International Baccalaureate Mathematics

Syllabus Content

Modelling skills: Use the modelling process described in the “mathematical modelling” section to create, fit and use the theoretical models in section SL2.5 and their graphs. Develop and fit the model: Given a context recognize and choose an appropriate model and possible parameters. Determine a reasonable domain for a model. Find the parameters of a model. Test and reflect upon the model: Comment on the appropriateness and reasonableness of a model. Justify the choice of a particular model, based on the shape of the data, properties of the curve and/or on the context of the situation. Use the model: Reading, interpreting and making predictions based on the model

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

Graph Plotter An online tool to draw, display and investigate graphs of many different kinds.

Here are some exam-style questions on this statement:

"While studying a new disease, scientists found that the number of toxic cells in the bloodstream increased over time, according to the model \(D(t)=12×(1.16)^t , t \ge 0\) where \(D\) is the number of the toxic cells in the bloodstream per litre and \(t\) is the time in hours." ... more

"The diagram show a wheelchair ramp from ground level to a height of 70cm." ... more

"Percy Cod and Fran Finklestein are both researchers working at different universities. They are each studying a different colony of bacteria which coincidentally start increasing in size at the same time." ... more

"The quantity of heat required to heat an amount of water is given by the formula:" ... more

"In a fantasy story the power value of a dream catcher varies depending on its length. The power values of various dream catchers are recorded in the following table:" ... more

"A Big Wheel at an amusement park has a diameter of length 70 metres which rotates at a constant speed. The bottom of the wheel is h metres above the ground. A seat starts at the bottom of the wheel.The wheel completes one revolution in 4 minutes. [The diagram is not to scale]" ... more

"A cup of hot tea is placed on a table to cool. The temperature of the room is 24^oC." ... more

"In a remote lake it was noticed by conservationists that a disease was rapidly spreading amongst two species of fish, R and S, which is reducing their numbers. The conservationists calculated that the numbers of each type of fish can be modelled by the functions:" ... more

"Fifty milligrams of a certain type of medicine has been shown to enter the bloodstream of an adult according to the following equations:" ... more

"Consider the function \(f\) defined by \(f(x) = 25e^{x-5}\) for \(x \in \mathbb{R}^+\)." ... more

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Click on a topic below for suggested lesson Starters, resources and activities from Transum.

Graphs This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts. A graph is a diagram which represents a relationship between two or more sets of numbers or categories. The data items are shown as points positioned relative to axes indicating their values. Pupils are typically first introduced to simple bar charts and learn to interpret their meaning and to draw their own. More sophisticated statistical graphs are introduced as the pupil's mathematical understanding develops. Pupils also learn about coordinates as a pre-requisite for understanding algebraic graphs. They then progress to straight line graphs before learning to work with curves, gradients, intercepts, regions and, for older pupils, calculus.

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If you use a TI-Nspire GDC there are instructions for finding a power regression equation and correlation.

This video on Functions: Overview and Types is from Revision Village and is aimed at students taking the IB Maths AI Standard level course.

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