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How do I not make any more mistakes in math?

I've tutored math and science for the last eight years. Rather than advise you to check your work or to try harder, I have a simple suggestion: Graph-paper.Use graph-paper — for ALL math — even when not graphing. Use it for taking class notes. Use it for all homework.It has to be the right kind of graph-paper, though:The lines have to be VERY light. Most are too thick or dark and actually obscure your own writing.I prefer spiral bound, but if I need to tear pages out, perforated — ideally both. (Mead makes two styles I recommend: their “100-sheet Quad Spiral Notebook,” and the “Cambridge Business Notebook.”)The grid-size needs to match your writing size. 4-per-inch is usually too big. I prefer 5-per-inch, but have used 8 or 10 also.Double-sided, ideally with the same grid-spacing on both sides.Try folding the sheet lengthwise in half or drawing a vertical line down the middle of the sheet, then working problems strictly within these columns. At the end of the first column, start the next problem at top of the second column.Use the grids to line up your writing, i.e. one grid per number, per minus sign, per equal sign, etc. Even use a grid for spaces to make it neater. Everything gets its own grid. It's like using a Mono-spaced font.Fractions are troublemakers. So, never write an entire fraction on the same line as non-fractions. Never use a diagonal line in your fraction; it should always be horizontal. All the other non-fractions really ARE fractions — their denominator is just “1”. So imagine a line under each regular term with a “1″ written below it. This shows you where to write your actual fraction: Only the numerator goes on the main line with everything else. The denominator always goes below the main line, where all those invisible 1's are at. Also, add parentheses around the entire fraction, whether they're needed or not, as a reminder to properly distribute any adjacent multipliers.When solving equations, it's critical to keep the equal sign in the SAME place for every step. This “centers” or “aligns” your work. And definitely DO write the equal sign at every step, keeping it lined up. This conveys that you're writing another step which is derived from the line above it, rather than something new or unrelated. If you can, try to keep all the terms lined up as well.Try to work on one side of the equation only, though this is not always possible.When a step involves a change on only one side, do NOT rewrite the unchanged other side. Leave it blank until something changes. (The blank space on one side of the equal sign implies “ditto-marks,” but do not actually write ditto-marks. :)Leaving the unchanged side blank saves MANY, MANY opportunities for mistakes. Write only on the changed side. It also makes checking and following your work much easier, both for you and for your teacher.At the final line, you can bring down the unchanged side and re-write it, before boxing the entire solution.Crowded work is difficult to follow or to spot mistakes, so leave some white space between problems. Your elementary-days of one-problem-per-line are long gone.—————As a bonus, you have graph-paper now handy at every spot on the page. No more finding separate graph-paper and attaching it or taping it on. And since you have the grids already, go ahead and sketch a small graph of EVERY problem, whether instructed to or not. If you graph the expression on each side of an equation individually, but on the same x-y axes, the point(s) where they intersect will show your answer.Don't waste time drawing tick-marks, as they just add clutter. Don't even label the axes. IGNORE** the grids and just get the SHAPE about right. Practicing making this connection between an expression and the general shape of its graph is HUGE.It trains your brain to think visually. It teaches you how to estimate. It allows you to easily spot a wildly erroneous answer. It also helps when going the other way, i.e. when the assignment is to come up with the equation from a given graph.—————**On graph-sketching, I actually find unlined PLAIN paper to be the best. Draw an x-y axis, but do NOT add any tick-marks or labels. Then first draw the shape freehand, and second, label ONLY the interesting points like minima, maxima, or x- or y-intercepts with their values. Add enough labels to definitely nail down the graph, but NONE others. It doesn't matter if it is drawn “to scale” or not. If the scale is wildly off, add “NTS” for an official disclaimer :)Hope this helps.One more thing: Use a decent eraser. You can thank me later ;-)The built-in erasers on number-2 wooden pencils are terrible. They smudge your work and tear your paper, or they harden and break off.Use either a separate rectangular eraser or a stick. It has to be the white ones, like the “Pentel Hi-Polymer” or the “Pentel Clic-Eraser.” For an all-in-one solution, try the “Pentel Twist-Erase Click” mechanical pencil. (The eraser in this one won't run out like they do on so many mechanical pencils.)Whatever form you choose, the white polymer material will erase cleanly and completely, will not tear your paper, and never hardens or dries out.(Mead and Pentel have not paid me to recommend anything, but maybe I should look into that… :)

How do I self-prepare for the IBPS and SBI PO 2019?

In theory, there is no difference between theory and practice. But in practice, there is.- Yogi BerraBefore you start your preparation you must be aware of the every nitty-gritty of this exam. Please, visit official website of IBPS, download IBPS-PO notification and go through it to know every crucial details about the exam like exam pattern, negative marking, scheme of examination etc.Examination structure consists of three phase:1. Preliminary Examination2. Main Examination3. InterviewBefore preparation, we must know the previous year cut-offs and type of questions asked in last year exam. So, please check previous year visit - PracticeMock Blog.The weight-age (ratio) of CWE (Main exam) and interview will be 80:20 respectively. If you do the math you will realized that merely qualifying the cutoff will not get you a job. If you want to see your name in the final list, you will need to score 15-20 marks more than cutoff of Main Examination considering average interview marks (around 60 out of 100).Now, let's start with the preparation part.We need to prepare for the 5 different sections viz.Quantitative Aptitude/Data Analysis & InterpretationReasoning Ability & Computer AptitudeEnglish LanguageGeneral/ Economy/ Banking AwarenessEnglish Language (Letter Writing & Essay)English Language● Topics to focus onReading Comprehension (Short/Long passage including questions related to tone/theme/inference etc.)Cloze TestSentence Correction and sentence ImprovementSpot the errorFill in the blanks (single filler & double filler )Para jumbles (Arrangement & odd one out)Vocabulary (synonyms & antonyms)Para completionMatch the followings (Grammar based, Emotions based)Tips for English Language:Start reading newspaper on daily basis. Benefits of reading Newspaper are multi fold, it will increase your reading speed, will build up your comprehension ability, and will enhance your vocabulary. It will also help you in preparing current affairs, understanding Critical reasoning questions, and writing better essay and letter in descriptive test.Reading from online sources will be more beneficial compared to reading paperback editions of newspaper/magazines/books etc. You can use The Hindu, New-York Times, time magazine and articles written by various economists. You can also read speeches and publications available on Reserve bank of India website.People can suggest you to read ‘wren & Martin for English Grammar’ and ‘Word Power Made Easy’. These books will surely help you in improving your English language, but if you haven’t read these books previously, I will not advise you to go for them with only 100 days in hand as rate for return will not be in your favour.For Grammar, Refer to Plinth of paramount by Neetu Singh or General English by SP Bakshi. Don't try to cram all the rules, just go through them and practice quizzes based on the rules. In examination hall, trust your instincts.Noun, subject- agreement, articles & preposition, these are some important chapters.Learn Vocabulary and idioms & phrases.For Vocabulary, you can also watch YouTube videos of Study IQ Education Channel.Start practicing different/new types of questions from a test series and from online quizzes.Reasoning Ability:● Topics to focus ona. Seating arrangement:Linear (Double rows/Tipple rows), Circular, square, rectangular, hexagonal etc. (Inside, Outside, In-out, with blood relation and with multiple variables). Arrangements with unknown number of people, with vacant seats, and with movements of people.b. Coding-Decoding (Old type/New Types)c. Mathematical Inequalities (Including Coded one)d. Blood relations (Including Coded one)e. Syllogism & reverse syllogism (Including cases of ‘few; and ‘only few’)f. Puzzles:Box, Floor (with vacant cases) with multiple attributes and blood relations as well.Grid Matrix Puzzles (with multiple variables)g. Direction and Distance ((Including Coded one)h. Classification/Analogyi. Series (Alphabetical, Number & mixed series)j. Ordering and rankingk. Machine Input-Outputl. Critical/Logical Reasoningi) Cause & effectii) Statement & Argumentiii) Statement and course of actioniv) Statement and Assumptionv) Drawing inferencesm. Data sufficiency (Two/Three Statements, and Redundant type)n. Computer Aptitude: Learn basics of Computer. But these days no questions are asked related to computer awareness but they ask questions involving computer aptitude with logic involvement of conversion of number systems or using flow diagram etc. Use test series to practice these types of questions.Tips for Reasoning:1. Learn how to approach each type of questions mentioned above, with the help of a teacher or from online YouTube channels. (Meritshine, Infinitesimal, Oliveboard etc.)2. While learning all these concepts, start solving memory based previous year papers. Practice quizzes from all the topics and Master them using latest pattern based test series. Practice is the only key.Quantitative Aptitude/Data Analysis & Interpretation:● Topics to focus on○ Simplification & approximation○ Percentage○ Profit, Loss & discount○ Time and Work○ Ratio and Proportion & partnership○ Interest (Simple and compound)○ Number Series (Missing & Wrong)○ Quadratic Equations○ Mixture & Allegation○ Time, speed & distance○ Boat & Stream○ Time & Work (Including Pipe & Cistern)○ Average & Ages○ Circle, Mensuration, Geometry, Algebra○ Permutation & Combination, Probability○ Number System○ Data interpretation■ Bar Graph■ Line Graph■ Pie-Chart■ Tabulation■ Mix diagrams■ Radar graph■ Caselets (Including Flow diagram caselet)• Types of Questions: Word Problems (Including Approximations, Fill in the Blanks, Multiple Options) Quantity Comparisons (Including Two/Three Quantities) Data Sufficiency (Including Two/Three Statements, Redundant Type, Consistent/Inconsistent Type) New types of Charts (Flow diagram based, Scatter Chart, etc.)Tips for Quantitative aptitude:1. Learn concepts of all the chapters mentioned with the help of Quantum Cat by Sarvesh K. Verma or Quantitative Aptitude by Arun Sharma or using YouTube Videos.2. Learn square of numbers up-to 50, cubes up-to 20 & tables up-to 25.3. Practice 50 questions of moderate to difficult level for each chapter, and then start practicing online quizzes and mock papers.General/ Economy/ Banking AwarenessThis section can be divided into three sections, Static GK, Banking Awareness, and Current Affairs.For static Banking Awareness & static GK, refer to booklet/pdf available online of any authentic source.● Glance through the newspaper every day. Read Business section thoroughly. Read editorials with special emphasis on articles related to Indian economy, finance, and budget.○ You will find a lots of fodder points below the images in newspaper.● Follow Reserve bank of India (RBI) websites religiously (Reserve Bank of India). Read FAQ of RBI Frequently Asked Questions● Go through the current affairs of at least six months before the exam date. (Starting from May 2019 to 25th November 2019 for IBPS-PO 2019). Read AffairsCloud or GKToday daily current Affairs, revise them weekly and monthly basis and suffice them with weekly/Monthly quizzes. You can also make notes of daily current affairs so that you can easily revise them before exam.● Practice Weekly quizzes on PraticeMock application and blog.● For last minutes revisions, refer to 500+ most probable questions of Practicemock (released before the Mains exam)● Use Financial Dictionary | Investopedia for investment/stocks knowledge.● You can also use YouTube Videos for monthly revision of current Affairs.English Language (Letter Writing & Essay): Learn the format of Formal and Informal Letters and practice some letters asked in previously conducted exams. Reading is going to help immensely in writing Essay. Most of the time topics of Essay is from the current Affairs. After reading an editorial, you can make a habit of writing the editorial in your own words. Practice writings some Essays before going to examination. Practice typing on computer keyboard, it will help you in completing Letter/Essay on time with required word limit with minimum typing errors. Watch your grammatical errors while practice writing.Test Series:PracticeMock & Olive board are best. Start writing Mock test from the very first day of your preparation. Learn by Practicing. Don’t miss to analyse test after attempting it. Don’t get disheartened by low marks, find your weak areas and master them with practice. Practice with two different test series. Always remember, a mock a day keeps the failure away.All the very best for your exam.Happy Practicing!

Are solar panels ugly in your opinion?

Hello Ansh,Not at all, many solar installations are aesthetically pleasing, especially the residential and rooftop installations. What’s not to like? The technology is simple, green, good for the world, and provides energy independence for the homeowner. In fact, we can all look forward to a renewable powered society by 2050 or even sooner. Or can we?Do you know the definition of the word meme?[1]an idea, behavior, style, or usage that spreads from person to person within a cultureSolar has become a very ugly meme. This idea that solar and wind will one day provide 100% of the world’s energy needs is, to a large extent, driven by what people believe about solar. Many see the simple green rooftop panels as a solution to all of our problems.This good looking meme has taken on a life of it own and is finding it’s way into the hearts and mids of folks at the state, nation, and world as evident by so many 2050 proclamations. It’s a good idea that pulls on the heartstrings, needs, and desires of us all. The only problem is, it’s wrong.It’s a problem of scale; we mortal creatures are not very good with large numbers. Make no mistake, the amount of energy we require for our modern society is staggering.I’ve spent a lifetime exploring the arts of electronics and I still have a hard time expressing these numbers. You can see some of my attempts at understanding here:Aaron Dahlen's answer to What are the main arguments against solar energy?Aaron Dahlen's answer to Why doesn't the whole world use solar power?Please leave a comment below if you would like to continue the conversation.Regards,APDahlenP.S. Please allow me to further explain my position. Solar is indeed beautiful especially in the hands of a master as seen elsewhere in this post. However, the OP asked for an opinion. While I do like the look of the technology, there is something deeper about solar that I find disturbing.First, climate change appears to be a real thing. Taking action now to prevent further degradation is something I believe we can and should do. On a personal level, I need to know that I did something about it. I need to look back and tell my children I did my best. Part of that is to research, reflect, and write about technology. Writing here on Quora has allowed me to understand the technology and reinforce clearly understand the limitations. Not because Quora is an echo chamber, precisely the opposite as you see by the unpopular stance I have taken.Second, the world is getting better.[2]Energy is a core component to this movement. I’ve made the analogy that we humans are like small leaves on a great tree that has roots firmly planted and nourished on coal, oil, and gas. This is what is keeping us alive today. Yet, it is also making us sick. It will be no simple task to transplant this tree without dropping leaves.My argument against solar and for nuclear can be explained with a simple graphic:Source: 15 Dec to 31 Dec 2017 from TopicsThis is real data. The only change is the addition of the teal box to emphasize the problem area. I ask you, how is solar is going to fill this box?Adding more solar is not the answer. I’ve made those arguments as clear as I can here on Quora[3]but don’t take my word for it. You can read more about it on page 124 in a excellent paper written by MIT:[4]“Even if PV generation becomes competitive at low levels of penetration, a substantial scale-up of PV deployment will reduce the per-kilowatt profitability of installed PV capacity until a system-dependent breakeven point is reached, beyond which further investments in solar PV are no longer profitable.”You can also read about the same problem described slightly differently on page 22 of this report by the NREL:[5]The rapid increase in marginal curtailment rates as a function of PV penetration is a significant limitation for PV to remain competitive with other sources of low-carbon energy once it achieves a certain penetration (in this case perhaps 15%–20% of annual demand). This challenge can be observed by examining the impact of curtailment on the levelized cost of energy (LCOE) of PV. As curtailment increases, and capacity factors decrease, the LCOE increases.Wind is not the solution. There will be times when the wind (on and off shore) is unavailable. That is evident in the German data - the teal box above. Also, as I have mentioned many times here on Quora, the good folks at the NREL show that we are nearly done building profitable wind.[6] Every projection they present shows wind growth as flat past about 2025. Could they be wrong. Sure, it’s a forecast, things can change. I suspect a major change to the wind predictions would not be good for us…The cost of storage on the time scales associated with that German graph is atrocious.[7] Pumped hydro is great if you have the resources. Geothermal and hydro are also wonderful technologies but are not economical or desirable in many location. We could make a good argument that they are already developed as much as they can be.HVDC power lines - no.[8]Ditto superconducting lines.[9]Doing without isn’t an option. Most folks live in the city. Without steady reliable power those places become literal death traps. There is some irony in this statement. With all their faults, our cities are the most economical places to live. This is something we should all encourage. Yet, the possibility of energy independence is challenging. As I write this, I think of my New York neighbors.Finally, I will not stand in judgment of humanity and tell other they will have to do without.What’s left after all of this is nuclear. Nuclear can easily provide the energy to fill the square. The argument of modulating the reactor to match the supply / demand curve is trivial compared to filling the box with solar and wind. There is no comparison, the little daily fluctuations are insignificant when compared to the bulk of the base load box. Nuclear is the low cost emission free solution.This is not a decision I take lightly. Becoming a proponent of nuclear was a long battle especially for a person who spent the early part of life dreaming about solar and off-grid independence. As evidence, you could find a few of my articles published in Home Power magazine. If you look really hard you can find a most unflattering picture of a younger me powering the TV on a pedal power generator…To make a statement about climate change is to look at my children and recognize that the sins of the father are visited upon the them for many generations. Each of us needs to examine this question for the next generation.A lifetime of study has shown me that solar has limitations and will not yield the [math]CO_2[/math] reduction we need for all of the reasons I have outlined. On the other hand nuclear can do the job with less emission, lower cost, and greater stability. It is the lesser of the evils.And now, a personal note:JD,This is something you will need to take care of. Your father did the best he could by weighing the options; all things considered, nuclear appears to be the best way forward. I wish you every success in this world. May your generation do better.Regards,APDahlenFootnotes[1] Definition of MEME[2] Gapminder Tools[3] Aaron Dahlen's answer to What are the main arguments against solar energy?[4] https://energy.mit.edu/wp-content/uploads/2015/05/MITEI-The-Future-of-Solar-Energy.pdf[5] https://www.nrel.gov/docs/fy16osti/65023.pdf[6] https://www.eia.gov/outlooks/aeo/pdf/AEO2018.pdf[7] Levelized Cost of Storage 2017[8] People often mention an electric power supergrid as the solution to the solar and wind intermittency problem. Is this a viable energy solution?[9] Aaron Dahlen's answer to What is the efficiency of a superconducting power transmission line when factoring in the cost of cooling?

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