Precalculus - Mathematics for Calculus Eight Edition by James Stewart, Lothar Redlin, and Saleem Watson
Search by ISBN on Amazon: 0357753631

Two years of high school algebra, plane geometry, plane trigonometry; obtaining required score on the Math Readiness Assessment.

This course has two weekly discussion sections. Student attendance and participation in discussion sections is mandatory. During discussion sections, students will work in small groups on worksheets to strengthen their understanding of course material.

• Lecture 1-2
  • Section 1.1 Real Numbers (intervals with set notation and absolute value)
  • Section 1.2 Exponents and Radicals (properties of exponents including n-th roots and rational exponents)
  • Section 1.3 Algebraic Expressions (expanding and factoring)
  • Section 1.4 Rational Expressions (compound fractions and rationalizing denominator or numerator)
• Lecture 3
  • Section 1.5 Equations (linear, quadratic, quadratic-type)
• Lectures 4-6
  • Section 1.7 Modeling with Equations
  • Section 1.8 Inequalities (linear, nonlinear, and absolute value inequalities; modeling with inequalities)
• Lecture 7-8
  • Section 1.9 The Coordinate Plane; Graphs of Equations; Circles (including distance and symmetry)
  • Section 1.10 Lines (including parallel and perpendicular lines)
• Lecture 9
  • Section 2.1 Functions (domain)
  • Section 2.2 Graphs of Functions (piecewise defined functions, vertical line test)
  • Section 2.3 Getting Information from the Graph of a Function (range, increasing/decreasing, local max/min, solving equations graphically)
• Lecture 10
  • Section 2.6 Transformations of Functions (including even and odd functions)
• Lecture 11
  • Section 2.7 Combining Functions
• Lecture 12
  • Section 2.8 One-to-One Functions and Their Inverses (including graphing)
• Lecture 13
  • Section 3.1 Quadratic Functions and Models (max and min of quadratic functions)
• Lecture 14
  • Section 3.2 Polynomial Functions and Their Graphs
• Lecture 15
  • Section 3.6 Rational Functions
• Lecture 16
  • Section 3.7 Polynomial and Rational Inequalities
• Lecture 17
  • Section 4.1 Exponential Functions
  • Section 4.2 The Natural Exponential Function
• Lecture 18
  • Section 4.3 Logarithmic Functions
  • Section 4.4 Laws of Logarithms
• Lecture 19
  • Section 4.5 Exponential and Logarithmic Equations
• Lecture 20
  • Section 4.6 Modeling with Exponential Functions
  • Section 4.7 Logarithmic Scales
• Lecture 21-22
  • Section 5.1 The Unit Circle
  • Section 5.2 Trigonometric Functions of Real Numbers
  • Section 6.1 Angle Measure
  • Section 6.2 Trigonometry of Right Angles
  • Section 6.3 Trigonometric Functions of Angles
• Lecture 23
  • Section 5.3 Trigonometric Graphs (including periods and shifts)
  • Section 5.4 More Trigonometric Graphs (tangent, cotangent, secant, and cosecant)
• Lecture 24
  • Section 7.1 Trigonometric Identities (including even/odd and cofunctions)
  • Section 7.2 Addition and Subtraction Formulas
  • Section 7.3 Double-Angle and Half-Angle
• Lecture 25
  • Section 7.4 Basic Trigonometric Equations
  • Section 7.5 More Trigonometric Equations
• Lecture 26
  • Section 5.5 Inverse Trigonometric Functions and Their Graphs

 

Note: Section 2.5 - Modeling with linear functions is covered in the discussion section worksheet.

If time permits:

• Section 1.6 Complex Numbers
• Section 1.12 Modeling Variation

This course is designed to prepare students for our calculus classes.

At the end of this course a student will be able to:

• Manipulate and simplify expressions algebraically
• Graph and analyze functions, including:
  • Piecewise, discrete, linear, power, polynomial, rational, exponential, logarithmic, and trigonometric functions
  • Translation, scaling, and reflection
  • Finding domain and range
  • Inverse functions
• Solve equations and inequalities involving linear, power, polynomial, rational, exponential, logarithmic, and trigonometric expressions and absolute values.
• Be able to use algebraic trigonometric formulas to represent geometric situations and problems
• Model and solve contextualized word problems, including:
  • Set up mathematical models using clear mathematical notation
  • Analyze, interpret, and use solutions in context
• Use appropriate and correct mathematical notation in all presented work
• Write organized and logical mathematical work

Students' progress in the course will be assessed using both formative and summative assessments. There are at least 2 midterms and a final as well as homework and discussion worksheets.