Effective: 2023-05-01

Course Description

The course outline below was developed as part of a statewide standardization process.

General Course Purpose

The general purpose of this one-semester course is to prepare students for the skills and level of rigor needed for successful study in a sequence of courses in calculus with analytic geometry.

Course Objectives

• Relations and Functions
• Distinguish between relations and functions.
• Evaluate functions both numerically and algebraically.
• Determine the domain and range of functions in general, including root and rational functions.
• Perform arithmetic operations on functions, including the composition of functions and the difference quotient.
• Identify and graph linear, absolute value, quadratic, cubic, and square root functions and their transformations.
• Determine and verify inverses of one-to-one functions.
• Polynomial and Rational Functions
• Determine the general and standard forms of quadratic functions.
• Use formula and completing the square methods to determine the standard form of a quadratic function.
• Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions.
• Identify zeros (real-valued roots) and complex roots, and determine end behavior of higher order polynomials and graph the polynomial, and graph.
• Determine if a function demonstrates even or odd symmetry.
• Use the Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine the zeros over the complex numbers.
• Identify intercepts, end behavior, and asymptotes of rational functions and graph.
• Solve polynomial and rational inequalities.
• Interpret the algebraic and graphical meaning of equality of functions (f(x) = g(x)) and inequality of functions (f(x) > g(x))
• Exponential and Logarithmic Functions
• Identify and graph exponential and logarithmic functions and their transformations.
• Use properties of logarithms to simplify and expand logarithmic expressions.
• Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms.
• Solve exponential and logarithmic equations using one-to-one and inverse properties.
• Solve application problems involving exponential and logarithmic functions.
• Systems of Equations
• Solve three variable linear systems of equations using the Gaussian elimination method.
• Trigonometric Functions
• Identify angles in standard form in both degree and radian format and convert from one to the other.
• Find the arc length.
• Find the value of trigonometric functions of common angles without a calculator using the unit circle and right triangle trigonometry.
• Use reference angles to evaluate trig functions.
• Find the value of trigonometric functions of angles using a calculator.
• Use fundamental trigonometric identities to simplify trigonometric expressions.
• Graph the six trigonometric functions using the amplitude, period, phase and vertical shifts.
• Use trig functions to model applications in the life and natural sciences.
• Analytic Trigonometry
• Use the fundamental, quotient, Pythagorean, co-function, and even/odd identities to verify trigonometric identities.
• Use the sum and difference, double angle, half-angle formulas to evaluate the exact values of trigonometric expressions.
• Determine exact values of expressions, including composite expressions, involving inverse trigonometric functions.
• Solve trigonometric equations over restricted and non-restricted domains.
• Applications of Trigonometry
• Solve right triangles and applications involving right triangles.
• Use the Law of Sines and Cosines to solve oblique triangles and applications.
• Conics
• Identify the conic sections of the form:Ax^2+By^2+Dx+Ey+F=0.
• Write the equations of circles, parabolas, ellipses, and hyperbolas in standard form centered both at the origin and not at the origin.
• Identify essential characteristics unique to each conic
• Graph equations in conic sections, centered both at the origin and not at the origin.
• Solve applications involving conic sections.
• Sequences and Series (Optional unit at the discretion of the department. Not required for transfer.)
• Identify the terms of geometric sequences.
• Find a particular term of geometric sequence.
• Determine the formula for the an term of geometric sequences.
• Find the sum of first n terms of finite geometric series.
• Find the sum of infinite geometric series.
• Introduce arithmetic concepts as time allows.

Major Topics to be Included

• Relations and Functions
• Polynomial and Rational Functions
• Exponential and Logarithmic Functions
• Systems of Equations and Inequalities
• Trigonometric Functions
• Analytic Trigonometry
• Applications of Trigonometry
• Conics