Maths at Home

Video Lesson: Calculating Percentage Error The Percentage Error Formula The formula to calculate percentage error is: Percentage Error = |[(Measured Value – True Value) / True Value]| x 100 Where the Measured Value is the value obtained through measurement or observation. Where the True Value is the actual, theoretical or accepted value of the quantity […]

Video Lesson: Proof by Induction with Matrices How to do Proof by Induction with Matrices To do proof of induction with matrices: Substitute n=1 into both sides of the equation to show that the base case is true. Substitute n = k into both sides of the equation and assume it is true to obtain

Video Lesson: Proof by Induction for Divisibility How to Prove Divisibility using Proof by Induction To prove divisibility by induction, follow these steps: Show that the base case (where n=1) is divisible by the given value. Assume that the case of n=k is divisible by the given value. Use this assumption to prove that the

I am Andrew and I am a High School Mathematics tutor offering both online tuition and face-to-face tuition (depending on location). I offer tuition in all branches of mathematics from Year 5 to Year 12 SACE including: I am a current Head of Mathematics in South Australia and have 9 years of mathematics teaching experience

Video Lesson: How to Use De Moivre’s Theorem to Find Powers of Complex Numbers What is De Moivre’s Theorem? De Moivre’s theorem is a formula used for finding powers of complex numbers. De Moivre’s theorem states that for any complex number z = r( cos(θ) + isin(θ) ), powers of this number can be calculated

Video Lesson: How to Find the Modulus and Argument of a Complex Number What is the Modulus of a Complex Number? The modulus is the distance of the complex number from the origin on the argand diagram. For any complex number z = a + bi, the modulus is calculated using the Pythagorean theorem with

Video Lesson: How to Calculate the Magnitude and Direction of a Vector How to Calculate the Magnitude of a Vector The magnitude of a vector is a measure of its size or length. To calculate the magnitude, use the formula |v| = √(x2 + y2) where x and y are the horizontal and vertical components

Video Lesson: How to Find a Vector Perpendicular to a Plane How to Find a Vector Perpendicular to a Plane from 3 Given Points To find a vector perpendicular to a plane from three given points A, B and C: Calculate the vectors AB and AC. Calculate the cross product of the vectors AB and

Video Lesson: How to Find the Vector Between Two Points How to Find the Vector Between Two Points To find the vector between two points, subtract the coordinates of the initial point from the coordinates of the final point. For example, the vector from A(2, 3) to B(4, 0) is found by subtracting A from

Video Lesson: How to Calculate and Interpret Z-Scores What is a Z-Score? The z-score describes how many standard deviations a raw score is above the mean. Negative z-scores indicate a position below the mean. For example, a z-score of 2 means two standard deviations above the mean and a z-score of -1 means one standard