Khan Academy
Khan Academy: Arithmetic and Pre Algebra: Adding Fractions With Different Signs
This video shows how to add three fractions, one of which has a negative sign. Practice problems are available. [6:22]
Khan Academy
Khan Academy: Linear Algebra: Subpsace Projection Matrix Example
An instructional video that works through a concrete example for how to find the projection of an arbitrary vector onto a specific subspace in R4. Uses a 4 x 2 basis matrix for the subspace. Matrix operations are used along with the...
Khan Academy
Khan Academy: Linear Algebra: Simpler 4x4 Determinant
Video demonstrating how to find the determinant of a 4x4 matrix by using row operations and row replacements to get the matrix into upper triangular form. [9:13]
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Khan Academy: Geometry: Intro to 30 60 90 Triangles
Solves an example problem in which the length of the hypotenuse is known and the length of a side must be determined. Explains the special relationship of the lengths of the sides of a 30-60-90 triangle using the Pythagorean theorem....
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Khan Academy: Differential Equation: Laplace/step Function Differential Equation
Video demonstrates using the Laplace transform and inverse Laplace transform to solve a differential equation. [19:12]
Khan Academy
Khan Academy: Linear Algebra: Proof of the Cauchy Schwarz Inequality
Video first explains what the Cauchy-Schwarz inequality is and then shows a proof of it. [16:55]
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Khan Academy: Calculus: 2011 Calculus Ab Free Response #5C
Video shows how to find the particular solution to a separable differential equation. [9:15]
Khan Academy
Khan Academy: Algebra: Proof of Quadratic Formula
Demonstrates how to derive the quadratic formula from the standard form of a quadratic equation by completing the square. This video also appears in the Algebra: ck12.org strand. [7:44]
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Khan Academy: Geometry: Similar Example Problems
Explains how to identify and use similar triangles in order to determine unknown side lengths in two given diagrams. Each diagram also applies knowledge of angles formed when parallel lines are cut by a transversal. [7:37]
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Khan Academy: Linear Algebra: Example of Finding Matrix Inverse
A video lesson that works through a concrete example to find the inverse of a 3 x 3 matrix. The original matrix is augmented by the identity matrix and then put in reduced row echelon form. The result of the row operations on the...
Khan Academy
Khan Academy: Algebra: Solving Rational Equations 2
A step-by-step breakdown on how to solve a rational equation with constraints. [4:08]
Khan Academy
Khan Academy: Linear Algebra: Proof of Formula for Determining Eigenvalues
Video beginning the process of finding eigenvectors and their eigenvalues by manipulating the equation for finding a transformation where the result is an eigenvector. Includes review of null space and linear independence and dependence...
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Khan Academy: Differential Equations: Convolution Thm for Initial Value Prob
Video shows how the convolution theorem can be used to solve an initial value problem and get it to an integral form. [12:14]
Khan Academy
Khan Academy: Differential Equations: Complex Roots of Characteristic Equation 3
Video shows example of using formula derived in previous video for general solution of a differential equation when characteristic equation has complex roots. Includes using initial conditions to determine a particular solution. Shows...
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Khan Academy: Linear Algebra: The Gram Schmidt Process
Video about the Gram-Schmidt process which is used to create an orthonormal basis from any basis. First an orthonormal basis is created in one dimension by normalizing the vector and then in two dimensions by building on the...
Khan Academy
Khan Academy: Pre Calculus: Introduction to Limits (Hd)
Instructional video explaining the concept of a limit. Does not provide a formal definition of limit. Includes graphical and numerical examples using both a virtual chalkboard and virtual graphing calculator. Includes link to practice...
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Khan Academy: Algebra: Conic Sections: Iit Jee Circle Hyperbola Common Tangent 3
The third video of five on solving an IIT JEE problem concerning a tangent line that is common both to a circle and a hyperbola. This video uses algebra to determine where the arbitrary line y = mx + b could intersect the given hyperbola...
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Khan Academy: Algebra: Conic Sections: Iit Jee Circle Hyperbola Common Tangent 5
The final video in the series on solving an IIT JEE problem concerning a tangent line that is common both to a circle and a hyperbola. The video first completes solving for the slope that began in the previous video and then substitutes...
Khan Academy
Khan Academy: Algebra: Factoring Trinomials by Grouping 5
Video demonstrates how to factor a given quadratic trinomial using the factor by grouping method. The given trinomial has a GCF and a leading coefficient greater than 1. [4:46]
Khan Academy
Khan Academy: Geometry: Exploring Medial Triangles
This video tutorial [11:32] explains what a medial triangle is and proves that the medial triangle divides the original triangle into four congruent triangles. Proof uses triangle similarity and triangle congruence postulates.
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Khan Academy: Calculus: 2011 Calculus Ab Free Response #6B
This video [5:15] shows how to write the derivative of a piecewise function as another piecewise function. Uses the derivative to find the value of x that gives a certain derivative value.
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Khan Academy: Linear Algebra: Proving Vector Dot Product Properties
Video shows proofs of vector dot product properties. Proves vector dot products hold true under the commutative, distributive and associative properties. [10:45]
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Khan Academy: Statistics: Bernoulli Distribution Mean and Variance Formulas
Video example of what a Bernoulli distribution is. Demonstrates how the general formulas for the mean and variance of the distribution are derived. [6:59]
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Khan Academy: Algebra: Conic Sections: Foci of a Hyperbola
A video lesson exploring the foci of a hyperbola. The formula for finding the foci is derived algebraically and then applied to a specific hyperbola equation. Shows that the foci of a hyperbola relate closely to the foci of an ellipse....