Physics and maths tutor
For each of the exam boards below, there are revision notes, cheat sheets, worksheets, questions by topic, and past papers. Solution Banks
|Core 1||Mechanics 1||Statistics 1||Further Pure 1|
|Core 2||Mechanics 2||Statistics 2||Further Pure 2|
|Core 3||Mechanics 3||Statistics 3||Further Pure 3|
|Core 4||Decision 1|
GCSEs & IGCSEs
|AQA||CAIE||Edexcel||OCR A||WJEC (England)|
|Edexcel (IGCSE)||OCR B||WJEC (Wales)|
UK Legacy A-levels
The RoadMap of Physics
So physics is a huge subject that covers many different topics going from galaxies in the depths of space right down to subatomic particles. And if you don’t already know physics its difficult sometimes to see how all these different subjects are related to each other.
So this is my attempt to show that in a map, so this is the map of physics. I hope you enjoy it. Physics can be broadly broken down into three main parts: Classical Physics, Quantum Physics, and Relativity. We’ll start with classical physics and a good person to start with is Issac Newton.
His laws of motion describe how everything made of matter moves about, and his law of universal gravitation tied together with the motion of planets in the sky with the falling of objects on Earth into one elegant and general description. He also invented calculus, a supremely powerful mathematical tool that has been used over the centuries to derive new physics.
Calculus is really part of mathematics but physics and mathematics are inseparable. Math is the language of physics, you can imagine it like the bedrock that the world of physics is built from. Newton also made strides in the field of optics which is the physics of light and how it travels through different materials. It explains, refraction seen in prisms and lenses which are used to focus light in telescopes, microscopes, and cameras.
Telescopes enabled us to peer into the depths of space and observe the wild array of objects there and develop astrophysics and cosmology. Optics is closely related to the theory of waves, which is basically how energy can travel through disturbances of a medium, like ripples on the surface of a pond or sound through the air. Light doesn’t need a medium to travel through, it can travel through the vacuum of space, but it still follows the same principles as all waves namely reflection, refraction, and diffraction.
This leads us to electromagnetism: the description of magnets, electricity, or more generally, electric and magnetic fields. It was a Physicist called James Clerk Maxwell who discovered that these are two aspects of the same thing and derived the wonderfully elegant rules of electromagnetism and theorized that light was an electromagnetic wave. Electromagnetism also explains all of electricity.
Jumping back a little bit, classical mechanics is related to Newton’s laws and covers the properties and motion of solid objects, how they move when forces hit them, what happens when they are joined together, like in gears or buildings, or bridges. Fluid mechanics is the description of the flow of liquids and gasses. Using fluid mechanics you can work out how much lift is generated from an airplane’s wing, or how aerodynamic a car is. Fluid mechanics is notoriously difficult, mostly because the motions of tiny things like molecules get really complicated really fast.
This leads us to the Chaos theory. Chaos theory is the description of large complex systems and how small differences in initial conditions can lead to very different final outcomes. Thermodynamics is the description of energy and how it passes from one form to another. It also includes entropy which is a measure of order and disorder and basically tells you how useful different kinds of energy are.
Energy is a fundamental property to physics and although I have written energy here, I should have written it everywhere on this map because everything has energy. So that is all of classical physics, the picture of the Universe we had around the year 1900. It told us we lived in the Universe where everything ran a sort of like clockwork, if you could measure everything accurately enough the future was kind of predetermined. However, not everything was solved, there were just a few holes in experiments that hinted at something more.
The orbit of Mercury was slightly too fast and some strange things happened on the smallest scales with electrons and light which were all unexplained. Physicists at the time thought that they would solve and explain these problems soon enough but poking at them they unraveled the new domains of relativity and quantum physics and turned our understanding of the Universe completely on its head. Albert Einstein was the genius who developed the theories of special and general relativity.
Special relativity predicts that the speed of light is constant for all observers which means that when you travel really fast weird stuff starts happening like time slowing down. It also states that energy and matter are different aspects of the same thing through the famous formula E=mc2. General relativity says that space and time are part of the same fabric called spacetime and that the force of gravity comes from objects bending spacetime, making other objects fall in towards them.
While relativity describes the very big, other physicists were busy at work on the very small in the world of Quantum Physics. Atomic theory probed the nature of the atom, and more and more detailed descriptions of the atom were developed. From a tiny sphere to electron orbits, to energy levels, and then to the electrons being wave-like charge distributions.
Condensed matter physics describes the quantum physics of many atoms together in solids and liquids, and is where many great technologies have come from like computers, lasers, and quantum information science. Nuclear physics describes how the nucleus of atoms behaves and explains radiation, nuclear fission, the splitting of the atom used in our nuclear power plants, and nuclear fusion which takes place in the Sun and will hopefully soon be harnessed here on Earth.
Particle physics probes even deeper to find the fundamental subatomic particles that everything is made of and are described in the standard model of particle physics. Quantum field theory captures all of quantum physics and combines it with the special theory of relativity and is the best description of the Universe we have.
Unfortunately, Quantum field theory doesn’t include gravity and so physicists don’t know how to join together quantum physics and the general theory of relativity leading to the giant chasm of ignorance. One day in the future we hope to close this chasm and come up with a theory of all of physics we call it quantum gravity, and there are many attempts to do this some examples are string theory or loop quantum gravity and there is many more. But quantum gravity isn’t the only thing we observe but don’t understand, there are also the major puzzles of dark energy and dark matter which seem to make up 95% of the Universe.
So all of our physics only really describes 5% of what we know about and everything else, at the moment, is a mystery. There are many other mysteries out there like the Big Bang, and no doubt there are things beyond that that we don’t even know that we don’t know.
Which gets to the lofty cloud which floats over all of physics: philosophy. Although many physicists make fun of philosophy, it is the big philosophical questions that motivate a lot of physics, like, “What is the fundamental nature of reality?” “How come the Universe even exists?” “Do we have free will if we are just made of physics?” or “How do we know that the way that we do physics and science actually gets to the fundamental truth of the Universe?” And, just, why is all of the physics the way it is? Well, those are the big questions, ones which we may or may never answer, but that is no reason to give up trying, after all, physicists are not quitters. And that was the map of physics.
The RoadMap of Mathematics
The mathematics we learn in school doesn’t quite do the field of mathematics justice. We only get a glimpse at one corner of it, but mathematics as a whole is a huge and wonderfully diverse subject.
The origin of mathematics lies in counting. In fact, counting is not just a human trait, other animals are able to count as well and evidence for human counting goes back to prehistoric times with checkmarks made in bones. There were several innovations over the years with the Egyptians having the first equation, the ancient Greeks made strides in many areas like geometry and numerology, and negative numbers were invented in China. And zero as a number was first used in India.
Then in the Golden Age of Islam Persian mathematicians made further strides and the first book on algebra was written. Then mathematics boomed in the renaissance along with the sciences. Now there is a lot more to the history of mathematics than what I have just said, but I’m gonna jump to the modern age and mathematics as we know it now. Modern mathematics can be broadly be broken down into two areas, pure maths: the study of mathematics for its own sake, and applied maths: when you develop mathematics to help solve some real-world problem. But there is a lot of crossovers.
In fact, many times in history someone’s gone off into the mathematical wilderness motivated purely by curiosity and kind of guided by a sense of aesthetics. And then they have created a whole bunch of new mathematics which was nice and interesting but doesn’t really do anything useful.
But then, say a hundred years later, someone will be working on some problem at the cutting edge of physics or computer science and they’ll discover that this old theory in pure maths is exactly what they need to solve their real-world problems! Which is amazing, I think! And this kind of thing has happened so many times over the last few centuries.
It is interesting how often something so abstract ends up being really useful. But I should also mention, pure mathematics on its own is still a very valuable thing to do because it can be fascinating and on its own can have a real beauty and elegance that almost becomes like art. Okay enough of this highfalutin, lets get into it. Pure maths is made of several sections.
The study of numbers starts with the natural numbers and what you can do with them with arithmetic operations. And then it looks at other kinds of numbers like integers, which contain negative numbers, rational numbers like fractions, real numbers which include numbers like pi which go off to infinite decimal points, and then complex numbers and a whole bunch of others.
Some numbers have interesting properties like Prime Numbers, or pi, or exponential. There are also properties of these number systems, for example, even though there is an infinite amount of both integers and real numbers, there are more real numbers than integers.
So some infinities are bigger than others. The study of structures is where you start taking numbers and putting them into equations in the form of variables. Algebra contains the rules of how you then manipulate these equations. Here you will also find vectors and matrices which are multi-dimensional numbers, and the rules of how they relate to each other are captured in linear algebra.
Number theory studies the features of everything in the last section on numbers like the properties of prime numbers. Combinatorics looks at the properties of certain structures like trees, graphs, and other things that are made of discreet chunks that you can count. Group theory looks at objects that are related to each other in, well, groups.
A familiar example is a Rubik’s cube which is an example of a permutation group. And order theory investigates how to arrange objects following certain rules like, how something is a larger quantity than something else. The natural numbers are an example of an ordered set of objects, but anything with any two-way relationship can be ordered. Another part of pure mathematics looks at shapes and how they behave in spaces. The origin is in geometry which includes Pythagoras and is close to trigonometry, which we are all familiar with from school.
Also, there are fun things like fractal geometry which are mathematical patterns that are scale-invariant, which means you can zoom into them forever, and they always look kind of the same. Topology looks at different properties of spaces where you are allowed to continuously deform them but not tear or glue them. For example, a Möbius strip has only one surface and one edge whatever you do to it. And coffee cups and donuts are the same things – topologically speaking.
Measure theory is a way to assign values to spaces or sets tying together numbers and spaces. And finally, differential geometry looks at the properties of shapes on curved surfaces, for example, triangles have got different angles on a curved surface, and brings us to the next section, which is changes. The study of changes contains calculus which involves integrals and differentials which looks at areas spanned out by functions or the behavior of gradients of functions.
And vector calculus looks at the same things for vectors. Here we also find a bunch of other areas like dynamical systems which look at systems that evolve in time from one state to another, like fluid flows or things with feedback loops like ecosystems.
And chaos theory studies dynamical systems that are very sensitive to initial conditions. Finally, the complex analysis looks at the properties of functions with complex numbers. This brings us to applied mathematics. At this point, it is worth mentioning that everything here is a lot more interrelated than I have drawn. In reality, this map should look like more of a web tying together all the different subjects but you can only do so much on a two-dimensional plane so I have laid them out as best I can.
Okay, we’ll start with physics, which uses just about everything on the left-hand side to some degree. Mathematical and theoretical physics has a very close relationship with pure maths. Mathematics is also used in the other natural sciences with mathematical chemistry and biomathematics which look at loads of stuff from modeling molecules to evolutionary biology.
Mathematics is also used extensively in engineering, building things has taken a lot of maths since Egyptian and Babylonian times. Very complex electrical systems like airplanes or the power grid use methods in dynamical systems called control theory. Numerical analysis is a mathematical tool commonly used in places where mathematics becomes too complex to solve completely. So instead you use lots of simple approximations and combine them all together to get good approximate answers.
For example, if you put a circle inside a square, throw darts at it, and then compare the number of darts in the circle and square portions, you can approximate the value of pi. But in the real world numerical analysis is done on huge computers.
The game theory looks at what the best choices are given a set of rules and rational players and it’s used in economics when the players can be intelligent, but not always, and other areas like psychology, and biology. Probability is the study of random events like coin tosses or dice or humans, and statistics is the study of large collections of random processes or the organization and analysis of data.
This is obviously related to mathematical finance, where you want to model financial systems and get an edge to win all those fat stacks. Related to this is optimization, where you are trying to calculate the best choice amongst a set of many different options or constraints, which you can normally visualize as trying to find the highest or lowest point of a function.
Optimization problems are second nature to us humans, we do them all the time: trying to get the best value for money, or trying to maximize our happiness in some way. Another area that is very deeply related to pure mathematics in computer science and the rules of computer science were actually derived in pure maths and is another example of something that was worked out way before programmable computers were built.
Machine learning: the creation of intelligent computer systems uses many areas in mathematics like linear algebra, optimization, dynamical systems, and probability. And finally, the theory of cryptography is very important to computation and uses a lot of pure maths like combinatorics and number theory.
So that covers the main sections of pure and applied mathematics, but I can’t end without looking at the foundations of mathematics. This area tries to work out the properties of mathematics itself and asks what the basis of all the rules of mathematics is. Is there a complete set of fundamental rules, called axioms, from which all of the mathematics comes from? And can we prove that it is all consistent with itself? Mathematical logic, set theory, and category theory try to answer this and a famous result in mathematical logic are Gödel’s incompleteness theorems which, for most people, means that Mathematics does not have a complete and consistent set of axioms, which mean that it is all kinda made up by us humans.
This is weird seeing as mathematics explains so much stuff in the Universe so well. Why would a thing made up by humans be able to do that? That is a deep mystery right there. Also, we have the theory of computation which looks at different models of computing and how efficiently they can solve problems and contains complexity theory which looks at what is and isn’t computable and how much memory and time you would need, which, for most interesting problems, is an insane amount.
Ending So that is the map of mathematics. Now the thing I have loved most about learning maths is that feeling you get where something that seemed so confusing finally clicks in your brain and everything makes sense: like an epiphany moment, kind of like seeing through the matrix.
In fact, some of my most satisfying intellectual moments have been understanding some part of mathematics and then feeling like I had a glimpse at the fundamental nature of the Universe in all of its symmetrical wonder.
Earn Money to Websites by Solving Maths Physics Problems
Start your tutoring career online with this website
How you can make your money by becoming one of our fraternity by becoming a teacher. See, first of all, it’s a lesser stressful job, as compared to other jobs, and this is me talking with a lot of experience, I have been into other jobs and I’m telling you, teaching is not that’s stressful because teaching there is self-satisfaction that you are helping somebody, you are helping a child, you are in a way nurturing a child.
So there is this satisfaction and it’s rewarding in that way. you feel good about yourself when you teach. Talking about money. Money is also good. It’s good. It is good. I know there is this notion that teachers don’t earn a lot, it’s not really true. If you teach privately, or you run coaching institutes I’m telling you there is pretty good money involved. So if you are planning on becoming a tutor or a teacher.
You can have my word. It is a good idea. So there is this portal by the name of MyFavTutor so MyFav, I don’t know how to pronounce that, but that is how it is. And I am writing the name here you can see the spelling. This portal, what does it do, it helps you it is like a mediator between the tutor let me take myself for an example, and let me take a student, let’s say, Sonia.
Let Sonia be a student. I am a teacher and Sonia is a student. Now, I am in my home, I want to teach someone and Sonia is at her place and she wants to study from somebody. She wants a tutor, so she doesn’t know me, I don’t know her. How will she know me, I mean, either I advertise myself. Okay, which is a difficult job, it involves a lot of money. So probably at the beginning of my career, or if I’m beginning to teach, I don’t think I would be able to afford that. So how can I get to know Sonia? So that is where this portal will help you. How will it help you? It is somewhere where Sonia will also log in and Aleena will also log in. Aleena, as a teacher. And Sonia as a student. Now, this portal is going to figure out if Sonia, or Aleena, are from the same locality. So it is basically connecting students with teachers of same locality.
And of course, there’s going to be a proper profile that will be maintained by the portal for me. So when I log in as a teacher so, I have to provide all my details in the portal and I have to complete the profile. I will explain that process in a screen recording later.
So first I will create an account for myself after the creation of the account, what will happen is, I have to create a proper profile for myself. Okay, just like the jeevansathi.com profile. No, no, no just kidding, not like that but yeah basic details like my educational qualification, my alma mater, my current address. When you mention all these things in your profile.
After that, you need to upload the documents for verification. Your educational documents will also be count as documents. Once your documents are verified that is when you become a tutor and you’ll get a batch, and you will be a verified tutor, and after becoming the verified tutor. Now you have a profile, a valid account on the portal, and several students can approach you and you can also approach several students in your locality. And that is how it works I think it’s pretty much explained.
Now, the next question that might pop into your head is how much am I going to earn? It’s completely up to you how much time are you ready to devote? Are you planning it as a side income? Are you just going to give it two hours or three hours of your day? Or you want to be a full-fledged teacher/full-fledged tutor? It’s completely up to you. The more time you give, the more you earn. Now another thing is, is this free or not, yes it’s completely free. Alright, but then there is a paid version also, again, up to you if you want to use the paid version, you can pay the fee of £30 for a year.
That is how you become the premium member, alright. And then you have the access to unlimited leads and all. Go into it, do your research on your own. I’m just here to give you a brief idea as to how things work here. I found it interesting and I wanted to share it with you.
So the next question that I would want to cover up here is what is the benefit of enrolling yourself as a tutor on the portal? The benefit is first of all it’s free of cost. Another thing is that you will have a rating from the students. So, of course, in the beginning, you’re not going to be rated, once you start taking lectures and you start teaching for some hours, probably in a matter of a month or so, maybe two months, you will be able to gather a proper decent rating for yourself.
And once you have the rating things really smooth out. Students will trust you more, you will have an authenticity to vouch for you. Another thing is that it’s not just for private people I mean private tutors, private tuitions, or private teachers it is also for the coaching centers.
So if you are a coaching center or you are planning on starting a coaching center then also you can enroll yourself over there, and you can generate leads from there, you can contact the students, and you can start your journey of becoming a teacher, or running yourself a proper successful career as a teacher. So let’s get into what I have to show you on the laptop.
Alright so first I’ll go to Google. And I’ve already typed MyFavTutor for you. That is the first link that you have to click right on the top. And then the website opens up. I’ll scroll a little down and show you around. So, these are the achievements, the various teachers and students, and reviews. Why MyFavTutor so there is something for the students.
so I would rather go to register now, which I’m going to take you to in a while. Then there are these testimonials there as these various cities where this website is working. There is this name of the company right at the bottom BlueWebMedia, so they own this website, and it’s comparatively a newer portal, it’s a newer website. So if you register now, it may actually add up to an advantage for you because you will be like the early birds.
Alright so what I’m going to do is I am going to take you through the link HOW IT WORKS. Please just read through it. It’s very informative I’ve already done my research. So I’m telling you from my experience, it is very, very well written and quite informative definitely read it, they’ve explained how exactly you have to complete your profile. I’ve already read this, they are going to take your address, they’re going to take your qualification, your experience and they will offer you a verified badge once they are done checking your documents, then you have the option of uploading your pictures and then basically you have to present yourself well.
So that more and more students trust you and they want to study from you. Then another thing that I want to show you is tutor registration so that is where I’m actually taking you right now, I’m going to… and before I get into it. I want to show you this. Two types of plants that they’ve talked about are their’s standard plan and the premium plan this is what I was referring to. Standard Plan is free, as of now till April sixth, as it says, and, after which it’s going to be £30 per year.
Okay, fine, then there is this premium plan, which is for £30 till the sixth of April and then it’s going to be ₹5000 per year. And under the premium plan, what get is you get the verified badge, which is important. And then there is this unlimited number of leads that you can get. Please do your research, I’ll create my account and show it to you, they are going to send you a verification code.
So there is this form that you have to fill. Okay, and then you have to verify your ID by 7th April, they are saying and today we are sitting at 31st of March so they are providing you with a week’s time, to fill in your profile and to get it verified.
So there is this early bird offer which is going on, till the sixth of April, you should enroll yourself if you’re interested in then because it’s free till then, I’ve already created my account. This is my profile, this is how my dashboard looks like. So there is this profile section, you have messages, contacts, reviews, and rating affiliates. Okay, another thing is this messages tab.
The messages tab would mean that if a person wants to be your student, he or she is going to send you a message, and it’s going to be reflected on the messages tab over here. And that is when you will be able to contact the person back. Alright, so the messages tab is very important you have to keep your eye over there, I think, more or less, I’m done. Please fill in your details.
Provide your educational background, your experience, and everything, I am not filling in everything since obviously, I’m sure you must have got the idea by now. I think this is a brilliant idea, it’s going to really help a lot of you becoming proper full-time tutors. And it will really help you in making good enough income for yourself.
I’ll see you again. Take care of yourself, stay home, stay safe. Bye-bye.