Divisibility rules

Divisibility rules:

• Numbers ending with 0‚ 2‚ 4‚ 6 or 8 are divisible by 2
• If the sum of the digits of a given number is divisible by 3, the number is divisible by 3.
• If the number formed by the end two digits of a given number is divisible by 4‚ then the number will be divisible by 4.
• Numbers ending with 0 or 5 are divisible by 5
• If the number formed by the end three digits of a given number is divisible by 8‚ then the number will be divisible by 8.
• If the sum of the digits of a number is divisible by 9, the number is divisible by 9.
• Numbers ending with 0 are divisible by 10
• If the difference of the sums of the digits in alternate places is divisible by 11, the number is divisible by 11.

Addition Rule of Probability

The Addition Rule:

Probability is the probably that event will happen – how likely the event will happen. The addition rule for probability: a statistical property that states the probability of one and/or two events occurring at the same time is equal to the probability of the first event occurring, plus the probability of the second event occurring, minus the probability that both events occur at the same time.
If events A and B are mutually exclusive or disjoint, then P(A U B) = P(A) + P(B)
Otherwise, P(A U B) = P(A) + P(B) – P(A ∩ B).

Quadrants

Quadrants:




Let X'OX and Y'OY perpendicular coplanar lines intersecting each other at O. We refer X'OX as x-axis and Y'OY as y-axis. It is clear from the adjoining figure, that these two lines divide the plane into four equal parts, each part is called a Quadrant.
The four Quadrants are:
XOY - first Quadrant
YOX' - second Quadrant
X'OY' - third Quadrant
Y'OX - fourth Quadrant

Trigonometry Heights and Distances

Trigonometry Heights and Distances:

• The word "Trigonometry" is derived from the two Greek words meaning measurements or solution of triangles. Trigonometry which is a branch of mathematics that deals with the ratio between the sides of a right triangle and its angles.
• Trigonometry is the study about relationships between the sides and angles of a triangle.
• Trigonometry is used in surveying and to determine Heights and Distances, in navigation it is to determine the location and the distances, and in the fields like nondestructive testing for determining things such as the angle for reflection or refraction of an ultrasound wave.

Types of Angles

Types of angles:

Algebra

Algebra is one of the main branches of mathematics. It explains the relations and properties of quantity by means of letters and other symbols. Algebra is used to simplify the long and very complicated statements. The basic algebra has the following subtopics are

1. Variables
2. Expressions
3. Terms
4. Polynomials
5. Equations.

Theorem in Mathematics

Theorem in Mathematics:

Congruent Supplements Theorem: When two angles are supplementary to the congruent angles or to the same angle, then the given angles are congruent.
Vertical Angle Theorem: Two angles are said as congruent even when they are vertical angles.
Alternate Interior Angle Theorem:Pairs of alternative interior angles are said as congruent when two parallel lines are cut transversely.
Consecutive Interior Angle Theorem:Pairs of consecutive interior angle are said as supplementary when two parallel lines are cut transversely.
Alternative Exterior Angle Theorem: Pairs of alternative exterior angle are said as congruent when two parallel lines are cut transversely.