Jun 07, 2023
MATH 1300 - Pre-Calculus
Course provides a rigorous treatment of graphs, inverses, and algebraic operations of polynomial, rational, exponential, logarithmic, and trigonometric functions, trigonometry and analytic geometry. The course also includes introductions to linear systems, polar coordinates, vectors, conic sections, sequences and series. Recommended only for students intending to enroll in MATH 2301 Calculus I. No credit for both this course and MATH 1322 (first course taken deducted).
Requisites: (C or better in MATH 1200 or MATH 1321) or math placement level 2 or higher WARNING: No credit for both this course and MATH 1322 (first course taken deducted)
Credit Hours: 4
General Education Code: 1M
Repeat/Retake Information: May be retaken two times excluding withdrawals, but only last course taken counts.
Lecture/Lab Hours: 4.0 lecture
Grades: Eligible Grades: A-F,WP,WF,WN,FN,AU,I
Course Transferability: OTM Course: TMM002 Pre-Calculus
College Credit Plus: Level 1
- Analyze the algebraic structure and graph of a function to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, etc.
- Define the six trigonometric functions in terms of right triangles and the unit circle.
- Determine algebraically and graphically whether the graph of an equation exhibits symmetry.
- Determine whether an algebraic relation or given graph represents a function.
- Express angles in both degree and radian measure.
- Find inverses of functions and understand the relationship of the graph of a function to that of its inverse.
- Identify and express the conics (quadratic equations in two variables) in standard rectangular form, graph the conics, and solve applied problems involving conics.
- Identify and express the general term of arithmetic and geometric sequences, and find the sum of arithmetic and geometric series.
- Perform basic vector operations both graphically and algebraically addition, subtraction, and scalar multiplication.
- Perform operations with functions addition, subtraction, multiplication, division, and composition.
- Perform transformations of functions translations, reflections and stretching, and shrinking.
- Represent functions verbally, numerically, graphically and algebraically, including linear, quadratic, polynomial, rational, root/radical/power, piecewise-defined, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
- Represent sequences verbally, numerically, graphically and algebraically, including both the general term and recursively.
- Represent vectors graphically in both rectangular and polar coordinates and understand the conceptual and notational difference between a vector and a point in the plane.
- Solve a system of linear equations graphically and algebraically by substitution and elimination, and solve application problems that involve systems of linear equations.
- Solve a variety of equations, including polynomial, rational, exponential, and logarithmic, trigonometric and inverse trigonometric, including equations arising in application problems.
- Solve a variety of trigonometric and inverse trigonometric equations, including those requiring the use of the fundamental trigonometric identities, in degrees and radians for both special and non-special angles.
- Solve application problems that involve trigonometric equations.
- Solve application problems using vectors.
- Solve polynomial and rational inequalities graphically and algebraically.
- Solve right and oblique triangles in degrees and radians for both special and non-special angles, and solve application problems that involve right and oblique triangles.
- Understand the difference between an algebraic equation of one, two or more variables and a function, and the relationship among the solutions of an equation in one variable and features of the graph.
- Use functions, including those listed in the first outcome, to model a variety of real-world problem solving applications.
- Use the Remainder and Factor Theorems for polynomial functions.
- Verify trigonometric identities by algebraically manipulating trigonometric expressions using fundamental trigonometric identities, including the Pythagorean, sum and difference of angles, double-angle, and half-angle identities.
- Write series in summation notation, and represent sequences of partial sums verbally, numerically, and graphically.
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