After the dust has settled after Year 7, Year 8 offers students the chance to take stock of their progress and understand their strengths and weaknesses.
Year 8 is an essential stage of Mathematical learning for you to acquire and consolidate the rest of the foundations for High School Maths.
Performing 1oth maths guide express in Year 8, or failing to 1oth maths guide express mastery of the basics, could condemn you to a lower stream. Before you can excel in Year 8 Maths, you must master the understanding of topics.
1oth 1oth Maths Guide News maths guide express may struggle to acquire and implement the content they learned last year in Year 7 because it still feels like a big leap from Primary. These are some of the reasons students struggle:.
This is especially true for Maths. Mastering Maths is a systematic process that begins with understanding the theory of each concept. You can also check your knowledge with checkpoint questions for each subject. These will let you test your skills. If you want to improve your marks in Maths, you must be methodical in your approach. Now it is time to familiarise yourself with the content of this Guide.
This is a resource that you should come back to consistently as you encounter the subjects at school during the year.
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Question 8. The perimeter of a certain sector of a circle is equal to the length of the arc of a semicircle having the same radius. Express the angle of the sector in degrees, minutes and 1oth Maths Guide Weight seconds.
Question 9. An airplane propeller rotates times per minute. Find the number of degrees that a point on the edge of the propeller will rotate in 1 second. Question What angle will it turn in 20 seconds? A circular metallic plate of radius 8 cm and thickness 6 mm is melted and molded into a pie a sector of the circle with thickness of radius 16 cm and thickness 4 mm.
Find the angle of the sector. Solution: Area of the circular plate melted. An athlete runs 4 times around a circular running track to describe m. What is the radius of the tract degrees subtended at the centre of the circle, after he has run a distance of m? So, what is the optimum strategy for prisoner A? In this version he should testify � because whichever strategy his partner chooses this gives prisoner A the best possible outcome.
Looking at it in reverse, if prisoner B testifies, then prisoner A would have been best testifying gets 5 years rather than If prisoner B remains silent, then prisoner A would have been best testifying goes free rather than 6 months.
This brings in an interesting moral dilemma � ie. This situation represents a form of plea bargaining � which is more common in America than Europe. Part of the dilemma arises because if both men know that the optimum strategy is to testify, then they both end up with lengthy 5 year jail sentences.
If only they can trust each other to be altruistic rather than selfish � and both remain silent, then they get away with only 6 months each. So does mathematics provide an amoral framework? Game theory became quite popular during the Cold War, as the matrix above represented the state of the nuclear stand-off. The threat of Mutually Assured Destruction MAD meant that neither the Americans or the Russians had any incentive to strike, because that would inevitably lead to a retaliatory strike � with catastrophic consequences.
The above matrix uses negative infinity to represent the worst possible outcome, whilst both sides not striking leads to a positive pay off. Such a game has a very strong Nash Equilibrium � ie. Could the optimal maths strategy here be said to be responsible for saving the world?
If someone is nasty to you on round one ie by testifying then you can punish them the next time. So with the threat of punishment, a mutually co-operative strategy is superior. You can actually play the iterated Prisoner Dilemma game as an applet on the website Game Theory.
Alternatively pairs within a class can play against each other. An interesting extension is this applet , also on Game Theory, which models the evolution of 2 populations � residents and invaders. You can set different responses � and then see what happens to the respective populations.
This is a good reflection of interactions in real life � where species can choose to live co-cooperatively, or to fight for the same resources. The first stop for anyone interested in more information about Game Theory should be the Maths Illuminated website � which has an entire teacher unit on the subject � complete with different sections,a video and pdf documents.
There are a lot of different games which can be modeled using game theory � and many are listed here. Some of these have direct applicability to population dynamics, and to the geo-politics of war versus peace. Simulations -Traffic Jams and Asteroid Impacts. This would be an interesting piece of data to test for the strength of correlation:.
Which clearly shows a strong positive correlation. For even more data, a club by club full breakdown is also provided by the Guardian here. I have also made the data above into a word document to be used as a some A4 posters � and you can download that here: Premier League Debt. An Investigation.
Why Study Maths? Careers Inspiration. This is inspired by a fantastic website � we use math � which has a massive amount of information about different careers using mathematics in a really well laid out format. According to a comprehensive careers survey by Careers Cast � which looked at over different jobs and ranked them for stress, pay, job stability and work environment � 6 of the top 10 jobs require or strongly prefer maths graduates or those with a good mathematical background.
From the we use math site there is information with interviews, maths required, job skills etc on about 50 maths related jobs � as well as some pretty impressive statistics about the usefulness of mathematics:. There is also an accompanying video with interviews from a large range of mathematicians talking about the jobs they have gone into:.
Michio Kaku � American Professor of Theoretical Physics and fantastic populariser of mathematics and physics takes us through a 40 minute journey on the importance of physics in explaining the universe:. April 15, in IB Maths , ToK maths Tags: Graham , Graham's Number , Grahams number literally big enough to collapse your head into a black hole , mathematics , teaching maths 4 comments. This is a great introduction to notation for really big numbers.
Numberphile have produced a fantastic video on the topic:. Which clearly can lead to some absolutely huge numbers very quickly. Therefore will there always be things in the Universe which are beyond full human understanding? Or can mathematics provide a shortcut to knowledge that would otherwise be inaccessible? How Are Prime Numbers Distributed? Twin Primes Conjecture � a discussion about the amazing world of prime numbers. If any number ends with the digit 0, it should be divisible by In other words, it will also be divisible by 2 and 5 as.
Prime factorisation of. It can be observed that 5 is not in the prime factorisation of. Hence, for any value of n , will not be divisible by 5.
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