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This is the British International School Phuket’s IB maths exploration page. This list is primarily for Maths Studies students (exam in 2020) and IB Maths Applications students (exam in 2021 onwards). If you are doing a Maths SL, HL exploration (exam in 2020), or are doing IB Maths Analysis (exam in 2021 onwards) then go to this page instead.

**NEW**

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. Written by an experienced IB teacher this guide talks you through:

- An introduction to the essentials about the investigation,
- The new marking criteria,
- How to choose a topic,
- Examples of around 70 topics that could be investigated,
- Useful websites for use in the exploration,
- A student checklist for completing a good investigation,
- Common mistakes that students make and how to avoid them,
- A worked example for the maths behind correlation investigations,
- A selection of some interesting exploration topics explored in more depth,
- Teacher advice for marking,
- Templates for draft submissions,
- Some examples of beautiful maths using Geogebra and Desmos.

**You can download this here.**

**IB Revision with** Revision Village

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. I would strongly recommend students use this as a resource during the course. You choose your subject (HL/SL/Studies if your exam is in 2020 or Applications/Analysis if your exam is in 2021), and then have the following resources:

The Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and each area then has a number of graded questions. What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial. Really useful!

The Practice Exams section takes you to ready made exams on each topic – again with worked solutions. This also has some harder exams for those students aiming for 6s and 7s.

The Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year. I would really recommend everyone making use of this – there is a mixture of a lot of free content as well as premium content so have a look and see what you think.

**Maths Studies and Applications IA Exploration Topics**

Make sure you read the Maths Studies guidance from the IB prior to starting your IA maths exploration – this linked site gives the full list of assessment criteria you will be judged against and also gives 9 full examples of investigations students have done.

Given the assessment criteria it’s probably easiest to conduct a data analysis investigation, though you can choose to explore other parts of the syllabus instead. To get good marks make sure you carefully follow the marking criteria points given by the IB and try and personalise your investigation as much as possible. Be innovative, choose something you are interested in and enjoy it!

**Primary or Secondary data? **

The main benefit of primary data is that you can really personalise your investigation. It allows you scope to investigate something that perhaps no-one else has ever done. It also allows you the ability to generate data that you might not be able to find online. The main drawback is that collecting good quality data in sufficient quantity to analyze can be time consuming. You should aim for an absolute minimum of 50 pieces of data – and ideally 60-100 to give yourself a good amount of data to look at.

The benefits of secondary data are that you can gain access to good quality raw data on topics that you wouldn’t be able to collect data on personally – and it’s also much quicker to get the data. Potential drawbacks are not being able to find the raw data that fits what you want to investigate – or sometimes having too much data to wade through.

**Secondary data sources:**

1) The Census at School website is a fantastic source of secondary data to use. If you go to the random data generator you can download up to 200 questionnaire results from school children around the world on a number of topics (each year’s questionnaire has up to 20 different questions).

2) If you’re interested in sports statistics then the Olympic Database is a great resource. It contains an enormous amount of data on winning times and distances in all events in all Olympics. Follow links at the top of the page to similar databases on basketball, golf, baseball and American football.

3) If you prefer football you can also find a lot of football stats on the Who Scored website. This gives you data on things like individual players’ shots per game, pass completion rate etc.

4) The World Bank has a huge data bank – which you can search by country or by specific topic. You can compare life-expectancy rates, GDP, access to secondary education, spending on military, social inequality, how many cars per 1000 people and much much more.

5) Gapminder is another great resource for comparing development indicators – you can plot 2 variables on a graph (for example urbanisation against unemployment, or murder rates against urbanisation) and then run them over a number of years. You can also download Excel speadsheets of the associated data.

6) Wolfram Alpha is one of the most powerful maths and statistics tools available – it has a staggering amount of information that you can use. If you go to the examples link above, then you can choose from data on everything from astronomy, the human body, geography, food nutrition, sports, socioeconomics, education and shopping.

7) Plotly is a great visual graphic site – you can create visually interesting infographics and analyse data from hundreds of other sources.

8) TSM – the Technology for Secondary Mathematics is something of an internet dinosaur – but has a great deal of downloadable data files on everything from belly-button ratios to lottery number analysis and baby weights.

9) Google Public Data – an enormous source for public data, which is displayed graphically and can be searched.

10) Nationmaster – another huge site with pretty much any statistic and data comparing countries. Currently they have 19 million data points – so you’re likely to find something useful!

11) Google word usage analysis – a great tool which allows you to track the usage of words over the centuries.

**Example Maths Studies IA Investigations:**

Some of these ideas taken from the excellent Oxford IB Maths Studies textbook.

**Correlations:**

1) Is there a correlation between hours of sleep and exam grades?

Studies have shown that a good night’s sleep raises academic attainment.

2) Is there a correlation between height and weight?

The NHS use a chart to decide what someone should weigh depending on their height. Does this mean that height is a good indicator of weight?

3) Is there a correlation between arm span and foot height?

This is also a potential opportunity to discuss the Golden Ratio in nature.

4) Is there a correlation between the digit ratio and maths ability?

Studies show there is a correlation between digit ratio and everything from academic ability, aggression and even sexuality.

5) Is there a correlation between smoking and lung capacity?

6) Is there a correlation between GDP and life expectancy?

Run the Gapminder graph to show the changing relationship between GDP and life expectancy over the past few decades.

7) Is there a correlation between numbers of yellow cards a game and league position?

Use the Guardian Stats data to find out if teams which commit the most fouls also do the best in the league.

8) Is there a correlation between Olympic 100m sprint times and Olympic 15000m times?

Use the Olympic database to find out if the 1500m times have go faster in the same way the 100m times have got quicker over the past few decades.

9) Is there a correlation between sacking a football manager and improved results?

A recent study suggests that sacking a manager has no benefit and the perceived improvement in results is just regression to the mean.

10) Is there a correlation between time taken getting to school and the distance a student lives from school?

11) Does eating breakfast affect your grades?

12) Is there a correlation between stock prices of different companies?

Use Google Finance to collect data on company share prices.

13) Does teenage drinking affect grades?

A recent study suggests that higher alcohol consumption amongst teenagers leads to greater social stress and poorer grades.

14) Is there a correlation between unemployment rates and crime?

If there are less work opportunities, do more people turn to crime?

15) Is there a correlation between female participation in politics and wider access to further education?

16) Is there a correlation between blood alcohol laws and traffic accidents?

17) Is there a correlation between height and basketball ability?

18) Is there a correlation between stress and blood pressure?

19) Is there a correlation between Premier League wages and league positions?

**Normal distributions:**

1) Are a sample of student heights normally distributed?

We know that adult population heights are normally distributed – what about student heights?

2) Are a sample of flower heights normally distributed?

3) Are a sample of student weights normally distributed?

4) Are a sample of student reaction times normally distributed?

Conduct this BBC reaction time test to find out.

5) Are a sample of student digit ratios normally distributed?

6) Are the IB maths test scores normally distributed?

IB test scores are designed to fit a bell curve. Investigate how the scores from different IB subjects compare.

7) Are the weights of “1kg” bags of sugar normally distributed?

**Other statistical investigations**

1) Does gender affect hours playing sport?

A UK study showed that primary school girls play much less sport than boys.

2) Investigation into the distribution of word lengths in different languages.

The English language has an average word length of 5.1 words. How does that compare with other languages?

3) Do bilingual students have a greater memory recall than non-bilingual students?

Studies have shown that bilingual students have better “working memory” – does this include memory recall?

4) Investigation about the distribution of sweets in packets of Smarties. A chance to buy lots of sweets! Also you could link this with some optimisation investigation.

5) 22) Using Chi Squared to crack codes – Chi squared can be used to crack Vigenere codes which for hundreds of years were thought to be unbreakable. Unleash your inner spy!

6) Which times tables do students find most difficult to learn? – Are some calculations like 7×8 harder than others? Why?

**Modelling using calculus**

1) How can you optimise the area of a farmer’s field for a given length of fence?

A chance to use some real life maths to find out the fence sides that maximise area.

2) Optimisation in product packaging.

Product design needs optimisation techniques to find out the best packaging dimensions.

**Probability and statistics
**

1) The probability behind poker games

2) Finding expected values for games of chance in a casino.

3) Birthday paradox:

The birthday paradox shows how intuitive ideas on probability can often be wrong. How many people need to be in a room for it to be at least 50% likely that two people will share the same birthday? Find out!

4) Which times tables do students find most difficult?

A good example of how to conduct a statistical investigation in mathematics.

5) Handshake problem

With n people in a room, how many handshakes are required so that everyone shakes hands with everyone else?

**Other ideas
**

If you want to do an investigation with a bit more mathematical content then have a look at this page for over 300 ideas for Maths SL and HL students.