Category: Mathematics

I am an IB student. This is for my Mathematics Applications and Interpretations course, it is my Internal Assessment, therefore extremely important. The guiding question is the following: How does the parabolic path of a horse change as jump height increases?. I have started the work, which I will attach below to give an idea but which you must absolutely not use as it contains AI. SOME INFO: Rationale and aim

Your aim should be clearly stated in this – make it bold or bullet point it or write on its own line.

Say what you are exploring and why. One paragraph should be enough. Be concise.

• Why have you chosen this topic?
• Why is it important to you?
• What do you hope to explore? Do NOT write a plan or method

Your aim may change during the exploration. This can be a GOOD thing! Explain any change – its important!

Do not use the word hypothesis here. It is a mathematical term relating to hypothesis testing

DO NOT WRITE A PLAN OR METHODOLOGY – THAT STOPPED WHEN THE IB COURSES CHANGED

Data collection

• This can be statistics (secondary data), a diagram (eg a photo in Geogebra with some coordinates), a survey and its results, a picture, a pattern, etc etc
• State where it comes from. You can add the weblink at the bottom of the page
• Make sure you have enough data points (at least 30 for statistics, less for modelling)
• Do you need a sample? If yes, how do you select the data? (random, systematic, cluster, convenience sampling) This is in your textbook.
• Do not let a data table exceed one page. If it does, cut the bottom and put it alongside the top of the table, or shrink the row height. If you have LOTS of data, put in the top of the data (say 3-5 rows) and put the rest in the appendix. If you have a multi-layered exploration, you can use another page for your second lot of data.

We need to see the whole survey – all the Qs need to be seen.

• Define your variables and use italic variables throughout the exploration. Remember to discuss independent and dependent variables if modelling or statistical. Do NOT refer to x and y. Use your variables. Keep the context of the aim throughout.

Analysis

This is obviously the bulk of your exploration.

Do NOT outline the whole plan – that was the old IB syllabus. Just explain as you go, like telling a story.

It may come in multiple parts:

• Say what you are going to do first AND WHY
• Do it
• Reflect on the findings in relation to your aim.

Then you repeat this for your next part. Never leave the reflection until the end. It needs to be throughout your exploration. No exceptions!

We love diagrams, screenshots of your GDC, labelled pictures, etc to help us follow your work. Using multiple forms of mathematical representationincluding tables, graphs, and equations helps convey your ideas effectively. Make sure the reader can see the diagram you are discussing.

Numbers should be exact or given to 3sf, just like in exams, or to a SPECIFIED rounding for your context.

For modelling, consider the fit with R2 AND how appropriate it is in theory. See the padlet for R2 info. You must explain before why youve chosen that type of model using its shape.

For Voronoi diagrams, explain the significance of vertices, edges, and regions within your context.

Use proper notation, no divide signs. See the padlet for writing mathematically. Use the equation editor:

Conclusion

• Summarise your results and refer to your aim.
• Are you surprised about your results?
• Comment on the validity – use domain and range (detail of this is in your analysis section
• How can your results be used by a wider audience? What implication might they have for mankind/our school/Milan/Italy etc?

You do not need to say what you could have done differently. If its important, do it. If its not, forget it! However, you CAN say what you could do to extend the exploration.

General points to remember

• There is a checklist in the – take a look! It includes the formatting of you title page & in general
• Your audience is your peers
• Repetition is bad as it reduces conciseness. Eg, you should explain ONE expected frequency in a chi-squared test to show understanding, then give the whole expected frequency table (from tech).
• For regression lines, consider removing the BIVARIATE outliers first (far away from clusters on a scattergraph or beyond the upper or lower bound (from formula) of BOTH data sets, or draw a box plot with outliers to find these. You could find the regression line before and after and make a decision.
• Do not write any formulae you are not using. For AI SL, use technology and take screenshots, eg your GDC, desmos, Geogebra.
• Genuine personal engagement means using novel mathematical approaches, an exploration driven by original questions, or unique insights. Not by gushing how interested you are! Authentic engagement needs to be demonstrated repeatedly and meaningfully throughout the exploration to achieve the highest marks. PE should drive the exploration in a distinctive and personal way, with thoughtful interpretation.
• Dont delete challenges – discuss them as part of your reflection. Ask your teacher if you are unsure.
• Label all your axes! Including when you have one axis such as box plots
• If you do a process that doesnt help with your aim, stop and delete it. Your exploration needs to be concise.
• No need to explain how you used your GDC or any tech.
• When you discuss a diagram, make sure the reader can see that diagram as they read.
• A result cannot just appear. Show the working or screenshot the technology used I ALSO ATTACHED BELOW THE MARKING CRITERIA, PLEASE TAKE INTO CONSIDERATION DEEPLY. FOLLOW IB CRITERIA. I WILL ALSO ATTACH A PAST IA WITH A SIMILAR QUESTION FOR REFERENCE, OBVIOUSLY DO NOT PLAGIARISE. I HAVE ATTACHED THE PHOTOGRAPHS THAT WILL NEED TO BE MODELLED ON THE IA DRAFT THAT I WROTE, THE ONE MENTIONED EARLIER , THIS WILL NEED TO BE DONE ON DESMOS. AS CAN BE SEEN IN THIS DRAFT I HAVE ALREADY ATTEMPTED TO DO SOME OF THEM BUT I AM NOT SURE IT IS CORRECT. INCLUDE ANY IMAGES OR SCREENSHOTS OF THIS IN THE ESSAY. YOU MAY ALSO INCLUDE GRAPHS, TABLES ETC.