Possibly Biased DataIt is often possible that different research studies concerning the same issue can produce very dissimilar or contradictory results. How can this happen? Aren’t all statistics “true”? While the names of these Universities are fictiti…

Probability Involving AND and ORLet’s examine AND first:In probability, an outcome is in event “A and B” only when the outcome is in both event A and event B. In Venn Diagrams, we learned that an element was in the intersection “A and B”, only when the e…

Function TransformationsThere are numerous ways to apply transformations to functions to create new functions. Let’s look at some of the possibilities. Remember to utilize your graphing calculator to compare the graphs of your functions and their transf…

Transformations – Notations and FormulasA transformation is an operation that maps an initial figure (pre-image) onto a final image called an image. Line ReflectionsA reflection is a flip. It is an opposite isometry – the image does not change size but…

How To Find The Area Of A Plane FigureThe area of the portion of the plane or shape can be defined as the amount of stuff required to cover it. For finding the area of a polygon, we consider the enclosed region of the polygon. Let us consider an illustra…

Length of a Line Segment (Distance)When working with Coordinate Geometry, there are many ways to find distances (lengths) of line segments on graph paper. Let’s examine some of the possibilities:Method 1:Whenever the segments are horizontal or vertical,…

The Concept of CongruenceCongruence – CongruentObjects that are exactly the same size and shape are said to be congruent. Congruent objects are duplicates of one another. If two mathematical figures are congruent and you cut one figure out with a pair o…

Error in MeasurementAny measurement made with a measuring device is approximate. If you measure the same object two different times, the two measurements may not be exactly the same. The difference between two measurements is called a variation in the m…

Constructions: Isosceles and Equilateral TrianglesDirections for constructing isosceles and equilateral triangles:Construct an Isosceles Triangle Using Given Segment Lengths:When constructing an isosceles triangle, you may be given pre-determined segment…

RotationsA rotation is a transformation that turns a figure about a fixed point called the center of rotation. Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. (notation Rdegrees ) An object and …