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 expanding brackets and collecting like terms. Answers can be revealed or hidden. Functions dealt with are linear, quadratic and reciprocal. The next sheet shows two linear functions which are combined in different orders, equations are set and the input required needs to be calculated by solving each equation. The final sheet is similar but the functions are one linear and one quadratic.

Cubics (Factorising and Graphing)
The first six sheets allow students to investigate the relationships between cubic polynomials, the factorised form and the graph. Initially the factors are of the form (x-n) but later sheets deal with factors which could be (x±n) and with repeated factors. The sheet with tab "Evaluate f(a)" is intended to allow students to quickly find factors by inspection using the Remainder Theorem or the Factor Theorem. The graph of the function can be revealed. The final interactive sheet "Evaluate f(b)" is similar but the coefficient of x³ could be 1,2 or 4. There are also five sheets of questions which may be suitable for duplication for class use.

Note: This program was designed by be viewed on a screen with a resolution of 1024 x 768. Users may have to adjust the resolution of their screen for the pages to display as was originally intended. The program uses macros which need to be enabled on users’ machine.