Many of you who are doing exams this year will be revising or starting to think about revising. As a tutor, I am often asked, “What should I revise?” The answer is, unfortunately, everything that you have covered in the course. No one except the exam writers know what is going to be in the exams in any single year, so always make sure that you cover everything.

Barnaby Lenon, an ex-headmaster at Harrow, has recently written in a blog that GCSE students should revise their course *at least* three times. The same applies for A level students, but officially there is no magic number given as to how many times you should do so. Usually, however, it will be more than once. Some lucky people, the exceptions, can read something once and it will “go in”, but more will have to go through the course over and over again for it to sink it. We are all different, and this is the main point with revising – what works for one person will not work for another.

With all this in mind, there are some tips below. Remember, some will work for you, some won’t.

• Find a good place to work. Some of you will like quiet, others will like some noise. We all work best in certain places. Some students may like to work in a library, others in their room, others in a coffee shop. Find a place that works well for you and stick to it.

• What time works best for you? Some people work better early in the morning, others in the afternoon, others late at night. Again, stick to what works for you. If you are a night owl, it’s pointless to try and force yourself to get up early and study – it just won’t work as well. Use your strengths and find the best time to suit you.

• Avoid distractions. There are so many distractions today: mobile phones, television, emails and so on. It can make it hard to study. If you are reading this now but also looking at your social media feed on your phone, for example, it’s doubtful all you are reading will go in. So avoid such distractions if you can. Turn off your phone. Turn off your emails. If you find it hard to do this, give yourself a time limit, “I will revise for one hour, then spend five minutes looking at my phone.”

• With the above point also in mind, some students find it hard to sit down and study for long periods. Others prefer it. Again, you should do what suits you best. If you do find it hard to sit for long periods, give yourself a reward. One student I worked with played volleyball at national level. He found it very hard to sit down for long periods and study. Consequently he was doing hardly any revision. We came up with a plan. He would revise for 50 minutes, then go outside and play with a ball or go for a jog for ten minutes. Then he would revise for 50 minutes again and so on. This worked well for him. You may find a similar reward works for you, looking at your phone, going for a walk, making a cup of tea, watching TV, phoning a friend and so on. Decide on your time limit and give yourself a reward.

• Aim to study for no more than two and a half hours without taking a break. You are probably not revising as well as you would if you carry on revising after that time.

• Making and reading notes and using flashcards can all work well for some students. Others can make recordings of their notes and listen back to them when they are going for a walk or even when they are sleeping at night – Mind maps and memory palaces can also be useful when revising. Again, find a method that works well for you and stick to it.

• If you are reading something and it isn’t sinking in or you don’t understand it. Try a few of the following techniques…

o Read it out loud. When you do this, sometimes it seems to make more sense.

o Try and explain it to someone else – You may find that you know far more than you think you do when you explain it to another person.

o Read it in another way. There are a lot of resources online today, so if you don’t understand your notes or textbook, look online and find another explanation.

• Making a revision timetable for when you intend to revise your subject is also useful. You may be revising for more than one subject, so work out when you are going to study and make a plan for each subject.

• Practice exam papers and old TMAs under “exam conditions.”

• Try to take off a day a week. You decide which day. Take some time off from all that studying.

• Try to start revising as soon as you can. The earlier you start to revise, the more revision you will do.

Remember, you have revised before. You know what has worked well for you and what didn’t. So if you have a good way of revising, stick to it. But if your way hasn’t worked so well, why not try another option from those listed above? There is also of course a lot of advice out there online and in books. The best way to revise is the way that works for YOU! So find your best method and stick to it.

Finally, though success in them is all about your hard work and revision, I am still going to wish you this – Good luck with your exams!

On April 11, 1970, at 7.13pm (US time), Apollo 13 was launched from the Kennedy Space Centre in Florida. Only two days later its crew, Commander James A. Lovell Jr, Command Module Pilot, John L Swigert Jr and Lunar Module Pilot, Fred W Haise Jr (pictured above, left to right), found themselves abandoning their planned landing of the module on the Moon, however, when an oxygen tank exploded.

Blowing out the side of the Service Module, the crew were left with only the Command Module and a series of life-threatening consequences. Suddenly they only had limited power, had lost the cabin heating system, and very soon they began to run out of water and food. Meanwhile, urgent repairs were needed to the carbon dioxide removal system, which threatened to flood the module with toxic fumes.

With a calmness that can only be marvelled at, Swigert and Lovell radioed Mission Control with the well known words, “Houston, we’ve got a problem.” Mission Control, led by flight director Gene Kranz, immediately switched its prime mission from exploration to getting all three crewmen back to Earth alive. Their first move was to shut down all essential systems. Even with this done however, there were only enough resources to keep two of them alive for two days; somehow they had to make them last four days – and then for all three men.

Mission Control worked hard on ways to get the lunar module’s filter system working to ensure the astronauts didn’t die of carbon monoxide poisoning by having the crew construct a makeshift system constructed from whatever they had to hand- in this case, duct tape, hosing and the command module’s surviving canisters; adapting them for lunar module use. They then had to make sure that the module remained in the Moon’s gravitation pull, so that as they travelled around it they would gain enough momentum to be powered back to Earth. Despite suffering from the cold of their situation, and a lack of food and water, the crew still managed to jettison the Service Module and fly the Command Module back into Earth’s orbit. They survived against all odds and eventually splashed down in the Pacific on April 17th.

Once the crew were safely on Earth, investigations began into what had gone wrong. It was discovered that a heating wire inside the liquid oxygen tank had lost its insulation and that as a result it gradually overheated – leading to an explosion the crew likened to a bomb going off.

Further work led to the conclusion that the initial design of the oxygen tank had played a part in the disaster. All the previous Apollo missions had flown without any oxygen tank problems but the tank on Apollo 13 had a troublesome history. As Space.com explains, “In October 1968, the Number 2 tank eventually used on Apollo 13 was at the North American Aviation plant in Downey, California. There, technicians who were handling the tank accidentally dropped it about two inches. After testing the tank, they concluded the incident hadn’t caused any detectable damage. The dropped tank was eventually cleared for flight and installed in Apollo 13. The tank passed all of its routine pre-launch tests. But at the end of March 1970, after a practice session called the Countdown Demonstration Test, ground crews tried to empty the tank — and couldn’t. “

The technicians “fixed” the problem by turning on heaters inside the tank to warm up the remaining liquid oxygen, turning it into gas which could then be vented to safety. The thermostat inside the tank was supposed to prevent the temperature from exceeding 80 degrees Fahrenheit. However, a surge of electricity caused the thermostat to weld shut without the technicians noticing. This meant that the continual intense heat damage to the internal wiring of the tank turned it into a small bomb, which was ignited when Apollo 13’s crew turned on the cooling fans inside the service module’s two liquid-oxygen tanks.

The Apollo 13 crew were all awarded the Presidential Medal of Freedom for their acts of heroism. Their story has been told many times, but most famously- and most accurately – in 1994 by Commander Lovell himself, who wrote about the mission in his book, *Lost Moon*. Such was the popularity of the book that director Ron Howard adapted it into the award winning film, *Apollo 13*, in 1995.

Scientist and mathematician Galileo Galilei was born on February 15th, 1564, in Pisa, Italy. A pioneer of maths, physics and astronomy, Galileo’s career had long-lasting implications for the study of science.

In 1583, Galileo was first introduced to the Aristotelian view of the universe, which was a religion-based view of how the world worked. A strong Catholic, Galileo supported this view until 1604, when he developed theories on motion, falling objects, and the universal law of acceleration. He began to openly express his support of the controversial Copernican theory, which stated that the Earth and planets revolved around the sun, in direct contrast to the doctrine of Aristotle and the Church.

In July 1609, Galileo learned about a telescope which had been built by Dutch eyeglass makers. Soon he developed a telescope of his own, which he sold to Venetian merchants for spotting ships when at sea. Later that year, Galileo turned his telescope toward the heavens. In 1610 he wrote* The Starry Messenger*, where he revealed that the moon was not flat and smooth, but a sphere with mountains and craters. He discovered that Venus had phases like the moon, and that Jupiter had revolving moons, which didn’t go around the Earth at all.

With a mounting body of evidence that supported the Copernican theory, Galileo pushed his arguments against church beliefs further in 1613, when he published his observations of sunspots, which refuted the Aristotelian doctrine that the sun was perfect. That same year, Galileo wrote a letter to a student to explain how Copernican theory did not contradict Biblical passages, but that scripture was written from an earthly perspective, and that this implied that science provided a different, more accurate perspective.

In February 1616, a Church inquisition pronounced Galileo as heretical. He was ordered not to “hold, teach, or defend in any manner” the Copernican theory regarding the motion of the Earth. Galileo obeyed the order until 1623, when a friend, Cardinal Maffeo Barberini, was selected as Pope Urban VIII. He allowed Galileo to pursue his work on astronomy on condition it did not advocate Copernican theory.

In 1632, Galileo published the* Dialogue Concerning the Two Chief World Systems*, a discussion among three people: one supporting Copernicus’ heliocentric theory of the universe, one arguing against it, and one who was impartial. Though Galileo claimed Dialogues was neutral, the Church disagreed. Galileo was summoned to Rome to face another inquisition, which lasted from September 1632 to July 1633. During most of this time, Galileo wasn’t imprisoned, but, in a final attempt to break him, he was threatened with torture, and he finally admitted he had supported Copernican theory. Privately, though, he continued to say he was correct. This ultimately led to his conviction for heresy and as a result he spent his remaining years under house arrest.

Despite the fact he was forbidden to do so, Galileo still went on to write *Two New Sciences*, a summary of his life’s work on the science of motion and strength of materials. It was another work that has helped cement his place in history as the world’s most pioneering scientist, even if he was not fully appreciated in his own time. Galileo Galilei died on January 8th, 1642.

Einstein was born in Germany in 1879 and, other than a short period spent studying in Switzerland, he lived there until 1933. He moved to the United States of America due to the rise to power of the Nazis under Adolf Hitler.

Why is he famous?

Many people use the word Einstein as a way of describing a genius. His most important work was the theory of general relativity which caused a huge sea change in our understanding of physics.

Unusual facts

Einstein studied for a mathematics and physics teaching diploma but struggled to find a job after graduation. He ended up spending some time working as a clerk in a patent office where he was passed over for promotion on at least one occasion. He was also turned down at one point when he applied for a job as a professor of mathematics.

In 1933 the Nazis organized mass burnings of books written by Jews and works by Einstein were among those set alight.

Einstein’s first wife was also a mathematician and some people have suggested that she may have made contributions to his works, although no evidence has been found of this.

Einstein had a huge respect for Isaac Newton and apparently had a picture of him on his wall. Newtonian Mechanics is now seen as a special case within Einstein’s theory of general relativity. People argue about which mathematician was the greater genius – there is even a Facebook page devoted to the argument.

Links to modern mathematics

Whilst much of Einstein’s work is way beyond Key Stage 3 and GCSE level you may well have heard of his famous equation E = mc² which links mass, the speed of light and energy. It is often used in exercises on rearranging formulae and substitution. You first need to understand algebra if you are to go on to understand the work of Albert Einstein.

Debby Gill

Tutor

For more information on Oxford Home Schooling’s home study courses please contact a student adviser on 0800 0 111 024.

In todays distance learning Maths blog an Oxford Home Schooling tutor looks at the life and work of Isaac Newton.

Isaac Newton is probably the most famous British mathematician. He was born in Lincolnshire in 1643 and spent most of his adult life in Cambridge.

Why is he famous?

Newton’s most famous work was a book called *Philosophiae Naturalis Pricipia Mathematica* or “Mathematical Principles of Natural Philosophy”. This is basically a book about how gravity acts on objects.

Unusual facts

Newton is famously supposed to have discovered gravity when an apple fell on his head. Some people say this is just a myth but you can visit trees in several places which are claimed to be “the” tree.

His work on calculus (a method for finding maxima and minima) caused him to be involved in a dispute with another mathematician called Leibniz over who invented it first. Most historians now believe calculus was actually discovered by them both independently and, while Leibniz’s notation is commonly used in Pure Mathematics today, Newton’s very different notation is often used in Mechanics and Physics.

Newton died in 1727 and was buried in Westminster Abbey. It is thought that he may have suffered from mercury poisoning in later life due to various experiments he had carried out as traces of mercury were found in his hair after his death.

Links to modern mathematics

Newtonian Mechanics is still studied today – his laws of motion are about force, velocity and acceleration. Much of it has been superseded by the work of Albert Einstein but, when studying motion on Earth for example, his laws are still very good approximations to what we see happen in real life.

Debby Gill

Tutor

For more information onhome study GCSE Maths and KS3 Maths courses please contact a student adviser on 0800 0 111 024.

In today’s distance learning Maths blog, an Oxford Home Schooling tutor looks at the life and work of Geralamo Cardano.

Cardano was born in Pavia, Italy in 1501. His mother had moved out of Milan in order to avoid the plague that was sweeping the city at that time. He spent much of his life in Italy although he did live in Scotland for a while.

Cardano wrote the first study of the probability of dice rolling, as well carrying out some ground breaking work in algebra and number theory.

Cardano was a successful doctor and his services were sought by many important people. The only person to persuade him to leave Italy was the Archbishop of St Andrews who paid him a large sum of money for his services and eventually made a full recovery.

In addition to being a physician Cardano was a renowned gambler and he used his understanding of probability to great advantage at dice and card tables. He also wrote some controversial articles which caused him to be jailed for heresy for a few months.

Cardano apparently correctly predicted his own date of death although many people think he “cheated” and committed suicide in Rome on 26th September 1576

Writing the probability of throwing a 6 on a 6 sided dice as 1/6 may seem obvious today but Cardano was the first person to formally do so. He also did a lot of work on solving equations.

Debby Gill

Tutor

For more information on Oxford Home Schooling’s home study courses please contact a student adviser on 0800 0 111 024.

Little is known about Euclid but it is thought that he lived around 300BC in Alexandria, Egypt.

Euclid wrote a collection of 13 books called *The Elements* which was basically a compendium of all known mathematics at that time. The section on parallel lines, points and angles is particularly famous and many people call him the “Father of Geometry” because of it. Many mathematicians like to misquote the famous line from Casablanca as “Here’s looking at Euclid” when referring to geometrical calculations.

Until part way through the twentieth century Euclid’s *The Elements* was the second best-selling book of all time (beaten only by the Bible). Today no one mathematician could hope to produce a book similar to *The Elements* by covering all known modern mathematics, because they would have to understand work at the frontiers of too many specialities. In the 1930s Nicolas Bourbaki began work on such a book. It later turned out however that Bourbaki was in fact a fictitious name used by a group of more than twenty French mathematicians.

The modern day geometry we learn in Key Stage 3 Maths and GCSE Maths is essentially Euclidean geometry, although non-Euclidean geometries have since been discovered. Einstein’s Theory of General Relativity implies that Euclidean space is a good approximation to physical space, where gravity isn’t too strong, and therefore Euclidean geometry is valid for most practical purposes in everyday life.

Debby Gill

Tutor

For more information about studying a distance learning Maths course with Oxford Home Schooling please contact a student adviser on 0800 0 111 024.

In blog 6 in our series for students studying distance learning maths an Oxford Home Schooling distance learning tutor looks at the life and work of Archimedes.

Archimedes was born in Sicily in about 287 BC. He was educated in Egypt and then returned to Sicily where he lived until his untimely death in around 212 BC.

Archimedes is probably most famous for his discovery that when placed in water a floating object displaces an amount of water equal in weight to the object itself. Legend has it that he realised this stepping into his bath so he shouted “Eureka!” and ran home without his clothes. He also wrote many important mathematical works on geometry and mechanics.

Archimedes is credited with the invention of the catapult and also the Archimedes Screw, which is becoming increasingly common as a water feature in children’s play areas.

A popular story tells how Archimedes died at the hands of a Roman soldier. He was working on a mathematical drawing in the sand when he was ordered to stop to meet the General. Archimedes refused saying he first needed to finish his diagram and so the soldier killed him. Some believe Archimedes’ last words were “Don’t disturb my circles.”

Much of Archimedes’ work is a foundation for modern mathematics. Calculations we do today involving the diameter and circumference of the circle are based on his discoveries. He developed an early approximation to the number we call pi.

Debby Gill

Tutor

To find out more about Home Education please visit our website.

For information on our maths courses visit the webpages for KS3 Maths, GCSE Maths, IGCSE Maths or A Level Maths.

Or you can contact a student adviser to discuss your home study options on 0800 0111 024.

In blog 5 in our series on famous mathematicians, an Oxford Home Schooling tutor looks at the life of Pierre-Simon Laplace.

Like Descartes, Laplace was born in France but over 150 years later in 1749. He was a member of the French Academy of Sciences and they cancelled their meeting on the day of his death in 1827 as a mark of respect.

Laplace is famous for his work in many areas of mathematics including calculus and probability as well as for his writings on what he called “celestial mechanics”, the motion of planets in the solar system.

Laplace was a contemporary of Napolean and was Minister of the Interior in his government. He was dismissed after six weeks, however, and while the first edition of his writings on probability is dedicated to Napolean later editions are not.

Laplace’s brain was reportedly smaller than average! It was removed after his death and displayed in a museum for some time – yuck!

Mathematical proofs by Laplace often contained lines such as “it is therefore obvious that…” indicating that he had either mislaid that part of the proof or not quite completed it. Such an approach is not recommended for students of mathematics today!

Laplace was one of the first people to formalise writing on probability. He popularised basic principles such as “the probability of an event occurring is equal to the number of favourable outcomes divided by the number of possible outcomes” which we still use at Key Stage 3 and -GCSE level today. Due to his more advanced work on calculus he has a transform and an equation named after him, which you are sure to meet if you study mathematics at university.

Debby Gill

Tutor

To find out more about home education visit the Oxford Home Schooling website.

For information on our maths courses visit the webpages for KS3, GCSE, IGCSE or A Level Maths.

Or you can contact a student adviser to discuss your home study options.