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...
Khan Academy
Introduction to Function Inverses
Starting from a brief look at functions and the mapping of domains to ranges, Sal starts out with an intuitive sense of what a function inverse is. He then, using an example, shows how to find the inverse of a function and also shows how...
Curated OER
Intro to 30-60-90 Triangles
As the fourth part of a series on the Pythagorean Theorem, Sal continues an exploration of the ways to calculate the length of sides of a right triangle using algebra. He also explores using this theorem to solve problems involving a...
Curated OER
Identifying Conics 2
In this video, Sal shows again how to write an equation of a conic section in standard form and identify the conic section it represents. This time, his example is of a hyperbola (not centered at the origin), which he also graphs.
Curated OER
Identifying Conics 1
After watching this video, you should be able to write an equation of a conic section in standard form, and identify the conic section from its equation. In an example problem, Sal reviews how to complete the square and graph an ellipse...
Curated OER
Fun Trig Problem
If solving trigonometric equations is your idea of fun, then this video is correctly titled. Here Sal uses trigonometric identities, the quadratic formula, and inverse trigonometric functions to solve a trigonometric equation sent in by...
Curated OER
Focus and Directrix of a Parabola 2
Continuing from a previous video, Sal takes the discussion of the focus and directrix of parabola further. Given the parabola, y=x2, he derives the focus and directrix by matching parts of the equation he found earlier. He then, comes up...
Curated OER
Foci of an Ellipse
The foci of an ellipse are explored in this video. First, foci are shown as the two points on the major axis such that the sum of the distance from a point on the ellipse and the foci points is the same as the distance from any point on...
Curated OER
Foci of a Hyperbola
In this video, Sal defines the vertex and the foci of a hyperbola, and shows how to locate both. By comparing the hyperbola to an ellipse throughout the video, the listener sees the similarities between these two conic sections. This...
Curated OER
Finding the 100th Term in a Sequence
The example problem is this video has a sequence of numbers that decrease by a fixed amount with each iteration, and one needs to find the 100th number in the sequence. Sal shows the listener how to find the pattern between the number...
Curated OER
Example of Solving for a Variable
Sal uses the formula for perimeter to show how the variables can be moved around to solve a problem. He demonstrates a few different ways to do this.
Curated OER
Equations of Sequence Patterns
An example of writing an algebraic equation of the pattern of blocks that grows at each iteration is shown in this video. Sal shows how to find the pattern by looking at the iteration number and number of blocks. He then continues this...
Curated OER
Domain of a Function
We look at a number of different examples of functions and see what their domain is. Sal writes the domain in set notion and shows how different functions can have different input values that cause the function to be undefined.
Curated OER
What is the domain of a function?
After defining a simple function from a word problem, a short video shows how one could find the domain and the range of that function. The instruction reinforces the definitions of domain and range with a concrete example.
Curated OER
Connection between even and odd numbers and functions
Are odd numbers connected to odd functions and even numbers to even functions? This video tries to clarify that connection. It also talks about functions that are neither odd nor even to give a more intuitive feeling about classifying...
Curated OER
Conic Sections: Intro to Hyperbolas
In this video, Sal starts with the equation of a hyperbola by first comparing it to the equation of the circle, and ellipse. He then shows how to find the equation of the asymptotes by solving for y. He also shows a few intuitive ways to...
Curated OER
Conic Sections: Intro to Circles
The equation of a circle is explored in this video by looking first at the equation of a circle with the center at the origin; then building upon that, equations of circles that are shifted off the origin.
Curated OER
Conic Identification 3
This is the last of three well-done videos on identifying and graphing conic sections from an equation. Here, Sal shows graphing a circle, not centered at the origin, and a parabola that opens downward.
Curated OER
Complex Numbers (Part 1)
In this video, a complex number is defined and graphed on the complex plane. Sal also shows how to add, subtract, and multiply two complex numbers. He starts showing how to divide two complex numbers, but runs out of time and continues...
Curated OER
Binomial Theorem (Part 2)
Sal shows two ways to quickly calculate the coefficients of a binomial expansion. With the first method, he shows the relationship between PascalÕs triangle and the coefficients, and in the second method, he shows an even faster way for...
Curated OER
Binomial Theorem (Part 1)
In this video, the Binomial Theorem is defined and used to expand (a + b) 4.
Curated OER
Basic Rate Problem
A simple rate problem is looked at in this video. The listener needs to compute whether four trains each going different distances over different amounts of time are moving at the same constant rate. This problem reinforces ones basic...