Curated OER
Slope and Rate of Change
Introducing slope as "a way of measuring the inclination of a line," Sal endeavors to provide a working knowledge of slope problems and problem solving. The video is framed as a review, but could be a good way to fill any holes in...
Khan Academy
Simple Equations
Basic algebraic equations of the form Ax=B are dissected. Sal encourages viewers to fully understand what the equations represent prior to learning how to manipulate them. Furthermore, he teaches students how to solve the equations...
Khan Academy
Similar Triangles (Part 2)
Building on concepts in the first part of the series on similar triangles, installment number two explores how to find the values for given angles in a triangle. These problems are solved by using algebra and ratios. A step-by-step...
Khan Academy
Scientific Notation Examples
The problems in this video contain additional examples of scientific notation, continued from the previous presentation. Viewers have the opportunity to see Sal work through several more problems using the same techniques he has been...
Khan Academy
Rhombus Diagonals
Delving into a proof that the diagonals of a rhombus are perpendicular to each other, this lecture evaluates the angles and sides of this figure. It would serve as a great test preparation activity.
Khan Academy
Refraction of Seismic Waves
Mr. Khan uses a metaphor of a car to help explain the change in direction of waves as they hit a boundary between two mediums. He then goes on to explain the relationship between the structure and density of the earth and the behavior of...
Khan Academy
Recognizing Odd and Even Functions
This video gives a formal definition of odd and even functions, as well as, an intuitive feeling for how they are different. By looking at the graphs of both types of functions, Sal shows the reflection properties of both functions....
Khan Academy
Range, Variance and Standard Deviation as Measures of Dispersion
Continuing his conversation about data sets from the previous video, Sal introduces range, variance, and standard deviation as means of dispersion. Those who are advancing in algebra or who are beginning a statistics class will benefit...
Curated OER
Pythagorean Theorem All
As the second in a series on the Pythagorean Theorem, this lecture delves into some more difficult problems. Primarily, it examines the process for finding the value of a hypotenuse. It is particularly helpful because the example problem...
Curated OER
Proof: sin(a+b)=(cos a)(sin b)+(sin a)(cos b)
Sal proves the sum of angles formula for sine, sin (a+ b) = cos (a) sin (b) + sin (a) cos (b), through a clear but rather non-intuitive proof. The proof is interesting as it not only uses the SOH-CAH-TOA model but requires one to recall...
Curated OER
Proof: lim (sin x)/x
By looking the expression (sin x)/x that is not defined at the limit value of 0, Sal uses the squeeze theorem to show that the function can by bound between two other functions that are defined at limit value so the limit can indeed be...
Khan Academy
Proof: Hyperbola Foci
In a video that is quite involved, algebraically, Sal proves that the distance of the foci from the center of a hyperbola is the square root of a2+b2. Since the algebra shown here is challenging, this video might be appropriate as an...
Curated OER
Proof: d/dx(x^n)
Using the binomial theorem and definition of a limit, Sal shows a proof that the derivative of xn equals nxn-1.
Curated OER
Proof: d/dx(sqrt(x))
Using the definition of a limit, Sal proves the derivative of x or x1/2 is equal to _ x-1/2.
Curated OER
Proof: d/dx(ln x)=1/x
Using the definition of a limit, various properties of logarithms, and a definition of e, Sal shows the proof of derivative of ln x = 1/x. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó has a clearer explanation of this...
Curated OER
Proof: d/dx(e^x) = e6x
Using the derivative of ln x, the chain rule, and the definition of a limit, Sal shows a proof that derivative of ex = ex. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó has a clearer explanation of this proof.
Curated OER
Proof: cos(a+b)=(cos a)(cos b)-(sin a)(sin b)
Using a similar method that he used to prove the sum of angles formula for sine, Sal shows the proof of the cosine sum of angles formula, cos (a+ b) = cos (a) cos (b) - sin (a) sin (b). This proof also uses the SOH-CAH-TOA model and some...
Curated OER
Polar Coordinates 1
In this introductory video, Sal defines polar coordinates and using basic trigonometry identities and the Pythagorean Theorem defines the relationships between Cartesian coordinates and polar coordinates.
Khan Academy
Patterns in Sequences 2
This video looks again at finding the algebraic pattern in sequences. In the example, we are looking at a figure where a number of toothpicks (or lines) are added each time, and you need to find how many toothpicks will be in the 50th...
Khan Academy
Patterns in Sequences 1
Faced with a series of numbers we need to find the next few values of the sequence. This short video shows an example of finding the next values in a sequence where we need to find the pattern of adding a specific number each time to...
Khan Academy
Parallel Lines 2
Can you tell, algebraically, if three lines are parallel? In this video, Sal demonstrates how to rewrite linear equations in slope-intercept form and compare the slope of each line.
Curated OER
Parabola Focus and Directrix 1
Starting with a point (focus) and a line below the point (directrix), in this video, Sal tries to find the set of all points (locus) equidistant to the point and the line. He shows, using the distance formula, that indeed, we have an...
Curated OER
Introduction to Logarithms Properties
Sal gets to the heart of the matter in this video, clarifying that it's important to understand math "so you can actually apply it in life later on and not have relearn everything every time." True to his word, Sal demonstrates ways to...
Curated OER
Introduction to Limits (HD)
Sal begins his explanation of limits with a few basic examples and takes a more intuitive point of view before looking at a formal mathematical definition in later videos. He starts by introducing the notation for limits and describes...