Let’s let the height of the box be $$h$$. 3) Chinese postman problem – This is a problem from graph theory – how can a postman deliver letters to every house on his streets in the shortest time possible? 16) Are we living in a computer simulation? In the examples to this point we’ve put in quite a bit of discussion in the solution. 5) Königsberg bridge problem: The use of networks to solve problems. As always, let’s start off with a quick sketch of the box. On occasion, the constraint will not be easily described by an equation, but in these problems it will be easy to deal with as we’ll see. 5) Knight’s tour in chess: This chess puzzle asks how many moves a knight must make to visit all squares on a chess board. We’ve worked quite a few examples to this point and we have quite a few more to work. 28) How to avoid a Troll – an example of a problem solving based investigation, 29) The Gini Coefficient – How to model economic inequality. In order to do it full justice, you need to begin early. The third method however, will work quickly and simply here. 4) Rocket Science and Lagrange Points – how clever mathematics is used to keep satellites in just the right place. If $$f''\left( x \right) < 0$$ for all $$x$$ in $$I$$ then $$f\left( c \right)$$ will be the absolute maximum value of $$f\left( x \right)$$ on the interval $$I$$. We also can’t forget to add in the area of the two caps, $$\pi {r^2}$$, to the total surface area.

Sketching the situation will often help us to arrive at these equations so let’s do that. Let’s also suppose that we run all of them through the second derivative test and determine that some of them are in fact relative minimums of the function. 20) The Coastline Paradox – how we can measure the lengths of coastlines, and uses the idea of fractals to arrive at fractional dimensions. However, suppose that we knew a little bit more information. 25) Euler’s 9 Point Circle. What is your best way of surviving the zombie apocalypse? The Shoelace Algorithm to find areas of polygons.

Are maths students better than history students? 11) The Monty Hall problem – this video will show why statistics often lead you to unintuitive results. So, let’s get the derivative and find the critical points. 4) Bluffing in Poker: How probability and game theory can be used to explore the the best strategies for bluffing in poker. Use computer graphing to investigate. Is Bitcoin going to keep rising or crash? ie 6 is a perfect number because 1 + 2 + 3 = 6. ( Log Out /

Written by an experienced IB teacher this guide talks you through: There’s a really great website been put together to help IB students with topic revision both for during the course and for the end of Year 12 school exams and Year 13 final exams. In the last two examples we’ve seen that many of these optimization problems can be done in both directions so to speak. Can you find the pattern behind it? If $$f'\left( x \right) < 0$$ for all $$x < c$$ and if $$f'\left( x \right) > 0$$ for all $$x > c$$ then $$f\left( c \right)$$ will be the absolute minimum value of $$f\left( x \right)$$ on the interval $$I$$. This particular problem was solved by Euler. 3) Stacking cannonballs – solving maths with code – how to stack cannonballs in different configurations.

You can download a 60-page pdf guide to the entire IA coursework process for the new syllabus (first exam 2021) to help you get excellent marks in your maths exploration. This is a function which is used in Quantum mechanics – it describes a peak of zero width but with area 1. One of the main reasons for this is that a subtle change of wording can completely change the problem.

For example, Mod 3 means the remainder when dividing by 3. 11) Zeno’s paradox of Achilles and the tortoise: How can a running Achilles ever catch the tortoise if in the time taken to halve the distance, the tortoise has moved yet further away? What is the Mordell equation and how does it help us solve mathematical problems in number theory? 3) Mathematical methods in economics – maths is essential in both business and economics – explore some economics based maths problems.

With some examples one method will be easiest to use or may be the only method that can be used, however, each of the methods described above will be used at least a couple of times through out all of the examples.