equations like y = kx on coordinate planes with varying axis scales. Learn to recognize when differently-scaled graphs actually represent the same relationship.

Representing numbers using powers of 10

2026-07-21T18:38:21.058934

Learn how to write very large and very small numbers as multiples of powers of 10. Practice converting numbers into this form to make their size easier to understand and compare.

Rules of input-output tables

2026-07-21T18:38:21.058934

Learn how input-output diagrams work, where a rule transforms each input into a corresponding output. Practice identifying the rule from given pairs and applying it to find new outputs.

Calculating dimensions of a cone

2026-07-21T18:38:21.058934

Given the volume of a cone and one dimension, use the cone volume formula to find the missing dimension. Explain the reasoning behind each step of the calculation.

Solving problems using powers of 10 in context

2026-07-21T18:38:21.058934

Work through real-world problems involving very large or very small quantities, identifying what information is needed to solve them. Use exponent rules and powers of 10 to organize the numbers and work out a solution.

Writing and graphing linear equations

2026-07-21T18:38:21.058934

Write an equation in the form Ax + By = C from a real-world context where two quantities trade off to keep a fixed total, then graph the relationship. This form fits naturally when neither variable depends on the other, since both simply vary together to maintain that constant total.

Calculating dimensions of a cylinder

2026-07-21T18:38:21.058934

Use the cylinder volume formula to solve for a missing dimension, height or radius, when the volume and other dimension are given. Work through a table of cylinder dimensions and look for patterns.

Large numbers on the number line

2026-07-21T18:38:21.058934

Use a number line to place very large numbers, coordinating their decimal forms with multiples of powers of 10. Practice matching the two representations to build a sense of scale.

Limits of piecewise functions: absolute value

2026-07-23T21:43:53.000000

Exercises to support the video on finding limits of piecewise functions that involve absolute value.

Understand: Watersheds and human activity

2026-07-23T19:47:28.000000

Check your understanding of watersheds and human activity in this set of free, standards-aligned practice questions.

Apply: The cellular basis of life

2026-07-23T16:10:33.000000

Apply your understanding of the cellular basis of life in this set of free, standards-aligned practice questions.

Apply: Organ system interactions

2026-07-23T16:10:15.000000

Apply your understanding of organ system interactions in this set of free, standards-aligned practice questions.

Vectors in 2D

2026-07-23T15:30:15.000000

Practice adding, decomposing, and finding vector angles using trigonometry from word problems.

Interpreting motion data

2026-07-23T15:28:19.000000

Practice interpreting motion data in this set of free practice questions.

GCF & LCM word problems

2026-07-23T14:04:34.000000

Solve word problems where you either need to find the GCF or LCM.

Understand: Cell parts and functions

2026-07-22T18:57:49.000000

Check your understanding of cell parts and functions in this set of free practice questions aligned to NGSS standards.

Understand: Humans and ecosystems

2026-07-22T16:11:11.000000

Check your understanding of humans and ecosystems in this set of free practice questions aligned to NGSS standards.

Square roots

2026-07-22T15:05:46.000000

Practice finding the square root of a perfect square positive integer.

Translate points

2026-07-22T14:59:55.000000

Relate side lengths and areas of squares

2026-07-22T14:32:34.000000

Find the area of a square given a side length with a square root, find the side length of a square given its area, and estimate the side lengths and areas of squares. Use square root notation to express side lengths.

Solve problems using powers of 10 in context

2026-07-22T14:30:07.000000

Use exponent rules and powers of 10 to multiply, divide, and perform multi-step calculations with very large and very small quantities in real-world contexts.

Estimate volume of hemispheres

2026-07-22T14:26:15.000000

Estimate the volume of a hemisphere by comparing it to shapes you know, like cylinders, cones, and prisms. Use these shapes to find upper and lower bounds and make a reasonable estimate.

Calculate dimensions of a cone

2026-07-22T14:21:59.000000

Find a missing dimension of a cone (radius, height, or area of the base) when given its volume and one other dimension.

Calculate dimensions of a cylinder

2026-07-22T14:13:41.000000

Find a missing dimension of a cylinder (radius, diameter, or height) when given its volume and one other dimension.

Interpret piecewise linear functions

2026-07-22T14:08:15.000000

Interpret piecewise linear graphs in real-world contexts by identifying, calculating, and comparing rates of change for specific intervals.

Graphs of functions in context

2026-07-22T14:06:55.000000

A graph can tell different stories depending on which quantities we choose to compare. In this exercise, we'll explore how real-world situations can be represented with graphs by matching stories to graphs, matching graphs to stories, and identifying independent and dependent variables within a context. We'll think carefully about which quantity is the input, which is the output, and how features like increasing, decreasing, or staying constant show what is happening in a situation.

Explore negative exponents with a base of 10

2026-07-22T14:01:31.000000

Explore what happens when powers of 10 have **negative exponents**. A negative exponent means the number gets smaller by dividing by 10 each time. Practice rewriting powers of 10 as decimals and fractions, combining expressions using exponent rules, and recognizing when different forms represent the same value. The goal is to understand how negative exponents follow the same patterns as positive ones!

Dilate figures on a circular grid

2026-07-22T13:40:09.000000

Create dilations of polygons on a circular grid by applying a given scale factor and center of dilation.