LibGuides: Math Applications and Interpretations DP SL: IA (2022)

Modelling (practical approach involving geometry and functions)

LibGuides: Math Applications and Interpretations DP SL: IA (1)

  • Packaging and geometrical shapes

  • Packaging and geometrical shapes (annotated)

Modelling (practicalapproach involving statistics and functions)

LibGuides: Math Applications and Interpretations DP SL: IA (2)

  • Microwave popcorn

  • Microwave popcorn (annotated)

Modelling (theoretical approach)

LibGuides: Math Applications and Interpretations DP SL: IA (3)

  • Ice cream

  • Ice cream (annotated)

Exploring mathematics

LibGuides: Math Applications and Interpretations DP SL: IA (4)

  • Zeno's arrow paradox

  • Zeno's arrow paradox (annotated)

How long should it be?

It is difficult to be prescriptive about mathematical writing. However, the Mathematics: analysis and approaches and the Mathematics: applications and interpretation guides state that 12 to 20 pages should be appropriate. An exploration may be less than 12 pages, however. A more common failing of mathematical writing is excessive repetition, and this should be avoided as such explorations will be penalized for lack of conciseness. It is recognized however that some explorations will require the use of several diagrams, which may extend them beyond the recommended page limit.

Are there any particular topics to be avoided?

A topic must be chosen so that the assessment criteria can be applied to it. Purely descriptive historical topics, for example, are not appropriate.

Is any particular format for the exploration to be used?

No particular format is required. Students may write both the text of explorations and draw graphs and/or tables by hand, or explorations may be fully or partially word-processed. Either form is acceptable as long as the exploration is clearly legible. In recent years, students have used various forms of technology (for example, spreadsheets) to present data, construct tables and graphs, and perform calculations.

Does the exploration need a title?

It is good practice to have a title for all pieces of work. If the exploration is based on a stimulus, it is recommended that that the title not just be the stimulus. Rather, the title should give a better indication of where the stimulus has taken the student. For example, rather than have the title “Number patterns”, the title could be “Number patterns—exploring patterns in final digits of prime numbers”.

What should the target audience be for a student when writing the exploration?

The exploration should be accessible to fellow students.

Can the students use mathematics other than that which they have done in class?

Yes, but this must be clearly explained and referenced, and teacher comments should clarify this.

Can students use mathematics that is outside the syllabus?

It is not necessary to do this to obtain full or high marks. If students decide to explore mathematics outside the syllabus it is recommended that the level is commensurate with the syllabus.

Is interpretation of results a separate section or should comments be made during the exploration?

Commenting on and interpreting results at the point at which these are used enhances the communication and should be summarized in a conclusion. This may also apply to comments on the validity of results.

Must students use external resource material?

There is no requirement for the use of external resource material. However, students often find it necessary to obtain material from other sources (for example, for obtaining data, or for using formulae). In these cases, students should acknowledge these sources and list them in a bibliography and state any sampling processes used when using secondary data.

What is personal engagement?

The exploration is intended to be an opportunity for students to use mathematics to develop an area of interest to them rather than merely to solve a problem set by someone else. CriterionC (personal engagement) will be looking at how well the student is able to demonstrate that he or she has “made the exploration their own” and expressed ideas in an individual way.

What is the difference between precise and correct?

As outlined in criterion E (use of mathematics), “precise” mathematics requires absolute accuracy with appropriate use of notation. “Correct” mathematics may contain the occasional error as long as it does not seriously interfere with the flow of the work or give rise to conclusions or answers that are clearly wrong.


  • Calculating beauty–the golden ratio

  • Colour preferences

  • Daylight in a classroom–architectural design

  • Is my mirror showing an accurate image?

  • M.C. Escher: Symmetry and infinity of art

  • Modelling the surface area of the glass dome of the Galleria Vittoriio Emanuele II in Milan, Italy

  • Searching for the ideal sound

  • Shadows and height

Business and finance

  • A comparative study of shares, real estate, bonds and banks

  • Analysis of stock market changes

  • Applications of calculus to the economics of firms

  • Buying a car or a house–payment options

  • Code breaking

  • Economic development and levels of income

  • Finding the lowest values of the dimensions of differently shaped storage rooms using differential calculus and optimisation

  • International phone call pricing

  • Statistics on flight information for an international airline

Food and drink

  • Costs of products bought online compared to local grocery stores

  • Dine in or dine out?

  • How many peas are there in a 500 gram box of peas?

  • Jelly bean study

  • The cookie problem–taste is all-important

  • The operation of a tuck shop

  • The volume of an egg

  • What is the greatest candy bar in the world?

Health and fitness

  • A comparison between calorie intake and gender

  • A comparison between lung capacity, age, weight and body fat

  • Aids awareness in Maseru

  • Blood pressure

  • Breakfast and school grades

  • Breast and cervical cancer–ethnic comparison

  • Infant mortality

  • Investigating reaction times

  • The SIR model in relation to world epidemics

Geometry and trigonometry

  • Geodesic domes

  • Graph theory–finding the shortest path

  • Newton-Raphson

  • Origami applications to mathematics

  • Sine waves in pitch frequencies

  • Spanning trees

  • Spherical geometry

  • Stacking bricks

  • The ideal cut of a diamond

  • The Ferris wheel

  • The open Knight’s Tour on a chessboard

  • Topography and distance

Nature and natural resources

  • Airfoil and lift force

  • Analysis of the cost and utility of gas versus electricity in an average domestic situation

  • Animal population

  • Calculating the time of sunrise and sunset

  • Chaos theory: universal prediction

  • Counting weeds

  • Earthquakes–can they be predicted?

  • Florence Nightingale and modelling spread of disease

  • Graphing the Pharmacokinetic Profile

  • How does population density affect the transmission of Ebola?

  • Is the swell of the sea influenced by the temperature?

  • Modelling Arctic Sea ice cover

  • Modelling rainfall

  • Modelling the cooling of a cup of tea

  • Optimum dimensions of an aluminium drink can

  • Predicting cooling times

  • Rainfall compared to grape vine yield

  • Statistical investigation of leaves

  • The quality of local water

  • The SIR model in relation to world epidemics

  • The volume of an egg

  • Sunspot cycles

  • What is the relationship between the duration of drainage and water height in my bathtub?


  • Approximation of pi

  • Cyclic situations and patterns through happy numbers

  • e, π

and φ

  • : are they related?

  • The golden number phi

  • What is e?

  • Euler’s totient theorem


  • Assuming a person has an 85% chance of meeting a soul mate during their lifetime, what does that mean about the number of potential soul mates in the world?

  • Correlation between divorce rate and financial uncertainty

  • Does gender influence choice of favourite animal?

  • Does the electoral college in the US truly represent the political choice of the people?

  • Effect on tipping percentages

  • Exploring the gamblers’ fallacy–why it can cause fatal decisions

  • Is film genre choice more dependent on nationality or gender?

  • Gender-based discrimination

  • Left-handed students

  • Memory

  • Perception of time

  • Relationship between a country’s human development index and infant mortality rate

  • Relationship between GDP and fertility rate in countries across the world

  • Relationship between income inequality and rate of corruption in a country

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

  • Relationship between unemployment and criminality in Sweden from 1988-1999

  • Relationship between women’s secondary education and fertility rates in developing countries

  • Statistical comparison of the number of words in a sentence in different languages

  • The birthday paradox

  • When can I use “swimmed” and “knowed” correctly?

  • Voter turnout

Sport and leisure

  • Baseball bat speed compared with body weight

  • Body proportions for track and field events

  • Does the team win when it was the dominating team during the match?

  • Effective short corners in hockey

  • Exploring card counting in blackjack using probability

  • Factors affecting athletic performance

  • Has sports performance improved more on land or in water?

  • Height, weight and swimming performance

  • How does the amplitude of a ski turn affect the speed of the skier?

  • How far do tennis balls roll?

  • The geometry involved in billiards

  • Modelling musical chords

  • Modelling the jump of a horse

  • Practice makes perfect

  • Relationship between skiing ability and distance travelled to ski

  • Resistance of fishing line

  • Rollerblading and the maths behind it

  • The Monty Hall problem

  • The Tower of Hanoi puzzle

  • Video games and response times

  • Will female swimmers ever overtake male swimmers?

Travel and transport

  • Cost efficiency of vehicles

  • Driving skills

  • How many bicycles are there in Amsterdam?

  • Petrol prices

  • Public transportation costs and car usage: a personal comparison

  • Running late and driving habits

  • Seat belt use

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

  • Traffic study of Schiphol International Airport

  • Transport safety in town centres

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