NEET Study TipsTeam Altis Vortex
For more than two years, an aspirant needs to imbibe a whole lot of topics; be it in Physics, Chemistry or Biology. Some say it’s tough to manage all of them together, some say it is impossible to do so, yet there are some who do it. The difference lies in how you manage your time, and how well you cover these topics sequentially. Doing them sequentially is important because otherwise, what you study won’t stay till the end. Therefore we will talk about some NEEET Study Tips.
An Overview of Preparation by NEET Toppers
A student has more time in class 11th to orient himself, than in class 12th. In our First NEET Study Tips, We would advise students of class 11th to first concentrate on each topic individually. Whilst in 11th, it is important to build your concepts and interests. Any doubts, get them cleared immediately. Often it is that this stage that students tend to develop a fear of chapters like Rotation, Gravitation, etc. And the fear thus developed troubles them throughout their preparations. MAKE SURE YOU DO THESE CHAPTERS PROPERLY IN CLASS 11TH, TO AVOID THE PHYSICS SCARE IN +1 AND +2. You might go wrong during solving the initial questions. But make that a reason to study more and improve yourself. Chapters like Mechanical Properties, EM waves etc. often seem very boring and difficult to retain. So keep studying these again and again, till you memorize them properly.
Even in chemistry, you’ll face similar problems and needs to study topics again and again. In our second NEET Study Tips, For physical Chemistry, you should know all the formulae and their proper application. Often, students aren’t comfortable using some particular formulae. But your aim should be to stay well versed with all of them. Organic chemistry calls for a very systemised approach. Each chapter in organic is linked to its previous one and forms a base for the next topics. The most typical organic questions, those with a series of reactions using one starting reactant and asking about the final product, test how systemised and directional your thinking is. So be it nomenclature and isomerism, or alcohol and phenols; make sure you devote proper time to each of these topics.
Inorganic Chemistry is tough to have a strong grip on. For AIIMS, every figure, bond diagram, and series/order in the NCERT is important. All uses given in the ncert should be learnt by heart. It would seem impossible initially, but if you keep doing it regularly, you’ll gradually learn it. And of course, Qualitative Analysis is a must for the AIIMS MBBS exam.
In our third NEET Study Tips, A similar approach should be adopted for Biology. Each topic, diagram and data should be learnt in a systematic manner, by heart. Yes, it would seem impossible if you look at the size of the syllabus; but as you do it again and again, you’ll realise memorising more than 80-90% of the syllabus is possible.
THE KEY HERE, IS TO UNDERSTAND AND LEARN TOPICS SYSTEMATICALLY; SO THAT EACH PRECEDING TOPIC PREPARES YOU FOR THE NEXT ONE.
Look up HC Verma for any doubt in Physics, OP Tandon in Chemistry and Trueman for Biology. At end of each topic, make sure you rethink all the major points you studied, and solve the end exercises. Often a tendency to solve questions days after doing the topic weakens a student’s grasp on the subject.
On the contrary, a student in class 12th often has to rush through subjects. We personally won’t recommend revising class 11th in the early months of class 12th… At least till August-September, a student in class 12th should aim at completing his +2 syllabus, at least most of it. And it must be done with utmost concentration without worrying about the 11th. After September, in the last months of your preparation, you will need to push forward all subjects together. That’s when you’ll need to balance your time management according to your needs. If one topic is weak and you are sitting down to improve on it, make sure the other subjects still stay in control.
A very common tendency of students is to go after books like Solomons, JD Lee etc. for Chemistry and other similar books for Physics. The mistake that students make here is that to study one specific topic, they actually start reading the whole text. In some cases, it might prove to be useful, but by and large, one should only look up very specific doubts from these books. Unnecessarily going through those texts won’t put your time and energy to their best use.
Class 11th and 12th present many hurdles to students; but if you maintain a constant level of interest and determination throughout, these two years of study could really be smooth sailing for you.
What to Study, When to Study What?
In this article, we shall discuss what to study, what not to study and when to study what? For premedical preparations, the amount of material available to do is much much more than you need to do. So, it is important to know what to spend your precious time in.
Regular studies are very important. Whenever you are taught any chapter in physics, chemistry or biology, you should be well versed with all the concepts and points of that chapter before the next chapter starts. For physics, practice MCQ questions as and when you study the topics. Read the NCERT simultaneously and highlight the important points so that it is easy when you read it the second time. It is also very important to clear whatever doubts you have about any concept or question without delaying it. Remember, writing down formulas will NOT do any good because without practising questions, your concepts will not be clear and you’ll end up being confused.
For chemistry, again, practice questions and read up the NCERTs as you are being taught chapters. It is very important to thoroughly learn the NCERT for Inorganic chemistry. Inorganic chemistry will involve quite a lot of ratification. For organic chemistry, practice as many questions as you can, especially of General Organic Chemistry (since if that is strong, organic will be much easier to understand). You need to remember all the named reactions given in the NCERT. And for the last chapters of organic (chemistry in everyday life, polymers etc.) you will have to resort to ratification.
So, each day, give at least an hour or two to the biology NCERT. Practice questions regularly, and it is equally important to clear your doubts.
In the last two/or three months before the exam, it becomes a priority to practice time-bounded test papers. Do the previous year’s papers of the last 8 years or so, and analyse the mistakes you make in them. Give a lot of tests and keep revising topics you feel you are weak in. Make sure you have the entire biology NCERT at your fingertips.
Do NOT commit the mistake of referring to a lot of books for questions, since that creates chaos. Stick to one or two books, and there is no need to go into a lot of detail. Studying the syllabus of the NCERT and the notes given to you by your institute teachers is enough theory. You will get additional knowledge as you practice questions. Do not waste time reading a lot of detail in inorganic chemistry, or doing high-level books like Solomons for organic. First focus on keeping your basics clear. Books like Solomons should be used only as a referral book, to understand some high-level concepts you might need.
During the Summer Vacations between class 11th and 12th, revise as much of the 11th course as you can, but this should NOT compromise your studies of the ongoing 12th course in any way. After you have finished with the 12th (by December) simultaneously revise the 11th and 12th in December and January while giving plenty of test papers. In February and March, focus your attention entirely on the 12th, for the preparation of the boards. As soon as the boards are over, get on to the 11th. In the last month, revise the entire course according to a plan, and do as many test papers as you can.
SO, keep yourself focused and remember that the quality of study is more important than the quantity.
What Books to Study
One question which comes to every medical aspirant’s mind is what books to study, what books to not study? Which books to use to practice questions? We are here to answer these questions
So, first and foremost…NCERT. If you haven’t heard it enough by now, the NCERT books are your ultimate path to success. Especially the biology NCERTs, they have to be read multiple times until you have every important point at your fingertips. All the diagrams, all the labelling, the description of the diagrams, and even the summary of each chapter are important. Doing previous year’s papers will give you a fair idea of the type of questions that come from them. As you read up the NCERTs, you’ll find certain lines which could come as Assertion Reason questions. Mark them. Other than that, You can practice with “NCERT Biology Gear UP” along with NCERT. YOu have not to need to read any other books except these both books as you will get past year question and crips notes in this book.
For Chemistry, let’s divide it into three sections. For physical chemistry, it is important to practise questions in order to clear your concepts. Other than the NCERT, practice a book with enough MCQs for each chapter. Some books we would recommend are
For Inorganic chemistry, studying the theory, again and again, is more important than doing questions. NCERT is very important for inorganic, all the reactions, reagents, and special properties of compounds should be crystal clear. You can make notes if you want to. Study the notes they give you at your institute.
For organic chemistry, again, you need to practice an ample amount of questions for getting a good grip on it. You should know the concept and reaction mechanism behind every question that comes from practice. Some books with enough questions are Selected Problems Organic Chemistry. NCERT questions are a MUST!! For getting your concepts of general organic chemistry, MS Chauhan is a good book for medical exams.
For Physical chemistry, numerical questions should be practised to get a strong grip. Some books for physical are OP Today or N.Avasthi.
For NEET NCERT based questions are a must. So you can take Chemistry NCERT Gear UP
Lastly for physics, practice is the only thing that can make you perfect it. Pradeep’s, S.L. Arora are some books which have a good question bank. “Concepts of Physics by H.C. Verma” is a very good book to build up concepts in order to tackle higher-level questions. Apart from this, NCERT of course is a must, especially the “points to ponder” given at the end of each chapter. In Physics, you need to do the following things: Read up and solve the NCERT, Solve the institute modules and then do a book with lots of MCQ questions. Then go for books like H.C. Verma if you get enough time. Practice the previous year’s questions and look up the extra topics that have been asked, like Camera and Laser.
For NEET, You can practice with Physics NCERT Gear UP
SO, basically, you need to practice as much as you can, have clear concepts and keep the NCERT (of all subjects) at your fingertips.
Whilst in an exam…
The mentality and methodology of a student determine to a great extent, his performance in the exam. It won’t be unusual for a student’s confidence and interest level to decline steadily, as he moves from question 1 to question 200 (AIIMS q. paper). The major problem this presents is that by the time the student reaches the tough questions of assertion-reasoning, a part of his brain already starts to feel tired. So naturally, the questions requiring clear thinking and logical reasoning start seeming tough to solve.
In physics, this often happens with questions of waves, gravitation, optics and modern physics. Such questions need to be thought over with a very clear and directional mind. In chemistry, the same trouble arises with assertion reason of physical chemistry titrations and organic chemistry. Biology presents relatively straightforward questions, but still, A & R questions of chapters like classical botany, human physiology etc. may need you to link facts.
The best way to tackle this problem is to look at the question paper in an organised manner. Before attempting the question paper, you should know what your weaknesses and strengths are. Your weaknesses will have seemingly tougher questions so it is always better to start off with those parts of the question paper. Generally, a student who is strong at calculations and logical thinking start with physics while a student who is good at recalling things starts with biology.
Physics in an AIIMS exam is often very calculative and tricky. So even a strong student can feel shaken by it. But the point is that solving every question of physics in an AIIMS exam isn’t possible in most cases. You just need to make sure though you’ll feel very tired after the 40 questions of physics MCQ, the assertion reasons must be approached with a fresh mind. If not immediately after the Physics MCQ, you may first complete all objective questions and then do all A & R questions together.
A big proportion of students also prefer to do biology first, so that they remain confident for most of the exam time. This probably is because a major part of biology is from the NCERT. But while adopting this sort of technique, the students should make sure they do not leave out Physics for the last. If you have to start with Biology, do so Then move over to Physics, then to chemistry and finally to the assertion reasons.
There are some points you should keep in mind during the last days of your preparations:
Students often remain tensed about questions in biology from Classical Botany (the Plant Kingdom/ classification of life) and Ecology. The questions from these chapters are primarily from the NCERT. Every table/ diagram of the NCERT must be at each student’s tip because these have the highest chances of being modulated and asked in some of the other forms. But it is always advised to the students to go through major happenings in the field of Ecology. Like the major summits and meetings and conventions and protocols. However, AIIMS primarily focuses on Plant and Human physiology. (Including Class 12th reproduction unit).
While writing the exam it isn’t necessary that you’ll remember all that you’ve read. Often we see questions that relate to something we’ve read before, but still can’t recall the answer. It is very important not to freak out under such circumstances. Just leave it question aside for a short while and move over to the next questions. Later after having solved most of the other questions, come back to that initial problem and think of it with a clear mind. If you’ve read it before, it will definitely stike you.
Also, always attempt GK at the end else it could get scary at times!! GK is mostly prepared at the last. Make sure you do the recent Nobel Prize winners, Important Dates, Important Sorbiquets, Heads of Important Govt. Offices, And the latest in Sports- Winners, Tournaments and trophies.
Whilst in the exam, just remember not to panic, believe in yourself and believe that what you have prepared would be enough to get you through.
What are those 10 ways to save time in NEET exam preparation?
- Time Management is a major aspect one needs to concentrate on while preparing for any exam. Every minute is precious to you and you can gain or lose a lot in just a minute or two. Therefore, utilize your time wisely. This will help diminish the burden, as well as additional pressure, just around the time your exam begins.
- To start with, plan out a timetable. You know your strengths and weakness. Give more time to the areas you linger behind and focus more on them. Don’t bundle it up and keep it aside. You will most likely be unable to finish it at the last minute and may very well need to skip it.
- Test yourself in recording things you can’t recall. Visual aids are always helpful in remembering. Devise easy techniques to remember things.
- Don’t just cram facts. You will be tested on your basic understanding of your studies. So don’t delay to clear questions when you have time.
- Don’t leave anything for the last-minute cramming. That is not exactly the way you approach an exam. This can only lead to failure and dejection.
- Get ready short notes for revision before exams. This will spare time and exertion as you will not have to go through the entire chapter when you are doing revision for the last time.
- Get eliminate distractions. Some people can concentrate solely on a very neat and tidy atmosphere. So set up the environment as you want for better concentration. It also depends on people as to what time of the day, suits them to put their maximum effort. So if you’re a nighttime fledgling, don’t be guilty, if you’re not hovering over your books throughout the day. Practice old sets of paper. Allot timings for each section.
- Try to follow the schedule. This will help you save time in the examination hall.
- Take regular breaks, so as to not pressurize yourself an excessive amount.
Top Dos and Don’ts for NEET Exam
Do’s (A Day before Examination)
- Checking the centre of the examination centre is crucial as it helps avoid last moment rush before the examination.
- Ensure yourself of the correct examination centre just in case the name of your examination centre is common. it would produce issues right at the last moment. therefore be extremely careful.
- Revise vital formulas and short notes.
- Have trust in yourself and keep patience.
- Eat right and balanced meals.
- Work out to remain healthy.
- Sleep well.
Don’ts (A Day before Examination)
- Don’t get nervous while preparing for the examination.
- Don’t lose faith in yourself.
- Don’t attempt anything new.
- Don’t neglect your health.
- Don’t hit the sack late.
- Don’t skip meals to spend more time on preparation for the big day tomorrow.
- Don’t oversleep.
Do’s (During the Examination)
- Read the problems on the question paper rigorously to avoid silly mistakes.
- Fill all of your particulars (such as names, roll no. etc.) within the paper properly.
- Check the queries on the question paper as per the extent of their issue.
- Attempt straightforward queries initially.
- Attempt troublesome questions later followed by the questions you’re unsure of
Don’ts (During the Examination)
- Don’t rush to reading questions.
- Don’t use a pen where a pencil is required.
- Never attempt difficult questions first.
- Don’t attempt any question randomly.
- Don’t rush to write an answer.
- Don’t waste too much time on any one answer.
Tips and Tricks for the AIIMS 2017 Examination Day
- Spend a while analyzing the question paper initial.
- Once you’re done reading the question paper, you want to mark the questions as per the extent of their problem.
- Now answer questions in sequence as per the extent of the problem.
- Obviously, try simple questions 1st followed by tough ones.
- Move to a different question if you’ve got already spent an excessive amount of time on one question.
- Don’t lose your focus while answering a question.
- Attempt questions from Biology 1st as they’re sometimes easier than Physics and chemistry.
- The best time management strategy throughout the examination is to aim at simple questions 1st followed by tough ones. In this manner, you save plenty of your time for yourself.
- Don’t let your energy wither.
- Don’t Panic.
How to make concise notes for revision on the eve of examination?
| Concise notes mean to make our study easier. They assist a student to remember and understand well the basic concepts, facts and figures. Numerous a period when previously earned knowledge is required to be reproduced promptly our memory trench us, rather underperforms under load. Simply put, just as a computer malfunctions when it is a bit too full of data and application programs, an individual’s brain is also clouded when it is replete with facts and figures. Under such circumstances, concise notes might return handy. They drastically cut back the time needed for recapitulating and reviving our cache of knowledge. Why are concise notes important?|
Students tend to feel tense and nervous on the eve of the examination. Anxiety overtakes and it, therefore, happens generally that a student who, in a very relaxed atmosphere, may need to be resolved a problem, couldn’t attain the same at the examination centre, so creating him ineligible for an otherwise deserved grade. it’s so, necessary to be in a very fairly stable and light mood throughout such tests or examinations or maybe interviews.
Concise notes instil confidence since one revises the targeted knowledge in a very short time, with ease and quite comprehensively. Conceptual points are also renovated within a short time and hence application of knowledge is better in the gruelling moments of a test. In today’s state of affairs wherever a test of overall knowledge and skills is mostly considered a lot of important than one of a specialised nature, it’s of utmost priority to retain the complete gamut of knowledge that one has acquired and retaining is indeed what’s provided by point-wise-notes. Intelligent students are determined to finish the revision of a complete course at intervals of a span of 3 to 5 hours. simply looking for about 3 minutes at a well tagged schematic diagram will assist you to revise a detail of about 2 pages Experienced teachers have revealed that a well ready note of about 2 pages is also enough to form a decent recollection of a complete chapter of eighteen pages. Thus we can find out easily what a marvel such notes can be! Various types of concise notes: Concise notes might be as bulleted sentences or numbered records. They may at times be in the form of schematic or labelled diagrams. Some students prefer notes in contrasting colours or highlights for vividity. Concise notes whose contents are imagined to be records or data for remembrance are in tabular forms. Typically a concise note is compiled in such the simplest way that every component of the note provides a clue to the next part. A concise note might also be in the style of symbols, somewhat like a shorthand, that act as memory aids. How to make such notes: First attempt to perceive the subject in detail. Make an understanding of your own. Analyze the articles constituting the topic from numerous angles of reasoning. Now create the notes by putting the points in your own words. Pay attention to avoid (a) missing any details and (b) repeating any point. The initial try ought to be thought of as a blueprint, then attempt to make it a lot crisp and proper in sequential steps of improvisation. Writing in your own handwriting is often a better option since it’s more possible to reside in memory for a longer period of time. Give enough gaps among different concepts, facts and figures. After completion, try recapitulating the whole chapter by reading the points. If it’s possible, the note is also considered a good one. If possible get it checked with an expert. More important and difficult areas should be highlighted. Notes may be aided with diagrams where ever necessary. Drawbacks of concise notes: Sometimes one tends to consult many books while making such notes which is not advisable. Maybe a couple of decent reference books along with the main textbook are quite sufficient for preparing effective notes.
A few students obtain such notes from other students or market and concentrate just these before the examination. This is a major drawback. Insufficient reading of the chapters and inadequate acquisition of concepts may play havoc with the overall ability of the student.
If the notes carry mistakes these mistakes may be sustained for the whole span of the course and the wrong concepts may cause a wrong understanding of the related material also. Hence a cross-check is always recommended.
Confidence is reasonable however one ought not to overflow out with confidence. Concise notes, it must be remembered, are only helping aids but one must practice enough numerical problems, reasoning tests etc. to gain good marks
Preparation One month before the exam…..
ONE MONTH before the exam can be divided into 4 weeks. What all you have to follow during each week is given below under each sub-heading
1ST WEEK –
- Revise all chapters rapidly
- Try to read up on all the small points that you have added on the sides of your textbooks
- Check assertion and reasons from NCERT very well
- Use keywords “because”, “since”, “thereby”, etc. to find A&R from PDF files of NCERT textbooks
- Try to make a note of all important points which are difficult to remember in one go
- Try to cover the notes that you have prepared in your class time course
- Do question papers daily
- Retrospective study of questions that you solve
- Write down weak potions you face while solving questions on papers
- Write down all mistakes you make while solving question papers
- Won’t give importance to time management during solving questions this week
- Read up weak portions you face while doing questions
- Try to read up all the short notes that you have prepared during the course
- Read up all the portions that you have marked in yellow, green and red markers in your textbooks which are important, very important and ultra-important portions respectively
- Do more questions from weak portions after revising it properly
- Do question papers with time management in mind
- Read up portions that you made mistakes early while doing in 2nd week
- Read up all short notes that you have prepared
- Read the points that you have marked in red and green in your textbooks which are ultra-important and important portions respectively
- Go through all chapters once rapidly
- Give more significance to weak portions and those portions in which you made mistakes
- Attempt to solve whole question papers 30 minutes before the actual time of paper
- Utilize the short notes that you arranged during your whole course
- read up the ultra-critical portions in the textbooks that you have set apart in the red sketch
Preparation On the eve of the exam…..
How to study?
Devise your own method of studying
Do not read reference books as it may lead to information overload
Try to avoid learning lying on the bed, you should use a chair and study table for it
Try to make good use of short notes that you have prepared
What to study?
- Go through all mistakes that you have committed while you were doing your test series
- Have a glance through the ultra-short notes that you have prepared
- Avoid studying big reference textbooks
- Do not try to study fresh topics on the eve of the exam
- Go through all the pictures and figures in NCERT
- Try to have a look into the tough biological terms and their explanations
- Read the topics marked RED in your NCERT which are ultra-important
- Physical chemistry – go through equations and formulae of all chapters
- Inorganic chemistry- go through the chemical equations and chemical formulae of important reagents and products of the chemical reactions
- Organic chemistry- Go through the organic reactions and the mechanisms of important ones
- Go through the equations, formulae and graphs of all chapters
- Do some numerical to get a flow to do questions during exams easily
Quality not quantity
It’s the quality of study that counts. You may spend hours at your books, but if your mind is not in them, it’s no point
One hour of good study is better than a whole night of mind-wandering
Reconfirm exam details
Make a quick call to a close friend to confirm the timing and centre of the paper. However, you don’t transform the call into a chatting session.
Take a break
Regular breaks between study sessions are a must. Do relaxation exercises like deep breathing
Take a walk in the garden or watch some news on television — but only for a while!
No exam talks at dinner-time!
As far as possible, eat with your family on the eve of the exam. Parents can enjoy their kids by cooking something unique. Avoid all talks of exams at the dinner table.
What to eat
Try not to stuff yourself with food or snack during your studies. This will just make you languid. Maintain a strategic distance from zesty and salty sustenance. Have lots of green leafy vegetables, fruits, salads and pulses.
Small meals prior to the exam will make you more alert during the exam.
Get some shut-eye
Try not to stay up the entire night in the expectations this would enable you to remember more. Those who sacrifice sleep end up feeling sluggish the next morning. Also, lapses in memory may occur due to an overtired mind.
Make a list
To avoid any last-minute hassles. Pack your bag on the eve of your examination day. Make sure you have the following:
- Hall ticket!!!!!!
- Board pad.
- Carry at least three pens. Not brand new ones, but those that have been tried and tested by you. You should have a flow while using those pens. Make sure the ink levels are full.
- A set of sharpened pencils.
- Carry a bottle of water or juice in a bottle to keep you hydrated during the exam.
- Note: Ensure there are no chits, old bills or receipts in your pen pack.
Preparation During examination!!!!!!
- Be calm, confident and cool
- Pray well before the exam begins and trust that you have done the maximum preparation you can
- Believe in yourself and your hard work
- Make sure you are very careful while bubbling the OMR sheet
- Even if you make a small mistake in the OMR sheet, try not to get tensed and ignore it even if the invigilator shouts at you for that. Understand that no OMR sheet goes unchecked even if you make any mistake in filling your details in it. NEVER GET TENSED BECAUSE OF THAT!!!!
- Start answering from the most comfortable portion you are with
- In the worst scenario, if you are not able to answer the first 5 questions you attempted from the easiest portion, then try to switch the subject and start doing that part without feeling anxious or tensed.Switching the portion will help you build up some confidence in yourself while answering.
- Mark/ encircle keywords in the question paper
- Read the question carefully and make sure you understand the question well
- The words like EXCEPT, NOT CORRECT, etc. need more alertness
- While attempting Picture based questions, try to see for which labelled part the question is meant.
- Read all the options clearly and see that other options can be eliminated before confirming an answer
- Note the options like “ALL THE ABOVE”, “BOTH A & B”, “NONE OF THESE”, etc. to avoid wrong markings
- Leave the numerical with complex calculations for doing last
- Do simple questions with simple calculations fast so as to save time doing the difficult level questions
- If the values in options match closely, then try to do the questions last as it needs perfect arithmetic calculations without any kind of approximations in values
- Whenever possible, do an approximation of values and make the arithmetic calculations easy and fast but make sure you don’t approximate it so much!!!
- All questions will be asked exclusively from NCERT textbooks
- Do those questions fast and save time for difficult questions involving more arithmetic calculations
- All questions are fact-based, so if you don’t know a particular question, never go for wild guessing
- Most questions are directly from NCERT
- Make sure whether they are asking about the intermediate product or the main product of the reaction
- Try to make a note of the temperature and catalyst involved while solving a chemical equation
- Mark key points in the question paper
- See whether the option values are close or not
- Do the rough work in the space provided. Try not to encroach into the questions section to avoid confusion. Do the rough works legibly but in small form so that you won’t use much space and also you can go back to the same calculations later if you feel any confusion
- Make sure you don’t make any arithmetic carelessness
- Check units while marking the answers
- Try to eliminate other options while marking the answers
- Try to use the trick of “DIMENSIONAL ANALYSIS” in very tough questions to get the answers. This concept works in many of those high-level questions
- If the values in options match closely, then try to do the questions last as it needs perfect arithmetic calculations without any kind of approximations in values