MAT 171 Pre-Calculus Mathematics

1. Solve linear equations with complex coefficients.
2. Solve quadratic equations by factoring, extracting roots, completing the square, and the quadratic formula.
3. Solve equations of the quadratic type.
4. Solve and graph inequalities: linear, quadratic, rational, absolute value.
5. Graph conic sections: circle, parabola, ellipse, hyperbola.
6. Graph rational functions including considerations of vertical asymptotes and horizontal asymptotes.
7. Find rule for the inverse of a function and graph the inverse.
8. Solve exponential and logarithmic functions.
9. Solve exponential and logarithmic equations.
10. Solve higher order polynomial equations using Remainder, Factor, Rational Root, and Conjugate Root theorems.
11. Solve systems of non-linear equations.
12. Solve 3x3 systems of linear equations: substitution, elimination of variables, Gauss-Jordan method, matrix inverses, Cramer’s Rule.
13. Matrices and Matrix Algebra: addition, subtraction, products, determinants.
14. Sequence and series: generate sequences, summation notation, arithmetic, geometric.
15. Binomial Theorem: expand, find n-th term.
16. Use the circular and triangular definition of trigonometric functions.
17. Find trigonometric functions of special angles and angles corresponding by reference.
18. Use amplitude, period, phase shift, and vertical shift to graph trigonometric functions.
19. Find inverse trigonometric functions of special values using domain restrictions.
20. Prove identities, simplify expressions, and solve equations using basic, Pythagorean, angle sum and difference, double angle, and half angle identities.
21. Solve triangles using Law of Sines, including use of the ambiguous case and solve associated word problems.
22. Solve triangles using Law of Cosines and solve associated word problems.
23. Graph, add, subtract, and find the dot product of vectors and solve associated word problems.
24. Add subtract, multiply and divide complex numbers in rectangular and trigonometric form and use DeMoivre’s theorem.
25. Convert between rectangular and polar coordinates.
26. Graph polar and parametric curves.

Objectives for MAT 171 Pre-Calculus Mathematics:

1. Identify and graph families of functions, find their inverses and zeros, and solve related equations.
2. Solve systems of equations, linear and non-linear, using an appropriate method including matrix methods.
3. Recognize equations of and sketch a graph of the conic sections.
4. Distinguish between general varieties and special types of sequences and series, and use appropriate formulas for finding summations and nth terms.
5. Generate a binomial expansion and find a specified nth term.
6. Recognize definitions and graphs of trigonometric functions and their inverses:
   evaluate and use to prove identities, solve equations, and solve triangles.
7. Apply trigonometry to solving problems involving vectors, complex numbers, polar coordinates, and parametric equations.