Name: __________________________________ Period: _____ A9

MATH STUDIES PROJECT

LIST OF SAMPLE TOPICS ............................... 3

DEADLINES ................................................... 4

COMMON FURTHER PROCESSES .............. 5 - 7

CHI-SQUARE CRITICAL VALUE TABLE ............ 8

ROUGH DRAFT DIRECTIONS .................. 9 – 10

ADVICE FROM IB ................................ 11 - 12

IB RUBRIC ............................................ 13 - 17

OVERVIEWFrom IB Curriculum Guide

The internal assessment is an integral part of the course and is compulsory for all students. It enables students to demonstrate the application of their skills and knowledge, and to pursue their personal interests, without the time limitations and other constraints that are associated with written examinations. It is an individual project and is a piece of written work based on personal research involving the collection, analysis and evaluation of data.

The specific purposes of the project are to:o develop students’ personal insight into the nature of mathematics and to develop

their ability to ask their own questions about mathematicso encourage students to initiate and sustain a piece of work in mathematicso enable students to acquire confidence in developing strategies for dealing with new

situations and problemso provide opportunities for students to develop individual skills and techniques, and to

allow students with varying abilities, interests and experiences to achieve a sense of personal satisfaction in studying mathematics

o enable students to experience mathematics as an integrated organic discipline rather than fragmented and compartmentalized skills and knowledge

o enable students to see connections and applications of mathematics to other areas of interest.

As part of the learning process, teachers can give advice to students on a first draft of the project. This advice should be in terms of the way the work could be improved, but this first draft must not be heavily annotated or edited by the teacher. The next version handed to the teacher after the first draft must be the final one. Each student must sign a declaration for the internal assessment to confirm that the work is his or her authentic work and constitutes the final version of that work. Once a student has officially submitted the final version of the work to a teacher, together with the signed declaration, it cannot be retracted.

The same piece of work cannot be submitted to meet the requirements of both the internal assessment and the extended essay. Work for this project must be separate from work for other courses’ internal assessments. Group work should not be used for projects. Each project is an individual piece of work based on different data collected or measurements generated. The internal assessment is an integral part of the mathematical studies SL course, contributing 20% to the final assessment in the course.

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Each project must contain:

o a titleo a statement of the task and plano measurements, information or data that have been collected and/or generatedo an analysis of the measurements, information or datao interpretation of results, including a discussion of validityo appropriate notation and terminology.

Students can choose from a wide variety of project types, for example, modelling, investigations, applications and statistical surveys.

The project should not normally exceed 2,000 words, excluding diagrams, graphs, appendices and bibliography. However, it is the quality of the mathematics and the processes used and described that is important, rather than the number of words written.

Students are expected to consult the teacher throughout the process. In developing their projects, students should make use of mathematics learned as part of the course. The level of sophistication of the mathematics should be similar to that suggested by the syllabus. It is not expected that students produce work that is outside the mathematical studies SL syllabus. The project is internally assessed by the teacher and externally moderated by the IB using assessment criteria that relate to the objectives for mathematical studies SL.

Each project is assessed against the following criteria. The final mark for each project is the sum of the scores for each criterion. The maximum possible final mark is 20.

Criterion A Introduction 3

marks

Criterion B Information/measurement 3

marks

Criterion C Mathematical processes 5

marks

Criterion D Interpretation of results 3

marks

Criterion E Validity 1 mark

Criterion F Structure and communication 3

marks

Criterion G Notation and terminology 2

marks

Students will not receive a grade for mathematical studies SL if they have not submitted a project.

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THEREFORE, STUDENTS CANNOT EARN THEIR IB DIPLOMA IF THEY HAVE NOT COMPLETED ALL OF THEIR INTERNAL AND EXTERNAL ASSESSMENTS. THIS

PROJECT IS AN INTERNAL ASSESSMENT.

MORE IMPORANTLY, ACCORDING TO THE STATUTES FOR THE STATE OF FLORIDA, STUDENTS IN THE IB PROGRAM OF STUDY WHO DO NOT COMPLETE THEIR

INTERNAL ASSESSMENTS CANNOT GRADUATE FROM HIGH SCHOOL. CERTAIN REQUIREMENTS (E.G.: ECONOMICS, GOVERNMENT, AND HOPE) ARE WAIVED FOR

IB STUDENTS THAT WOULD NEED TO BE MET IN ORDER TO GRADUATE.

LIST OF SAMPLE TOPICS

The following list gives the titles of some projects that attained a variety of marks. Some titles are more descriptive than others and in most cases the original wording has been retained.

Aestheticso Calculating beauty-----the

golden ratioo Colour preferenceso Daylight in a classroom-----

architectural designo Is my mirror showing an

accurate image?o Origami applications to

mathematicso Shadows and heighto M.C. Escher: symmetry and

infinity of art

Business and financeo A comparative study of

shares, real estate, bonds and banks

o Analysis of stock market changes

o Buying a car-----payment options

o Economic development and levels of income

o Mortgage loans

o Running a restaurant and dance club

o Investigating mobile phone traffic

o Analysis of basic U.S. stocks over the period 1980---1999

o Investing in a hotel in Costa Rica

o Organising a wedding

Food and drinko A comparison between calorie

intake and gendero Dine in or dine out?o High school luncheso Jelly bean studyo Take the cola challengeo The cookie problem-----taste is

all-importanto The operation of a tuck shopo Investigating eating trends of

today’s youtho Costs of products bought

online compared to local grocery stores

Health and fitnesso Breakfast and school gradeso Breast and cervical cancer-----

ethnic comparisono BMI (body mass index)o Infant mortalityo Investigating reaction timeso A comparison between lung

capacity, age, weight and body fat

o Aids awareness in Maseruo Blood pressure

Nature and natural resourceso Analysis of the cost and utility

of gas versus electricity in an average domestic situation

o Calculating time of sunrise and sunset

o Earthquakeso The quality of local watero A statistical investigation of

leaveso The affect that different

temperatures have on the

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level of growth of bacteria in water from a garden pool

o Sunspot cycleso Animal population

Peopleo Characteristics of federal

prisonerso Gender based discriminationo Perception of timeo The psychology of memoryo Voter turnouto Correlation study of TV versus

sleep timeso Power to weight ratioo A study of the effect of colour

on human emotionso Which type of movies do

males/females prefer?o Does gender influence choice

of favourite animal?o Relation between

unemployment and criminality in Sweden from 1988---1999

o Relations between international and bilingual students: jobs, pocket money and spending behaviour

School-based titleso Girls’ sport and gradeso Left-handed studentso Performance of local students

compared with foreign students

o Searching for the ideal sound

Sport and nationalityo Sporto Baseball bat speed compared

with body weighto Effective short corners in

hockeyo Factors affecting athletic

performanceo Height, weight and swimming

performanceo How far do tennis balls roll?o Resistance of fishing lineo Stoppage times in National

Football League (NFL) gameso Will female swimmers ever

overtake male swimmers?o Comparing heights from

sports datao Rollerblading and the maths

behind ito The effect of sport on grade

point average (GPA)o Olympic Games in Sydney

2000: track and field times

Travel and transporto Cost efficiency of vehicleso Driving skillso Petrol priceso Seat belt useo Traffic movement in an urban

areao Transport safety in town

centreso Running late and driving

habitso Traffic study of Schipol

International Airport

o The effect of blood alcohol content law on the number of traffic collisions in Sacramento

o Public transportation costs and car usage: a personal comparison

Miscellaneouso Average puppy weights in the

first few weekso Counting weedso International phone call

pricingo Memoryo Practice makes perfecto Predicting cooling timeso Sine waves in pitch

frequencieso Spanning treeso Topography and distanceo Video games and response

timeso The Ferris wheelo The geometry involved in

billiardso Investigation into different

brands of batterieso Statistical comparison of the

number of words in a sentence in different languages

o How many peas are there in a 500 g box of peas?

o Correlation between women’s participation in higher education and politics from 1955---2000

As stipulated in the curriculum paper, you will earn grades within the first two quarters from deadline work. A grade for the final project will be included in the fourth quarter (a quarter that has very few grades). NO PROJECTS WILL BE ACCEPTED AFTER THE FINAL DUE DATE.

Work (in the form of a physical copy) is due when it is collected in class. Work submitted electronically is due by 11:55 PM the day before the physical copy is due. Late work for the project is immediately docked 10% for each day it is late, up to 50% off. If a deadline requires both electronic and physical work, both copies must be turned in on time for the work to be considered on time. The first copy that is late starts the clock on the late work penalty. All previous assignments must be complete for any assignment to receive on-time credit.

Deadline (Electronic

Copy)

Deadline (Physical

Copy)Work Points

September 4 Initial Planning Form 10

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October 12 Statement of the Task and Plan Refer to the deadline’s rubric on the class website for all requirements.

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November 1 at 11:55 PM EST

November 2 Raw Data/MeasurementsRefer to the deadline’s rubric on the class website for all requirements.

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December 12at 11:55 PM EST

Rough DraftRefer to the deadline’s rubric on the class website for all requirements.

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January 29at 11:55 PM EST

January 30 Final ProjectRefer to the deadline’s rubric on the class website for all requirements.Submit electronically as one Word file (.doc, .docx) through the required online platform.You need one printed copy in class on the deadline. It should not be stapled.Partially based on the official IA grade using the IB rubric (20 points).NO PROJECTS WILL BE ACCEPTED AFTER THE FINAL DUE DATE.

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COMMON FURTHER PROCESSES

The one-variable statistics covered in chapters 6 and 10 are “simple processes”. Most students will accomplish their required “further process” using two-variable statistics. Although you are expected to do the work by hand, you are welcome to use Excel to structure the work and your GDC to ensure accuracy. Use your notes for chapter 11 (available on the class website) for assistance with the following steps. If you need further guidance, use the textbook and avoid online sources. Too many students find unreliable, incorrect, or inappropriate statistical formulas and guidance online.

REGRESSION MODEL

1. Start by creating and interpreting a scatter plot using the raw data for two quantitative variables. Do not create scatter plots for categorical variables or for class midpoints of quantitative variables. It may be relevant at this point to determine if there are any outliers, but you must give sound reasons before disavowing data.

2. If the correlation does not appear to be at least moderate in strength:a. If the scatter is roughly linear, you can choose to find Pearson’s correlation

coefficient (r) and the coefficient of determination (r2) by hand and SEPERATELY interpret each value using your notes for 11A and 11B (or p. 321 and p. 326 of your textbook).

b. If the strength is not at least moderate, do not find the linear regression equation and therefore do not graph the line on the scatter plot. Doing so is an incorrectly worked process. You can still use your scatter plot and your work to find r and r2 as one SIMPLE process. Skip steps 3-5.

3. If the scatter is linear and the correlation appears to be at least moderate in strength:a. Find Pearson’s correlation coefficient (r) and the coefficient of determination

(r2) by hand and SEPERATELY interpret each value using your notes for 11A and 11B (or p. 321 and p. 326 of your textbook).

b. If the strength is at least moderate, use your notes for 11D to find by hand and interpret the linear regression equation. You should add the graph of the line to your scatter plot. All work up to this point is considered one FURTHER process. Skip to step 5.

4. If the scatter is quadratic, cubic, or exponential and the correlation appears to be at least moderate in strength:

a. You may use Excel or your GDC to find the model’s equation and r2 (r is for linear). Using only technology to create a scatter plot and to find a regression equation is one SIMPLE process.

b. The coefficient of determination (r2) still indicates the correlation’s strength. Use the table to the side to interpret r2, but only if the shape is non-linear. If the strength is at least moderate, you should add the graph of the model to your scatter plot. If not, do not graph the model on the scatter plot. To do so is an incorrectly worked process. Move on to step 5.

5. Regardless, be sure to interpret your findings. Use the factors listed in your notes for chapter 11 to examine how well the equation represents the association. As is often

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the case, you may also find that interpolation and extrapolation using the model is appropriate for your investigation to find optimal values. These can be good opportunities to include your project’s required statement on validity.

CHI-SQUARE TEST OF INDEPENDENCE

There is one type of χ2 test you are required to know for Math Studies. The chi-square test of independence is used for two categorical (qualitative) variables to see if they are independent of each other. In some cases you can also use this for quantitative data, as long as you “categorize” and group it. For example, age is really quantitative but you can classify people as young, middle-aged, or senior. Be careful with notation. “x”, “x”, “X , and “Χ” are not the same as “χ” let alone “χ2”.

1. State your null (H0) and alternative (H1) hypotheses.H0: statement that the two variables are independent (“is independent of”)H1: statement that the two variables are not independent (“is not independent of”)

2. You need to organize the data into a contingency table of observed values. You should then calculate expected values for each “cell” in a second table.

a. Find all row and column sums, and the “total total” and put them in the contingency table.

b. Calculate each expected value using f e=row∑ ∙column∑ ¿total

¿ . You only

have to show the work by hand for one of the expected values. c. YOU CANNOT PROCEED unless all expected values are at least 5. To do so

would mean you have an incorrectly worked process. This issue never occurs on an IB exam, but often happens with projects. If any of the expected values are less than five, you have two possible remedies.

i. You might try changing the contingency table to have fewer categories for one or both of the variables. The new categories must still be appropriate for your investigation. You would then recalculate the values in the expected frequency table to ensure that all expected values are at least five.

ii. You could collect more data but you must do so with as much planning and intention as the first round of data collection. This would also mean you need to revise the introduction of your project to account for the revisions to your data gathering process.

3. Find the degrees of freedom using df=(number of rows−1)(number ofcolumns−1) . Do not include the rows and columns that contain the sums.

4. Choose a significance level, usually 1%, 5%, or 10%. On an IB exam you will be given a significance level. The lower the significance level, the more stringent you are in allowing a “significant discrepancy” in your data and the more confident you can be that the conclusion is correct. Therefore, the more confident you are with quality and quantity of your data, the lower you can go with the significance level and the more confident you can be with your conclusion. Be sure to give a reason for your choice of a significance level. You might choose to analyze its impact on your findings (which may be a good opportunity to include the required statement on validity). Most

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students choose 5% (the scientific norm) unless they have a reason to be more or less stringent (and consequently more or less certain with their conclusion).

5. If df=1a. The χcalc2 and p-value that your GDC gives you are not statistically sound and

should not be used. You must find the χcalc2 and perform the chi-square test of independence by hand using Yate’s continuity correction (FURTHER process).

χcalc2 =∑ (|f o−f e|−0.5)2

f eb. Use your df and significance level to find the critical value in the critical

value table. Compare the χcalc2 to the critical value.c. State a conclusion by replacing the brackets with the values.

Since [chi-squared statistic] > [critical value], we reject H0. [variable] is not independent of [variable].Since [chi-squared statistic] < [critical value], we do not reject H0. [variable] is independent of [variable].

6. If df >1, use either of the two methods below.a. Determine the χcalc2 by hand using the regular formula (FURTHER process) or

using your GDC (SIMPLE process).

χcalc2 =∑ ( f o−f e )2

f ei. Use your df and significance level to find the critical value in the

critical value table. Compare the χcalc2 to the critical value.ii. State a conclusion by replacing the brackets with the values.

Since [chi-squared statistic] > [critical value], we reject H0. [variable] is not independent of [variable].Since [chi-squared statistic] < [critical value], we do not reject H0. [variable] is independent of [variable].

b. Determine the p-value using your GDC (SIMPLE process).i. Compare the p-value to the decimal form of the significance level.ii. State a conclusion by replacing the brackets with the values.

Since [p-value] < [significance level], we reject H0. [variable] is not independent of [variable].Since [p-value] > [significance level], we do not reject H0. [variable] is independent of [variable].

7. Now that you have your conclusion and a reason, interpret what the conclusion means in the context of your investigation! If you failed to reject the null hypothesis, then there was not enough evidence to reject it. If you did reject it, there is enough evidence to support the alternative hypothesis’ claim. Having evidence to suggest that two variables are not independent indicates a possible, but not definite, association.

CHI-SQUARE CALCULATOR PROCEDURE (TI-83+, TI-84)

1. Using your MATRIX key, go to EDIT for matrix [A].2. Put in the size of your table, and then enter the observed values.

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3. Go to STAT, and then TEST. Choose χ2−TEST . (It is easier to scroll up to find it than down.)

4. Press ENTER. Highlight CALCULATE. Press ENTER.5. It will give you the χcalc2 , the p-value and df.6. Also, go back to MATRIX, EDIT, [B] and all the expected values will magically appear.

Recall, they need to be greater than 5. Note: For the IB exam, you are allowed to use your GDC but must still be able to find the degrees of freedom and one expected frequency by hand.

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ROUGH DRAFT DIRECTIONS

Prepare your rough draft by assembling the sections in the order below.

1 Title Page Centered horizontally and vertically, you need to list (in this order) your exploration title and “IB Math Studies SL Project”. Each item should be on separate double-spaced lines. Including the title page, you must use the same font and size (plain; 10 or 11 point) and double-space throughout your entire exploration. This section should not have a page number. DO NOT INCLUDE YOUR NAME OR CANDIDATE/SESSION NUMBER.

2 Table of On a new page, title the top of the page with a bolded, centered “Table of Contents Contents”. This section must be double-spaced and use

the uniform font size. You will list the subtitles and page numbers for every section of the remaining areas of your paper (including the introduction, all relevant subtitles, conclusion, bibliography, and appendix). This section should not have a page number.

3 Body This section must be double-spaced and use the uniform font size. On a new page, you will begin numbering the pages in the upper right side of the header with a page number, starting with “1”. Use the directions on the next page of this booklet to set up the page numbers correctly. Section the body of your project with subtitles starting with your introduction. Indent each paragraph. Don’t use contractions. Each of the three required processes should have their own subtitle and within each you should appropriately organize the data (e.g.: a frequency table), process the data (show work once and repeat as is relevant), and interpret the results. It is vital that you include reasons and interpretations throughout. Use the equation editor built into your word processing program for all mathematical notation and formulas. The work for your processes must be in the body of your project. Be sure to include at least one statement on validity where it’s appropriate. Using the word “valid” or “invalid” is a great way to indicate your analysis on your process’s or interpretation’s validity. The recommended structure of the body is:

Introduction (statement of task and plan; include your survey if applicable)Mathematical Process: “ ” (SIMPLE)Mathematical Process: “ ” (SIMPLE)Mathematical Process: “ ” (FURTHER)Conclusion

4 Bibliography Title the top of a new page with a bolded, centered “Bibliography”. You still need page numbers at the top of each page. You will include sources you cited within the body of your paper and sources you only consulted. You need to cite your sources in MLA format which includes double-spacing, hanging indentation, and alphabetical arrangement. For IB, internet sources need a date of access and a complete URL.

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INTERPRET! Don’t just “plop” mathematical processing in without explaining what it

means and indicates.

Give REASONS as you are completing each step of your plan (e.g.: justify groups when

organizing data, explain choice of significance level in chi-square test). The project

should flow well. Anyone with an understanding of the

mathematics should be able to comprehend what you are doing and why you are doing

it as they are reading the project.

When interpreting, “most” or “majority” means more than half. Modal value or interval does not have to be more

than half.

Avoid using “effect”.

“Correlation” can be used for two

quantitative variables.

Otherwise use

5 Appendix Include a table in an appendix with your raw data. Title the top of a new page with a bolded, centered “Appendix” and include page numbers. If you need to refer to the raw data in the body of your paper, you may reference the appendix. If applicable, put a copy of your survey in your introduction, not the appendix. If you have tables that include your workings, you should put those tables in the body of your project, but you must have the raw data in your appendix.

The directions below work for Microsoft Word 2010, 2013, and 2016.

Set Up Headers and Page Numbers Correctly

Make sure that all sections of your project are in one Word document. Delete anything in your headers by double-clicking in the header area, selecting the text, and deleting.Your introduction should start with an “Introduction” subtitle and be at the top of the page after your table of contents. Put your blinking cursor in front of the subtitle.In the menu at the top of the window, select the “Page Layout” tab.Select the “Breaks” drop-down option.Under “Section Breaks”, select “Next Page”.Double-click in the header area on the page with your introduction. You should now be able to see the “Design” tab at the top of the window.De-select (turn off) the “Link to Previous” option.Select the “Page Number” drop-down option.Hover over “Top of Page” and then select the option with the page number on the right side of the page.You need to fix the page number if it is not “1”. Highlight the page number in the header.Select the “Page Number” drop-down option in the menu at the top of the window.Select “Format Page Numbers”.Choose “Start at” and set it at 1. Click “OK”.Make sure the header’s font and size are the same as the rest of your essay.

Hanging Indentation for Bibliography

Type in your MLA formatted sources. Press enter once after you have finished a source and want to add another.Highlight all of your sources (but not the “Works Cited/Consulted” heading) with your cursor.At the top of the window, select the “Home” tab.To the side of the word “Paragraph”, click the small arrow to open a dialog box.Under the “Special” drop-down box, choose “Hanging” and make sure the “By” amount is 0.5. Click “OK”.

How to Set Tabs for Table of Contents

Type in your subtitles on different lines. When finished, highlight all of the subtitles with your cursor.At the top of the window, select the “Home” tab.To the side of the word “Paragraph”, click the small arrow to open a dialog box. Select the “Tabs” button.Enter “6.5” as the tab position, “Right for alignment”, and select “Set”. Click “OK”.

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Next to each subtitle, press the space bar and then press “Tab” on the keyboard. Press the space bar and then type the page number(s).

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ADVICE FROM IB

It is important for the candidate to write a clear plan explaining what they are going to do, what mathematical processes they are going to use in the project and give reasons as to why they are using these processes. This will help them to focus and will prevent them from including any irrelevant processes in their project.

As is the case every year, most candidates chose to write a statistical project. Other types of projects using modelling, optimization, probability, trigonometry, sequences or finance were few and far between. A few candidates used statistical tests outside the syllabus and, even when the mathematics was accurate it appeared that they did not always fully understand the tests that they were using.

Nearly all projects contained data which varied from a few pieces to hundreds of pieces. It should be noted that having a lot of data does not necessarily mean that it is quality data. Some candidates did not include their raw data. This makes it impossible for the moderator to know if it is quality data or to check that the tables are set up correctly or if the mathematical processes are accurate. Also, some candidates forgot to include a copy of their questionnaire or survey. When using a random sample of data, the candidates should give an explanation of their method of choosing the “random” sample.

The simple mathematical processes were often done using technology without any explanation. The candidate should give an example of how to find a mean or show how to calculate the angles at the centre of a pie chart. A few candidates did not include any simple processes and jumped right into a chi-squared test and, as a result, their chi-squared test was counted as their first simple process and they did not score well in criterion C. The main errors in the sophisticated processes were, as always, in the chi-squared test (no null hypothesis stated, raw data or percentages instead of frequencies in the table of observed values, too many entries less than 5 in the table of expected values) and regression (drawing or calculating the regression line when the correlation coefficient was not moderate or strong). Also, there were a number of instances of chi-squared test being performed without any discussion of how the boundary limits for the cells were arrived at. There should be some discussion of whether the mean, median or some other value has been used and the reason for this choice discussed. Much use was made of technology with results occurring often without working, interpretation or justification. It is difficult for the moderator to verify that the candidates knew what they were doing.

Criterion A

Teachers should stress the importance of writing a clear statement of the task and a clear and detailed plan of how they are going to achieve this. This focuses the candidate and usually results in a project that is clear and follows a logical order. Most candidates explain how they are going to collect their data but do not describe the mathematical processes that they are going to use in the project. Those with clear statements of task and plan generally wrote more successful pieces of work.

Criterion B

Few candidates describe their sampling method. Candidates who are using data from the internet or other secondary sources must also remember to identify the source in their bibliography. They also need to think about the relevance of this data for their project. All raw data must be included in the project in order for the moderator to check the accuracy of tables and mathematics. A sample of the questionnaire used must also be included along with the raw data so that the moderator can check the accuracy of any tables of values included in the project.

Criterion C

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The mathematics used in the project needs to be done in a relevant and meaningful manner. Some projects contained many mathematical calculations, some of which were meaningless for the actual project. In many of the projects the mathematics was done using technology. All mathematical processes using technology only are considered as simple processes. All processes such as mean, median, pie charts, chi-squared test, correlation and line of regression could all have been demonstrated by hand showing the moderator that the candidate knew what they were doing. Some candidates missed out any simple mathematical processes and only did a chi-squared test or line of regression. When no simple processes are present then the first sophisticated process is counted as simple. It is important for the candidate to realize this. As mentioned above there are still many errors in the chi-squared test and candidates are still drawing lines of regression on diagrams where there is little or no correlation present. This makes the process irrelevant and lowers the mark awarded for this criterion.

Criterion D

The project flows better if partial conclusions are made after every mathematical process and then an overall conclusion given at the end. Most candidates managed to give at least one interpretation that was consistent with their analysis but fewer could produce thorough explanations of their calculations. Some candidates attempted to justify their results based on their own personal beliefs rather than the mathematics that they had performed.

Criterion E

Candidates are now commenting more on their data collection, their results and giving suggestions for extensions or improvement. Few are able to comment successfully on the validity of the mathematical processes that they have used throughout their project. Many candidates are now including their remarks about validity under a heading “Conclusions/Validity” as if they were two sides of the same coin. Candidates need help to understand that they need to choose which techniques to use and which not to use. Commenting on why they did or did not use a certain technique shows a good understanding of validity.

Criterion G

Many projects had a reasonable structure but, due to errors in notation and terminology, only receive 1 mark for this criterion. The most common errors are: * for multiplication, ^ for “power of”, X2 for χ2, E for “10 to the power of”, mixing up Pearson’s correlation coefficient (r) and the coefficient of determination (r2).

Reminders

Check that the mathematics used in the project are relevant.If using technology, give an example by hand of what you are doing before you start to do any mathematics on the calculator.

Pay more attention to detail such as labels and scales on graphs, spelling mistakes, typos, and computer notation.Include all raw data in an appendix.Include simple mathematical processes in your project.

List of Common Pitfalls

The chi-square test with expected values that are less than 5. Would need to collect more

data or combine/create groups to increase expected values.

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The chi-squared test with 2 × 2 contingency table (degrees of freedom = 1) and the Yates’s continuity correction not applied.Omitting labels on graphs.Inappropriate use of regression line. Calculation of equation of regression line

despite the scatter diagrams or value of r indicating weak or no correlation.Raw data not provided, so no mathematical calculations can be verified.Repetition of the same work for the same process.Use of calculator notation.

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Simple

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Further

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