MATH 1300 - Pre-Calculus

• 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.