Trachtenberg Speed Maths - Pdf

Friends, today we are giving you one of the useful books on mathematics. That is The Trachetenberg System of Speed Maths. And before going to download and read the book, lets read a small story of our hero Jakow Trachtenberg (The inventor of a system of rapid mental Calculation known as The Trachtenberg System). He created the Trachtenberg system of mathematics, whilst a political prisoner in Hilter's concentration camps during the second world War. To keep himself sane whilst living in an extremely brutal and harsh environment, Trachtenberg immersed his mind in a world of mathematics and calculations. As concentration camps do not provide books, paper, pen or pencils nearly all of his calculations had to be performed mentally. This forced Trachtenberg to develop methods and shortcuts for performing calculations mentally. Trachtenberg developed his discoveries into a complete system of mathematics.

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Speed Maths shortcuts - Pdf version

Friends, we've got tremendous response to our previous pdf post of the shortcuts about Squares, Square roots and Cube roots. First of all thanks for the support. So many of our users have asked to upload the shortcuts for doing basic maths like additions, subtractions, multiplications and divisions etc.   So for you we are posting the shortcut tricks for mental maths. In this post you will get the shortcuts for finding almost all the mathematical problems (including square roots and cube roots). Hope this post will help you in improving your problem solving skills. You can get more downloads here. Please LIKE our facebook page here for frequent updates. Happy Reading :).

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Speed Improvement Test - Day 8

Recommended Time : 15 Mins

First to these tests? Start the tests from Day 1

Percentages

1. 55.55% of 468 = ?
2. 15.88% of 510 = ?
3. 34.09 % of 792 = ?
4. What percentage of 933 is 588 ?
5. By what percentage is 412 more than 322 ?

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Key - Speed Improvement Test - Day 8

Recommended Time : 15 Mins

<< Read Questions Here

Percentages

1. 55.55% of 468 = 260
2. 15.88% of 510 = 80.988
3. 34.09 % of 792 = 270
4. What percentage of 933 is 588 = 63%
5. By what percentage is 412 more than 322 = 27.95%

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Data Interpretation for IBPS PO VII Exam 2017

Data Interpretation,  the one of the easiest, time taking and scoring topic of the Bank Exams.  Everybody knows this fact... but people pay less attention on this area. But unfortunately in IBPS PO VII Exam, the complete aptitude section will depend on Data Interpretation. So you should concentrate more on this area.

In this post, we shall discuss about the basics Data Interpretation.  The Data Interpretation is also called as comprehension of mathematics. Because, in reading comprehension, we have to study the passage and answer the questions followed by that passage. In the same way, in Data Interpretation, some data is given in the form of graphs, charts and tables followed by questions. We have to study, understand and analyze the data to solve the questions. Here we have to keep in mind that, even a 10th standard boy can solve these problems. But you've to solve these problems IN TIME.

So you have to practice well so that you can do the small calculations (like additions, subtractions, and simple multiplications) with a glance (see here for shortcuts in mental maths). Now lets have a look at some basic details of Data Interpretations.

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Line Graphs

The line graph is another important type of graph. The line graph displays information as a series of data points connected by some straight line segments (or simply lines). You can simply say that the Line Graph is the graph which uses points connected by lines to show how something changes in value. Lets have a look at an example Line Graph so that we can understand the topic in detail.

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Multiple Bar Diagram

This model is also same as the simple Bar Diagram. But the difference is, here we have to encounter more than one bar... I mean, we have to do problems with two or more vertical or horizontal bars. In these type of diagrams normally they will give the information of two different organizations (like the production of soaps of two different companies) or the information of two different items of the same organization (like the production of the soaps and shampoos of the same company) and asks questions on the given data. Have a look at an example.

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Simple Method for Calculating Shortcut for Square - Part 2

We've already seen how to find the squares of numbers which are one more than those whose squares we already know (eg 25, 30, 35 etc).Read that post Here. Similarly, we can find the squares of numbers which are one less than the numbers whose squares are known already to us. For Example,

292 = 30 - 30th odd number = 900 - 59 = 841

392 = 40 - 40th odd number = 1600 - 79 = 1521

342 = 1225 - 69 = 1156

542 = 3025 - 109 = 2916

742 = 5625 - 149 = 5476

942 = 9025 - 189 = 8836

2142 = 46225 - 429 = 45796

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Shortcut for Square - A Simple Method

We have already discussed a method for finding the squares of the given number (check that method Here). Now we shall discuss another simplest method to calculate square of the given number. First of all one thing you should keep in mind, for you r convinience we've mentioned each and every step in detail. But You should do all these calculations MENTALLY. I mean without using pen or pencil. So practice well to do these problems orally. Now lets go to the topic, Finding the square of a number ending in 5 is very simple. If the last digit of the number is 5, then the last two digits of the square will be 25.What ever is the earlier part of the number multiply it with one more than itself and that will be the first part of the answer. (The second part of the answer will be 25 only).

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Shortcut for Multiplication (Base Number Method Part 2)

We've already discussed about the Shortcut Method (Base Number Method) for doing multiplications. In the earlier post we've discussed doing the multiplication by taking the base as 100 (Click Here to read that). I mean, you can do the multiplication for the numbers nearer to the 100. Then what about the remaining numbers? Well, being the Guide 4 Bank Exams we have solutions for all Banking Problems... So, lets have a look at some more approaches of the Base Number Method so that it will be easier for you to multiply any number with any number :)

Find the product of 117 and 88

117   --->   +17

  88   --->   -12

____         _____

105             -204           Ans : 10296

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Shortcut for Multiplication (Base Number Method)

We've already discussed some short cut tips for Multiplications. You can check that post Here. Now we shall discuss another  Simple and Useful method for Multiplication. In this method we take a base (according to the given numbers) and do the multiplication according to that base. Assume that you have to multiply 97 with 92. The power of 10 to which these two numbers are close is 100. We call this 100 as the base. Now write these two numbers with the difference from the base. 

97 ------>  -3  (because 97 is obtained as 100 - 3)

92 ------> -8 (because 92 is obtained as 100  -8)

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Speed Improvement Test - Day 5

Recommended Time : 15 Mins

<< Read Shortcut Techniques Here

Additions / Subtractions

1. 3972 + 7646 + 8791 + 2763 + 9437 = ?
2. 7149 + 3487 + 2983 + 6731 + 8971 = ?
3. 545 - 32 + 217 + 49 - 117 + 81 =?
4. 642 + 717 - 84 + 343 - 119 + 420 = ?
5. 2636 - 1742 + 8346 + 73 - 514 = ?

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Speed Improvement Test - Day 4

Recommended Time : 15 Mins

<< Read Shortcut Techniques Here

Additions / Subtractions

1. 4321 + 64319 + 54321 + 709126 = ?
2. 5321 + 6741 + 8091 + 4678 + 2132 = ?
3. 432 + 216 + 509 + 723 - 625 - 416 = ?
4. 40965 + 60978 - 31241 - 20986 = ?

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How to improve Maths / Aptitude Calculation Speed

Calculation Speed plays a very very very important role in Bank Exams. Some people think that, people should have the natural ability to do calculations fast, of course that is true at some extent. But that doesn't mean the other ordinary people like you and me need not feel bad.

According to Aerodynamics Laws based on Weight and the Size of the wings, some species only do have the ability to fly. If we strictly apply their laws, a Bee cant fly. Because its weight is More and Wing's length is very less when compared to its Weight. But still it is flying very comfortably and enjoying the Honey in almost every flower.

Sometimes Old rules and blind beliefs remain worthless. Forecasters' predictions become wrong. Only The Belief in You and Hard work will create wonders. Trust me, it is very easy to develop good calculation speed in a relatively short period of time. All you need is Hardwork, Little Amount of time and Good Material to Prepare... You give us the first TWO, we will provide you with the Third one... 

30 x 30 : Just spend 30 minutes a day for 30 days. You will definitely find the difference in your calculation speed. Your practice involves basic Additions, Subtractions, Multiplications, Percentage Calculations, Comparing Fractions and Calculating Squares. 

How can this blog help me? We post some examples on calculations. Solutions for these
examples indicating the short-cuts that you need to learn and implement. Which will help you to solve problems mentally in less time .

How to use this blog? Before you start involving with our posts, make sure that you are thorough with the following (Mandatory) :

• Multiplication Tables (Up to 20 x 10)
• Squares (Up to 30)
• Cubes (Up to 15)
• Powers of 2 (Up to 12)
• Powers of 3 (Up to 6)
• Reciprocals of numbers (Up to 12)
• Complements of 100 
• (I mean, the difference between 100 and the given 2 digit number).

Some Useful Shortcuts of Basic Maths :

• Addition Shortcuts
• Subtraction Shortcuts
• Multiplication Shortcuts
• Division Shortcuts
• Decimals

What should I do for this : Nothing, just open this page daily when ever you free. You can find a post containing 20 questions on calculations (Additions, Subtractions, Multiplications etc) . Just try to solve them mentally in the recommended time. Just put away your Calculators, Pens, Pencils and Papers. 

While taking these tests, please follow the below instructions.

• Take One test every day.
• Check the starting time and keep in mind the time that has been allotted for the particular exercise.
• Don't use calculator.
• Write as little as possible on paper. You should try doing as much of the calculation as possible mentally.
• Some questions require precise calculations whereas some other questions require only approximate calculations. Please remember that the level of accuracy to which you should work out the calculations will depend on the answer choices given in the post itself. So, do not spend more time than is necessary on each question. 
• Stop the test as soon as the Prescribed time is Over.
• After you Complete each exercise, spend time working out the questions that you could not complete in the given time. Then, check for the correctness of your answers. Rework all the questions in the test to see whether the method that you adopted was the best/shortest.
• Check the answers to see whether you have approached the calculations correctly. Use the learning that you gain in one Exercise in working out the next Exercise.
• Even after you use up all the tests given in this Blog, you should continue similar calculation practice on a regular basis to ensure that your calculation speed does not drop.  

Have a look at some basic techniques which will help you to improve your speed of Mental Maths....

☞ Mental Maths (Additions)

☞ Mental Maths (Subtractions)

☞ Mental Maths (Comparison of Fractions)

Click Here to take our Daily Speed Improvement Test Series

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