The Basic Elements of GeometryYou are familiar with some terms like triangle, square, cube, cuboid, etc. These are examples of geometrical figures. To make these geometrical figures we need to know some basic elements. These basic elements are as follow…

Simplifying Complex Fractions  (multiplying by common denominator)Method 1: This is one of two methods for simplifying complex fractions.To Simplify a Complex Fraction by Multiplying by a Common Denominator. 1. Find the least common denominator (LCD) of …

Factoring by Grouping with a Grid BoxLet’s look at factoring This time, let’s use our grouping process written in a grid box.When “factoring by grouping”, dealing with the signs may be problematic. To avoid this confusion, many students find the creati…

Completing the SquareAn equation in which one side is a perfect square trinomial can be easily solved by taking the square root of each side. Consider the example at the right: It is this method of solution that is the basis of a process called “complet…

Absolute Value InequalitiesSolving an absolute value inequality problem is similar to solving an absolute value equation.Start by isolating the absolute value on one side of the inequality symbol, then follow the rules below: If the symbol is > (or &g…

Radicals | Simplification, Properties, Addition and Multiplication of RadicalsA radical or the principal nth root of k: k, the radicand, is a real number. n, the index, is a positive integer greater than one.  Properties of Radicals: Simplifying Radicals…

Adding and Subtracting Rational (Fractional) ExpressionsFractions are fractions!It doesn’t matter if the fractions are made up of numbers, or of algebraic variables, the rules are the same! The Basic RULE for Adding and Subtracting Fractions:Get a Commo…

Vertically Opposite AnglesTwo angles are called a pair of vertically opposite angles, if their arms form two pairs of opposite rays. Let two lines AB and CD intersect at a point O. Then, two pairs of vertically opposite angles are formed. (i) ∠AOC and ∠B…

Linear Pair Of AnglesTwo adjacent angles are said to form a linear pair of angles, if their non-common arms are two opposite rays. In the adjoining figure, ∠AOC and ∠BOC are two adjacent angles whose non-common arms OA and OB are two opposite rays, i.e.…

What Is Arithmetic MeanIf three or more than three terms are in A.P., then the numbers lying between first and last term are known as Arithmetic Means between them.i.e. The A.M. between the two given quantities a and b is A so that a, A, b are in A.P. i.…