Algebraic Surds

LEARNING OBJECTIVES:  To define algebraic surds To perform operations involving surds To simplify and rationalize surds MATH CONCEPTS SURDS- It is a root of a positive real quantity where its value cannot be exactly determined. It is an irrational number which cannot be simplified and usually in the form of , n is the order … Read more

Arithmetic Series

LEARNING OBJECTIVES: To define and illustrate arithmetic seriesTo solve for the value of an arithmetic seriesTo apply the concepts of arithmetic series to solve real-life problems MATH CONCEPTS ARITHMETIC SERIES – it is the sum of the terms in an arithmetic sequence/progression. GENERAL FORMULA FOR ARITHMETIC SERIES – It is a formula to be used … Read more

Proof by Exhaustion

In this section, we will learn about “Proof by Exhaustion”. After reading this article we will be able to prove any statement by exhaustion. Introduction As we have studied before, that “proving a mathematical statement is an art”. There are many techniques to prove the mathematical statement. In this section, we are going to discuss … Read more

Proof by Deduction

In this article, we will learn “how to prove a statement by deduction?” Content Introduction Definition Methodology Practical Examples Summary Introduction In mathematics proving some statement is always a critical work. Because any statement in mathematics has its significance. Here we are discussing one of the techniques to prove whether the statement is true or … Read more

Disproof by Counterexample

In this article, we will learn “How to disprove a statement by counterexample?” Introduction Some time in mathematical science we find a statement that looks true but in actual it is not true due to some reason. We need just an example to show that, the given statement is not true is called disproof by … Read more

Complete the Square

In this section, we will learn, “how to complete square of the quadratic equation” and able to find the “solution of the quadratic equation”. Introduction Completing the square of any quadratic equation helps us to find the solution of the quadratic equation and gives us a vertex form of any quadratic equation. By vertex form, … Read more