Fast Arithmetic Tips : Addition

1. Addition of 5
When adding 5 to a digit greater than 5, it is easier to first subtract 5 and then add 10.
For example,

8 + 5 = 13.
Also 8 - 5 = 3; 3 + 10 = 13.

12 + 5 = 17.
Also 12 - 5 = 7; 7 + 10 = 17.

2. Subtraction of 5
When subtracting 5 from a number ending with a a digit smaller than 5, it is easier to first add 5 and then subtract 10.
For example,

26 - 5 = 21.
Also 26 + 5 = 31; 31 - 10 = 18.

23 - 5 = 18.
Also 23 + 5 = 28; 28 - 10 = 18.

23 - 5 = 18.
Also 23 + 5 = 28; 28 - 10 = 18.

Division by 5
Similarly, it's often more convenient instead to multiply first by 2 and then divide by 10.
For example,

1375/5 = 2750/10 = 275.

980/5 = 1960/10 = 196.

Multiplication by 5
It's often more convenient instead of multiplying by 5 to multiply first by 10 and then divide by 2.
For example,

140×5 = 1400/2 = 700.

135×5 = 1350/2 = 675

120×5 = 1200/2 = 600

it's more quick right ?!

Division/multiplication by 25
Use operations with 4 instead.
For example,

37×25 = 3700/4 = 1850/2 = 925.

Add a sequence from one to a selected
1-digit number and back

Choose a 1-digit number.
Square it.


If the 1-digit number selected is 7:
To add 1 + 2 + 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4 + 3 + 2 + 1
Square 7: 49
So the sum of all numbers from 1 through 7 and back is 49.

See the pattern?

If the 1-digit number selected is 9:
To add 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
Square 9: 81
So the sum of all numbers from 1 through 9 and back is 81.

Basic statistics formulas

Statistics is a mathematical science pertaining to the collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities; it is also used and misused for making informed decisions in all areas of business and government. (
its include histogram graphics theory, probability, ANOVA, Summarizing data, deviation, Correlation and causation, etc.

Download Basic Statistics Formula List
it include : Measures of Location, Sets, Probability, Measures of spread, deviation, Normal density function, Confidence intervals for the mean, Hypothesis test for the mean , and Simple linear regression

Basic Practice of Statistics

it include : Exploring Data: Distributions, Producing Data, Probability and Sampling
Distributions, Basics of Inference, Inference About Means, The Chi-Square Test, One-way Analysis of Variance: Comparing Several Mean, Inference for Regression.

Introduction to Statistics formula sheets
this document include : Descriptive statistics, Scienti c notation on the calculator, Statistical inference, Normal curve

Trygonometric Delights, and introduction of trygonometry free books

in this post I provide a simple review of the two free books that I found after browsing about trigonometry, there is no end to the discussion of the triangle, we can explore a part of this mathematics ranging from history, until a new theory about the true triangle, two books that can be download for free following a discussion about two different things but actually interrelated, the first book can be downloaded at the following link

This Book Begins by examining the "proto-trigonometry" of the Egyptian pyramid builders. It shows how Greek astronomers developed the first true trigonometry. It traces the Slow Emergence of modern, analytical trigonometry, recounting its Origins in Renaissance Europe's quest for more accurate Artillery, more precise clocks, and more pleasing musical instruments.
The following book reveals history from time to time regarding the development of a triangle formula as well as its application in building the history of human civilization, for example about, Recreational Mathematics in Ancient Egypt, Epicycloids and Hypocycloids, more information, please read and downloaded directly on the link provided.
Download Link

An introduction to TRIGONOMETRY
The next is a book that should be compulsory reading for lovers or for beginners to learn trygonometry, why because this book presents the complete formula, an explanation of the basics trygonometry very important to understand.for exampleTrigonometric circle and AnglesTrigonometric numbers of a real number tBasic formulasRelated valuesTrigonometric functionsInverse trigonometric FunctionsSum formulasTrigonometric equationsfor more details please read and learn more at the link below
Read Online

Best mathematics Integral help website

Integration is an important concept in mathematics and, together with differentiation, is one of the two main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integral.
to learn more about integral, here i write some list that i think best online help of integral.

1. Wolfram Integral
The Wolfram Mathematica Online Integrator is powered by webMathematica, so it expects input to be in Mathematica syntax, it very easy to solve integral problem, just write your mathematics integral then click Compute, the results will display in a second.
before write your mathematics expression, learn the expression and syntax first

2.Edu Media
this website provide trial graph of integration, A graphic illustration of the integral of a function. You can change the limits of integration and the number of rectangles employed for the approximation. by Click and drag the limits of integration then select a function and the number of rectangles to be used for the approximation.

3. SOS MATH one my favorite website in mathematics, SOS math provide various type of integral function and formula.The tables will be organized by topics

4. Mathematics Reference
we can get Essential rules for integration in this website from basic integral, trigonometry integral, Hyperbolic trigonometry, and others

5. Inmath
this site give us to explores some of the techniques for finding more complicated integrals, By studying the techniques in this chapter, you will be able to solve a greater variety of applied calculus problems.

6. Lamar.Edu
this side also provide integral list in pdf format, so we can download it easily and free,from basic, common formula, until trigonometric formula.

so after learning the function, try to finish some question and math problems below

integral calculus -

best online calculus help website

various online help of calculus available in internet, every those website have their advantage, we can choose which website that can fit with what we need.
below some list calculus website with their unique facilities

this website provide various facilities with unique multimedia tutorial, problem's this week can become interactive tutorial source, available from 1998 until 2003,you can see those example at
other interactive multimedia tutorial available at calculus phobe, Understanding that enormous tome is just as plausible as whittling a canoe from a giant redwood tree. Welcome to your oasis of understanding. The tutorials that follow explain calculus audio-visually, and are the equivalent of a personal tutoring session. More than just boring lectures, the topics come alive with Flash animation. see more at

i will vote that this website is the best online tutorial for calculus, with their slogan "Get calculus help, a calculus tutor is online to help you"
We use the computer, which your child associates with entertainment and fun, to make learning more interesting.

The student works one-on-one with a professional tutor in a secure web environment using your existing computer, web browser and broadband Internet connection - no special equipment or software is needed.

Using the virtual whiteboard workspace both tutor and student draw and write to share problems, solutions and explanations, and work with simulations and animations to maximize learning. but you need about $99.99/month flat rate to get online help for 24 our.

this website special for any body that need various link to learn more about calculus, because at this website we can find a lot of link calculus tutor, interactive link for learn calculus, sample exam's, calculus applet's, link for online text, vector calculus, and calculator link for calculus like derivatives and others.

this website also have special feature, on this website we can solve the calculus problem online, for example to solve derivative we can go to , the java-script that installed on that website will generate step by step to solve the problem that we type on that website.

this website provide topic by topic tutorial of calculus, begin with functions with e
exponents,fractions,factoring, trigonometry until antiderivatives and integrals
integrals in particle movement, substitution, integrals for area.

Linear Methods of Applied Mathematics free book

Linear Methods of Applied Mathematics

Orthogonal series, boundary-value problems, and integral operators
Evans M. Harrell II and
James V. Herod

Copyright 1994,1995,1996, 1997, 2000 by Evans M. Harrell
II and James V. Herod. All rights reserved.

This is a WWW textbook written by Evans M. Harrell II and James V. Herod,
both of Georgia Tech. It is suitable for a first course on partial differential equations,
Fourier series and special functions, and integral equations. Students are expected
to have completed two years of calculus and an introduction to ordinary
differential equations and vector spaces. For recommended 10-week and
15-week syllabuses, read the

This text concentrates on mathematical concepts rather than on details of calculations,
which are often done with software, such as Maple or Mathematica.
It is not necessary to have experience
Maple or Mathematica
in order to read this text, nor is it the goal of this
text to teach software, but there are links in the text to
Maple worksheets and Mathematica notebooks, which perform calculations
and provide some supplementary instructive material. The supplementary
material exists both in a "flat" form, which can be read with Netscape, and
also in an active form, requiring mathematical software.

If you have access to mathematical software, you
may wish to take this opportunity to
set up the latest
version of Netscape to launch Mathematica or Maple automatically when appropriate.

You are welcome to browse, but if you make more than casual use, such as downloading
files or using them as study materials, certain restrictions and fees apply. Before
proceeding, please

Diagnostic quiz
Please take this before embarking on a course from this book.

Links to review materials on

ordinary differential equations

linear algebra


Also available in an
Adobe Acrobat version

The geometry of functions
Also available in an
Adobe Acrobat version

The red syllabus and the yellow syllabus continue with Chapter III
The green syllabus continues with

Chapter XIII
Fourier series. Introduction.
Also available in an
Adobe Acrobat version (without links)

Calculating Fourier series.
Also available in an
Adobe Acrobat version (without links)
test at this stage.

Differentiating Fourier series.
Also available in an
Adobe Acrobat version (without links)

The red syllabus continues with Chapter VI
The yellow syllabus continues with
Chapter XIII
Notes on a vibrating string.
Also available in an
Adobe Acrobat version (without links)

Traveling waves.
Also available in an
Adobe Acrobat version (without links)
test at this stage.

Mathematics of hot rods.
Also available in an
Adobe Acrobat version

PDEs in space. (includes potential equations)
Also available in an
Adobe Acrobat version (without links)

PDEs on a disk.
Also available in an
Adobe Acrobat version (without links)

test at this stage.
Great balls of PDEs.
Hunting for eigenvalues.

Geometry and integral operators.
Solving Y = KY + f.
test at this stage.

Ordinary differential operators.
Finding Green functions for ODEs.
test at this stage.

Green functions, Fourier series, and eigenfunctions.
Partial differential operators - classification and adjoints.
The free Green function and the method of images
test at this stage.
The fundamental solution of the heat equation
Using conformal mapping to construct Green functions.
Some advanced topics.

Multivariable Calculus

This is a textbook for a course in multivariable calculus. It has been used for the past few years here at Georgia Tech. The notes are available as Adobe Acrobat documents,

this book also available online at, written by George Cain and James Herod

Title page and Table of Contents

Table of Contents

Chapter One - Euclidean Three Space

1.1 Introduction

1.2 Coordinates in Three-Space

1.3 Some Geometry

1.4 Some More Geometry--Level Sets

Chapter Two - Vectors--Algebra and Geometry

  2.1 Vectors

  2.2 Scalar Product

  2.3 Vector Product

Chapter Three - Vector Functions

  3.1 Relations and Functions

  3.2 Vector Functions

  3.3 Limits and Continuity

Chapter Four - Derivatives

  4.1 Derivatives

  4.2 Geometry of Space Curves--Curvature

  4.3 Geometry of Space Curves--Torsion

  4.4 Motion

Chapter Five - More Dimensions

  5.1 The space Rn

  5.2 Functions

Chapter Six - Linear Functions and Matrices

  6.1 Matrices

  6.2 Matrix Algebra

Chapter Seven - Continuity, Derivatives, and All That

  7.1 Limits and Continuity

  7.2 Derivatives

  7.3 The Chain Rule

Chapter Eight - f:Rn-› R

  8.1 Introduction

  8.2 The Directional Derivative

  8.3 Surface Normals

  8.4 Maxima and Minima

  8.5 Least Squares

  8.6 More Maxima and Minima

  8.7 Even More Maxima and Minima

Chapter Nine - The Taylor Polynomial

  9.1 Introduction

  9.2 The Taylor Polynomial

  9.3 Error

  Supplementary material for Taylor polynomial in several variables.

Chapter Ten - Sequences, Series, and All That

  10.1 Introduction

  10.2 Sequences

  10.3 Series

  10.4 More Series

  10.5 Even More Series

  10.6 A Final Remark

Chapter Eleven - Taylor Series

  11.1 Power Series

  11.2 Limit of a Power Series

  11.3 Taylor Series

Chapter Twelve - Integration

  12.1 Introduction

  12.2 Two Dimensions

Chapter Thirteen - More Integration

  13.1 Some Applications

  13.2 Polar Coordinates

  13.3 Three Dimensions

Chapter Fourteen - One Dimension Again

  14.1 Scalar Line Integrals

  14.2 Vector Line Integrals

  14.3 Path Independence

Chapter Fifteen - Surfaces Revisited

  15.1 Vector Description of Surfaces

  15.2 Integration

Chapter Sixteen - Integrating Vector Functions

  16.1 Introduction

  16.2 Flux

Chapter Seventeen - Gauss and Green

  17.1 Gauss's Theorem

  17.2 Green's Theorem

  17.3 A Pleasing Application

Chapter Eighteen - Stokes

  18.1 Stokes's Theorem

  18.2 Path Independence Revisited

Chapter Ninteen - Some Physics

  19.1 Fluid Mechanics

  19.2 Electrostatics

Design by Free WordPress Themes | Bloggerized by Lasantha - Premium Blogger Themes