KEY POINTS FROM MATRIC MATHEMATICS

COROLLARY: These are formulas or Statements derived from main Formula / Theorem.

• Theorem may have many proofs.

• For convenience Figures may be shown separately from main figure.

• Pythagoras' theorem can be proved using proportionality of the sides of two similar triangles. Its converse can be proved using Congruent Triangles (SSS).

How to prove the basic theorems in geometry?

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1. Use the previous theorems, postulates, definitions and properties you already learned to prove new theorems. That's the principle of geometry, as you go by the lessons, you use what you learned before to learn new lessons.

2. Label the Drawing

3. Know where you are going (Given and Have to Prove)

Actually you can use two kinds of proving:

1. Direct and
2. Indirect.

In direct, you prove step by step until you come up with the desired statement.

In the other hand, indirect proving is when you prove the opposite of what you want to prove.

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Geometry Lesson: Postulates, Theorems and Proofs (Simplifying Math)

Calculating Time using Casio Calculator for IGCSE, O' Level Mathematics Paper

Calculator Skills

Calculating Time using Casio Calculator for IGCSE, O level Mathematics Paper

This video demonstrate Calculating Time Taken for O'Level, IGCSE Mathematics Paper using Casio Calculator.

Student can find such question in their Mathematics paper in topic like:
1. Time Taken
2. Travel Graphs
3. Distance, Time and Speed 

F.Sc Mathematics

F.Sc Mathematics

Math City

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Ilm Ki Dunya

Society of Higher Education & Industrial Research

Muslim Mathematician

Muslim Mathematician

Abu Ja'far Muhammad ibn Musa Al-Khwarizmi

Born: about 780 in possibly Baghdad (now in Iraq)

Died: about 850

This is taken from a stamp from the former USSR

Rate (mathematics)

In mathematics, a rate is a ratio between two measurements with different units. If the unit or quantity in respect of which something is changing is not specified, usually the rate is per unit time. However, a rate of change can be specified per unit time, or per unit of length or mass or another quantity.

A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%) or fraction or as a multiple.

An average rate can be calculated using the total distance travelled between a and b, divided by the travel time

An instantaneous rate can be determined by viewing a speedometer.

Minimum Point of a Quadratic Graph

Minimum Point of a Quadratic Graph

Differentiating the function and setting its derivative to 0 is the fastest way however if you do not know calculus then an alternate method is to complete the square. 

But for any quadratic in the form ax^2 + bx +c, where a, b and c are constants: the lowest point is when 

x = -b/2a.

The Rule of Four

The Rule of Four

Mathematics should be expressed in the following four ways:

1. Algebraically

2. Numerically

3. Graphically

4. Verbally

In order to understand mathematics holistically, it is important that students connect each concept with the rule of four.

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The beauty of this way of understanding mathematics is that it is so versatile; students can work with information presented in any one way and manipulate that information to find or interpret the information in other ways.

All students can learn

Three goals for the students:

1. Work accurately with basic operations:

2. Be able to apply basic operations to more complex problems.

3. Incorporate technology with the goal of higher level mathematics.

First and foremost my job is to ready my students for the next level of mathematics. Often, the level of mathematics dictates teaching methods.

When working with college-prep 9th graders in algebra, I focus heavily on a deep understanding of basic operations. The focus is essentially rote learning initially, and then we move to more involved problems. I teach and re-teach the basic skills that students will need to be successful when they reach algebra 2 and tackle the complexity therein.

When working with students in pre-calculus or calculus, I teach basic ideas fairly quickly and then move to complex applications of knowledge with the use of technology. I expose my students to the most rigorous IB or AP problems I can find or produce and sometimes much of class is spent discussing ideas rather than crunching numbers.

"In order to understand Math, you must do Math."

Having too much fun with the graphing calculator!

"Understanding of math is more than following examples.  It is the conceptual 'why' and 'how' and being able to apply that."

"The Rule of Three: Every topic should be presented geometrically, numerically and algebraically."