Maths at Home

Video Lesson: How to Calculate Variance What is Variance? Variance is a measurement of the variability or spread in a set of data. It is calculated as the average of the squared deviations from the mean. The larger the variance, the more spread a set of data is. The variance is the square of the […]

Video Lesson: Calculating the Volume of a Spherical Cap Volume and Surface Area of a Spherical Cap Calculator The calculator below calculates the volume and surface area of a spherical cap. Simply enter the following values: ‘h’ is the height of the spherical cap ‘r’ is the radius of the sphere ‘a’ is the radius

Video Lesson: Sketching the Derivative Graph of a Function What is the Graph of the Derivative Function? The derivative is the value of the gradient of the original function. The y coordinates at each point on the derivative function show the value of the gradient at the corresponding point on the original function. For example,

Video Lesson: Average Rate of Change What is the Average Rate of Change The average rate of change is defined as the average change in a function per unit over a given interval. It is the gradient of the secant line connecting the endpoints of the interval. It describes how one quantity changes with respect

Video Lesson: How to do Dominance Matrices What are Dominance Matrices? A dominance matrix is a numerical representation of which person or team has dominance over others within round-robin competitions. The value of 1 is written in the matrix if an entity has dominance over another and a 0 is written if they do not.

Video Lesson: What are the Double Angle Formulas? Video Lesson: How to Use the Double Angle Formulas What are the Double Angle Formulae? The double angle formulae are: sin(2θ)=2sin(θ)cos(θ) cos(2θ)=cos2θ-sin2θ tan(2θ)=2tanθ/(1-tan2θ) The double angle formulae are used to simplify and rewrite expressions, allowing more complex equations to be solved. They are also used to find

Video Lesson: How to Do Differentiation from First Principles What is Differentiation by First Principles? Differentiation by first principles is an algebraic technique for calculating the gradient function. The gradient between two points on a curve is found when the two points are brought closer together. The gradient is given by the equation f'(x)=limh→0[f(x+h)-(fx)]/h. Derivation

Video Lesson: The Number of Paths Algorithm How to do the Number of Paths Algorithm To do the Number of Paths Algorithm: Decide on the two directions of travel from start to finish. From the start node, write 1s at each outer node in the two directions of travel. At each inner node, add the

Video Lesson: Forward and Backward Scan to Find the Critical Path Video Lesson: Critical Path Analysis on a Network Diagram What is the Critical Path? The critical path is the longest sequence of tasks from project start to finish. The sum of the times on the critical path is equal to the project minimum completion

Video Lesson: How to Construct a Precedence Network from a Prerequisite Table What is a Precedence Network? A precedence network is a visual diagram used for representing the tasks required for completing a project. Arrows are used to show the dependencies of the tasks in relation to one another. The tasks are labelled on each