Read these books to excel in maths

Knowing how to do maths is an important skill that can help you excel in many different areas of life. 


To succeed, you’ll need to make time for reading, practice your skill on a consistent basis, and take advantage of all the resources available to you. Here are three of the best books for math learners.


This book is designed for people who want an introduction to the beauty of mathematics and how it connects with other fields like accounting, finance, physics, engineering and economics. 


It’s not designed as a lecture on proofs or details about how mathematicians solve problems; instead it focuses on what makes math interesting and fun.


Macl Edge has some more information about reading books to excel in maths.


Here are some books names discussed to read in maths-

1. The Loss of Certainty – From Pythagoras to Gödel by William Thurston


He describes the history of mathematics, how it has evolved and is progressing, and discusses philosophical questions such as the nature of proofs and the relationship between mathematics and science.


2. A Mathematician’s Lament by John Allen Paulos


He is a professor at Temple University and his book is a must read for those who want to go beyond just studying math. He also talks about the loss of rigor and unscientific elements in math education.


3. The Magic of Reality by Richard Feynman


Feynman is one of the most renowned scientists of all times; he developed the theory of quantum electrodynamics (QED), was part of the Manhattan Project, won the Nobel Prize for Physics, and was a brilliant teacher. 


His interest in philosophy led him to write on many interesting subjects, including ghosts and reality. 


This book on Feynman is written with great humor; it’s not meant to be taken completely seriously or read out loud, but it’s an enjoyable way to learn more about the man who discovered QED.


4. An Introduction by Carl B. Boyer and Uta C. Merzbach


This book is a general history of mathematics and it has been used as a textbook in schools for years. 


It covers the development of math from prehistory to the 20th century and is very reliable for anyone who wants to read up on the subject.


Mathematics: The loss of certainty is an excellent book, but it’s not meant for people who want to learn math or need to quickly refresh their memory about various topics; it’s more suited for students who want to become a master mathematician or a tutor, or just someone who wants a better understanding of how math works.


5. Real World Math by George W. Hart


Hart is a professor of mathematics at Harvey Mudd College in Claremont, California. He has created art installations, poems, and soap operas that are only mathematical in nature to make the subject more fun for students. 


The book includes math puzzles and problems to make learning more interesting.


6. A Bigger Reason to Read Mathematics by I.J. Good


This is a hard-to-find book but it’s very similar to A Mathematician’s Lament because it talks about the same subjects in the same ways, with the same sense of humor. 


It’s not much different from A Mathematician’s Lament because Good also talks about the history of mathematics and its connection with other fields, but if you’re interested in mathematics, this is still a good read.


7. The Book of Proofs by Steven Hales


This is one of the easiest books to read about proofs because it explains how mathematicians have found them throughout history and describes their importance to mathematicians. 


It’s a good introductory book to the topic, but it won’t help you quickly refresh your memory about a specific proof.


8. The Little Book of Mathematics by Martin Gardner


In this book, Gardner discusses mathematical wonders from infinity to giant prime numbers and the latest ideas in the field. 


He also talks about how math has been used in literature, religion and philosophy. 


If you want a book that will help you discover the most interesting aspects of mathematics, this is a good option because it spans different topics and centuries of development.


It also looks at math from different viewpoints that aren’t always focused on proofs or techniques.


9. Mathematician’s Mind by William Thurston


He talks about how mathematicians think and what they consider when they’re developing a proof. 


He also explains the relationship between math and science, and includes philosophical elements in his explanations of proofs. 


He was a member of the American National Academy of Sciences and he won many awards for his work.


10. A Very Short Introduction by Peter Bylund, Deborah J. Gordon


This book is an easy way to start learning about math from everyday life examples, even if you don’t have much background in the field or aren’t sure you want to pursue it as a career option.



How to Study for Class 11th Maths


Contrary to what most students expect of their life after a busy 10th standard, 11th is not a year one can afford to take lightly. It lays the foundation of the ever-important 12th standard exam and covers essential concepts which are then further built upon in future years. It is thus imperative that students pay full attention to the subject and try and score as high as possible. Although most friends around you might tell you that 11th standard scores don’t count for much and it’s enough that you just pass, scoring well should still be a priority. This will not only make you study hard but also build up a strong core that will be helpful in the future.


Before you begin your preparation, go through the syllabus once and create a rough timeline for you to follow. Ask your teachers about the sequence in which they plan to teach the chapters and you can start briefly reading about them before the lecture. Make a detailed chart which consists of everything from the date of your examination to all festive holidays, and pen down how you plan on covering up the syllabus. While you’re at it, make sure to leave some time out for yourself, for light and casual workouts and also for some revision sessions.

Get your basics right

One can’t hope to score good marks and get a good grasp of the concepts with a questionable hold over previously taught concepts. like the student will realise moments after attending the first lecture, the 10 standard concepts are still very much a part of the curriculum and you cannot do away with them. Thus, if one doesn’t feel confident about them, there is no shame in going back after a few steps, picking up an old book and revising a few chapters. This might feel like a waste of time initially but will account for much more in the longer run.

Make your own notes as you learn

While textbooks and other reference materials are amazing sources to study from, it doesn’t hurt to not down the set of formulas and important points, simultaneously as you learn them. In the process of making these notes, not only are you writing the formulas by yourself but also subconsciously memorizing them. Your personalized notes will always help you to quickly brush up on a few topics whenever you need to come back to them. You can also note down interesting observations and even write your own derived formulas, for a certain type of problem that occurs too often.


The rule of thumb when preparing for the 11th standard math exam, or any other math exam in general is to solve as many problems as you can. Many students commit the mistake of simply reading a few problems from reference books without ever trying to solve them themselves. This approach will trick you into believing that you’ve actually studied a particular problem when the reality is you are not ready to solve it in the actual paper. Multiple websites and coaching institutes provide daily practice problems for students to get a hold of every chapter one at a time.

Identify your strengths and weaknesses

Solving multiple problems every day will give you a good enough idea of the topics that you are comfortable with and the areas you need to further work upon. Once you’ve done this analysis and successfully identified the chapters and type of problems that you are not too good at solving, you can try implementing a different approach, revising the topic, studying them again or asking your teacher for help. Target one weakness at a time and do not move further down the list unless you turn it into a strength.

Time management

The math paper is known to test students not only on their ability to solve questions by applying formulas but also on if they are successfully able to allot appropriate time for each question and finish the paper within the given time. The students must be fully prepared with a plan to solve each section of the paper in a specific amount of time. The students must practise performing calculations quickly and also solve a problem using the shortest path possible. Care must be taken that time is not being wasted in solving optional sums, before the paper is completed.

Extra Study Material

Once you are done studying the textbook and feel the need for more problems to solve, you can refer to external sources, multiple of which are available. These study materials also come bundled with solution sets, to enable you to check your answers. The 11th Class RD Sharma Solutions would make a good example of one such book.

Revision is key

Even though you are confident about a particular chapter and don’t feel the need to go through it again, a brief revision session is always recommended just to make sure you don’t miss out on scoring marks in your strong areas, owing to the lack of revision.


While most students start the paper with clean and neat handwriting, as pages get filled, it becomes more and more shabby and unpresentable. This is completely natural and also unavoidable at times, however, it is always advised to at least make sure that everything written is legible and there is no ambiguity regarding the content matter. Underlining the final answer and starting a new question on a different page are a few things that one can do to help maintain the answer sheet pleasing to the eye. That being said, time must not be wasted in making the paper look cleaner than necessary.

Keep calm and perform

No matter how much you’ve prepared, if you are unable to keep calm during the day of the examination and succumb to the pressure, you will end up not scoring up to your expectations or potential. To avoid this one must meditate daily and also practice giving mock tests in an atmosphere as close to the real exam as possible.

Keeping all these points in mind, you are now ready to start preparing for your maths paper. Since everybody has their own set of preferences and restrictions, you need not follow every advice to the T and rather take this as a reference, make modifications and find out what works best for you!


How to prepare chemistry for JEE

How to Prepare for JEE Main in the Last One Month A serious applicant immaculately must have completed the syllabus by now. The following points would still count. Time Operation proper planning is most important for timely medication and dealing with the study pressure. By now serious scholars must have established their medication or been informed about the same by their preceptors. So, this is the time to consolidate your medication and ensure that you do extremely well in the factual JE (Main) test. All the three subjects are drugs, Chemistry & Mathematics are inversely important. So, divide these Pharoah remaining weeks aptly into the three subjects. 

Prepare a chapter-wise topic-wise modification schedule. Produce short notes and all formulas & points to remember. This will help in quick modification before the examination Correct Methodology The correct approach for those appearing for the first time or alternative time is to stick to one source and not to the multitude of books/ study material. To reap the benefits, the scholars should remain focused throughout the medication period with a positive station to study with the utmost attention. In the last two weeks, it’s only brushed up through & notes flagged important problems with twists. Taking a mock test on the factual pattern is recommended at this time. Focus on your Thing The key to the right medication is proper and timely planning. Cappers learn from their weak areas and exercise well in time to get better by all possible means. Correct station and acute focus are the keys to being a crusher. Cappers divide their medication time consequently. They stick to a single system of medication and have faith in themselves. Therefore, they traditionally make up their confidence position and are geared up to crack any delicate question. They ensure working all former times isn’t papers keeping their generalities clear.

Study Material & Important Midfs One must not start any new books at this stage. Still, one can still relate to standard books for conception clearing. This stage should be employed further for problem working, developing shortcuts, and learning formulas, understanding one’s strengths & sons. Applicants must take up Mock Tests in CBT (Computer Based Test) mode to develop bones, confidence & test disorder. Time Management is important to score further marks in the factual JE (Main).Important Mosques in Physics, Chemistry, & Mathematics

.Mathematics Quadratic Equations & Expressions, Complex Figures, probability, Vectors, Matrice; in AlgebraCircle, Parabola, Hyperbola in Coordination Figure; FigureFundamentals, Limits, Durability and Differentiability, Operation of Destination, Definitely in Math.

Expert tip_ Try to do as important as quality problems as possible to develop a sound confidence position. Drugs, Solemnity, Fluids, Heat & Thermodynamics, Swells & Physics & Electronics, Electronics, Electronics Electronics, Electronicist, Electronicist, Opagnetics, Electronicist, Oprix In production, Opagnetics, Opagnetics, Opagnetics, Optix In production, Oprix In production, Opagnetics, Opagnetics, Opagnetics, Opagnetics, Opagnetics, Opagnetics & Physics  Physics  Physics  Physics  Physics  Physics  Physics  Physics  Physics  Electronics, Electronic, Electronics, Electronic, Electronic  Physics  Physics  Physics  Physics  Electronic, Electronicist, Electronicist, Electronic  Electronics, Electronics, Electronicist, Electronicist, Electronicist, Electronic  Physics  Electronics, Electronics, Electronic  Physics  Physics  Electronics, Electronicist, Electronics, Electronicist, Electronicist, Opagneticist, Electronicist, Magnetic  Physics  PhysicsTip ▁Expert Hearing quality problems is the key to success in this subject. However, also this subject becomes more intriguing, If the generalities are clear. Chemistry, Electrochemistry, Chemical & Ionic Equilibrium, Mole Concepts in Physical Chemistry and Organic Chemistry.

The expert tip will be to Just go through the Periodic Table in general. For the Organic part, first makeup all your introductory generalities and also start doing lots of practice. And for the Physical part, the practice has as many numerical as you can. Recommended Schools are advised to avoid picky studying Physics, Chemistry, and Mathematics. Generally, all motifs are covered as mentioned in the syllabus .https://www.Nedentu.Commit-/je /jee-main-chemistry-important-questions.JEE Main Chemistry Important Questions with Solutions. Still, the following points should be kept in my mind

  1. Remain focused and maintain a positive station while studying.

   2. Developing speed by working quizzes


How to crack the physics section in neet

It is critical to achieve a high NEET All India Rank by performing well in the physics area of the NEET 2022 exam paper. According to last year’s study, a decent score in NEET 2022 Biology and Chemistry would not be sufficient for admission to elite medical colleges. Candidates must understand how to study Physics for NEET 2022 in order to pass with a 600+ mark.

The Physics part has questions ranging in difficulty from low to moderate, based on last year’s NEET difficulty level. The NEET-UG Physics subject includes questions ranging from simple formula applies to complex computations. As a result, while studying Physics for NEET 2022, gaining conceptual clarity is essential. To restart your NEET preparation, read the well-detailed article below to learn how to study Physics for NEET 2022 and to get some valuable tips.

How to study Physics for NEET 2022 is a prevalent issue among NEET aspirants. As a first step in studying physics for the NEET UG 2022 exam, candidates should dispel the myth that physics preparation is tough. 

Let’s have a look at some of the ways through which the Physics section for NEET 2022 can be covered efficiently.

  • Concepts should be grasped rather than muddled. You will be ready for the next phase if you have a firm understanding of each idea. Understand the subject to the point that you can envision it. 
  • Students should thoroughly study the NEET Physics Important Questions with Solutions 
  • You have 180 minutes to answer 180 questions, but not necessarily 1 minute per question due to the varying difficulty levels of each topic. It has been discovered that practically all questions are pulled from the NCERT books based on prior years’ examinations. They are the top books for studying for the NEET. However, you can solve certain higher-level questions using a few additional common books. This will increase your self-assurance. You’ll also get a good notion of how prepared you are, and you’ll be able to revise accordingly. Remember that NEET Physics Preparation necessitates constant revision. 
  • Well, we all are well aware of one fact, that is, The backbones are formulas – Learning formulas is one of the finest ways to gain an advantage in physics when faced with a variety of mathematical and numerical difficulties. With limited time, keep a short handwritten note of formulas and revise them on a daily basis.
  • Practice questions with a clear concept — Because the NEET 2022 exam may not always follow a predictable pattern, it’s critical to answer as many questions as possible while maintaining concept clarity. Also, rather than answering too many questions for NEET 2022 Exam, concentrate on clarifying the principles.
  • It has been widely observed that The majority of NEET aspirants have made it a habit to learn everything. This strategy will probably work for NEET Biology, but definitely not for NEET Physics. When you attempt to study Physics not just for NEET, but for any competitive exam without including a practical component into your study schedule, you may believe that you have grasped all of the concepts, but you will be unable to apply them during your examinations and hence won’t be able to solve the questions in the NEET exam.
  • Physics for NEET 2022, With only a few months remaining to prepare for the many themes under the Physics section, candidates must expedite their studies for all subjects. Compared to Biology and Chemistry, Physics is more numerical and mathematical in nature, thus students must devote sufficient time to prepare. There are a few things you may do to prepare for the Physics component of the exam effectively.
  • Because physics is a conceptual subject, you will need to ensure that your understanding of the many topics in the subject is clear in order to pass the examination with flying colours. To get a decent grade on the exam, you need to understand the concepts of the topics in Physics. While NCERT can help you comprehend all of your ideas, going to one of the other reference books can help you understand them better.
  • Theoretical questions in Physics will be one of the free-marks options, as the questions will all be based on distinct concepts and theories. Securing a decent mark in physics will be a cakewalk for any applicants with clear notions.
  • As previously said, utilising various reference books and sources will aid in the removal of doubts and the clarification of concepts. However, if you use too many books at once, the opposite can happen. It is preferable to understand the principles through one book initially and then use a couple more books to supplement your knowledge of the subject if you become confused.
  • In the reference, underline the most important points. When you finish your reading and begin rewriting, it is simple to scan over the points. Use doodles to retain complicated concepts and colours to organise your notes to be more creative when taking notes.
  • When you’ve finished a topic for NEET 2022, read over all of the solved examples to make sure you understand the solution. If there are any other answers to difficulties, try to comprehend them. As many issues as feasible should be practised. To comprehend a situation, you must envision it and connect it to the applicable topic you’ve already learned. It is much easier to solve sample questions accurately in less time if you have practised solving them in each topic. Also, examine the exam pattern so that you can solve issues in a logical manner.


Add advanced methods to your preparation plan to help you succeed even more. You should never use a calculator to speed up your problem-solving process. Create your own superior problem-solving strategies. Don’t get stuck answering a question for an extended period of time; instead, return after completing problems of lesser difficulty. Keep a firm understanding of which formula to use in which case. The Physics section of NEET can be faced and solved properly by following the tips given above.


Calculating the Square Root of 4, its Value and Method

The symbol for square root is ‘√ and the square root of 4 is denoted by ‘√4. Not all the numbers are a perfect square. However, the number 4 is a perfect square. This makes it easy to find the square root of 4 like for other numbers that are a perfect square. The numbers that are not a perfect square have to be calculated by a complex division method to get their root value.

What is the Square Root of 4? The square root of 4 is 2. This square root could be a positive or a negative number. So basically there are always two roots of the same number. So if you consider the number 4 then the square root of 4 is /- 2. This means that the square root of 4 could be 2 or -2.

The square root in simple terms is the answer that you get when a number is multiplied by itself. Like for example, when you find the square root of 4 then ( 2)*( 2) =4 or (-2)*(-2) = 4. So you see both are the square roots of the number 4.

Let us quickly glance at some of the square roots.

  • 16 = 4 x 4 = 42
  • 36 = 6 x 6 = 62
  • 49 = 7 x 7 = 72
  • 64 = 8 x 8 = 82

This article widely explains the square root of 4. First, let us begin with some basics that relate to a square root.

Perfect square- What does it mean?

A perfect square is a number whose square root is a whole number. To understand whether or not a number is a perfect square, follow this simple rule.

  • If the number ends with either 2,3,7 and 8 in its unit place then it cannot be a perfect square.
  • If the number has 1,4,5,6 or 9 in its unit place then the number is a perfect square. However, the vice versa or this is not possible. Like you have 25 as a perfect square but 45 is not a perfect square.

The square root of 4

In maths, it is not difficult to square a number. But to find the square root of any number is however complicated. You will have to figure out what the original number was which was squared to get the answer.

So 5 and -5 are the square roots of 25. If the numbers are non-negative real numbers it will have a non-negative square root. This is called the principal square root and is written as √a. √ is a symbol that is used to represent square rot. So the √25 = 5 because 5*5 =25. The number that is written under the radical symbol is the radicand. Here the number 25 is a radicand.

The numbers 2 and -2 are the square roots of the number 4 and this is because the 2 squares are 4. If the number is a non-negative real number then it will have no negative square root.

The square root of 40

40 is formed when you multiply 4 and 10. The square root of 4 is equal to 2 but how do you go about finding the square root of 10. 10 is not a perfect square and thus the square root of 10 has to be found using the long method of square root division.

Value of the square root 40 = √40 = √4 x √10 = 2 √10

Now, √10 = 3.162 , Using the long division method

Hence, √40 = 2 x 3.162 = 6.324

The square root of 400

If you need to find the square root of 400 then 

4 x 100 = 400

Both 4, as well as 100, are the perfect squares. This makes it easy to find the root value of 400. √400 = √4 x √100 = 2 x 10 = 20

Hence the square root of 400 is 20.

Square Root of 4000

4000 can be written as 400*10. We know the square root of the number 400 is 20. Now the square root of 10 can be found with the long division method.

Thus the square root of 4000 = 20*3.162 = 63.24

Square root from the numbers 1 to 50

Below we list the square roots of the number 1 to the number 50.

NumberSquare Root Value

Understanding how to find the square root through the division method is important to carry out several calculations in mathematics. The table above can be an easy reference point when you need to find the square root of a number between 1 to 50.

Solved examples

What is the square root of the number 4?

The number 4 has a perfect root which is 2. The square root however can be a positive or a negative number. This means that every number will have a positive as well as a negative square root. The square root of 4 can be 2 or it could be -2.

How to find the square root of 40000?

To find the square root of a number try to break it down into its multiples.

So you can write the number 40000 = 400*100

Now you know that 400 = 4*100

Thus 40000 = 4*100*100

Let us now write down the square roots of these numbers.

‘√ 40000 = ‘√4*‘√100*‘√100 = 2*10*10 = 200

Thus you see how breaking down a number makes it easy to find its square root.

Why learn the square root

The square root is an important topic and a very simple practical example of the square root is to compute the area. So if you hear that the room is 400 sq feet then it is a 20 by 20 feet room. Square roots also let us understand what irrational numbers are.

Have you ever seen an advertisement in the newspaper which states that the house for rent is of say 625 square feet or the hotel for sale is 10000 square feet? Well, this is a direct application of square roots. So you know that the house is 25 by 25 feet and the hotel on sale is 100 by 100 feet.

You use square roots to find the pendulums peril. You use square roots in the Pythagoras theorem. It is used to find out the length of the shadow of the pole.

Thus it is clear why the study of square roots is important. Practice makes one perfect so make sure to solve a number of questions on square roots to get a good grasp of this topic which will be used throughout your study of maths.


The square root is an important topic in mathematics that will be used not just in your class examination but also in your competitive examinations. If you decide to study maths in college and take up this subject for higher studies even then you will see a lot of applications of square root. Thus it is important to get the basics right and understand the methods of calculating square root which will make it easy to tackle questions related to this topic.


What is the difference between a Concave and Convex Lense?

The lens enables us to look at things around us and differentiate between different objects. Our eyes have a crystalline biconvex lens. Lenses are transparent. Convex and Concave are two types of lenses that vary in shape as well as in properties. Lenses are based on the principle of refraction.

When the ray of light hits on the surface of the lens, it then bends the rays passing through the principal axis. This leads to convergence or may lead to divergence in the path of light. Convergence of light means concentration of light at one place; divergence means the scattering of the light ray.

These optical lenses mainly differ in terms of light refraction. When a light ray hits a concave lens, it diverges it, whereas a convex lens converges the rays of light passing through. The shape of the lens leads to distinct applications and different properties.

Here is how you can differentiate between concave lens and convex lens.

Differentiating between a convex and concave lens

Convex and concave lenses can be differentiated on the below criteria:

  • Optical Surface

The optical surface is the look and feel of the lens, which leads to the refraction of light. Convex lenses are thick at the centre of the lens and thinner at the edges. On the contrary, a concave lens is thinner in the middle and thicker on the edges, giving it an inward curve and bulging ends. The concave lens has only one curved surface, whereas the surface is curved inwards. In a convex lens, both sides of the lens bulge outwards. The optical surface is responsible for the convergence or divergence of convex and concave lenses.

  • The behaviour of the lens

Concave lens diverges the path of light, whereas convex lens converges the light. Since the light ray is scattered to multiple paths, the path is traversed behind the lens to find the focal point of a particular lens. Since the light ray is converged to a single path, the singular point where the rays are bent is called the focal point. Thus, in convex lenses, the focal point is on the other side of the place where the rays are falling.

  • Type of Image formed

Since the behaviour of the lens determines the type of light refraction, the image formation is different too. Since the focal point of a concave lens is on the same side of the lens from where the light rays are falling, the image formed is always virtual and erect the projected image of the object looks smaller and situated at a great distance. Whereas the focal point of a convex lens is on the opposite side of the lens from where the rays are falling, this leads to real and inverted images. In most cases, the projected image of the object appears to be closer and larger in appearance.

  • The polarity of focal length

A positive focal length indicates that the system is converging light, i.e., the convex lens has a positive focal point. Since Convex lenses have a real focal point, it is positive. In contrast, concave lenses have virtual focus since the focal point is on the other side. Hence the focal length is negative in the concave lenses. The power of the lens is the reciprocal of the focal point. Therefore the power of vision is also associated with polarity.

  • Vision correction in Concave And Convex lens

Lenses are mainly used for the correction of various issues related to sight and vision. Since the concave lenses diverge in nature, they are used to cure myopia. Myopia or nearsightedness is a common visual impairment condition in which a person can see objects nearer to them. Still, the objects that are farther away are not very well visible. This condition occurs to a person when a person’s shape of the eye is oblong, which causes the light rays to refract incorrectly, which leads to focusing of images in the front of the person’s retina instead of on their retina. A concave lens can easily rectify this problem.

The convex lenses help in correcting hypermetropia conditions. Hypermetropia, also known as long-sightedness or hyperopia, is a vision condition where the distant objects can be seen clearly, but the nearer objects appear to be blurred. The blurred effect is caused due to the incoming ray of light focusing behind the retina, instead of on it, due to an insufficient accommodation caused by the lenses. This is when the eyeball is not oblong enough, so the image isn’t made on the retina. 

Due to magnifying abilities that Convex lenses hold, they cure farsightedness. On the contrary, the nature of the concave lens makes the body of a nearer object. It appears to be distant and is rather smaller than the actual object itself.

Different uses of the concave and convex lens

Concave lenses are used for diverging incident rays. This helps in creating a virtual image on the other side of a refracting surface. Therefore, the lenses used in telescopes, binoculars, flashlights, cameras, and eyeglasses. Our eyes have concave lenses too. Convex lens, due to its magnifying nature, is used for telescopes, microscopes, and peepholes.

Different types of Convex and Concave lens

Different types of convex lenses are:

  • Concave-convex
  • Biconvex lens
  • Plano-convex

Different types of concave lenses are:

  • Concave-convex
  • Biconcave
  • Concavo-Plano


Thus, the above discussion concludes that concave and convex lenses have different physical configurations and form different images when the rays of light are incident on it. Therefore, they have different applications. The Concave and Convex lenses are mostly used to produce clear and sharper images according to the requirement. Both are used in different experiments, and most of the eye lenses are combinations of concave and convex lenses. These lenses have led to many innovations of new devices and helped a lot of visually impaired people with proper vision. Both convex and concave lenses make various types of images, both real and virtual. These two lenses have a wide variety of applications in the real world.


How to Prepare for Class 8 Math Olympiad

An Olympiad is a competition in which students take part at the age of 13 in mathematics, natural sciences, and/or literature. These are directed at public and worldwide levels. The Olympiad tests are conducted at the school level for all classes from 1 to 10. The intention behind the Olympiads is to evaluate understudies’ abilities and make them ace ideas that are educated in school. Understudies can choose subjects according to their decision. It is probably the best test to distinguish shortcomings and work upon them. 

Preparing for the class 8 math Olympiad is a daunting task for many students. To give yourself the best chances of success at this competition, it’s important to do as much as you can to prepare. Some key factors include ample practice, choosing effective methods of studying and reviewing, and managing your time. In this article, let’s check out some tips on how to overcome these difficulties and prepare for the competition. Keep in mind that these tips are not meant to be followed “lock-step” but rather to be used as general guidelines.

1. Keeping A Practice Journal

As a student prepares for a mathematics Olympiad competition, a useful technique is to keep a practice journal. A practice journal is a notebook or document where you can write down solutions, explanations, and problems you have worked on. By writing down how you solved problems, and especially by writing down why you solved them in a particular way, it will be much easier to solve similar problems in the future.

2. First Try To Solve Answers On Your Own

One effective method for working through an Olympiad problem set is to first try to solve it on your own. After you do this, look at the answers and see what methods were used and what answers were obtained. You can then apply these methods to other similar problems. For example, if you have a question about the derivative of the function f(x) = x^4 + x^3 – 4x^2 + 2, as a function of 1/x, as shown in the figure below, you can first solve this problem yourself by finding x from the left side of the equation and solving for y from there.

3. Participate In Month To Month Olympiads:

Month-to-month Olympiads are probably the most ideal way of rehearsing for yearly Olympiad tests. Indian Talent Olympiad directs month-to-month Olympiads that are like false tests or demo tests that are conducted each month for Science, Maths, English, GK, Drawing, and Essay. These tests are led online each fourth Saturday. The month-to-month Olympiads are led in part by astute inquiries that make it simple for understudies to get ready for various sections. Online month-to-month tests have ended up being extremely useful to all Olympiad members. 

4. Start As Ahead Of Schedule As Could Be Expected:

Understudies who plan for Olympiads should begin their training toward the start of the year. Olympiad tests are typically conducted during November-December, so understudies who start early will finish the prospectus well on schedule. It permits them to rehearse an assortment of inquiries that might be posed in the yearly Olympiads.

5. Get To Know The Prospectus: 

Indian Talent Olympiad has clarified the Olympiad prospectus exhaustively regarding its matter page. Kindly visit the individual subject page to find out about the specific schedule. 

6. Plan Every Day: 

Olympiads don’t expect understudies to concentrate on anything extra, yet expect them to rehearse each day. It is a positive routine to have a review design and be ready for the part. Work out the absolute number of days needed to finish every point. The last month should be put aside for correction. 

7. Manage Time For Various Subjects:

Time usage assumes a huge part in covering the whole prospectus for various subjects. Understudies should keep a plan where they would designate a separate time plan for reading for the Olympiad tests. 

8. Refer To Olympiad Exercise Manuals:

Indian Talent Olympiad gives exercise manuals in different subjects of Olympiads. These exercise manuals give thorough data on various themes. Understudies can rehearse an assortment of inquiries from these exercise manuals and plan for the Olympiads. The books have legitimate clarification of subjects with models for wagering understanding. 

9. Practice Test Papers:

Indian Talent Olympiad offers IMO Class 8 2011 Question Paper and many other sample papers for the students. Understudies can rehearse these example papers to comprehend the kind of inquiries posed at the end of the year tests. It assists them with knowing the degree of trouble of the test, to plan as needs are. Understudies can likewise see the number of inquiries they can address inside the given time limit, which is quite possibly the most basic part of the Olympiad. Understudies can purchase earlier year’s inquiry papers sets online from the Indian Talent Olympiad. 


Practice is the way to prevail in any assessment throughout everyday life. The more you practice, the better understanding you have about basics. Modification is basic for any test planning. Practice is the solution to your inquiry, “how to get ready for Olympiad tests”. Getting hung on the right substance, giving time, and keeping an inspirational perspective assists you with prevailing in Olympiads. 

11. Know The Important Olympiad Books: 

Understudies need to get ready from their coursebooks proposed by their educational committees (ICSE/CBSE/State sheets). Furthermore, understudies can allude to and request the Indian Talent Olympiad’s exercise manual, Olympiad study application presented from the Indian Talent Olympiad, Previous year question papers, and test papers for each Olympiad assessment. Indian Talent Olympiad likewise gives practice books to each class, so understudies can set up the thinking and coherent area.


Dedicate separate times for various parts. Prepare a daily practice to plan for the test. Understand Maths Olympiad prospectus and become more acquainted with what is asked in the test. Purchase Indian Talent Olympiad’s Maths Olympiad exercise manuals and test paper sets. Understand the degree of trouble of each question to rehearse appropriately. Practice various inquiries from the coherent thinking segment. Identify troublesome formulae and practice for those independently. Practice assortment of word issues by alluding to various review material by the Indian Talent Olympiad. Track your advancement, check the number of inquiries you could endeavour accurately inside the given time limit.


What all you need to know to prepare for the class 6 maths Olympiad

Class 6 Olympiad examinations serve as a foundation for competitive tests. It is essential that parents provide their children with a solid foundation in the form of these tests. In comparison to prior classes, students in class 6 are expected to solve a greater number of problems. The time restriction, however, stays the same at 65 minutes. Each student is given 50 questions divided into three portions. The first portion is the subjective pattern, which contains 30 questions, part two is the High Order Thinking portion, also known as the HOT section, which contains 5 questions, and the third section is the logic and reasoning section, which contains 15 questions.

Most of us have walked out of an examination hall thinking, “Oh, I knew the solution to that problem, but due to time constraints, I skipped it!” or ‘well, I was all set to write additional sentences for that question, but I ran out of time since I spent so much time on the last one!’ Such incidents occur throughout our student life, whether we are in primary school or preparing for the NEET exam. To avoid all these things the following are all of the vital secrets to prepare for the class 6 Olympiad test.

  1. Choose which Olympiads to compete in: In an academic year, there are six SOF Olympiads, as previously indicated. As a result, you should pick ahead of time which Olympiads you wish to compete in based on your area of interest. Academic Excellence Award is given to students who participate in all Olympiads and get merit places. As a result, you should think about competing in all six Olympiads.
  1. Keep hold of your syllabus: The second step is to locate the whole material for a certain Olympiad test type that corresponds to your grade. The test content will be based on the school curriculum established by the individual organizations. As a result, for an aspirant, clarifying the ideas about the syllabus will be a top concern.
  1. Make a detailed schedule and stick to it: Designing a timetable is the third stage that you must know for Olympiad preparation. Only the most successful people make a schedule and stick to it. They create their hard work routine more concentrated and productive. In this situation, you’ll also need to make a schedule so that you can finish your schoolwork and sit for the Olympiad tests in 2020. All you have to do is maintain a healthy level of balance in all aspects of your life. You must concentrate and devote time to the Olympiad preparation in addition to the school test.
  1. Start with Known Questions: It’s usually advisable to start with something you’re familiar with in order to maintain your confidence and give your paper a great start. Once you have a good handle on the question paper, you may start strategically dividing your time. You must allocate time to each question wisely depending on its relevance.
  1. Keep yourself energetic and at ease: When you’re taking a sample Olympiad test, make it a habit to stay fresh and calm. Also, Look for a peaceful area where you won’t be disturbed. This may be a library, a café, a room in your home, or someplace else where there isn’t a lot of noise or distractions. Avoid going to areas where you could meet with your buddies. You may train your brain to resist worrying and to handle all of the hard questions during the exam the above way.
  1. Sample papers must be solved:  Make sure you practise as often as possible once you’ve completed the full curriculum. Solve simulated examinations and previous year papers to evaluate your performance and identify areas where you might improve. You also get a good concept of the exam structure and the topics that are the most important. As a result, you should solve sample problems on a frequent basis to stay motivated throughout your exam preparations. These Previous Year Paper for IMO Class 6 Maths 2013 will help anybody for better preparation for Olympiad. 
  1. Maintain a healthy lifestyle: Your concentration, potential, and performance are all affected by poor health. As a result, it’s critical that you be physically and mentally fit. When it comes to staying active, a well-balanced diet is essential. Also. take frequent brief rests to rejuvenate your thoughts. These breaks are critical for recharging your batteries and relaxing your mind in preparation for another study session. Furthermore, it is vital to work out and meditate in order to boost your memory. Make sure you exercise every day to keep your brain healthy and get enough sleep to recharge your batteries.
  1. Practice more questions: Even after knowing the exact right answers, it has been noticed that the majority of children are unable to perform well on the exam. So, make sure you rehearse a lot of questions so you can answer them quickly. With this, you will be able to attempt the exam properly and finish it on time.
  1. Organize your time: When it comes to studying for Olympiad exams, one of the most important things to remember is to manage your time. While studying for your exams, you must strike a balance between academics and other activities, such as relaxation, sleep, eating, and studying the school syllabus etc. You will never finish your syllabus on time, no matter how much work you put into studying for the examinations if you do not know how to manage your time effectively. As a result, be sure you learn to efficiently adjust your time in order to excel in your exams.
  1. Take the Chance and Suppose: Take the Chance and Suppose: One of the nicest things about an Olympiad test paper is that it does not have any negative marks. So, you may certainly take a guess and tackle questions about which you are unsure. It might turn out to be the correct answer, and if it doesn’t, you’ve got nothing to lose.

Interesting ways to learn class 8 maths

The core study of maths of high school begins in class 8. The maths in class 8 consists of many concepts that are the basis of geometry and algebra. It provides a deep understanding of the basic concepts which helps the students to know about the core of maths. These concepts are important for the overall knowledge and success at the education level. Practicing the various concepts helps to attain fluency and a good score in maths. The syllabus of class 8 maths includes computing numbers, expressions, equations, geometry, and functions. The students are expected to understand and interpret these concepts. They must use a variety of skills to practice these concepts to score high marks in maths exams. Mastering over various diverse topics can be achieved only through consistent practice and reinforcement of the concepts with the related study materials.

A comprehensive and easy way to prepare for the class 8 maths exam is to follow the NCERT books. It helps the learners to revise for the exam quickly by saving a lot of time for preparation. Following the right study material help the students of class 8 to prepare the most important topics and questions that are required for scoring high marks in maths. The NCERT books for class 8 maths cover the entire syllabus of class 8 maths prescribed by the CBSE board. NCERT solutions help the students to gain an understanding of the basic concepts and make them study efficiently. Students can also use some online resources that are prepared by the maths experts.

Along with these study materials, there are certain things to be followed to score good marks in the class 8 maths. Here are some of the interesting ways to learn maths and score high.

Planned revision

It is not only important to cover the entire syllabus but also the students need to revise them precisely before the examination. Planning for revision is the foremost thing to be done during the preparation of the examination. Making a list of important topics prevents the students from skipping any topic in revision. This will also help to identify which topic needs more concentration and practice. The students should make a revision plan by allocating time for each topic. Once it is done, the students can execute their revision plan. This would reduce the revision time. It would help to avoid last-minute revision mistakes and errors.

A planned and quick revision helps to secure more marks in the examination. There may be certain concepts that are not included in the study plan. The students should not try to learn new things during revision because revision is only meant for studying again the known topics in a better way. This would help to score more marks in the maths examination.

 Practice sample papers

Practicing the previous years’ question papers helps to score good marks in the maths examination. One of the best ways to score more in the maths exam is by practicing. It helps in self-evaluation and figures out the errors that are made. So that it will not be repeated. Solving the questions enhances the speed and efficiently manages the time during examination on each question. Thus practicing helps in completing the entire exam in the stipulated time with 100% accuracy.

Write concepts and formulas

When a student wants to make a good attempt in a maths exam, it is necessary to know all the concepts and the formula related to them. It is better to derive the formulas as mugging up will not help often. Many new formulas can be formed on deriving the old ones. Writing is a good practice to revise them. Writing also enhances learnability and makes the concepts stronger. 

Take expert help

For scoring good marks in class 8 maths, it is necessary to know whether the learner is well versed in the basic concepts and formulas. If they are not, they can seek help from some subject experts or teachers to learn the concepts. It is because a teacher knows how to make children get into the concept with utmost concentration. Many resources are available to provide online tutoring to the students of class 8 to teach the concepts in an understanding way. Taking the expert help makes the students visualize the solution to some of the difficult problems. 

Prioritize the questions

Managing the time properly helps the students to complete the exam. This can be achieved by prioritizing the questions that are needed to be solved. The students must try to solve the questions within a limited time. This would prevent the last-minute rush and stress. They must categorize the questions based on the marks allotted and must strictly follow the schedule to finish the questions. Only this helps in revising the answer sheet one last time to prevent the mistakes before the closure of the exam duration. 

Focus on NCERT

To obtain a good score in the maths examination. The students should not miss out on the NCERT maths books. It provides the latest solved problems that help the students in practicing more. It covers all the topics that are in the curriculum of the class 8 maths subject. It gives a bunch of questions behind every unit for the students’ practice. These important questions that are categorized by NCERT are the frequently asked questions most of the time in the examination.


Learning maths interestingly helps to reduce the stress of the children during the examination. The students exhausted with exam pressure tend to perform less in the examination. Frequent practice helps them to overcome the stress created in the examination hall. The students must also be given short breaks during the preparation of the exams to prevent them from the fear of exams and from stressing them much. If the students follow the above ways of learning irrespective of the circumstance without any fail, then they surely would do wonders in the examination by securing high marks in maths.


Affordable Pricing Provides Programming Homework Help From Different Professionals

Getting the best programming homework help online isn’t easy. Often times the resources available may prove to be less reliable or fail to give you the sufficient privacy you deserve. That’s why it’s so important to find the right sources for getting programming homework help from. A programming homework help guide is often a valuable resource to have if you’re struggling with a subject in school. Many students end up having to take extra classes and even weeks off of work because they can’t keep up with all of the homework assignments on their own. With the right resources, you’ll be getting the very best programming homework help and ensuring that you’re well protected from any issues that could arise.

You should always get programming homework help from an experts, whether you’re asking for advice about one assignment or an entire class. Ask your teachers for assistance and they’ll likely direct you to some sort of professionals who can help you. It’s a good idea to seek out some of the advice from outside of the school because many individuals are used to teaching and know the right questions to ask when working with students. Some teachers will also be able to refer you to individuals who can help you out with any specific assignments. Having an expert around will make finishing your assignment much easier.

Try To Find A Professional Person For Help

Other than just finding an individual or individuals who can give you programming homework help, you may also benefit from finding professionals in your field. For example, if you’re an aspiring computer programmer, then you may want to find computer programmers who have experience dealing with certain programming languages. Having experts around can give you the confidence needed to complete the tasks involved in the program you’re working on. You might even find an individual who can give you insider information or tips about how to become a better programmer or work with programming languages on your own.

Many times, students don’t really enjoy completing their assignments or waiting until their assignments are due. That’s why it can be beneficial to find some type of programming homework help from an expert. An experienced professional can take a look at an assignment and immediately know what has to be done and what could be improved upon. This type of assistance is often priceless for many students who simply don’t have enough time to dedicate to their assignments.

Different Kinds Of Professional Programming Homework Services

Getting the best programming homework help online isn’t easy. Often, the available resources may prove to be less reliable or fail to give you the sufficient privacy you deserve. That’s why it’s so important to find suitable sources for getting programming homework help. A 

Programming homework help guide is often a valuable resource to have if you’re struggling with a subject in school. Many students have to take extra classes and even weeks off of work because they can’t keep up with all of the homework assignments on their own. With the right resources, you’ll be getting the very best programming homework help and ensuring protection from any issues that could arise.

You should always get programming homework help from an expert, whether you’re asking for advice about one assignment or an entire class. Ask your teachers for assistance, and they’ll likely direct you to some professionals who can help you. It’s a good idea to seek out some advice from outside of the school because many individuals are used to teaching and know the right questions to ask when working with students. Some teachers will also refer you to individuals who can help you out with any specific assignments. Having an expert around will make finishing your project much more straightforward.

Try To Find A Professional Person For Help

Besides just finding individuals who can give you programming homework help, you may also benefit from finding professionals in your field. For example, if you’re an aspiring computer programmer, you may want to see computer programmers who have experience dealing with specific programming languages. Having experts around can give you the confidence needed to complete the tasks you’re working on in the program. You might even find an individual who can provide you with insider information or tips about becoming a better programmer or working with programming languages on your own.

Many times, students don’t enjoy completing their assignments or waiting until their projects are due. That’s why it can be beneficial to find some programming homework help from an expert. An experienced professional can look at an assignment, and it will be it immediately and what could be improved. This type of assistance is often priceless for many students who don’t have enough time to dedicate to their assignments.

Different Kinds Of Professional Programming Homework Services

Many professionals offer programming homework help services to students in a variety of different fields. These include web developers, content editors, teachers, professors, and researchers. Their goal is to ensure that every assignment is done correctly and according to the specifications of the assignment provider. To help their clients, they often provide mock interviews and sample writing samples to give them some idea about writing a project.

To find the most affordable pricing, tutors often recommend taking advantage of available resources on the internet. These online resources allow users to get help from various professionals, including web developers, educators, and programmers. In many cases, it takes all of the effort and time that an individual will put into an assignment to access information that can help them get the job done right.