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These are the Transum resources related to the statement: "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.

- Direct and Inverse Proportion A self-marking exercise in solving direct and inverse variation problems.
- Equation of a Line Through Points Match the equations of the straight line graphs to the clues about gradients and points.
- Graph Equation Pairs Match the equation with its graph. Includes quadratics, cubics, reciprocals, exponential and the sine function.
- Graph Match Match the equations with the images of the corresponding graphs. A drag-and-drop activity.
- Graph Patterns Find the equations which will produce the given patterns of graphs.
- Graph Plotter An online tool to draw, display and investigate graphs of many different kinds.
- Plotting Graphs Complete a table of values then plot the corresponding points to create a graph.

Here are some exam-style questions on this statement:

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*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 - "
*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*" ... more^{o}C. - "
*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

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

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