International Baccalaureate Mathematics

Syllabus Content

Modelling with the following functions: Linear models. Quadratic models (including axis of symmetry, vertex, zeros and roots, intercepts on the x-axis and y-axis). Exponential growth and decay models. Equation of a horizontal asymptote. Direct/inverse variation: Cubic models: Sinusoidal models i.e. f(x)=asin(bx)+d, f(x)=acos(bx)+d

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

Plotting Graphs Complete a table of values then plot the corresponding points to create a graph.

Graph Equation Pairs Match the equation with its graph. Includes quadratics, cubics, reciprocals, exponential and the sine function.

Graph Patterns Find the equations which will produce the given patterns of graphs.

Direct and Inverse Proportion A self-marking exercise in solving direct and inverse variation problems.

Graph Match Match the equations with the images of the corresponding graphs. A drag-and-drop activity.

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

Equation of Line through Points Video A short video showing how to find the equation of a line that passes through given points.

Equation of a Line Through Points Match the equations of the straight line graphs to the clues about gradients and points.

Domain, Range and Asymptotes Match the functions with their features. A drag and drop activity.

Here are some exam-style questions on this statement:

"Richard studies fish populations in a lake." ... more

"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 cross-section of a fish pond is drawn on a set of axes shown below. The edge is modelled by \(y=ax^2+c\) and the cross section is the same for the whole of its length. The curve touches the x-axis at the origin." ... more

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

"Doctor Octothorpe investigated the decreasing population of a colony of ants in a remote province of China. His investigation took place in 1958." ... 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

"In medical imaging, the radioactive isotope Technetium-99m is used due to its short half-life of 6 hours. After being introduced into the body, the isotope decays, and the amount of Technetium-99m present can be tracked over time to study the function of specific organs." ... 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

See all these questions

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.

Furthermore

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

If you use a TI-Nspire GDC there are instructions for finding asymptotes.

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

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.