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Circles

This Excel file has a series of sheets which illustrate the link between the equation of a circle and the corresponding graph. It goes on to deal with the intersection of a circle with a straight line.

The first interactive sheet shows the equation and graph of circles centred on the origin where the radius...

Functions

Composite Functions
The first five sheets all have a similar format. A number is operated on by two functions, one after the other. The output after each operation can be revealed. Beneath the numerical example the algebraic form for gf(x) is shown and simplified by...

Exponential and Logarithmic Functions

e
This file has five sheets. The first shows how the value for e is derived from the binomial series for (1+x)n and this is used on the second sheet to derive the series for ex. The third sheet finds the derivative of ex...

Ellipse

This program deals with various aspects of the coordinate geometry of an ellipse. The first two sheets show the connection between ellipse and the auxiliary circle and also the focus/directrix definition of the ellipse. Subsequent sheets trace an interesting loci derived from tangents and normals. Parameters can be...

Hyperbola

This program begins with graphs of the hyperbola in the form x2/a2 -y2/b2 =1. The constants a and b can be altered and the changes in foci, directrices and...

Inverse Functions

Inverse Functions. Linear
This file starts with an example of how to find the inverse of a linear function. New examples can be generated and the graphs of both functions are shown on the next sheet. The next interactive sheet shows sets of linear functions for students to find...

Modulus Functions

This interactive program deals with the modulus function applied to linear, quadratic, reciprocal and sine functions. The graph of each function is shown as well as the unreflected sections of the graphs.

The first interactive sheet shows the graphs of functions in the form y=|mx+c|. The gradient and...

Parabola

Parabola

This file provides a well illustrated introduction to the properties of a parabola. It begins by illustrating the locus of a parabola. A point on the curve can be moved to clearly illustrate that the distance from the focus is equal to the distance from the directrix....

Polar Coordinates and Curves

This file has worksheets showing seven polar coordinate diagrams. The first allows students to explore simple polar coordinates by either inputting values for r and θ or stating those values for computer generated points. This is followed by two interactive sheets showing the locus for a circle and straight line...

Proof

This interactive workbook begins with a sheet which illustrate properties of odd, even and consecutive numbers. These properties are illustrated numerically and algebraically. The next two sheets deal with properties of the sum, difference and product of these numbers and again these are explored numerically and...

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