# 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.

1. Solve quadratic equations, equations of quadratic form and miscellaneous equations.
2. Solve quadratic, rational, compound and absolute value inequalities writing solutions in interval notation.
3. Graph families of functions using transformations and state domain and range in interval notation.
4. Solve higher-degree polynomial equations using the Remainder, Factor, Rational Root, Conjugate Root Theorems, Bounds Theorem, and the Intermediate Value Theorem.
5. Simplify difference quotients including polynomial, rational and radical functions.
6. Graph rational functions identifying vertical and horizontal asymptotes, including use of limits.
7. Find the rule for the inverse of a function and graph the inverse.
8. Graph exponential and logarithmic functions.
9. Solve exponential and logarithmic equations.
10. Solve systems of non-linear equations and inequalities.
11. Solve 3 x 3 systems of linear equations using Gaussian elimination, inverse of a matrix and Cramer’s Rule.
12. Perform matrix algebra operations including addition, subtraction, products and the evaluation of determinants by the minor-cofactor method.
13. Graph conic sections including circles, parabolas, ellipses and hyperbolas.
14. Find terms of a sequence using recursion and explicit formulas, and find the nth term formula for arithmetic and geometric sequences.
15. Use summation notation, find the sum of a finite arithmetic series and find the sum of finite and infinite geometric series.
16. Use the binomial theorem to expand a binomial.
17. Define the trigonometric functions using the circular and triangular definitions.
18. Convert between degree and radian measure.
19. Locate and find trigonometric functions of special angles and angles corresponding by reference.
20. Use amplitude, period, phase shift and vertical shift to graph trigonometric equations.
21. Identify the range restrictions for the inverse trigonometric functions and find inverses.
22. Prove and use basic, Pythagorean, angle sum and difference, double angle and half angle identities to simplify expressions, verify identities and solve conditional equations.
23. Graph, add and subtract vectors and solve associated applications.
24. Prove and use the Law of Sines and the Law of Cosines, and solve associated applications.
25. Convert between rectangular and trigonometric form of complex numbers.
26. Multiply and divide complex numbers in trigonometric form, and use DeMoivre’s theorem and the Nth-Root theorem to find integer powers and roots of complex numbers.
27. Convert between rectangular and polar coordinates and equations and graph common polar equations.

#### Office Hours

8 a.m.-4:30 p.m. Monday-Friday

#### Office Location

Administration Building, Room 1242

#### Office Phone Number

636-922-8496

Phyllis Marchand
636-922-8496
phyllis_marchand@stchas.edu

Joseph (Joe) W. Howe
636-922-8318
jhowe@stchas.edu