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MAT 1370 - Pre-Calculus
5 credit hours

MAT 1370 is an alternative to MAT 1350-1360 for qualified students. Topics include: polynomial functions and theory of equations; exponential and logarithmic functions; systems of equations, inequalities, and matrices; sequences, summation, induction, and binomial theorem; trigonometric functions; analytic trigonometry; applications of trigonometry in right triangles, oblique triangles, vectors, complex numbers, polar coordinates, and parametric equations; conic sections; analytic geometry in 3‑dimensions; and applications. Replaces MAT 137.
Prerequisite: Grade of A or B in MAT 1040 [formerly MAT 104] in addition to completion of high school level geometry and trigonometry, or qualified for MAT 2410 on the basis of SAT or a score at least 87 on Accuplacer College-Level Mathematics (CP4). Students must have a graphing calculator.

Books:

Outcomes:
Upon successful completion of the course, each student should be able to demonstrate the ability to use symbolic, numerical, and visual skills to find and verify solutions of algebra problems and algebra applications (of college-level difficulty) in the following areas:

1. Performing operations with and simplifying:

• Algebraic expressions involving real and complex numbers, including complex numbers in trigonometric form, integer and rational exponents, radicals, and absolute values.
• Transcendental expressions involving exponentials and logarithms.
• Polynomial, rational, radical, exponential, and logarithmic functions, including related composite and inverse functions.
• Trigonometric functions, including related composite and inverse functions.
• Vector expressions in two- and three-dimensions.

2. Solving:

• Linear and nonlinear equations and inequalities in one and two variables.
• Applications involving exponential and logarithmic functions.
• Trigonometric equations.
• Trigonometric applications that involve right triangles, oblique triangles, and angular motion.
• Applications of systems of equations in two and three variables using algebraic, matrix, and determinant methods.
• Problems involving sequences, summation, mathematical induction, and the Binomial theorem.
• Applications of vectors in two- and three-dimensional space.

3. Graphing and analyzing:

• Polynomial, rational, radical, exponential, and logarithmic functions, including related composite and inverse functions.
• The six basic trigonometric functions (sine, cosine, tangent, cotangent, secant, and cosecant) and their inverses (including shrinking, stretching, and translating).
• The four basic conic sections (parabola, circle, ellipse, and hyperbola - including translating but not rotating).

4. Graphing equations in rectangular, parametric, and polar form, and converting equations from any one of these forms to any other form.

5. Evaluating trigonometric functions and their inverses in degree and radian modes:

• For any angle using a calculator (approximate).
• For all multiples of 30, 45, 60, and 90 degrees without a calculator (exact).

6. Applying and verifying:

• Trigonometric identities.
• Trigonometric sum, difference, multiple-angle, and half-angle formulas.
• DeMoivre's theorem.