The Math Studies The Math Studies Project for Internal Project for Internal

AssessmentAssessmentA good project should be able A good project should be able

to be followed by a non-to be followed by a non-mathematician and be self mathematician and be self

explanatory all the way explanatory all the way through.through.

Length Length

The project does not have a word The project does not have a word limit. It is the limit. It is the qualityquality of the of the mathematicsmathematics and the and the processesprocesses used and used and describeddescribed that is that is important, rather than the number important, rather than the number of words written. of words written.

CommitmentCommitment

The project is a substantial piece of The project is a substantial piece of work (counts for 20% of the final IB work (counts for 20% of the final IB grade)grade)

The project should demonstrate a The project should demonstrate a commitment of time and effort by commitment of time and effort by the studentthe student

Choice of TopicChoice of Topic

The choice of topic must give The choice of topic must give students sufficient scope to students sufficient scope to demonstrate their mathematical demonstrate their mathematical ability.ability.

StatisticalStatistical Chi-Squared test for IndependenceChi-Squared test for Independence Correlation/Linear regressionCorrelation/Linear regression Student ‘t’ testStudent ‘t’ test Spearman’s rank order correlationSpearman’s rank order correlation

Choice of TopicChoice of Topic

Algebraic ModellingAlgebraic Modelling QuadraticQuadratic ExponentialExponential TrigonometricTrigonometric

CalculusCalculus i. Optimization Problemsi. Optimization Problems ii. Modelling ii. Modelling

Choice of TopicChoice of Topic

Number and algebraNumber and algebra i Sequences and seriesi Sequences and series ii Linear programmingii Linear programming Sets, Logic and ProbabilitySets, Logic and Probability i Venn diagramsi Venn diagrams ii Probabilitiesii Probabilities Financial MathematicsFinancial Mathematics

Title pageTitle page

The Project must have a clear title The Project must have a clear title Candidate’s nameCandidate’s name Candidate’s numberCandidate’s number DateDate SubjectSubject Teacher’s Name Teacher’s Name

Table of contentsTable of contents

Page numbering where each part of Page numbering where each part of the project can be foundthe project can be found

A: IntroductionA: Introduction Task:Task: What is the aim of the project?What is the aim of the project? The task must focus on a distinct objective with The task must focus on a distinct objective with

a clear hypothesis or direction a clear hypothesis or direction The task must be clearly statedThe task must be clearly stated Plan:Plan: What must be done to achieve this What must be done to achieve this

aim?aim? Include as much detail as is necessary to be Include as much detail as is necessary to be

clear clear Include a description of method of data Include a description of method of data

collection including any sampling techniques, collection including any sampling techniques, this will be useful for validitythis will be useful for validity

Include a description of the mathematical Include a description of the mathematical processes to be used and the reason for processes to be used and the reason for choosing these processeschoosing these processes

B: Information / B: Information / MeasurementMeasurement The information/measurements collected may come from a The information/measurements collected may come from a

survey, internet, calculation, etcsurvey, internet, calculation, etc The information/measurements must be sufficient in The information/measurements must be sufficient in

quantityquantity When the information/measurements is to be split, as in the When the information/measurements is to be split, as in the

chi squared test, more than 50 pieces of data is necessary chi squared test, more than 50 pieces of data is necessary to avoid small expected values, rendering the test invalid.to avoid small expected values, rendering the test invalid.

The information/measurements must be relevantThe information/measurements must be relevant The information/measurements must be organisedThe information/measurements must be organised The information/measurements should be reorganised each The information/measurements should be reorganised each

time, to suit calculations being done eg. Male, female time, to suit calculations being done eg. Male, female categories categories

If a questionnaire is used then include this in the projectIf a questionnaire is used then include this in the project A questionnaire should be designed to collect A questionnaire should be designed to collect

multidimensional mathematical datamultidimensional mathematical data Raw data must be included to determine the accuracy of Raw data must be included to determine the accuracy of

calculationscalculations

C: Mathematical ProcessesC: Mathematical Processes Always include some Always include some relevantrelevant simplesimple math math

processesprocesses What is the mathematical process used? What is the mathematical process used?

Explanation of mathematical techniqueExplanation of mathematical technique Why is this particular procedure useful? Why is this particular procedure useful?

Relevance/validity of mathematical techniqueRelevance/validity of mathematical technique Always state formulae used and do one Always state formulae used and do one

calculation by hand. The GDC can be used to calculation by hand. The GDC can be used to perform further similar calculations perform further similar calculations

Always check the accuracy of your resultsAlways check the accuracy of your results Interpret results/draw conclusions from the Interpret results/draw conclusions from the

results of the calculationsresults of the calculations (Standard deviation is often calculated but (Standard deviation is often calculated but

not used or commented on.) not used or commented on.)

C: Mathematical ProcessesC: Mathematical Processes Apply Apply relevant sophisticatedrelevant sophisticated processes as processes as

thoroughly as for simple process.thoroughly as for simple process. Interpret results/draw conclusions from the results Interpret results/draw conclusions from the results

of the calculationsof the calculations Comment on validity of resultsComment on validity of results Check the accuracy of the resultsCheck the accuracy of the results

For Chi-squared tests to be valid:For Chi-squared tests to be valid: Frequencies must be used, not raw data or Frequencies must be used, not raw data or

percentagespercentages No more than 20% of the expected cells should No more than 20% of the expected cells should

have a number less than 5have a number less than 5 No expected cells should have a number less than No expected cells should have a number less than

11 For Linear correlationFor Linear correlation

There is no point in finding the correlation There is no point in finding the correlation coefficient or regression line if the scatter graph coefficient or regression line if the scatter graph shows that there is no correlationshows that there is no correlation

D: Interpretation of resultsD: Interpretation of results

Always give a thorough and detailed Always give a thorough and detailed analysis and discussion of resultsanalysis and discussion of results

E: ValidityE: Validity

Validity of mathematical processes Validity of mathematical processes usedused

Validity of results obtained from Validity of results obtained from these processes these processes

F: Structure and F: Structure and CommunicationCommunication

The project should include the The project should include the discussion in the body of the workdiscussion in the body of the work

Appropriate mathematical language Appropriate mathematical language should always be usedshould always be used

The project should be presented The project should be presented correctly and in a systematic manner.correctly and in a systematic manner.

All sources should be acknowledgedAll sources should be acknowledged Include website addresses in Include website addresses in

bibliographybibliography Include raw data in body of document Include raw data in body of document

or in appendixor in appendix

ConclusionConclusion

Did the data and calculations Did the data and calculations support your task?support your task?

Discuss limitations in its Discuss limitations in its applicability within the project.applicability within the project.

Scope for improvement /extension of Scope for improvement /extension of the projectthe project

BibliographyBibliography

State websites State websites Footnotes as necessaryFootnotes as necessary Other sources of informationOther sources of information

AppendicesAppendices

Raw data collected can be placed Raw data collected can be placed herehere