Math 2 - Precalculus

Description

An intensive preparation for calculus. This course is intended for computer science, engineering, mathematics and natural science majors. Topics include algebraic, exponential, logarithmic and trigonometric functions and their inverses and identities, conic sections, sequences, series, the binomial theorem, and mathematical induction.

Prerequisites

Math 20 and Math 32

How It Transfers

UC, CSU IGETC AREA 2 (Mathematical Concepts)

Textbook

Stewart, Redlin, Watson Precalculus: Mathematics for Calculus, 5th Ed., Thomson Brooks/Cole, 2007

Entry Level Skills

 

Skills the instructor assumes you know prior to enrollment in this course

• Simplify advanced numerical and algebraic expressions involving multiple operations. 
• Perform operations on polynomials.
• Solve literal equations for a designated variable. 
• Solve and graph inequalities involving absolute value. 
• Solve polynomial equations by factoring. 
• Solve quadratic equations by using quadratic formula and completing the square. 
• Complete the square. 
• Solve rational and radical equations. 
• Use interval notation to express the solution to a linear, quadratic or rational inequality. 
• Solve application problems using equations. 
• Find the domain and range of linear, quadratic and absolute value relations. 
• Find domain of rational and square root functions. 
• Perform operations on functions including composition of functions.
• Determine the inverse of a function 
• Perform operations on complex numbers. 
• Convert between exponential and logarithmic forms.
• Evaluate and graph exponential and logarithmic functions. 
• Solve elementary logarithmic and exponential equations.
• Graph parabolas and circles by completing the square. 
• Solve systems of linear equations in three variables by elimination and matrices.
• Graph systems of linear and quadratic inequalities. 
• Evaluate simple expressions involving sigma notation. 
• Graph simple functions by vertical and horizontal translation.
• Define basic geometric terms. 
• Distinguish between hypothesis and conclusion. 
• Describe the relationship between a theorem and its converse, inverse and contrapositive. 
• Set up and complete simple direct and indirect proofs. 
• Perform basic geometric constructions. 
• Apply geometric theorems involving similar and congruent triangle; parallel lines; parallelograms and their properties; lines and circles and their properties; lines and circles and their relationships; right triangles (Pythagorean theorem).

Course Objectives

Skills to be learned during this course

• Simplify advanced numerical and algebraic expressions involving multiple operations.
• Solve linear, quadratic, rational and absolute value inequalities, graph their solution sets, and express the answer in interval notation.
• Solve literal equations for a designated variable.
• Apply algorithms of completing the square, rationalizing the denominator, and long division and synthetic division of polynomials. 
• Solve linear, quadratic form, simple cubic, radical, rational, absolute value, elementary exponential, and elementary logarithmic equations.
• Perform operations on complex numbers.
• Perform operations on functions including composition of two functions and determine the domain of the resulting function. 
• Use proper mathematical notation to evaluate functions and obtain their inverses.
• State and apply the fundamental properties of exponents and logarithms.
• Demonstrate knowledge of standard vocabulary associated with graphing, including but not limited to slopes of lines, intercepts, vertex of parabola, asymptotes, and interplay between graph and functional notation.
• Given its graph, determine whether a relation is a function and whether it is one-to-one, and determine its intercepts and domain and range.
• Graph using horizontal and vertical translations and determine the domain and range of linear, quadratic, simple cubic, radical, reciprocal, absolute value, exponential and logarithmic functions. 
• Graph circles and parabolas using horizontal and vertical translation. 
• Evaluate simple expressions involving summation notation.
• Set up and solve practical applications of the algebraic material.
• Define basic geometric terms. 
• Distinguish between hypothesis and conclusion. 
• Describe the relationship between a theorem and its converse, inverse and contrapositive. 
• Set up and complete simple direct and indirect proofs. 
• Perform basic geometric constructions. 
• Apply geometric theorems involving similar and congruent triangle; parallel lines; parallelograms and their properties; lines and circles and their properties; lines and circles and their relationships; right triangles (Pythagorean theorem).