How to solve trigonometric problems based on complimentary anngles?(concept-3)

IB Maths tutors give great importance to Trigonometry.

Trigonometry is one of the fascinating branches of Mathematics. It deals with the relationships among the sides and angles of a triangle.Word trigonometry was originated from the Greek word, where, ‘TRI‘ means Three‘GON‘ means sides and the ‘METRON’ means to measure. It’s an ancient and probably most widely used branch Mathematics. For basic learning, IB Maths Tutors divide trigonometry in two part:-

1. Trigonometry based on right triangles

2. Trigonometry based on non-right triangles.

Here, we are discussing trigonometry based on non-right triangles only.

In the third article of this series, we will discuss problems based on complementary angles

In the third article of this series, we will discuss problems based on complementary angles

<img src="right triangle.jpg" alt="right triangle">

In this right triangle Sin A=BC/AC & Cos C=BC/AC   clearly: Sin A=Cos C  In the given triangle A+C=90° so we can write C=(90°-A). This gives us freedom to write Sin A=Cos (90°-A) similarly we can write these relationships     Read more

How to solve basic problems in trigonometry?(concept-2)

Mathematics tutors give great importance to Trigonometry

Trigonometry is one of the fascinating branches of Mathematics. It deals with the relationships among the sides and angles of a triangle.Word trigonometry was originated from the Greek word, where, ‘TRI‘ means Three‘GON‘ means sides and the ‘METRON’ means to measure. It’s an ancient and probably most widely used branch Mathematics. For basic learning, I am dividing trigonometry in two part:-

1 Trigonometry based on right triangles

1 Trigonometry based on non-right triangles.

In this post, we will discuss problems based on trigonometric ratios of a few specific angles like 0°,30°, 45°, 60° and 90°. Mathematics tutors use different tricks to form this table. I will discuss my tricks in a separate post

<img src="trigonometric table.jpg" alt="trigonometric table"> Read more

How to solve basic problems in trigonometry?(concept-1)

Mathematics tutors give great importance to Trigonometry

Trigonometry is one of the fascinating branches of Mathematics. It deals with the relationships among the sides and angles of a triangle.Word trigonometry was originated from the Greek word, where, ‘TRI‘ means Three‘GON‘ means sides and the ‘METRON’ means to measure. It’s an ancient and probably most widely used branch Mathematics. For basic learning, I am dividing trigonometry in two part:-

1 Trigonometry based on right triangles

1 Trigonometry based on non-right triangles.

In this post, I will only discuss Trigonometry based on right triangles.

In a right triangle, there are three sides hypotenuse (the longest side), adjacent side(base) and the opposite side(perpendicular).

                             <img src="right triangle.png" alt="right triangle"> Read more

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.

How to represent irrational numbers on number line

irrational number

Representation of irrational numbers on number line
Before understanding representation of irrational numbers on number line first, we need to understand Pythagoras’ theorem
Pythagoras’ Theorem:: Over 2000 years ago there was an amazing discovery about triangles:
When a triangle has a right angle (90°) and squares are made on each of the three sides then the biggest square has the exact same area as the other two squares put together!

irrational numbers

pythagorus theorem

Or Read more

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

Teaching Maths-Classroom discussions

"class room"

Teaching Mathematics is an art but there are certain factors about it that we can learn and improve our academic delivery.

Creating productive classroom discussions is one of them

Lecture method may work very well for some subjects but not all the time in  Mathematics classes.
Engaging students by constantly asking them some questions is a nice method but only when the explanation and the questions are Mathematical. Reasoning and justifying are good habits of mind but they are only productive if they are based on Mathematical theories.
Creating a productive classroom discussion is probably the most difficult part of Mathematics teaching. I suggest five methods for moving beyond Lecture methods in teaching Mathematics.
I have always tried to practice these methods in my own teaching whether with students or with teachers and I have found them very useful

1. Predict the Pupils’ Responses of Mathematics
All the teachers should know about each and every student how he/she is going to react to the instructional tasks(s) that they are asked to work on. 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

Advantages of Class 10th Cbse Board Exams

img src="img/10thresult.jpg"

Class 10th board exams are far more beneficial for students  in comparison to school exams,here we have a few benefits:

Benefits Of Boards :

1) These exams give students a fair idea about the exams far away from the home atmosphere of their schools and teachers.

Students will find them better mentally prepare for other out school competitive exams

2).A student will find a level playing field across the country and can prepare him/her self for a pan India competition.

There are chances of  discrimination in school exams because some school exam papers might be really easy while some might be very difficult.

3) There is a scope of improvement in marks/grades for a student who work hard through out the year.

Because final marks-sheet  is based on single board exam conducted at the end of year while its based on comprehensive system in c.c.e system

4)A student has to write test for whole syllabus so he/she has to revise it many times ,it helps him/her make a strong academic base.

5)Board exams provides students and parents a fair idea about student’s strengths and weaknesses and help them decide about their future studies and streams

besides all these benefits,uniformity in the whole system makes it easy to deliver for teachers too so lets enjoy boards and get us best prepared for coming academic session