Some Mathematical Tips for the New Year

Happy New Year everybody! At this time last year I suggested some new year resolutions to help you in your studies. They are of course valid at all times, and if you didn't see them, then have a look now. This time I've got some tips which you might want to note down; they cover specific areas of the syllabus, although they aren't applicable to all of HL, SL, and Studies. Degrees or Radians? Well, it depends on what the question is asking you ...

Oligarchy and Democracy (Part 2)

Plato regards the descent of political regimes into tyranny as a gradual process in which each type of government is transformed into an even more unjust or imperfect state. The oligarchic man is the son of the timarchic man who has lost his reputation and fortune ‘in some political disaster’. Reduced to poverty, his son neglects the dialectic power of reason which he uses instead to further his selfish materialistic ends. In his craving for money, the oligarchic man ‘is ...

Concerning Leap Years

Who Introduced the Leap Year? Julius Ceasar, believe it or not. The Roman calendar had got seriously out of date with the solar calendar, even though Roman officials were supposed to introduce an extra month every so often. So Caesar consulted his top astronomers who worked out that the solar year—the time it takes for the Earth to do exactly one rotation around the sun—was 365.25 days. So, by maintaining a calendar with 365 days, and adding one extra day every ...

Drawing Graphs on the TI-84

A previous post on solving equations with the TI-84 has proved very popular, so here are some tips and tricks when using the GDC for drawing graphs and associated functionality. Pre-set scales It's easy enough to type in an equation and then press the graph button. However, the most important thing to do which helps make sense of any graph is to set up the correct window: the minimum and maximum value of the displayed coordinates, and the associated scale marks. The ...

Rise in Infections Due to Chickens

The rising trend of raising backyard chickens in US cities and suburbs is bringing with it huge increase in the number of illnesses from poultry-related diseases, at least one of them fatal. Between January 2017 and October 2017, over 1,100 people contracted salmonella poisoning from chickens and ducks in 48 states, according to the Centers for Disease Control (CDC). Almost 250 were hospitalized and one person died. The rate was four times higher than in 2015. The CDC estimates that the actual ...

What’s the difference between an expression and an equation?

Well, I’ll answer that in a moment. More generally, you should be familiar with algebraic terminology since relevant words are used in exam questions—you need to know exactly what they mean. Let’s start at the beginning and build up… Constants and variables A constant is a fixed number, such as 2. A variable is a letter which can take on different values, such as $x$. To complicate things, letters can sometimes be used to stand for constants! For example, I can define ...

Electric Vehicles in China

China wants to lead the world in the manufacture and use of clean-energy cars, and to achieve this it will need to ensure research and development in battery production. Batteries have become vital to the manufacture of clean energy cars. As part of China’s industry development plan (April 2017), the government pledged to promote research and development of key battery cell parts and improve management structures in the industry. Batteries are at the heart of clean energy vehicles because they are ...

Muhabbat Sharapova, Mathematician – and Hero of Uzbekistan

To be named as a "Hero of Uzbekistan" is to be awarded the highest national honour in that country. Recently, Muhabbat Sharapova, one of the country's top mathematicians, received the award - not for her mathematical prowess, but because she has turned down job offers from many leading universities and institutions in favour of remaining a maths teacher in her small home town. In an interview for the BBC's 100 women initiative, she says: "Mathematics is the mother of all sciences." ...

Collision theory and mechanisms – linking it together

I’ve just started teaching the kinetics topic to my students and so far we have focussed on the collision theory. Have you heard of this? The collision theory explains to us what happens during chemical reactions in terms of the collision of particles. In order for a chemical reaction to occur, particles need to come together (collide) with sufficient energy (speed). This is called the activation energy (and is defined as the minimum amount of energy required for a chemical reaction). If ...

Chocolate industry destroying rainforest in Cote d’Ivoire

The world’s chocolate industry is driving deforestation on a devastating scale in West Africa. As global demand for chocolate booms, ‘dirty’ beans from deforested national parks have entered big business supply chains. As much as 40% of the world’s cocoa comes from Cote d’Ivoire, and the rainforest cover has been reduced by more than 80% since 1960. The chocolate industry has many small-scale farmers who grow cocoa on plantations, many of which are illegal as they are in national parks or protected ...