Mathematics Active Learning

This worksheet involves a series of problems involving applications of quadratic functions including projectile motion, area and economics. To complete these problems students should know the quadratic formula and the formula for the x value of the vertex (-b/2a).

Students plot the graph of rational functions after algebraically identifying y-intercept, hole(s), x-intercept(s), vertical asymptote(s), horizontal asymptote or other asymptote and end behavior. Includes synthetic division in a couple problems as well as vertical and parabolic asymptotes.

Practice worksheet wherein students graph polynomials in factored form or find the roots using the factor theorem, synthetic division and the quadratic formula as necessary without using a calculator. Y-axes are unnumbered.

This includes a series of functions of rational, square root, absolute value and piecewise functions that are plotted by hand. It is a good review for advanced classes or a learning experience for lower level classes.

Students arrange values of five trig functions in ascending order. The first page involves functions of radian measures from 0 to 2pi. Twelve of the functions involve the same trig function, while two involve a mixture of trig functions. The second page involves functions of positive and negative angles in degrees and radians. Eight involve the same trig function, while six involve a mixture of the six trig functions.

Students evaluate f(x) given specific values. In addition they evaluate piecewise functions and function combinations that re similar to the definition of the derivative. This can be used as review, summary or diagnostic, depending on the level of the students.

Given the graphs of rational functions, students identify intercepts, holes and vertical and horizontal asymptotes. This is best used before locating these features given a function equation.

This is a series of problems involving domain restrictions in rational and square root functions and composition of functions. Some of the composition problems involve algebraic compositions and some involve numerical compositions.