#logarithm class 11 maths

[mr-shrimp]

It's September now, and I wanted to write about r*ssian schools, and I even had a draft about it, but I deleted it accidentally :(

Btw it's not a big deal, so enjoy this bullshit from typical r*ssian student <3

I want to do this bc I'm pretty tired of this, and I just want others to know that.

This post gonna be smth like QA format, bc it is a lot of easier to write ¯\_(ツ)_/¯

Russian school core(I guess). Let's go!

First things first. How long do you need to study?

-> Well, if we talk about ordinary school, then you can study 9 years or 11 years(this is optional). In year it's 9 months for studying and 3 for rest(nice joke). After 9th grade you can go to the high school or go to the college and then to university as well. After 11th grade you can go right to university(but here is option to go to college after 11th grade). In university system is not different from European with Bachelor degree, but as I know in this year or maybe in the next one they want to remove this and make only specialty degree. It sucks bc your specialty diploma will be invalid in countries with Bachelor degree. And with specialty degree you need to study about 5-6 years.

How old must be child?

-> In most of the cases it is like 6-7 y.o. Some schools have pre-school studying, here children are about 5 years. In the end of your execution in school you may be like 15-16(9th grade) or 17-18(11th grade)

Does children also have such a fucked lessons table?

-> Nah, they have like 3-5 lessons about 35-40 mins. First 4 grades are such a relax, hah

What about exams?

-> in the end of the 4th year you need to pass two exams(as I remember): rssian language and math. In the end of 9th grade you need to pass 4 exams: rssian, math and two optional disciplines. And in the end of the 11th grade you need to pass at least 3 exams: rssian, math(base or profile), and 1-5 optional. Maybe now max number of optional exams has changed, but I don't care.

Which exams did you choose?

-> I gonna write biology and chemistry in any way, bruh. Maybe sociology, too, bc I also into law(not new laws they are bullshit) and this kind of thing. Or maybe I should be a designer, I like money and I like to draw:) my doodles pretty cute hah

What about rest? Holidays? Weekends?

-> Okay, this is pretty interesting. In most of moscow schools we have 5-1 system, which means 5 weeks of studying and 1 week of holidays. Also, we have a lot of holidays for all country such as new year holidays or may 1st and may 9th. It is really a lot of holidays in r*ssia, tho. Although I said it is 3 month of holidays, but for real you need to study and here. Why? It's pretty complicated. You need to read a lot of books, you need to practice all disciplines, you need to prepare to your exams and smth like this, bc if you not gonna do it... well, it would be sad. Weekends don't exist in rssia you just sleep. Really, you tired as fuck after this weekly five-day-in-a-row executing. And you even need to do your homework, but all that you can is sleeping.

What about study program?

-> It's hard. Really. I'm at the last grade, and this is my lessons for every week(in two versions, look at pics below). And if you want to know, math in r*ssian schools is like math in a lot of math universities in America or England or any of European countries. And it is not about math only, it is about all disciplines. Like, in 10th grade we learning about sinuses and logarithms(fckng bllsht)

-> In mscow schools we have special programs like medicine class(here I am), IT-class and more more others(Pic below, translate it by yourself). They call it "project classes". And for every project class it is its own main disciplines. For example, in medicine class it is chemistry and biology, but they added prof math for some hecking reason and I hate this shit, but BTW.

-> As for daily classes table, this is really tough. We starting at 8:15 a.m. and ending at 3 p.m. or even at 4:40 p.m. This is NOT optional. You must go for all classes even if you don't need physics or prof math. You just MUST. We have lessons every for 40 mins and breaks for 20 mins. And no, we haven't any special long break for eating. If you late to your classes you gonna be scolded, bc "why can't you eat faster???". Oh well, maybe because I just can't hah? Anyway you need to go from cabinet to another cabinet and try to eat if you want. And the most absurd that we have special breaks for eating, but they also lasts 20 minutes.

-> As for holiday, you can't relax either, bc this is a lot of homework. For example, my friend(from IT-class) in last year had about 400 mathematical equations to solve for homework for 1 week. Wild, isn't it? Ofcourse not all teachs like that, but anyway. Our literature teach said to write essay about 400-500 words(okay ngl she like to make us write it even if it not holidays).

What about food?

-> Oh yeah cockroach it my oatmeal and juice with water, love it. Not gonna lie, we really have cockroachs in our dining room at school. And I guess teachs like "well until cockroachs not fall from ceiling to children food it's alright"(no, it's not). I really like to eat, even if it just an apple, I like food, and food at school is really bad. You have a choice: first to not eat, second to eat at dining room, and third to bring your homemade food. In any case you don't have time for really enjoy the food :(

What about "ins" of school?

-> in mscow schools pretty okay, in my school we even have green room with a lot of plants, we call it "winter garden". Cabinets are okay, but light is bad like they older then me. But in other regions it like very old house that may fall at every second. And some of them don't have bathrooms. I didn't joke. Or it is a toilet like a.. erm.. hole in floor? Yea, something like this I guess. And some regions(villages, for example) don't have schools.

-> As for lessons, it is just very strict teachs and really hard program. Okay, let's talk about "conversation about important things". As you all know in 2022 rssia started a w*r with Ukraine, and from this moment in all schools started this shit. In short this is something like patriotic lessons where they just lie to you how good our country is and how good that we live here and how bad another world is. Well, smth like this was at ussr time, too, as i remember this right. But you know, this lessons are necessary even if they don't have marks for it. You just need to know that all people in the world are bad and only rssia are innocent and saint(/sarc). Fucking bullshit.

What about project classes?

-> Well, Idk for other classes, but in medicine class we have pretty hard program. You need to know all chemistry and biology, make an individual project, go to medicine college(uh um hello I go to high school bc I don't want to go to college guys what's wrong with u), go to lessons in university like RUDN, Pirogov RNRMU(rssian national research medicine university) and etc. And this is all after your ordinary classes, ofcourse :)

And what about college?

-> Nothing special, we just were riding the subway there 1 hour, then studied for 3 or 4 hours at college and were riding the subway back for 1 hour. And for sure it sucks, bc I returned home at 9 p.m.(or even 10 p.m.) every Monday. And our teach said that we were lucky bc they could make our college classes at Saturday. And in the end we can get our diplomas in the end of the 11th grade. Why? For what? Idk.

What about program? You always say this is hard, but why?

-> So, biology(molecular, botanic, anatomy, ALL biology), organic chemistry, prof math, probability theory, physics and more other. All this university level. And a lot of home work after which you don't even have strength for yourself.

What about attitude towards mental health? And health as well?

-I have diagnosed severe depression and I'm still studying full-time education program. No one cares if you can stand, even if you have a fewer. But at least tech can send you to nurse or back to home. In rssian schools no one really cares about your mental health, your pronounces and other individual things. Well not all teachers stop bulling towards kids, and some of them are bullies themselves. I think that's enough to understand this.

Well, that's all, I guess. It is really a lot of issues that I didn't say. Please repost or reblog as much as possible. As for living in rssia it is like, you know, living in "1984", just read latest news and new laws in 2022-2024 period and add to this w*r with innocent country.

And stay safe all of you♡

Yes somewhen I make this rq please don't beat me :(

[mathyug]

https://youtube.com/ashishkumarletslearn

[haunted-van-au]

Roman pinched the bridge of his nose, focusing on the rose he was drawing in his notes rather than the math lesson happening in front of him. Logan would definitely be annoyed if he knew. Roman was already behind by a year in math and had been hearing about it since he came to live at Miss Morris’s. It had only gotten worse since they declared their truce. For someone who claimed not to care about anything (except for Patton when he was forced to answer directly), Logan certainly could be a fusspot.

Roman finished his drawing and glanced at the board. Well… it was too late now. He didn’t even know what ‘ln’ meant. Weren’t they talking about logarithms? He turned back to his notes, looking for an empty area to squeeze in another drawing, when he heard whispering behind him. Apparently, he wasn’t the only person not paying attention to math today.

“No, seriously, my cousin in Pamola City said the military’s in the street there,” a girl said behind him. Roman tuned into the conversation. “Something’s going on.”

“Rabid vampires?” her friend asked. Roman pulled his sweater sleeves over the bite mark scars on his wrists.

“Maybe,” the first girl replied, “but it’s so widespread. How could a coven get that far. Did you see the video?”

“Yeah, but channel 11 just said it was a silver drunk werewolf.”

“It didn’t look like a werewolf.”

“Well, it wasn’t the full moon…”

Roman bit his lip and glanced at the teacher before turning back halfway. “What video?” he asked in a whisper.

The girls stared at him like he was a gorgon who forgot his hat. Which was fair, because he didn’t think he’d ever spoken in this class other than to say ‘here’ during attendance.

“The man eater video they say is from Kutterville. It was posted yesterday but keeps being taken down. People think it’s either a hoax or a werewolf.”

So, that’s what Roman had heard whispers of throughout school today. No one really talked to him, but even he’d known something was going on.

“Mr. Royal. Ms Johnson, do the two of you have a comment?” Mrs. White asked from the board.

Roman winced and turned back.

“No ma’am,” the girl behind him said. Mrs. White turned back to the chalkboard.

Roman found himself tapping the desk with his pencil. He saw the guy next to him shoot him a nasty look but couldn’t manage to stop himself. He glanced at the clock. Ten minutes before school ended.

Roman is now open for questions.

[elvish-sky]

What sort of things do you do in algebra 2 if you don't mind me asking? I'm English and doing maths at A Level and I'm just curious to know the differences??

hey Anon!! sure, i don’t mind! so i don’t know anything about the English systems and all that (although it sounds a lot better, stupid USA). but currently we are working on graphing and functions. (so like plotting, using graphing calculators, finding the best-fit line, etc) later in the class we do more quadratics, rational expressions, and logarithms. and i don’t know what year you take A-Level in (or if it’s even by year) but for context i’m a sophomore in high school (which i think is Year 11 in England?) and i’m on the regular math track at my school. sorry if this was confusing Anon and thank you for the ask!!!

[shubhascbsescholars]

What are the important topics for IIT JEE in 11th Standard?

With the passion to pursue engineering from a premier institute like IIT, a lot of students aim at cracking the IIT JEE to live this dream right from their 11th standard. Considered as one of the most difficult entrance exams across the globe, not many know how to prepare for JEE and lack correct guidance. Here we will discuss, how one needs to divide and dedicate time for important topics in 11th standard to score maximum marks in IIT JEE.IIT JEE consists of thirty multiple choice questions from Maths, Physics and Chemistry. With equal weightage given to all three subjects, one should know how to prepare for IIT and what topics to emphasize on to be able to answer most questions correctly in the assigned time.

To help students understand and prepare better, we have curated a list of important topics for JEE Mains from each subject for them to prioritize topics based on it.. Have a look.

Mathematics

Probability: Being one of the most important topics, one needs to cover Conditional Probability, Law of Total Probability and Bayes theorem in detail to score maximum marks in this subject.

Coordinate Geometry: One needs to be thorough with Circle

Logarithm: Basic Logarithm questions are only asked

Permutation and Combination: Important topics to cover here are circular permutation, Integral solution of linear equation and Division/ Arrangement of Groups

Quadratic Equation: One needs to focus on roots of an equations coefficients and most importantly on roots of an equation.

Physics

Units & Dimension: All concepts under this topic needs to be covered.

Rotational Motion: One should draw their focus on the concept of rigid body dynamics.

Kinematics of SHM: Questions asked on this are to test the understanding of Simple Harmonic Motion and one can expect around 3 questions from this concept.

Newton s Law of Motion: Application of the three laws of motion needs to be understood and effectively used in solving the questions.

Chemistry

Chemical Equilibrium: One needs to focus on concepts like Law of Mass Action, Acids and Bases and Solubility product.

Atomic Structure: Atomic structure preparation and atomic mass concepts are important . Theories like the Thomson, Bohr and Rutherford should be concentrated on.

Stoichiometry: Focusing on topic like the Mole and equivalent concept is very important in class 11th.

Gaseous State: States of matter, compressibilty factor and van der Waals equation are concepts to be focused on.

Chemical Bonding: One should focus on periodicity concept.

Organic Chemistry: Basic concepts of Organic Chemistry from 11th standard is usually asked. Hence one shouldn t ignore it and emphasize on the basics.

We advice students to be through with all three subjects mentioned above and give additional attention to these important topics of class 11 for IIT JEE mains to score maximum marks. Good Luck!

[reid-fiction]

I assume that you were an average student in high school, that you are blond-haired and that you enjoy being with pets (idk i just guessed this whole stuff:/)

I was actually pretty much a straight-A student in high school until I got to AP Math 11 and 12. My school was dumb and, in order for me to do AP, I had to do both math classes at the same time in grade 11. One would have been hard enough, but trying to balance two at the same time that covered completely different subject matter was brutal! I still have a vendetta against logarithms. The plus side is that I did end up getting a 4 on my AP English exam in grade 12 (beating out the top 2 students in my class) which was basically my crowning achievement! (I’ll end this humble brag now ;) )

My hair is a medium brown shade. I was super blonde as a kid, but it got darker over time. I’ve also dyed it black a few times so I have no idea which part is my natural color anymore.

I LOVE animals! I currently don’t have any pets (hooray for apartment living!) but I used to have a dog and a rabbit. I had to give my rabbit away when I moved, and my dog passed away about a year and a half ago. But, eventually, I would love to have more pets!

Send assumptions about me based on my blog!

[deepinstitute]

What Are The Important Topics For IIT JEE In 11th And 12th Standard?

With the passion to pursue engineering from a premier institute like IIT, a lot of students aim at cracking the IIT JEE to live this dream right from their 11th standard. Every year, about 1.2 million candidates appear for the JEE Main exam, out of which, a fraction of students qualify to appear for the JEE Advanced exam.  Considered as one of the most difficult entrance exams across the globe, not many know how to prepare for JEE and lack correct guidance. ISS coaching in Lucknow will discuss in this article, how one needs to divide and dedicate time for important topics in 11th standard to score maximum marks in IIT JEE.

IIT JEE consists of thirty multiple choice questions from Maths, Physics and Chemistry. With equal weightage given to all three subjects, one should know how to prepare for IIT and what topics to emphasize on to be able to answer most questions correctly in the assigned time.

To help students understand and prepare better, we have curated a list of important topics for JEE Mains from each subject for them to prioritize topics based on it.. Have a look.

Mathematics

Generally, the weightage of topics of class 11 mathematics is 40% to 50% in JEE.

·         Probability: Being one of the most important topics, one needs to cover Conditional Probability, Law of Total Probability and Bayes theorem in detail to score maximum marks in this subject.

·         Coordinate Geometry: One needs to be thorough with Circle

·         Logarithm: Basic Logarithm questions are only asked

·         Permutation and Combination: Important topics to cover here are circular permutation, Integral solution of linear equation and Division/ Arrangement of Groups

·         Quadratic Equation: One needs to focus on roots of an equations coefficients and most importantly on roots of an equation.

·         Complex Number

·         Conic Section

·         Circle

·         Calculus

·         Vector & 3 D

·         Trigonometric Equation

·         Properties of Triangles

·         Quadratic Equation

·         Sequence and Series

 Physics

In Physics, the weightage of the syllabus of class 11 and 12 is almost equal -- it is around 50% for each. Some important chapters of Physics in class 11 include Waves, Simple Harmonic Motion, Units and Dimensions, Rotational Motion, and Newton’s Laws of Motion. The class 12 Physics topics that carry heavy weightage in JEE include Electrostatics, Magnetism, Current Electricity, Optics, Modern Physics.

·         Units & Dimension: All concepts under this topic needs to be covered.

·         Rotational Motion: One should draw their focus on the concept of rigid body dynamics.

·         Kinematics of SHM: Questions asked on this are to test the understanding of Simple Harmonic Motion and one can expect around 3 questions from this concept.

·         Newton s Law of Motion: Application of the three laws of motion needs to be understood and effectively used in solving the questions.

Chemistry

In JEE chemistry, generally, the weightage of the class 12 syllabus is more than that of class 11. Generally, the weightage of the class 11 chemistry syllabus in JEE is around 30% to 40%. Many topics that are taught in class 11 are the basic ones and serve as a foundation for a deeper understanding of many class 12 topics. So, even though the weightage of the class 11 syllabus is slightly on the lower side, the topics taught in class 11 should not be ignored or taken for granted.

·         Chemical Equilibrium: One needs to focus on concepts like Law of Mass Action, Acids and Bases and Solubility product.

·         Atomic Structure: Atomic structure preparation and atomic mass concepts are important . Theories like the Thomson, Bohr and Rutherford should be concentrated on.

·         Stoichiometry: Focusing on topic like the Mole and equivalent concept is very important in class 11th.

·         Gaseous State: States of matter, compressibility factor and van der Waals equation are concepts to be focused on.

·         Chemical Bonding: One should focus on periodicity concept.

·         Organic Chemistry: Basic concepts of Organic Chemistry from 11th standard is usually asked. Hence one shouldn’t t ignore it and emphasize on the basics.

·         Electrochemistry

·         Coordination compound

·         Salt analysis

·         Ionic equilibrium

·         Thermodynamics & thermochemistry

·         Aldehydes and ketones

·         Aromatic hydrocarbons

·         GOC isomerism

·         Liquid solutions

·         Alkyl halides and aryl halides

JEE Main Important Topics 2021- Best Books to Cover

Students should cover all the JEE Mains 2021 important topics and chapters from the below best-recommended books by various subject experts, previous year JEE Main toppers and many test takers. Students are advised to follow only one or two books for each subject and do not refer to so many books. Beside all the recommendations, NCERT books is highly recommended for JEE Main preparation.

JEE Main Best Books 2021

I.        Subject : Mathematics

Recommended Books:

1)     NCERT Class 11 and 12 Textbooks

2)     Differential and Integral Calculus by Amit M Aggarwal

3)     Trigonometry and Coordinate Geometry by SL Loney

4)     Complete Mathematics for JEE Main by TMH Publication

5)     Algebra by Dr.SK Goyal

 II.     Subject : Physics

Recommended Books:

1)      NCERT Class 11 and 12 Textbooks

2)      Concepts of Physics by HC Verma (Volume 1 and 2)

3)      Fundamentals of Physics by Halliday, Resnick & walker

4)      Problems in General Physics by I.E Irodov

 III.   Subject : Chemistry

Recommended Books:

1)       NCERT Class 11 and 12 Textbooks

2)       Organic Chemistry by OP Tandon

3)       Physical Chemistry by P Bahadur

4)       Inorganic Chemistry by JD Lee

5)       Modern Approach to Chemical Calculations by RC Mukherjee

 JEE is a very tough competition, where the difference of even 1 mark can cause a lot of damage to one’s rank. Hence, it is important to be equally proficient in all the topics, both from class 11 and class 12. Even though it may seem like that a majority of JEE questions are from the class 11 syllabus, however, you must notice that JEE questions generally involve a mix of several concepts, and hence, you should be comfortable with all the concepts involved to apply them in a single question. Generally, in class 11, the foundations of several advanced concepts are laid. Hence, you should pay equal attention to the syllabus of class 11 and 12, both.

We advice students to be through with all three subjects mentioned above and give additional attention to these important topics of class 11 for IIT JEE mains to score maximum marks. Good Luck!

[shilkaren]

Python Numbers

In this article, you'll find out about the various numbers utilized in Python, how to change over from one data type to the next, and the numerical tasks upheld in Python.

Number Data Type in Python

Python upholds integers, floating-point numbers and complex numbers. They are defined as int, buoy, and complex classes in Python.

Integers and floating points are isolated by the presence or nonappearance of a decimal point. For instance, 5 is an integer though 5.0 is a floating-point number.

Complex numbers are written in the structure, x + yj, where x is the genuine part and y is the imaginary part.

We can utilize the type() capacity to realize which class a variable or a worth has a place with and isinstance() capacity to check in the event that it has a place with a specific class.

How about we take a gander at a model:

a = 5

print(type(a))

print(type(5.0))

c = 5 + 3j

print(c + 3)

print(isinstance(c, complex))

At the point when we run the above program, we get the following yield:

<class 'int'>

<class 'float'>

(8+3j)

Valid

While integers can be of any length, a floating-point number is exact simply up to 15 decimal places (the sixteenth spot is inaccurate).

The numbers we manage each day are of the decimal (base 10) number framework. Be that as it may, software engineers (for the most part inserted developers) need to work with binary (base 2), hexadecimal (base 16) and octal (base 8) number frameworks.

In Python, we can address these numbers by suitably placing a prefix before that number. The following table records these prefixes.

Number System Prefix

Binary '0b' or '0B'

Octal '0o' or '0O'

Hexadecimal '0x' or '0X'

Here are a few models

# Output: 107

print(0b1101011)

# Output: 253 (251 + 2)

print(0xFB + 0b10)

# Output: 13

print(0o15)

At the point when you run the program, the yield will be:

107

253

13

Type Conversion

We can change over one type of number into another. This is otherwise called compulsion.

Activities like expansion, deduction pressure integer to coast verifiably (consequently), in the event that one of the operands is glide.

>>> 1 + 2.0

3.0

We can see over that 1 (integer) is forced into 1.0 (glide) for expansion and the outcome is additionally a floating point number.

We can likewise utilize worked in capacities like int(), buoy() and complex() to change over between types expressly. These capacities can even change over from strings.

>>> int(2.3)

2

>>> int(- 2.8)

- 2

>>> float(5)

5.0

>>> complex('3+5j')

(3+5j)

While converting from buoy to integer, the number gets shortened (decimal parts are eliminated).

Python Decimal

Python worked in class skim plays out certain estimations that may astonish us. We as a whole realize that the amount of 1.1 and 2.2 is 3.3, however Python appears to conflict.

>>> (1.1 + 2.2) == 3.3

What is happening?

Incidentally, floating-point numbers are carried out in PC equipment as binary divisions as the PC just understands binary (0 and 1). Because of this explanation, the majority of the decimal divisions we know, can't be precisely put away in our PC.

We should take a model. We can't address the division 1/3 as a decimal number. This will give 0.33333333... which is infinitely long, and we can just surmised it.

Incidentally, the decimal division 0.1 will bring about an infinitely long binary part of 0.000110011001100110011... and our PC just stores a finite number of it.

This will just rough 0.1 however never be equivalent. Thus, it is the impediment of our PC equipment and not a blunder in Python.

>>> 1.1 + 2.2

3.3000000000000003

To defeat this issue, we can utilize the decimal module that accompanies Python. While floating-point numbers have accuracy up to 15 decimal places, the decimal module has client settable exactness.

We should see the distinction:

import decimal

print(0.1)

print(decimal.Decimal(0.1))

Yield

0.1

0.1000000000000000055511151231257827021181583404541015625

This module is utilized when we need to do decimal computations as we learned in school.

It additionally saves importance. We realize 25.50 kg is more exact than 25.5 kg as it has two huge decimal spots contrasted with one.

from decimal import Decimal as D

print(D('1.1') + D('2.2'))

print(D('1.2') * D('2.50'))

Yield

3.3

3.000

Notice the trailing zeroes in the above model.

We may ask, why not carry out Decimal without fail, instead of buoy? The main explanation is effectiveness. Floating point activities are done should quicker than Decimal tasks.

When to utilize Decimal instead of buoy?

We for the most part utilize Decimal in the following cases.

At the point when we are making financial applications that need definite decimal portrayal.

At the point when we need to control the degree of accuracy required.

At the point when we need to carry out the thought of critical decimal spots.

Read our Latest Blog: Tuples in Python

Python Fractions

Python gives tasks involving partial numbers through its portions module.

A portion has a numerator and a denominator, the two of which are integers. This module has support for levelheaded number math.

We can make Fraction objects in different manners. How about we view them.

import portions

print(fractions.Fraction(1.5))

print(fractions.Fraction(5))

print(fractions.Fraction(1,3))

Yield

3/2

5

1/3

While creating Fraction from drift, we may get some surprising outcomes. This is because of the defective binary floating point number portrayal as examined in the past area.

Luckily, Fraction permits us to instantiate with string too. This is the favored choice when using decimal numbers.

import parts

# As buoy

# Output: 2476979795053773/2251799813685248

print(fractions.Fraction(1.1))

# As string

# Output: 11/10

print(fractions.Fraction('1.1'))

Yield

2476979795053773/2251799813685248

11/10

This data type upholds every fundamental activity. Here are a couple of models.

from parts import Fraction as F

print(F(1, 3) + F(1, 3))

print(1/F(5, 6))

print(F(- 3, 10) > 0)

print(F(- 3, 10) < 0)

Yield

2/3

6/5

Bogus

Valid

Python Mathematics

Python offers modules like math and random to do diverse mathematics like geometry, logarithms, likelihood and measurements, and so on

import math

print(math.pi)

print(math.cos(math.pi))

print(math.exp(10))

print(math.log10(1000))

print(math.sinh(1))

print(math.factorial(6))

Yield

3.141592653589793

- 1.0

22026.465794806718

3.0

1.1752011936438014

720

Here is the full rundown of capacities and properties accessible in the Python math module.

import random

print(random.randrange(10, 20))

x = ['a', 'b', 'c', 'd', 'e']

# Get random decision

print(random.choice(x))

# Shuffle x

random.shuffle(x)

# Print the rearranged x

print(x)

# Print random component

print(random.random())

At the point when we run the above program we get the yield as follows.(Values might be diverse because of the random conduct)

18

e

['c', 'e', 'd', 'b', 'a']

0.5682821194654443

Read Full Article: Python Numbers

[scotianostra]

A new one on me, Colin Maclaurin mathematician died on June 14th 1746.

I hated maths at school, I was okay at counting and remember getting put in a class in third year that was for maths and arithmetic, I was way over my head with the maths part, geometry and algebra, logarithms.....nah they meant nothing to me, not this guy though, he was mates with Isaac Newton!!! Oh I was better at spelling than the guy that wrote the short bio below  and know how to spell Isaac!! MacLaurin started University in Glasgow aged 11 and got his degree at just 14. He died after falling ill fleeing the Jacobites and is buried in is buried in Greyfriars kirkyard, I'll have a wee look for him when I next pass.  More info on him and his maths nonsense on the link.  http://www.mhhe.com/math/calc/smithminton2e/cd/tools/timeline/maclaurin.html

[onlyjihoons]

dream knight; l.j.n

a/n omg guys,, it has been so so long since i have written something, and im so sorry omg,, my school term is getting more hectic than it was before, and also i would like to sincerely apologise to  akutagawahakuryuunosuke im so sorry for taking so long to complete your request bb im almost done and i hope its not too shitty asnsosfo

and also this is a spinoff from @cremethorns Hydrochloric Acid,(i hope you don’t mind!) except it doesnt involve spillage of liquid on jeno and a shirtless jeno bc pg13, also highly based on true events that might have costed my innocence, i couldve caused an acid spill on my classmate lol.

disclaimer: this fic has nothing to do with royalty. or knights.

genre: in the context of The Inheritors,, fluff

synopsis: your crush had to see you at your worst, fainting in home econs, and spraining your ankle at dance, and you thought it was only one sided, and only jeno’s duty as a student councilor to bring you to the infirmary, it all changed when you nearly spilled acid on your crush’s oh-so-perfect face.

Lee Jeno. Student Councilor. Member of the school’s dance team. Visual. Most sought after chaebol, also heir to one of Korea’s biggest broadcasting companies. He had connections and friends, lots of them, from idols to even influential friends abroad, he has everything.

And you? Heir to your mom’s clothing brand, you had your fair share of inheritance to your name to be honest. But you were low-profile, only making friends with the people you trust. Everyone in your school was either filthy rich or a heir to some company or both. And most of the people had connections, not friends. Even the poorest student in your school lived in a swanky condominuim complex. You were pretty decent looking if you were compared to those of neighbourhood schools, but if you compared yourself to your classmates, you would be one of the less-better-looking ones. Make-up was part of it, plastic surgery is another.

Your crush and yourself were sort of polar opposites. Jeno was friendly and kind-hearted, making girls stop by his classroom just to marvel at his annoyingly good looks, one of the minority that hasn’t gone under the knife and yet this beautiful. He was also a talented human being, he can dance, sing and rap, and on top of that good grades and an mouth-watering amount of inheritance when he graduates from college. You had decent grades, looks and money, but your eyes shot glares at strangers, and the queen of comebacks. Last but not least, the formidable ‘ice queen’. You cursed at your genes for making your resting bitch face really bitchy, you got it from your mom. But under that ‘ice queen’ title was a really really really kind-hearted Y/N, which people failed to believe as they only made connections. You haven’t gone under the knife yet, as your mother chose to believe in au naturael. You didn’t want to either, not like you had to use your face in any kind of situation. You weren’t a model anyway.

Ever since you set foot into the school, you were classmates and tablemates for homeroom with Jeno, not like you were complaining. You easily made friends with Jeno, as he found you really nice to hang around with and one of the few not making connections. Exchanging smiles whenever you passed by each other, a simple, platonic friendship. At least that’s what you thought, at the beginning of high school.

Slowly, your teenage hormones got the better of you and you found yourself constantly looking at Jeno. Your heart started beating at the thought of the boy, and you were practically his partner for every single practical lesson for every subject in school. “Stars align and zodiacs match”, smirked Chenle, your cousin and closest friend in school. 

There was once you and Jeno were paired up for home econs, you thought you would make a good team, as you guys were already comfortable with each other. The school’s kitchen was incredibly humid and hot, while stir-frying the pasta, you passed out due to heat exhaustion. The humidity and the added heat from the gas stove was overbearing for your weak body. Being your partner and a member of the Student Council, (you were too, the both of you are the only student councils in your class) he kindly carried your limp body on his back, and constantly worrying about you. It was super sweet of him to even stay in the infirmary with you until you regained consciousness, recalling his big, brown worried orbs staring into your own. Black locks disarray and sweaty, and then flashing a relieved smile which melted you once again.

4 months later and your crush on him only deepened, you hit yourself mentally for choosing the same co-curricular activity as Jeno. He shot you a big grin when he saw you warming up on the first day of dance, offering to help you stretch, which you politely declined because you didn’t was to scare him off with your flexibility. But alas, the instructor decided to have some weird ‘flexibility evaluation’ which you vowed not to fail, due to your pride and reputation of a ballerina of 11 years. Contrary to your expectations, Jeno only eyed you with adoration? respect? shock? You didn’t want to get your hopes high.

Your instructor was impressed, placing you in the ‘top’ team. Your team bravely chose Gfriend’s Fingertip, also a choreography you had wanted to learn in the longest time. Jeno was in the ‘top’ team for the boys too, they chose BTS’ Not Today. You bit your lip, your teammates voted you to be the centre, SinB. You were flattered, they thought so highly of your dance skills, but you were also pressured to grasp the choreography fast and right, so that you could look the best and also help your teammates too.

While learning the dance break, your legs moved faster that your body could react, the inertia sending you to the laminated wooden floor, producing a small thump on your ankle. You groaned as the excruciating pain shot your ankle like a bullet, srunching your nose. Your teammates rushed to your side, worried as the team’s ace got hurt. Jeno’s team heard the commotion, and rushed to surround you as well. Jeno pushed through them, picking you up bridal style, causing ooh-ahhs, swoons(from the top teams) and glares(mostly from the girls) from the other teams. You instinctively wrapped your arms around his neck, afraid to fall again. Your instructor was puzzled when Jeno approached her with you in his arms, but she then hurriedly waved the both of you off lest your sprain got worse.

“Put me down, Jeno, I can walk,” You tried to wriggle out of his arms, but to no avail as Jeno suddenly ‘dropped’ you, producing a surprised yelp from you and curious gazes from students.

“Your sprain will worsen, princess,” Jeno whispered almost flirtatiously, sending shivers down your spine, “and I’m not Do Bong Soon, you’re not that light either.”

You scoffed, “I’m underweight, Jeno, how could you--” You gasped as Jeno’s faced inched slowly towards yours.

“I’ll kiss this pretty face of yours if you can’t stop talking till we get to the infirmary.” Jeno’s eyes darkened, causing you to gulp.

As much as you wanted his lips on yours, you shook your head profusely, Jeno’s eyes immediately crinkled into crescents, lightheartedly walking towards the infirmary.

In the end, stupid Jeno stayed to help ice your sprain, luckily not serious. The both of you missed dance, but none of you cared, you two were two busy giving each other playful banter to keep track of time.

“Your grades are gonna drop at this rate you are daydreaming in class because of Jeno,” Chenle snapped his fingers, startling you from your daydream.

You rolled your eyes, “Who was the one that got 16/20 for her math test and who was the one that got 12/20 for his math test?”

Chenle raised his hands in defeat, “Serves me right for not studying,”

“Neither did I,” You batted your eyelashes innocently as Chenle glared at you.

The school bell rang, signalling break time.

You and Chenle actually made the effort to pop by the snack shop to get some snacks together, usually it was decided through Rock Paper Scissors to who was the unlucky one to pay for the snacks and make the unwanted trip down. Neither of you actually bothered this time, as Logarithms sucked up all of the brain juice you had replenished during recess.

“Did you hear?” Chenle sipped on his banana milk, “We are getting our permanent lab partners for Chemistry today.”

“Mhmm,” You hummed as you munched on a churro snack, “I’ll probably get Jeno again, what’s new.”

“You see, Y/N, that’s the problem with you!” Chenle snapped suddenly, shocking you.

“P...problem?”

Chenle pinched the bridge of his nose, and hissed, “The reason why you’re always complaining that you can’t get Jeno to be your boyfriend, lies in the actions you do yourself, Y/N. At this rate, your crush on Jeno will be brought to your deathbed, the whole world knowing except him.”

You frowned, “So what is your point here, Chenle, do you want me to splash hydrochloric acid on him so i can see him shirtless? Hmm? Then after that expecting him to sweep me off my feet and plant a kiss on my lips? Like the ones in dramas and fanfictions?”

“Just... confess to him.” Chenle resumed sipping on the artificially flavoured drink, “I mean like, you have been liking him since forever, and besides, he has so many girls going after him. This is your golden chance, couz. And I highly doubt that your feelings for him are one-sided.”

You blinked your eyes, slowly absorbing Chenle’s words. You sighed, Chenle was right, even though you aren’t sure about the one-sided part. 

“Y/N and Jeno. Alright class, please take your seats beside your partner at the designated tables and wait for further instructions.” Your teacher waved the class off, and girls bursting into whiny sobs as they failed to get Jeno as their lab partner, again. It was a simple acid-base titration with hydrochloric acid and sodium hydroxide today, your teacher demonstrated the previous lesson and she wanted to let the class “have a go at it” as she believed in the whole “practical sessions helps with understanding” thing. It did help, in a way, but it was an opportunity for you to stare at Jeno up close, other than homeroom lesson. 

You hid your face in your hands as you saw Jeno approaching your seat with his signature eyesmile, you knew you were a stumbling mess in front of his smile, and your plans of confessing to Jeno would go down the drain.

“Y/N-ie~”Jeno sang as he settled down beside you, “We’re lab partners again.”

Don’t look at him, Don’t ever look at him, you chanted a silent mantra to yourself as you closed your eye in case you spilled your feelings too quickly.

“Y/N?” Jeno called out to you worriedly, “Are you alright? You look very out of it today.”

“It’s just the Logarithms that make me feel very blank in general,” You excused clumsily, “I’m just really tired.”

“Do you want me to be in charge of the burette or...”

“Actually, Jeno, I have something to tell you, and--”

“Alright class, please start now.” Your teacher instructed as students began to measure the amount of acid needed.

“Using a pipette, transfer 20.0cm3 of sodium hydroxide into a cornical flask. Add 2-3 drops of methyl orange into the sodium hydroxide. Describe the colour of the methyl orange.” Jeno read, “Do you want me to do it?”

You nodded slightly, recalling your phobia of handling equipment. It was in middle school, where you kindly helped the teacher to wash the petri dish, but your hands turned butter and the petri dish shattered, startling you. It was a measly petri dish, but it was kind of a big deal to the then you, and from then on you were very cautious around the cleaning of equipment.

“Y/N?” Jeno’s voice snapped you out of your reverie, “Its your turn to add the methyl orange.”

You unscrewed the cap carefully, then cautiously dripping exactly 3 drops of the indicator. So far so good.

“Sodium hydroxide is an alkali,” Jeno noted as he wrote the answer down in the instruction sheet, “Do you want to pour the hydrochloric acid?”

You complied, feeling bad that Jeno had to see this vulnerable side of you today. You poured 30.0cm3 of hydrochloric acid into the beaker, then placing a funnel at the top of the burette. Unfortunately, the burette was taller than your height of 5″2, and you needed to stand on the footrest of your stool to reach to that height.

You carefully poured the acid into the burette, heaving a sigh of relief as you emptied the beaker. Your ‘good’ day shattered when you lost your balance upon descending, and you expected to hit the hard concrete floor of the science lab.

But you didn’t. You were in fact supported by a pair of strong arms, and those arms belonged to none other than your crush, Jeno. His eyes bore a worried look as you hoisted you upright and rubbed your back soothingly.

“You must’ve been really tired Y/N,” Jeno sighed. “I think we should get back to class once we complete this.”

“O-okay.”

“So what is it that you wanted to tell me at the science lab?” Jeno rested his chin on his hands, expectantly waiting for an answer.

“I-I...” You wrung your hands nervously, Jeno nodded for you to continue, “I like you, Jeno-ah.”

Jeno’s eyes widened, but his face was unreadable, “Since when did you begin to like me?”

“I don’t know... since we cooked pasta i guess?” You smiled sheepishly, then slumped in your seat, “Its okay if you can’t reciprocate my feelings, Jeno. I’m fine with it.”

“But I’m not fine with it,” Jeno’s expression darkened, a side you have rarely seen.

“Wh-why?”

“Because I want you to be my girlfriend.”

You blinked your eyes, and also attempting to dig whatever earwax you had out of your ears. Did you hear him right, Lee Jeno wanted to be your boyfriend.

Jeno’s face inched closer to yours, then softly placing his hand on your cheek, “May I...?”

You nodded slightly, and without hesitation, Jeno leaned in and placed his soft lips on yours, an immense feeling of euphoria erupting in your chest. Your hands magically found its way to Jeno’s black locks, pulling him slightly closer to slightly deepen the kiss.

Seconds later, you pulled away, a faint red dusting your cheeks, “I’m sorry I shouldn’t have done that.”

“Its alright, like it was my first kiss so...” Jeno looked away shyly.

“It was mine too.” You confessed, immediately regretting your words as Jeno smirked, “Can I be your last too?”

“Maybe,” You shrugged.

Jeno brought you into his chest, red dusting your cheeks again, “What about now?”

“...Okay.”

Well, no one said that your dream knight has to be in shiny armour, he could be in school uniform too.

[juudgeblog]

How to prepare Maths for CLAT

This article is written by Anmol Singla of RGNUL.

CLAT is an exam which tests students analytical ability, mathematical skill, reasoning ability, language skills, general awareness and application of legal phenomena. Mathematics is one of the major differentials in one’s score as a lot of students fail to do well in this section. It is for some reason the most hated subject of most of the aspirants. This article will focus on how to target that eternal enemy and conquer it to score well in the exam.

Students who have a strong grasp of fundamentals of mathematics will find this section quite scoring. As long as you avoid silly calculation mistakes, concepts related to CLAT math section are easy. Make sure you cover these topics in mathematics:

• Number system

• Roots

• Decimals and fractions

• Surds and indices

• Average

• HCF and LCM

• Approximation

• Ration and proportion

• Logarithm

• Profit and loss

• Discounts

• Interest calculation

• Areas and volumes

So coming to it, 20 questions out of 200, exactly 10 percent of the total marks. It seems so little. Why do I need to do it? Well, it is a subject purely based upon your skill and practice. If you practice it with due diligence it will never betray you.

The questions asked in the examination are usually based upon the following topics:

Number system

Example – The number obtained by interchanging a two-digit number is 27 more than the original number. If the sum of the two digits is 13, what is the original number?

1) 63         2)74     3)85           4)58

Anita had to multiply two positive integers. Instead of taking 35 as one of the multipliers, she incorrectly took 53. As a result, the product went up by 540. What is the price of the new product?  

1) 1050

2) 540

3) 1440

4) 1520

5) 1590

RootsIn a class, each of the students contributed as many paise as there are number of students. If the total collection was Rs. 64, what is the number of students in the class?                        

1) 90

2) 82

3) 80

4) 40

Decimals and Fractions

(⅖  of 0.5 + ⅜ of 4.8) x ( ⅞ of 2.4 + 6/11 of 5.5 ) =

13.28

14.28

14.18

14.26

Average

The average weight of three men ‘X’, ‘Y’ and ‘Z’ is 75 kgs. Another man ‘A’ joins the group and the average weight now becomes 80 kgs. If another person ‘B’ whose weight is 5 kgs more than ‘A’ replaces ‘X’, then the average weight of ‘Y’, ‘Z’, ‘A’ and ‘B’ will be 85 kgs. What is the weight of ‘X’?

80 kgs.

84 kgs.

82 kgs.

78 kgs.

Areas and Volumes

A circular park, 42 m in diameter, has a path 3.5 m wide running around it on the outside.

Find the cost of gravelling the path at Rs. 4 per m2

Ans.

Rs. 1672

Rs. 1652

Rs. 2002

Rs. 2048

Ratio and proportion

Gold and copper are as heavy as water by 19 and 9 times respectively. The ratio in which these two metals be mixed so that the mixture is 17 times as heavy as water is:

2:3

3:2

4:1

3:4  

Profit and Loss

A trader sells rice at a profit of 20% and uses weights which are 10% less than the correct weight. The total gain earned by him is:

33 1/3%

22 2/9%

30%

35%

Interest Calculation

A man buys Rs. 20 shares paying 9% dividend. The man expects to have an interest of 12% on his money. The market value of each share is?

Rs. 18

Rs. 15

Rs. 12

Rs. 21

As we can see that all of the topics are taught in elementary school and are not difficult by any means. All it needs is the dedication to practice on a regular basis. How to do that?

Play with numbers in your daily life

If you are going outside, check out the number plate of the vehicles. Play with the numbers by finding out the sum and product of each number plate. Add variations like finding the difference of the squares, dividing the product of three numbers by third and more.

In case you are visiting shops, especially during sales, try to calculate the prices of all the products by adding up the discounts. Similarly apply your numerical knowledge in other real-life scenarios like a cricket game or a football game, dealing with debts and much more. This way you will be familiar with the core mathematical operations and will find your calculation speed increasing gradually.

This link will lead to you to another fun game to improve maths while you are outside.

Practice daily for at least three months before the exam

Make it a goal to solve at least 20 relevant questions daily. Go with practising specific topics for the first two months and mixed topics for the whole of the last month. Time yourself regularly. If you are diligent enough and grasp the concepts you should be able to solve most of the questions within a minute as you approach the end of your preparation.

Memorize all the formulas and relevant tricks by applying them thoroughly

Every topic has its own formulas and certain tricks that can help you to save time. Prepare a formula sheet and stick it at some place you can look at daily. Keep the tricks in mind while solving the questions. A few tricks for average, ratio and proportion have been given in this article.

Analyze your mistakes and work on them

Don’t just practice, EVALUATE YOURSELF! As you proceed with the topics you will start to identify your strong and weak areas. A common mistake made by candidates is that they tend to overdo their weaknesses and ignore their strengths. You have to make consistent efforts to work on both and not lose your grasp.

A few useful tips:

Memorize tables upto 20, squares upto 30 and cubes upto 20. This will be useful in both maths as well as the logical reasoning section.

Work upon the variations in the practical usage of formulas. For example, in mensuration, the formulas need to be applied judiciously to arrive at the right result.

Out of the 20 questions, at least 10 can be solved in under 1 minute. Identify them first, to maximize your score.

Don’t spend more than 15 minutes on this section unless you have completed the rest of the exams already.

Some of the recommended books are

Quantitative Aptitude by RS Aggarwal

NCERT textbooks for classes 8,9 and 10.

At the end of the day, maths is all about making efforts but making them smartly. One doesn’t need to be scared or feel like one has to move mountains. It is just another section of the exam which is feared way too much. If you are able to incorporate the given methodology into your preparation, you will surely do well in this section. As most of the students have relatively low scores in this section, a score of above ten can really increase your chances of securing a good rank and getting into your dream Law University.

To conclude there’s a quote, not from any old philosopher but from the idol of millions of youth in our nation, Virat Kohli:

“Self-belief and hard work will always earn you success.”

The post How to prepare Maths for CLAT appeared first on iPleaders.

How to prepare Maths for CLAT syndicated from https://namechangersmumbai.wordpress.com/

[loyallogic]

How to prepare Maths for CLAT

This article is written by Anmol Singla of RGNUL.

CLAT is an exam which tests students analytical ability, mathematical skill, reasoning ability, language skills, general awareness and application of legal phenomena. Mathematics is one of the major differentials in one’s score as a lot of students fail to do well in this section. It is for some reason the most hated subject of most of the aspirants. This article will focus on how to target that eternal enemy and conquer it to score well in the exam.

Students who have a strong grasp of fundamentals of mathematics will find this section quite scoring. As long as you avoid silly calculation mistakes, concepts related to CLAT math section are easy. Make sure you cover these topics in mathematics:

• Number system

• Roots

• Decimals and fractions

• Surds and indices

• Average

• HCF and LCM

• Approximation

• Ration and proportion

• Logarithm

• Profit and loss

• Discounts

• Interest calculation

• Areas and volumes

So coming to it, 20 questions out of 200, exactly 10 percent of the total marks. It seems so little. Why do I need to do it? Well, it is a subject purely based upon your skill and practice. If you practice it with due diligence it will never betray you.

The questions asked in the examination are usually based upon the following topics:

Number system

Example – The number obtained by interchanging a two-digit number is 27 more than the original number. If the sum of the two digits is 13, what is the original number?

1) 63         2)74     3)85           4)58

Anita had to multiply two positive integers. Instead of taking 35 as one of the multipliers, she incorrectly took 53. As a result, the product went up by 540. What is the price of the new product?  

1) 1050

2) 540

3) 1440

4) 1520

5) 1590

RootsIn a class, each of the students contributed as many paise as there are number of students. If the total collection was Rs. 64, what is the number of students in the class?                        

1) 90

2) 82

3) 80

4) 40

Decimals and Fractions

(⅖  of 0.5 + ⅜ of 4.8) x ( ⅞ of 2.4 + 6/11 of 5.5 ) =

13.28

14.28

14.18

14.26

Average

The average weight of three men ‘X’, ‘Y’ and ‘Z’ is 75 kgs. Another man ‘A’ joins the group and the average weight now becomes 80 kgs. If another person ‘B’ whose weight is 5 kgs more than ‘A’ replaces ‘X’, then the average weight of ‘Y’, ‘Z’, ‘A’ and ‘B’ will be 85 kgs. What is the weight of ‘X’?

80 kgs.

84 kgs.

82 kgs.

78 kgs.

Areas and Volumes

A circular park, 42 m in diameter, has a path 3.5 m wide running around it on the outside.

Find the cost of gravelling the path at Rs. 4 per m2

Ans.

Rs. 1672

Rs. 1652

Rs. 2002

Rs. 2048

Ratio and proportion

Gold and copper are as heavy as water by 19 and 9 times respectively. The ratio in which these two metals be mixed so that the mixture is 17 times as heavy as water is:

2:3

3:2

4:1

3:4  

Profit and Loss

A trader sells rice at a profit of 20% and uses weights which are 10% less than the correct weight. The total gain earned by him is:

33 1/3%

22 2/9%

30%

35%

Interest Calculation

A man buys Rs. 20 shares paying 9% dividend. The man expects to have an interest of 12% on his money. The market value of each share is?

Rs. 18

Rs. 15

Rs. 12

Rs. 21

As we can see that all of the topics are taught in elementary school and are not difficult by any means. All it needs is the dedication to practice on a regular basis. How to do that?

Play with numbers in your daily life

If you are going outside, check out the number plate of the vehicles. Play with the numbers by finding out the sum and product of each number plate. Add variations like finding the difference of the squares, dividing the product of three numbers by third and more.

In case you are visiting shops, especially during sales, try to calculate the prices of all the products by adding up the discounts. Similarly apply your numerical knowledge in other real-life scenarios like a cricket game or a football game, dealing with debts and much more. This way you will be familiar with the core mathematical operations and will find your calculation speed increasing gradually.

This link will lead to you to another fun game to improve maths while you are outside.

Practice daily for at least three months before the exam

Make it a goal to solve at least 20 relevant questions daily. Go with practising specific topics for the first two months and mixed topics for the whole of the last month. Time yourself regularly. If you are diligent enough and grasp the concepts you should be able to solve most of the questions within a minute as you approach the end of your preparation.

Memorize all the formulas and relevant tricks by applying them thoroughly

Every topic has its own formulas and certain tricks that can help you to save time. Prepare a formula sheet and stick it at some place you can look at daily. Keep the tricks in mind while solving the questions. A few tricks for average, ratio and proportion have been given in this article.

Analyze your mistakes and work on them

Don’t just practice, EVALUATE YOURSELF! As you proceed with the topics you will start to identify your strong and weak areas. A common mistake made by candidates is that they tend to overdo their weaknesses and ignore their strengths. You have to make consistent efforts to work on both and not lose your grasp.

A few useful tips:

Memorize tables upto 20, squares upto 30 and cubes upto 20. This will be useful in both maths as well as the logical reasoning section.

Work upon the variations in the practical usage of formulas. For example, in mensuration, the formulas need to be applied judiciously to arrive at the right result.

Out of the 20 questions, at least 10 can be solved in under 1 minute. Identify them first, to maximize your score.

Don’t spend more than 15 minutes on this section unless you have completed the rest of the exams already.

Some of the recommended books are

Quantitative Aptitude by RS Aggarwal

NCERT textbooks for classes 8,9 and 10.

At the end of the day, maths is all about making efforts but making them smartly. One doesn’t need to be scared or feel like one has to move mountains. It is just another section of the exam which is feared way too much. If you are able to incorporate the given methodology into your preparation, you will surely do well in this section. As most of the students have relatively low scores in this section, a score of above ten can really increase your chances of securing a good rank and getting into your dream Law University.

To conclude there’s a quote, not from any old philosopher but from the idol of millions of youth in our nation, Virat Kohli:

“Self-belief and hard work will always earn you success.”

The post How to prepare Maths for CLAT appeared first on iPleaders.

How to prepare Maths for CLAT published first on https://namechangers.tumblr.com/

[aphilosopherchair]

[Hey, That’s Her] The Riemann Sphere is Her Mirror on the Wall

                                   MBC 드라마 《신입사관 구해령》 (2019)

There may be such a woman.

For at least eleven hours a day, her analytical, artistic, emotional and ethical minds are collectively locked up in a Taylorist cell block where the mantra is familiarly simple: Don’t question, don’t tell. Every reasonable client is aware that this is a dog-eat-dog world, so it is up to him or her to look out for personal interests not yet covered by contract law or even fiduciary law. If you value your principles and dreams over your corporation’s needs, you are a selfish hypocrite. Oh, and complain all you want at the water cooler; just remember to put back your angel mask and keep your head low at meetings.

That much is not really astonishing. No one in this place is a one-day-old. What stuns more is the utterly dim calaboose she toils away at her daytime lockup to return her body to every night, where broken bottles and suspicious pools of liquids bedeck the streets, literal rock concerts never cease, homeless druggies openly spread their limp bodies on pavements, and drunken Cinderellas and Cinderfellas bang on random doors when the clock strikes twelve. 

Change might come with time but, given a burgeoning workload and an increasingly creepy cardiac rhythm, it must come soon. So, one night, she decides that if all jobs are this suffocating, she might as well take the best-paid one. It’s time to head back to graduate school, except that, this time, economic logic shall prevail over passion and intrigue.

As part of her research on Wealth and Investment Management MScs, she hunts down sample class videos from different business schools. Nestled among the suggested clips accompanying one search result, though, is a familiarly curious title that hypnotizingly whispers to her, Shopaholic Louis-style. It is the name an adviser, frowning over yet another overloaded course plan from her, pressed her into canceling out all those years ago right when meeting times for the semester did not conflict with those of her core classes. And soon, before her eyes, is an entire playlist for her narrowly missed destiny.

What harm could playing the introductory video at 2x do? Business schools’ admissions websites would not vanish in 30 minutes’ time. Ah, that was a collegiate equivalent of a soulful tearjerker but covered mostly basics she learnt in other classes. Application deadlines are half a year away, so there is ample room for a second lecture. Cool! The plot thickened pretty fast. Her college and graduate school debts are still badly in arrears. Can she be certain that she truly understands everything without attempting an unseen problem? Fetch homework sets from the official homepage tomorrow. Had she been bolder in imagination, she would have gotten question 7 right. Try harder for lecture three’s assignments. She has run out of eligible guarantors for a third loan. Lecture 11. Course completed. What a satisfying visual feast! Hey, the blurb of the follow-up course sounds fascinating too. It is not that she does not love investment banking. How about challenging herself at that course while the material of this course is still fresh in her mind? It is that she loathes investment banking. Mathematical logic has trumped economic logic. 

  How do you hold every number up to infinity in the palm of your hand without a poetic soul? Scoop out a round piece of dough and fancy being able to spread it so thin that it stretches to infinity. But instead of actually spreading it, roll up the edge to form a sphere. Let the bottom tip represent zero and the top tip represent infinity. As a point on the surface moves up from the bottom, it can have components that are each positive or negative, real or imaginary, depending on which pairs of opposite longitudes you assign the real number line and imaginary number line (recall: e.g. …, -10i, -9.99i, … , 0, … , 9.99i, 10i, …, where i is the square root of -1) to. The rise in value of each component accelerates with height, such that the physical gap representing any given numerical difference shrinks infinitely on the surface of the sphere as infinity approaches, making it harder and harder to advance and actually reach infinity. You are now cradling a physical version of the Riemann sphere.

© Jean-Christophe BENOIST, modified under the permission of CC BY-SA 3.0. P(A), around 1.5 in value, on the sphere corresponds to A on the grid, which represents the same numerical system in a typical boundless, regularly spaced 2D format. Similarly, P(B), around -0.5 in value, on the sphere corresponds to B on the grid.

 The macrocosm of universal random structures, infinite products, manifolds and many more is a dearly missed oracle that reveals her inadequacies for what they are, without miserliness, patronizing sugar-coating, or, ironically, calculation: her inflexibility, her inattentiveness, her impatience and her indolence. “Shortcuts and cookie-cutter approaches cannot be your default,” it states plainly. So long as they do not cross a certain line, tactful hypocrites, on the whole, seem to be treated better by their surrounding adult peers than sharp-tongued, straight-talking observers with pure intentions in her circle. Yet the more she experiences of the grown-up world, with the heightened stakes and heightened awareness of interpersonal dangers that deter verbalization of contrarian opinions on the one hand and massive clots of intractable ills on the other, the more she wishes to cherish many of those straight talkers. The ideal living beings are, of course, the severely scarce breed who efficiently marry the circumspection, civility and altruistic strategizing that come with tact with the determination to convey, where necessary, uncomfortable truths. 

For all its uninhibited criticism, mathematics gives credit where it is due and those who converse with it are frequently safe in the knowledge that it means its flattery. It reassures this corporate internee who feels increasingly stuck in her ways that she still has what it takes to master new grammars and vocabularies. It rewards her finesse at plugging gaps in background knowledge by improvising from scratch techniques taught only in later, simpler courses. What if these skills could let her pivot directly to some sector slightly less lucrative but also less odious to her than investment banking, never mind exactly how competitively relevant her prior higher education and corporate experience are?

Far more certain is that her deliciously madcap approach to this discipline with a matchingly rebellious streak has magically quietened the rock concerts and the intoxicated fairy tales and almost erased the jail bars. Nonetheless, as the faded bars unveil more and more vistas stretching beyond the horizons, she starts to wonder if she will live long enough to look a little further, if she will ever squirrel away enough bucks—after all those deductions for debt payments, taxes, food, rent, basic maintenance and transport—to hike a little closer, and if her wrinkled, financially secure self will continue to have the visual and cognitive acuities to deconstruct or even remember the sights a little longer. The jail bars resolidify to some degree.

Still, if positive infinity and negative infinity have been rendezvousing in a dimension invisible until intrepid mind adventurers outed them, and if functions as diverse as trigonometric functions, inverse polynomials and logarithmic functions share the same class of undercover identities, i.e. infinite sums of terms with increasing powers, maybe, she thinks, escape hatches exist somewhere nearby after all.

There may be such a woman. There may be such a snowless ending by a grilled window.

Note: This work of fiction commemorating Pi Day was inspired by an old Dramabeans guest post campaign, a few heartfelt entries of which have appeared in the admin’s Twitter feed. There is no intention, however, to establish any kind of association with the site. Interested readers can find slightly similar math-life themes in the book versions of Kim Ji-young, Born 1982 (82년생 김지영) and The Devotion of Suspect X (容疑者Xの献身).