# Math 111 Precalculus

### Objectives / Learning Outcomes

Welcome to the webpage for Math 111 Spring 2020.

Math 111 Objectives and Learning Outcomes
The primary goal of MTH 111 is to prepare you for calculus (MTH131 or MTH141). The calculus sequence is often an essential step toward degree and career objectives, so MTH 111 is also such a step. Thus MTH 111 is aimed at the student for whom it will be the first of an important series of courses rather than a last math course. The prerequiste requirement for MTH131 and MTH141 is earning a C- or better in MTH 111. This course completely fulfills the general education requirements for Mathematical, Statistical or Computational Strategies, (MSCS) A,B and C elements and for Knowledge Outcome: STEM Discipline (STEM) elements. However, this course is NOT a good choice simply to fulfill a general education requirement. It demands a very substantial amount of hard work for 3 credits.

In order to succeed in this course and future math courses, you will have to master the following 10 Precalculus Competency Areas (PCA).
Inequalities – Solve and graph simple linear inequalities, compound inequalities, absolute value inequalities quadratic inequalities and rational inequalities Rubric Elements – A.1, A.2, B.2, STEM1, STEM2
Graphs and Graphing – Find the distance between and midpoint of two points. Calculate and graph x-intercepts and y-intercepts. Graph horizontal and vertical lines. Identify families of functions and shifted graphs for linear, quadratic, cubic, square root, cubic root and greatest integer functions. Transform the graphs of linear, quadratic, cubic, square root and step functions by identifying the horizontal and vertical shifts, stretches, shrinkages and reflections. Discern symmetry from a graph. Graph piecewise functions. Determine and notate increasing, decreasing and constant intervals. Rubric Elements – A.2, A.2, B.1, C.3, STEM1, STEM2, STEM3, STEM4
Linear Equations and Lines – Calculate and identify the slope of a line, slopes of parallel and perpendicular lines, and slopes of vertical and horizontal lines. Create the equation of a line given two points or given a point and a slope or the line parallel or perpendicular. Detect the slope of a line given the graph of the line. Rubric Elements – A.1, A.2, B.1, B.2, STEM1, STEM2, STEM3
Functions – Test whether a given relation is a function for sets, graphs and equations. Use function notation. Evaluate the value of a function. Explain piecewise functions. Perform basic operations with functions. Determine the domain and range of a function. Compute the difference quotient of a function. Compose two or more functions. Test whether a given function is even or odd algebraically. Explain how to determine one-to-one functions for sets, graphs and equations. Find the inverse of a given function. Verify inverse functions using composition. Find the inverse of a mathematical model. Rubric Elements – A.1, A.2, B.1, B.2 C.1, C.2, C.3, STEM1, STEM2, STEM5, STEM6. STEM7
Polynomials – Factor polynomials, expand/multiply polynomials. Convert from the standard quadratic form to the standard parabola form by completing the square. Find the vertex, axis of symmetry, and other properties of a parabola represented by given quadratic function. Perform basic operations on complex numbers. Solve quadratic equations with real and imaginary roots. Divide two polynomials by both the long division and synthetic division methods. Recognize and apply the Zero Factor Theorem. Interpret and apply the Remainder Theorem. Interpret and apply the Rational Roots Theorem. Interpret and apply Descarte’s Rule of Signs. Graph higher order polynomials. Determine the end behavior of a polynomial function using the Leading Coefficient Test. Find all roots of a higher order polynomial. Determine the behavior of a polynomial function at the x-intercepts. Create the polynomial given its roots (both real and complex). Understand and apply the Complex Conjugate Theorem. Graph higher order polynomial functions. Rubric Elements – A.1, A.2, B.1, B.2, STEM1, STEM2, STEM5, STEM6
Radicals and Exponents – Perform basic operations on radical expressions. Explain the domain of exponential functions. Graph exponential functions and the associated family of functions. Simplify exponential expressions. Transform between radical, fractional and exponential forms. Rubric Elements – A.1, A.2, C.1, STEM1, STEM2, STEM5
Rational Expressions – Identify the domain of a rational expression. Evaluate rational expressions. Determine the vertical and horizontal asymptotes. Graph rational equations including asymptotes and ‘holes’. Rubric Elements – A.1, A.2, B.1, B.2, STEM1, STEM2, STEM5, STEM6
Trigonometric Functions – Evaluate basic trigonometric functions. Convert angles to degrees or radians. Find the domain and the range of the trigonometric functions. Understand Sine and Cosine functions from unit circle. Memorize and recall the trigonometric values at important angles based on unit circle. Understand and identify the graphs of trigonometric functions. Calculate the values of all other trigonometric functions. Transform and graph Sine and Cosine functions including phase shifts, periodicity and amplitude. Determine the values and graph inverse trigonometric functions. Solve right triangles and use right triangle trigonometry to solve application problems involving angle of elevation and angle of depression. Memorize and recall the Pythagorean Identities, Odd and Even Identities, Sum and Difference Identities, Double-Angle Identities and Half-Angle Identities. Simplify trigonometric expressions and prove equivalent expressions using trigonometric identities. Rubric Elements – A.1, A.2, B.1, C.1, C.2, STEM1, STEM2, STEM5, STEM6, STEM7
Logarithms – Evaluate logarithms. Apply logarithmic rules to simplify an expression. Solve logarithmic equations. Solve exponential equations. Understand and apply the properties of exponential functions and logarithmic functions. Apply mathematical methods and properties of exponential and logarithmic functions to solve real world application problems of compound interest calculation and radioactive decay. Rubric Elements – A.1, A.2, B.1, B.2, C.1, C.2, C.3, STEM1, STEM2, STEM3, STEM5, STEM6, STEM7
Problem Solving – For all PCA’s, justify solutions and the problem solving process. Verify, interpret and communicate solutions with respect to the original problem. C.2, C.3, STEM7