We are delighted to announce the publication of our new study and revision guide for IB Environmental Systems and Societies (ESS). Written for the requirements of the 2017–2023 exam sessions, this revision guide offers succinct coverage of the whole syllabus for Environmental Systems and Societies, with extensive self-test material to help students prepare for mocks and final exams. Clearly structured to match the curriculum, it offers exam tips and original case studies. Here’s what author Adrian Palmer said about his book: I have ...

## Understanding the Chain Rule

Most students are first introduced to the chain rule when shown how to differentiate a function such as y = (3x - 2)5. The problem is that is tempting to try and fit all chain rule differentiations into that format, for example trying to differentiate e3x - 2 in the same way. What is the chain rule? It's a calculus formula with a wide range of uses, just one of which is differentiating a 'function of a function.' Quite simply, differentiation concerns the rate ...

## Straight Line Curves

It's a really relaxing bit of recreational mathematics (albeit with some serious theory behind it), creating beautiful curves just by drawing straight lines. I can only give a glimpse in this blog, but the possibilities are endless. If you're tempted to have a go, one word of caution: be as accurate as you can since the final result can be disappointing if you are careless, or work too fast. My first example is probably about the simplest you can do. I've ...

## Great Mathematicians 5: Al-Khwarizmi

Not heard of him? Born in 780 in what was then Persia, he became one of the learned men of the House of Wisdom in Baghdad. He lived to the age of 70 and, because of the breadth of his work in mathematics and the sciences, he must have been an amazing person to know. The House of Wisdom acquired and translated scientific and philosophical treatises, mainly from Greek, as well as publishing original research. Al-Khwarizmi's first major publication was The ...

## 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 ...