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- MAT 171 Pre-Calculus

**Exit Skills: **

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.
- Graph families of functions using transformations and state domain and range in interval notation.
- Solve higher-degree polynomial equations using the Remainder, Factor, Rational Root, Conjugate Root Theorems, Bounds Theorem, and the Intermediate Value Theorem.
- Simplify difference quotients including polynomial, rational and radical functions.
- Graph rational functions identifying vertical and horizontal asymptotes, including use of limits.
- 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.
- Use the binomial theorem to expand a binomial.
- Define the trigonometric functions using the circular and triangular definitions.
- Convert between degree and radian measure.
- Locate and find trigonometric functions of special angles and angles corresponding by reference.
- Use amplitude, period, phase shift and vertical shift to graph trigonometric equations.
- Identify the range restrictions for the inverse trigonometric functions and find inverses.
- Prove and use basic, Pythagorean, angle sum and difference, double angle and half angle identities to simplify expressions, verify identities and solve conditional equations.
- Graph, add and subtract vectors and solve associated applications.
- Prove and use the Law of Sines and the Law of Cosines, and solve associated applications.
- Convert between rectangular and trigonometric form of complex numbers.
- Multiply and divide complex numbers in trigonometric form, and use DeMoivre’s theorem and the N
^{th}-Root theorem to find integer powers and roots of complex numbers. - Convert between rectangular and polar coordinates and equations and graph common polar equations.

8 a.m.-4:30 p.m. Monday-Friday

Administration Building, Room 1242

636-922-8496

Phyllis Marchand

636-922-8496

phyllis_marchand@stchas.edu

Joseph (Joe) W. Howe

636-922-8318

jhowe@stchas.edu

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