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IB Math SL Exploration Outline Information Name_________________________ Outline Due:_______________________ Outline Criteria: The outline MUST BE TYPED and include the following… Aim of the paper - One or two sentences that summarize your entire paper. This will also appear in your paper. Rationale of why you picked this topic. A list of the key parts of your paper, what kind of math you will be looking at, and where/how that math will be addressed in the paper. o Along the way (or at least in the last part of your paper), you should include a reflection of your exploration. Also include somewhere how you will incorporate “personal engagement.” 2 Examples: Outline for Medical Test Accuracy and Statistics Aim of the paper: What does it mean for a medical test to be 97% accurate or 99% accurate? Rationale (why did you pick this topic): I am interested in looking at how probability is used in the medical field. I want to look at how much error is acceptable in medical tests and what those errors mean. Key Parts of the Paper: 1. Look at some made-up data and address what it means for test results to be true negatives or false positives. In what cases do people actually have the disease (whether diagnosed or not). 2. Use conditional probabilities to compare the test result people are given vs. what it actually is. 3. Use data from the HIV/AIDS virus and conditional probabilities to see how many people are possibly misdiagnosed. Use this data to verify the accuracy that the test claims to have. 4. Reflect on what this data means. Mr. Peterson’s Sample Outline Aim of the paper: To show how can calculus be used to find the “volumes” of 4 dimensional objects. Rationale (why did you pick this topic): I’ve always been interested TV shows such as the Twilight Zone and movies such as Interstellar that mess with your mind. This led me to an interest in the fourth dimension – we can’t see it, but mathematically we can discover many of the properties of it. I want to dig deeper into the fourth dimension and explore the amount of space 4D objects take up. Key Parts of the Paper: 1. Explain what the fourth dimension is and various ways to understand what it would look like. 2. Start with the area of a square, volume of a cube, and lead in to the 4D-volume of a hypercube. 3. Show how calculus can be used to find the areas of a circle (2D) and volume of a sphere (3D). 4. Use calculus to show how to get the formula for the 4D-volume of a hypersphere and use it to find an actual 4D-volume. 5. Reflection on the paper. (Options: Look at what the results of the 4D-volume mean, or look at applications, or ask questions about the 5th dimension.)