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Topic module: Core

De’ Morgan’s Laws

De Morgan’s Laws are two results relating intersection, union and complement of two intersecting sets.

Algebra of sets

Here I introduce you to Sets and the algebra of set operations Definitions and notation Types of Set Intersection, Union, and Complement

Area bound by a curve and y-axis

Integration can be used to find the area bounded by a curve y = f(x), the y-axis and the lines y=a and y=b but care must be taken when the area is on either side of the y-axis as the video shows.

Linear interpolation method for locating a root in a given interval

The linear interpolation method for locating a root in a given interval is a simple extension to the change of sign method. The following video example demonstrates this method. Example: Find an approximation to the root of x3 + 2x – 2 = 0 using linear interpolation twice over, given that the root lies between 0 and […]

Bisection method for locating a root in a given interval

The bisection method is a simple extension to the change of sign method where an interval in which a root lies is continually bisected (cut in half) until the root is found to the required degree of accuracy. The following example is used to demonstrate this: Example: Find the root of to 1 decimal place […]

Stationary points

In this tutorial I show you how to find stationary points to a curve defined implicitly and I discuss how to find the nature of the stationary points by considering the second differential. Both methods involve using implicit differentiation and the product rule. Example: Nature of the Stationary Points

Stationary points

In this video you are shown how to find the stationary points to a parametric equation.

Proving identities using the factor formulae

Here I introduce you to the factor formulae. These are identities, given without proof are useful when adding or subtracting two sine angles or cosine angles and creating one term from the two. Hence, factor formulae. The examples which follow are typical of the kind of questions you can get that uses the factor formulae. […]

Graphing y=f(|x|)

Remember: f(|x|) reflects the graph to the right of the y-axis in the y-axis. Ignore the left hand side part of the graph In this video I show you how to draw graphs of the form y=f(|x|) using the modulus function and give you three graphs to try. Examples in the video: Sketch the following

Infinite integrals

In this tutorial I show you how to handle integrals where a limit is infinite as in the example below. Example:

The remainder theorem

The Remainder Theorem Rule to remember: If a polynomial is divided by then the remainder is . In the video tutorial I demonstrate this. Finding the remainder when a cubic polynomial is divided by x+1 In the videos that follow, I run through some typical remainder theorem questions that you are likely to encounter. I […]