Mrs. M. Knobel                                                                         Room # 417


Course Description:


              In Pre-Calculus, students continue to build on the k-8, Algebra I, Algebra II and Geometry foundations as they expand their understanding of mathematics. Students will use functions, as well as, symbolic reasoning to represent and connect ideas in geometry, probability, statistics, trigonometry and calculus to model physical situations. Finally, students will use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools and technology (including, but not limited to calculators with graphing capabilities, data collection devices and computers) to model functions and equations and solve Real-Life problems.


Course Objective: Pre-Calculus students will acquire and demonstrate knowledge of concepts, definitions, properties and applications of topics listed below. The main goal of Pre-Calculus is to help students obtain critical thinking and decision making skills that will allow them to connect concepts, develop computational skills and learn strategies needed to solve mathematical problems.


Course Assessment:

             60% Exams

             40% Other Assignments


                   Chapter 1  Graphs

1.1 The Distance and Midpoint Formula

                             1.2 Intercepts: Symmetry: Graphing Key Equation
                             1.3 Solving Equations Using a Graphing Utility  

                     Chapter 2   Functions and Their Graphs
                              2.1 Functions

                              2.2 The Graph of a Function
                              2.3 Properties of Functions  
                              2.4 Library of Functions: piecewise-defined Functions                  

                              2.5 Graphing Techniques: Transformations   
                              2.6 Mathematical Models: Building Functions

    1. Chapter 3   Linear and Quadratic Functions

                3.1 Linear Functions and Their Properties

                3.2 Linear Models: Building Linear Functions from Data

                3.3 Quadratic Functions and Their Properties

                3.4 Build Quadratic Models from Verbal Descriptions and from Data

                3.5 Inequalities Involving Quadratic Functions


      Chapter 4   Polynomial and Rational Functions

                4.1 Polynomial Functions and models

                4.2 The Real Zeros of a Polynomial Function

                4.3 Complex Zeros: Fundamental Theorem of Algebra

                4.4 Properties of Rational Functions

                4.5 The Graph of a Rational Function

                4.6 Polynomial and Rational Inequalities



      Mid Term Exams


      Chapter 5 Exponential and logarithmic Functions

                5.1 Composite Functions

                5.2 One-to-One Functions: Inverse Functions

                5.3 Exponential Functions

                5.4 Logarithmic Functions

                5.5 Properties of Logarithms

                5.6 Logarithmic and Exponential Equations

                5.7 Financial Models

                5.8 Exponential Growth and Decay Models

                5.9 Building Exponential, Logarithmic, and Logistic Models


      Chapter 6 Trigonometry Functions

                6.1 Angles and Their Measure

                6.2 Trigonometric Functions: Unit Circle Approach

                6.3 Properties of the Trigonometric Functions

                6.4 Graphs of Sine and Cosine Functions

                6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

                6.6 Phase Shift: Sinusoidal Curve Fitting


      Chapter 7   Analytic Trigonometry

                7.1 The inverse Sine, Cosine, and Tangent Functions

                7.2 The Inverse Trigonometric Functions (Continued)

                7.3 Trigonometric Equations

                7.4 Trigonometric Identities


      Chapter 8 Applications of Trigonometric Functions

                8.1 Right Triangle Trigonometry: Applications

                8.2 The Law of Sines

                8.3 The Law of Cosines

                8.4 Area of Triangle

                8.5 Simple Harmonic Motion; Damped Motion: Combining Waves



      ***If time permits, then the following lessons will be cover***



      Chapter 9 Polar Coordinates; Vectors

                 9.1 Lines

                 9.2 Polar Equations and Graphs

                 9.3 The Complex Plane; De Moivre’s Theorem


      Chapter 12 Sequences; Induction; the Binomial Theorem

                12.1 Sequences

                12.2 Arithmetic Sequences: Geometric Series

                12.3 Geometric Sequences; Geometric Series


      Chapter 14 A Preview of Calculus: The Limit, Derivative, and Integrals

                 14.1 Finding Limits Using Tables and Graphs

                 14.2 Algebra Techniques for Finding Limits

                 14.3 One-Sided Limits; Continuous Functions

                 14.4 The Area Problem; The Derivative

                 14.5 The Area Problem; The Integral


      Wish you a successful school year!!!

 Note: Please see new grading district policy
College Readiness Course Syllabus

Mrs. Knobel                                                                        Room # 417



College Readiness

Course Syllabus


Mayra Knobel



(956) 580-5300 ext. 1178


3rd 11:21-12:51


MW 4:00-4:30

According to the Texas House Bill 5, each student needs to be college readiness before exiting high school. Major universities will no longer offer remedial courses and therefore is up to each student to have their prerequisites before entering any university. In response to the Texas House Bill 5, in particularly the mandate that the course be co-developed with the partnering institutions, UTPA is offering the use of their WebWork server. WebWork is free and open-sourced software written by a grant from the National Science Foundation and currently supported by the Mathematical Association of America and numerous mathematics departments around the country. We will be partnering with UTPA to assist you to acquire the necessary skills to be successful on the TSI exam.

UTPA has been maintaining a WebWork server since 2001, and has in-house expertise on the software. We will use WebWork based homework assignments and will test. In addition we will use this homework system to deliver the final exam to all participating classes. We will be working with computers on a daily bases so the expectations to respect and take care of our equipment is imperative. 

**In order to receive a one year waiver you must obtain greater that a 70 in the course and 70 in the midterm and final exam. **

Even though this course is linked to the local universities and colleges, we will still follow Sharyland Independent School Districts Grading Policy.

Grading Policy:

60% Major Assignments: Test, Reports, Projects

40% Minor Assignments: Classwork, Homework, Quizzes


Statement for Academic Dishonesty: Academic integrity is fundamental to the activities and principles of our school.  No student shall cheat or copy the work of another.  Plagiarism, the use of another person’s original ideas or writings as one’s own without giving credit to the true author, will be considered cheating, and the students will be subject to academic disciple that may include loss of credit for the work in question. 


Tentative Course Schedule

Course A

  • Numbers

1.1 Commutative, Associative, and Distributive Laws
1.2 Fractions
1.3 Positive and Negative Real Numbers
1.4 Addition of real numbers
1.5 Subtraction of real numbers
1.6 Multiplication and division of real numbers
1.7 Exponential Notation and order of operations
1.8 Applications with percents

  • Algebra

2.1 Introduction to Algebra
2.2 Solving linear equations
2.3 Using addition and multiplication principles together
2.4 Formulas
2.5 Read graphs, plot points, and scaling graphs
2.6 Graphing linear equations
Approximate Six Week Goal
2.7 Graphing and intercepts
2.8 Rates of change
2.9 Slope
2.10 Slope-intercept form
2.11 Point-slope form

  • Solving inequalities

3.1 Solving inequalities
3.2 Solving applications with inequalities

  • Exponents and Polynomials

4.1 Exponents and Properties
4.2 Negative exponents and scientific notation
4.3 Polynomials
4.4 Addition and subtraction of polynomials

Approximate 12 week goal
4.5 Multiplication of polynomials
4.6 Special products
4.7 Polynomials in several variables
4.8 Division of polynomials
5.1 Introduction to factoring polynomials
5.4 Factoring perfect square trinomials and differences of squares

  • Rational Expressions

6.1 Rational Expressions
6.2 Multiplication and division of rational expressions
6.3 Addition, subtraction of rational expressions and the least common divisor

  • Radical Expressions

8.1 Radical Expressions
8.2 Rational numbers as exponents
8.7 Distance and midpoint formulas and applications


Course B

There is significant overlap between Course A and Course B. The assignments used will have some problems in common; however the expectation of student work will be higher. One reason for the repetition is that these topics represent the most important material for future mathematics and science courses the students will take.

Topics in green are duplicated from Course A.

  • Polynomials

2.2 Solving linear equations
Graphing linear equations
Graphing and intercepts
Addition and subtraction of polynomials
Multiplication of polynomials
Special products
Polynomials in several variables
Division of polynomials

  • Solving inequalities

3.1 Solving inequalities
Solving applications with inequalities
3.3 Inequalities and domain
3.4 Intersections, unions, and compound inequalities

  • Factoring Polynomials

5.1 Introduction to Factoring
5.2 Factoring Trinomials with leading coefficient one
5.3 Factoring Trinomials with leading coefficient not one
Factoring Perfect Square Trinomials and differences of squares
5.5 Factoring sums and differences of cubes
5.6 Factoring general strategy
5.7 Solving polynomial equations by factoring
5.8 Solving applications
Approximate 6 week goal

  • Rational Expressions

6.1 Rational Expressions
Multiplication and division of rational expressions
Addition and subtraction of rational expressions, and the least common divisor
6.4 Addition and subtraction of rational expressions with unlike denominators.
6.5 Complex rational expressions

  • Systems of Equations

7.1 Systems of equations in two variables
7.2 Solving systems using substitution or elimination
7.3 Applications of systems of two variables
** Optional ** 7.4 Business and Economics applications of systems of equations
7.5 Inequalities in two variables

  • Radical Expressions

8.1 Radical expressions and functions
8.2 rational numbers as exponents
8.3 Multiplying radical expressions
8.4 Dividing radical expressions
8.5 Expressions with several radical terms
8.6 Solving radical equations

Approximate 12 week goal

  • Functions

9.1 Introduction to functions
9.2 Domain and range of functions
9.3 Graphs of functions

  • Quadratic Equations and Graphs
9.4 Complex numbers
9.5 Quadratic Equations
9.6 The quadratic formula
9.7 Quadratic functions and graphs
9.8 More graphing quadratic functions