Khan Academy
Khan Academy: Linear Algebra: Exploring the Solution Set of Ax=b
Video first graphs the transformation image of a specific transformation. Then examines the solution set for a couple particular points in the image. Shows that the solution set is a shifted version of the null space. [16:34]
Khan Academy
Khan Academy: Geometry: Challenging Perimeter Problem
Demonstrates how to solve a problem from the 2000 American Invitational Mathematics Examination which involves finding the perimeter of a rectangle covered by nine overlapping squares. [9:56]
Khan Academy
Khan Academy: Arithmetic and Pre Algebra: Mixed Numbers and Improper Fractions
This video teaches how to convert between improper fractions and mixed numbers. Practice problems are available. [9:14]
Khan Academy
Khan Academy: Geometry: Incenter and Incircles of a Triangle
Explains that the intersection of the three angle bisectors of a triangle form the incenter of the triangle. [7:58]
Khan Academy
Khan Academy: Linear Algebra: Introduction to Projections
Video reviews how to use vectors to define a line. Gives an intuitive sense of what a projection is, then explains step-by-step where the formula for projections comes from. Shows an example of calculating a vector projection. [14:37]
Khan Academy
Khan Academy: Calculus: 2011 Calculus Ab Free Response #2 (C & D)
Video shows how to calculate the definite integral using a table of values and interprets what the definite integral represents in terms of the situation. Also shows how to use the definite integral to determine the value of a function...
Khan Academy
Khan Academy: Arithmetic and Pre Algebra: Recognizing Divisibility
This video explains how to test whether a number is divisible by a list of other numbers under 10. Practice problems are available. [6:26]
Khan Academy
Khan Academy: Arithmetic and Pre Algebra: Proper and Improper Fractions
This video explains the difference between proper and improper fractions. Practice problems are available. [1:41]
Khan Academy
Khan Academy: Statistics: Pearson's Chi Square Test (Goodness of Fit)
Video gives an example of the step by step process of using a Pearson's chi-square test to accept or reject a hypothesized data distribution. [11:48]
Khan Academy
Khan Academy: Linear Algebra: Transpose of a Matrix
Video explaining that the transpose of a matrix is created by switching rows and columns. The idea is shown abstractly and specifically with 2x2 matrix and 4x3 matrix. Also shows that the transpose of a transpose is the original matrix....
Khan Academy
Khan Academy: Algebra: Substitution Method 2
This video demonstrates how to solve a given system of equations by using substitution. [3:44]
Khan Academy
Khan Academy: Algebra: Recognizing Direct and Inverse Variation
Video showing how to manipulate sample equations to see if they represent direct or inverse variation or neither. Gives examples of values that make the equations true to explore further what is happening with the equations. Includes...
Khan Academy
Khan Academy: Linear Algebra: Determinant When Row Multiplied by Scalar
An instructional video explaining what happens to the determinant when one row in a matrix is multiplied by a scalar. Proves that the new determinant will simply be the scalar times the original determinant. Also addresses the case when...
Khan Academy
Khan Academy: Differential Equations: Laplace Transform 2
Video gives another example of using the Laplace transform to find Laplace transform table values. Includes an example of what it means for the Laplace transformation when the improper integral diverges and shows the connection between...
Khan Academy
Khan Academy: Geometry: Proof Rhombus Area Half Product of Diagonal Length
Demostrates how to prove that one way to find the area of a rhombus is by taking half the product of the diagonals. [5:07]
Khan Academy
Khan Academy: Arithmetic and Pre Algebra: Recognizing Prime Numbers
This video solves a problem asking to determine whether presented numbers are prime, composite, or neither. Practice problems are available. [4:40]
Khan Academy
Khan Academy: Chemistry: Types of Decay
The various ways a nucleus can decay, including Alpha, Beta and Gamma decay as well as positron emission. [17:02]
Khan Academy
Khan Academy: Linear Algebra: Eigenvectors and Eigenspaces for a 3x3 Matrix
Video finding the eigenspace for the two eigenvalues for the specific 3x3 matrix from the previous video. Part of the process of solving requires finding a null space by getting a matrix into reduced row echelon form. The resulting two...
Khan Academy
Khan Academy: Geometry: Problem Involving Angle Derived From Square and Circle
Demonstrates how to solve a challenging geometry problem about finding the measure of an angle that is formed by different segments in a square which intersect with part of a circle. Solution depends on creating triangles in the diagram...
Khan Academy
Khan Academy: Differential Equations: 2nd Order Linear Homogeneous Equations 4
Video shows using the foundation shown in previous videos how to more quickly find a solution to a second order linear homogeneous differential equation. Includes using initial conditions with the general solution to find a particular...
Khan Academy
Khan Academy: Differential Equations: Laplace Transform to Solve an Equation
Video shows example of using the Laplace transform to solve a differential equation. Problem is continued in next video. [10:51]
Khan Academy
Khan Academy: Linear Algebra: Finding Eigenvectors and Eigenspaces Example
Video defining eigenspace as the set of all the eigenvectors of a matrix with a specific eigenvalue. Finds the eigenspace for the two eigenvalues found in the previous video. Part of the process of solving requires finding a null space...
Khan Academy
Khan Academy: Algebra: Dividing Monomials
Video demonstrates how to divide a monomial by a monomial. [0:56]
Khan Academy
Khan Academy: Algebra: Fractional Exponent Expressions 2
Video simplifying an algebraic expression with fractional exponents and a square root. [7:32]