What is a Permutation? Can Permutations have Repetition?Definition of permutation: The ways of arranging or selecting a smaller or an equal number of persons or objects at a time from a given group of persons or objects with due regard being paid to the …

Division Algorithm For PolynomialsIf p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = q(x) × g(x) + r(x) where r(x) = 0 or degree of r(x) < degree of g(x). The result is called Division …

What Is Irrational NumberA number is irrational if and only if its decimal representation is non-terminating and non-repeating. e.g.√2, √3, π ……………. etc. Rational number and irrational number taken together form the set of real numbers.If a and b are t…

Graphing Linear Inequalities If you can graph a straight line, you can graph an inequality!Graphing an inequality starts by graphing the corresponding straight line. After graphing the line, there are only two additional steps to remember. Choose a point…

Permutations and CombinationsLet’s review what we already know about the counting principle and permutations, and introduce the term “combination”.Fundamental Principle of Counting: (also known as the multiplication rule for counting) If a task can be pe…

Normal DistributionA normal distribution is a very important statistical data distribution pattern occurring in many natural phenomena, such as height, blood pressure, lengths of objects produced by machines, etc. Certain data, when graphed as a histogr…

General “Transformation” VocabularyThe following vocabulary terms will appear throughout the lessons in the section on Transformational Geometry.Image: An image is the resulting point or set of points under a transformation. For example, if the reflectio…

Pythagorean TheoremTHEOREM: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. (c2 = a2 + b2) It is believed that this theorem was known, in some form, long before the time of P…

Angle InformationAn angle is the intersection of two rays with a common endpoint.Remember that an angle is named using three letters, where the middle letter corresponds to the vertex of the angle. The angle at the right is ∠ABC or ∠CBA. If it is perfec…

Midpoint of a Line SegmentThe point halfway between the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two equal segments. By definition, a midpoint of a line segment is the point on that line segment that divi…