The Math Studies Project for Internal Assessment A good project should be able to be followed by a non-mathematician and be self explanatory all the way through.

Length The project does not have a word limit. It is the quality of the mathematics and the processes used and described that is important, rather than the number of words written.

Commitment The project is a substantial piece of work (counts for 20% of the final IB grade) The project should demonstrate a commitment of time and effort by the student

Choice of Topic The choice of topic must give students sufficient scope to demonstrate their mathematical ability. Statistical Chi-Squared test for Independence Correlation/Linear regression Student ‘t’ test Spearman’s rank order correlation

Choice of Topic Algebraic Modelling Calculus i. Optimization Problems Quadratic Exponential Trigonometric Calculus i. Optimization Problems ii. Modelling

Choice of Topic Number and algebra i Sequences and series ii Linear programming Sets, Logic and Probability i Venn diagrams ii Probabilities Financial Mathematics

Title page The Project must have a clear title Candidate’s name Candidate’s number Date Subject Teacher’s Name

Table of contents Page numbering where each part of the project can be found

A: Introduction Task: What is the aim of the project? The task must focus on a distinct objective with a clear hypothesis or direction The task must be clearly stated Plan: What must be done to achieve this aim? Include as much detail as is necessary to be clear Include a description of method of data collection including any sampling techniques, this will be useful for validity Include a description of the mathematical processes to be used and the reason for choosing these processes

B: Information / Measurement The information/measurements collected may come from a survey, internet, calculation, etc The information/measurements must be sufficient in quantity When the information/measurements is to be split, as in the chi squared test, more than 50 pieces of data is necessary to avoid small expected values, rendering the test invalid. The information/measurements must be relevant The information/measurements must be organised The information/measurements should be reorganised each time, to suit calculations being done eg. Male, female categories If a questionnaire is used then include this in the project A questionnaire should be designed to collect multidimensional mathematical data Raw data must be included to determine the accuracy of calculations

C: Mathematical Processes Always include some relevant simple math processes What is the mathematical process used? Explanation of mathematical technique Why is this particular procedure useful? Relevance/validity of mathematical technique Always state formulae used and do one calculation by hand. The GDC can be used to perform further similar calculations Always check the accuracy of your results Interpret results/draw conclusions from the results of the calculations (Standard deviation is often calculated but not used or commented on.)

C: Mathematical Processes Apply relevant sophisticated processes as thoroughly as for simple process. Interpret results/draw conclusions from the results of the calculations Comment on validity of results Check the accuracy of the results For Chi-squared tests to be valid: Frequencies must be used, not raw data or percentages No more than 20% of the expected cells should have a number less than 5 No expected cells should have a number less than 1 For Linear correlation There is no point in finding the correlation coefficient or regression line if the scatter graph shows that there is no correlation

D: Interpretation of results Always give a thorough and detailed analysis and discussion of results

E: Validity Validity of mathematical processes used Validity of results obtained from these processes

F: Structure and Communication The project should include the discussion in the body of the work Appropriate mathematical language should always be used The project should be presented correctly and in a systematic manner. All sources should be acknowledged Include website addresses in bibliography Include raw data in body of document or in appendix

Conclusion Did the data and calculations support your task? Discuss limitations in its applicability within the project. Scope for improvement /extension of the project

Bibliography State websites Footnotes as necessary Other sources of information

Appendices Raw data collected can be placed here