The following exit skills were developed with the assumption that the student has a good grasp of all intermediate algebra skills and that word problems and applications are an integral part of any algebra course.
- Solve quadratic equations, equations of quadratic form and miscellaneous equations.
- Solve quadratic, rational, compound and absolute value inequalities writing solutions in interval notation.
- Solve higher-order polynomial equations using the Remainder, Factor, Rational Root and Conjugate Root Theorems.
- Graph rational functions identifying vertical and horizontal asymptotes.
- Find the rule for the inverse of a function and graph the inverse.
- Graph exponential and logarithmic functions.
- Solve exponential and logarithmic equations.
- Solve systems of non-linear equations and inequalities.
- Solve 3 x 3 systems of linear equations using Gaussian elimination, inverse of a matrix and Cramer’s Rule.
- Perform matrix algebra operations including addition, subtraction, products and the evaluation of determinants by the minor-cofactor method.
- Graph conic sections including circles, parabolas, ellipses and hyperbolas.
- Find terms of a sequence using recursion and explicit formulas, and find the nth term formula for arithmetic and geometric sequences.
- Use summation notation, find the sum of a finite arithmetic series and find the sum of finite and infinite geometric series.
- Identify and graph families of functions, find their inverses and zeros and solve related equations.
- Solve systems of equations, linear and non-linear, using an appropriate method including matrix methods.
- Recognize equations of and sketch a graph of the conic sections.
- Distinguish between general varieties and special types of sequences and series and use appropriate formulas for finding summations and nth terms.