Maths IA – Maths Exploration Topics:

Scroll down this page to find over lots of maths IA exploration topics and ideas for IB Applications SL mathematics students doing their internal assessment (IA) coursework.  Topics focus on statistics and data analysis – but also include other ideas!

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Also make sure to download a completely free 63 page Exploration Guide pdf packed full of essential advice about how to get excellent marks on your coursework:  You can download this for free here.

Essential resources for IB teachers:

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IB Teacher support with A new website for teachers at international schools.

If you are a teacher then please also visit my new site:  My new site has been designed specifically for teachers of mathematics at international schools.  The content now includes over 2500 pages of pdf content for the entire SL and HL Analysis syllabus and also the SL and HL Applications syllabus.  Some of the content includes:

  1. Original pdf worksheets (with full worked solutions) designed to cover all the syllabus topics.  These make great homework sheets or in class worksheets – and are each designed to last between 40 minutes and 1 hour.
  2. Original Paper 3 investigations (with full worked solutions) to develop investigative techniques and support both the exploration and the Paper 3 examination.
  3. A large number of enrichment activities such as treasure hunts, quizzes, investigations, Desmos explorations, Python coding and more – to engage IB learners in the course.

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 at least 50 pieces of data 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.

Useful programs/sites for data collection:

1) TSM – the Technology for Secondary  Mathematics has got one of the best link directories for downloadable data statistics files on everything from exam board data, weather data, baby weights, ice cream sales and much much more!

2) If you are interested in the environment, The National Oceanic and Atmospheric Administration (NOAA) has collected a large amount of environmental data for use.

3) If you like 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.   For example you can find out sports data on individual player pass completion rates in basketball.

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

8) Nationmaster – another huge site with pretty much any statistic and data comparing countries.  Currently they have 19 million data points!

 9) Desmos – a great online graphing site

10) Geogebra – another very powerful graphing application (also does 3D)

 11) Tracker software will allow you to track data from a video and then produce graphs. 

IB Exploration Guide

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I’ve written a comprehensive IB exploration guide which contains the Exploration Guide Essentials (63 pages), Statistics for Explorations (55 pages) and Modeling for Explorations (50 pages).  Get top tips from an IB examiner to help you get excellent scores on your coursework!  You can download from here.

Example Applications SL IA Investigations:

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


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.