How to Prove quadratic formula?

Many ib mathematics tutors consider quadratic equations as one of the most important topics of ib maths. There are following ways to solve a quadratic equation

► Factorization method

►complete square method 

► graphical method

► Quadratic formula method

<img src="ib mathematics tutors.png" alt="ib mathematics tutors>

The quadratic formula is the strongest method to solve a quadratic equation. In this article, I will use …… steps to prove the quadratic formula

Given equation: ax²+bx+c=0

Step-1: transfer constant term to right side

ax²+bx=-c

Step-2: divide both sides by coefficient of x²

x²+bx/a=-c/a
Step-3: write (coefficient of x/2)²     that is (b/2a)²=b²/4a²
Step-4: Add this value to both sides
x²+bx/a+b²/4a² =-c/a²+b²/4a²
(x+b/2a)²=b²-4ac/4a²
now, take square root on both sides
x+b/2=±√b²-4ac/a²

x=-(b/2a)±√b²-4ac/2a

x=-b±√b²-4ac/2a

This formula is known as quadratic formula, we can put values of a, b and c  from any equation and find the value of x (the variable) by directly using this formula.
IB Mathematics tutors can also explain the concept of conjugate roots with the help of quadratic formula. In a quadratic equation,
                                                              ax²+bx+c=0
if a, b and c are all rational numbers and one root of the quadratic equation is a+√b then the second root will automatically become a-√b. that can be understood easily as we use one +ve and one -ve sign in quadratic formula.
These types of roots are called Conjugate Roots.

IB Tutors-useful pdfs

I am sharing few documents prepared by experienced IB Tutors

 

Below is a past year paper for ib mathematics

 

ib_elite_tutor.com

 

Below is an important worksheet for Differentiability of Functions

 

Worksheets_on_Differentiability_(22-09-15)

 

Below is an important worksheet for logarithms

 

Worksheets_on_Log

 

Below is an important worksheet for maxima and minima value of Functions

 

Worksheets_on_Maxima_&_Minima_(22-09-15)

IB Mathematics Tutors- types of mathematical function(part-1)

IB Mathematics Tutors should give a fair number of hours in teaching functions.This is my third article on functions in the series of ib mathematics

For the sake of a comprehensive discussion, some standard functions and their graphs are discussed here

For the sake of a comprehensive discussion, some standard functions and their graphs are discussed here
1.Constant Function-
                                                F(x)=k
Domain= ℝ    

                                            Range    = {k}                                       

<img src="constant-function.jpg" alt="constant-function">

constant-function

                                   
Range    = {k}

Read more

IB Mathematics (part-2)-Domain and Range of a function

In IB Mathematics both HL and SL, functions are one of the most important areas because they lie at the heart of much of mathematical analysis.here I am discussing domain and range of a function

Domain of a Function

Suppose I say that f is a real function.This means that for real input, the output should be real. For example

 F(x)=√x

if F is real, then x can only take non-negative values because only then the output will be real. Set of all real values of R is called domain

“Domain is the set of all possible inputs for which the output is real ”

In some cases, x is defined explicitly. for example,

                                     y=f(x)

                                       =x²;    1<x>2 here domain is defined explicitly as (1,2)

If no domain is mentioned explicitly, the domain will be assumed to be such that “F” produces real output

These are a few examples

  1. y=f(x)=√x
    Domain D= x≥0

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Classroom conflicts

"classroom conflict"

 CLASSROOM  CONFLICT-

Classroom conflict is a general problem. Every teacher should be ready to face it.

  • As a teacher, we should be supportive, encouraging, and respectful of student ideas in the classroom. We should provide them proper space to put their views, we should correct their wrong answers, we should point out their academic weaknesses but we should never discourage our students.
  • We should always listen to our students carefully and we should respond to them properly whenever they offer an idea.
  • We should not dismiss a weak or incorrect idea immediately, we should ask our pupil to clarify it using the class material. Often, they can talk their way into a more thoughtful response.
  • We can try some funny things in the classroom to engage our students but we should know that this act require extra care as it can easily be misunderstood

We are also less likely to fall into conflict with our pupils if we resolve any mixed feelings we have about our superiority as a teacher. Students expect us to set clear boundaries and to hold them to their academic responsibilities.

TRICKS FOR MANAGING CHALLENGES-

Arguments in Class

When arguments erupt in class, or when a pupil makes any wrong comment, our role as the teacher is to save the learning atmosphere of our classroom. This task is two-fold: Read more

Pi day-14th March

In the whole history of Mathematics, the calculation of the ratio of a circle’s circumference and diameter is one of the biggest challenges.
This value is represented by the Greek letter π (pie). From ancient civilization of Babylonia to present age of supercomputers, Mathematicians have been trying to calculate this mysterious number.

They have searched for exact fractions value, formulas, and, more recently, patterns in the long string of numbers starting with 3.14159…….. which is generally shortened to 3.14.

Its an irrational number in Mathematics. Read more