MTH 1080A - Precalculus Mathematics

• Perform basic arithmetic operations with numeric and algebraic expressions, demonstrate correct use of order of operations, and simplify results
• Simplify algebraic expressions (rational, radical, exponential expressions, including negative and rational exponents)
• Factor polynomial and polynomial-like expressions
• Demonstrate use of the Laws of Exponents
• Evaluate algebraic and piecewise-defined functions with correct use of function notation
• Identify visually the domain and range of a function, using appropriate notation
• Identify visually the intervals where a function is increasing, decreasing, and continuous
• Be familiar with the graphs of simple power, radical, and reciprocal functions
• Combine functions using algebraic operations and composition
• Find equations of lines using point-slope form
• Develop a linear model of a real-life situation and interpret slope as the average rate of change
• Identify and apply transformations of functions and graphs
• Perform polynomial long division
• Perform arithmetic operations with complex numbers
• Solve quadratic, quadratic-like, and higher-degree polynomial equations
• Develop a quadratic or polynomial model of a real-life situation and interpret the features of the graph
• Visually determine if a function is one-to-one and identify the graph of its inverse function
• Find a formula for the inverse function of a one-to-one function
• Perform algebraic operations with rational functions and simplify results
• Simplify complex rational expressions
• Evaluate and simplify the difference quotient involving a polynomial or rational function
• Identify end-behavior of a polynomial function
• Identify asymptotic behavior of a rational function including determining if a discontinuity is removable or infinite
• Graph a piecewise-defined function and determine the intervals of continuity
• Evaluate and graph exponential functions and identify growth vs. decay
• Evaluate and graph logarithmic functions and interpret as the inverse of an exponential function
• Use algebraic properties of logarithms to simplify or expand logarithmic expressions
• Solve exponential equations
• Develop an exponential model for an application and interpret the results
• Convert angle measures between radians, degrees, and revolutions
• Find circular arc-length and sector area, converting to radians if necessary
• Sketch angles in standard position given their radian measure
• Evaluate trigonometric functions given information about an angle
• Evaluate trigonometric functions at special values using the reference angle
• Use technology to evaluate trigonometric functions
• Use right triangle trigonometry to solve an applied problem
• Apply basic trigonometric identities (ratio, reciprocal, Pythagorean, odd/even) to evaluate or simplify trigonometric expressions
• Interpret sine, cosine, and tangent in the context of the unit circle
• Sketch the graph of sine, cosine, and tangent
• Evaluate inverse trigonometric functions at special values
• Sketch the graph of arctangent
• Apply the addition formulas to evaluate or simplify trigonometric expressions
• Sketch the graph of a sinusoidal curve (sine or cosine with transformations) including finding the phase angle
• Derive other trigonometric identities (e.g. difference formulas, double angle identities, half-angle identities) from known identities with guidance
• Solve trigonometric equations
• Identify the type, determine the features of, and sketch a conic section
• Solve simple systems of equations analytically and graphically, including linear/linear and linear/quadratic
• Apply common geometric and physical formulas emphasizing dimensional analysis (area, volume, distance/rate/time, etc…)

• Basic algebra and geometry

• The real number system, order of operations, intervals, and inequalities
• Exponential notation and the laws of exponents
• Functions and modes of representation (algebraic, numerical, graphical, etc…)
• The coordinate plane and graphing functions
• Monotonicity and continuity
• Transformations of functions and their graphs
• Combining functions (algebra of functions, composition)
• Even and odd functions
• Difference quotients
• One-to-one and inverse functions
• The complex number system
• Linear, quadratic, and polynomial functions and models
• Factoring and solving polynomial equations
• Rational functions and asymptotic behavior
• Absolute value and piecewise-defined functions
• Exponential functions and models
• Logarithmic functions and their properties
• Solving exponential equations
• Angles and their measures, arclength and sector area
• Trigonometric functions
• Right triangle trigonometry
• Basic trigonometric identities
• Addition formulas and related identities
• Inverse trigonometric functions
• Graphs of trigonometric functions; sinusoidal models
• Solving trigonometric equations
• Conic sections
• Systems of equations