Mikel Haug » PRECALCULUS: 2nd PERIOD

PRECALCULUS: 2nd PERIOD

Precalculus Syllabus

Course Description:  The primary focus of pre-calculus is to prepare students for further studies in math and science and lay the foundation for calculus by developing a better understanding of mathematics and an intuitive grasp of the functions and their graphs studied in calculus. Multiple representations of problems and topics and the connections between them will be stressed as will the communication of mathematical concepts. Justification of solutions will be emphasized and varied approaches to a problem will include physical, verbal, numerical, graphical, and analytical techniques.  Students in Pre-Calculus extend their learning from Geometry and Algebra.  Precalculus combines the geometric, algebraic, and trigonometric techniques and strengthens students’ conceptual understanding of problems.  Attention is devoted to mathematical reasoning in solving problems, understanding concepts and the application of those concepts.  Students focus on the use of technology, modeling, and problem solving. Functions studied include polynomial, exponential, logarithmic, rational, radical, piece-wise, and trigonometric and circular functions and their inverses. Areas of discrete mathematics, and infinite sequences and series are also studied as well as an introduction to limits. 

 

Instructional Strategies:  Most instruction consists of interactive lecture with student involvement and questioning encouraged for clarity.  PowerPoint slides are often part of the instruction.  The presentations are typically followed by one or two days of assignments based on the topics and extensions.  Mathematics processes are emphasized, allowing students to engage in problem solving, decision making, critical thinking, and applied learning.  Students should learn to use a variety of ways to represent data, to use a variety of mathematical tools. Technology is used to enhance teaching and learning, not to replace the mathematics required.  Calculator problems are designated.  Students are expected to use multiple approaches to problems and communicate the connections between them with an emphasis on written communication.

 

Homework is an important part of learning mathematics and will be assigned regularly.  Every assigned problem should be attempted. You are encouraged to discuss problems with other students or friends.  However, it is not permissible to copy another student's work.  Do your best to think through the problems and understand why things work the way they do.  Doing homework may make you frustrated. That is ok. I am hoping that the homework will challenge you to think.  Thinking is part of learning!  The key for student success is that they come to school prepared daily and do their homework.  Since most of mathematics depends on concepts taught in prior lessons, it is much easier to stay current than to catch up.  Students are expected to work problems on the board and explain their solutions to their classmates.  This provides feedback on which students need additional help and which topics need additional reinforcement.  Students should grade their own homework making corrections and notes for later review.

 

Assessment:  Quarter grades are calculated as follows: the test/summative assessment average is weighted 35%, the quiz/formative assessment average is weighted 50%, and the daily participation average is weighted 15%.  For each semester average, the quarter grades are averaged and for the year, the semester grades are averaged.

 

Tutorials:  Precalculus is rigorous and I have high expectations.  I will be here by 7:15 each morning, during WIN with advanced notice, and after school as late as need be most days to assist you in rising to the challenge.

 

Procedures and Expectations:

  • You are expected to come to class prepared and on time. Prepared means having all materials and completed assignments.  On time means ready to work when the bell rings, not starting to get your materials unpacked.  You are expected to present work on the board.

 

  • Cell Phones and earbuds are not allowed in class. When you enter the class, you should turn your phone off and place it in your backpack or purse.  If you are caught with your cell phone during class, it will be turned over to the teacher and held until Friday after school, (if collected on a Friday, it will be held until the following Friday).  If needed sooner, a parent may come in to retrieve it.

 

  • You should treat yourself, your classmates, your instructor, and any guests with respect. listen to and follow directions the first time they are given, and follow the student code of conduct.

 

.Course Outline

  • In Unit 1, students study functions and their properties. Functions and their representation on the Cartesian plane are addressed. Students begin the unit by applying the distance and midpoint formulas and by identifying intercepts, symmetry, and slope of graphs. These are used to compare/contrast and categorize functions and transform these functions.  Topics of study include parent functions, combinations of functions, inverses of functions, and transformations. Students devise and implement a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Students learn to effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language and incorporating rational argument.
  • In Unit 2, trigonometric functions are applied to real world situations. Students learn how to evaluate and graph the trigonometric functions, their inverses, and reciprocals. The unit begins by introducing radian measure and the definition of trigonometric functions of the unit circle and using reference angles to find the trigonometric functions for any angle. The chapter also covers graphing trigonometric functions, reciprocals, and inverses, using their basic characteristics. Students use trigonometric ratios to solve problems in a variety of contexts.  Strategies for simplifying expressions and solving equations by using trigonometric identities are implemented. Students learn how to rewrite/simplify trigonometric expressions using identities and how to verify identities. Trigonometric equations written in quadratic form and equations containing more than one angle will be solved, followed by equations containing sums and differences of angles. Students will rewrite trigonometric expressions that contain functions of multiple or half-angles.  Students also use the law of sines and the law of cosines to solve problems.
  • In Unit 3, students extend their understanding of polynomial and rational functions. In this unit, the student learns to analyze and graph polynomial and rational functions. The chapter begins with identifying key characteristics and creating graphs of quadratic and other polynomial functions.  Students learn to find real and complex roots, asymptotes, intercepts, and holes as they graph polynomial and rational functions and problems using nonlinear inequalities
  • In Unit 5, students extend their understanding of exponential and logarithmic functions. This unit begins with writing, graphing and recognizing the basic characteristics of exponential and logarithmic functions. Students use these functions to model real-world problems, including compound interest and radioactive decay, among others from a variety of contexts. They expand their skills by using the properties of logarithms and exponents to manipulate expressions and solve equations.  
  • In Unit 6, students explore different aspects of discrete mathematics, including counting principles, the binomial expansion theorem, and sequences and series. Students analyze sequences and series and expand binomials. (The probability of events will be covered only as time allows.) Methods of representing sequences and series, including summation notation are studied for arithmetic, geometric and other sequences. Students expand binomials by using Pascal’s triangle and the Binomial Theorem. Proofs by mathematical induction will be included.
  • In Unit 7, Students are introduced to limits and continuity, the basis of Calculus. This unit is a compact introduction to calculus. It defines the limit of a function and covers the techniques of finding limits. Students learn to find the limits of functions at infinity and convergence and limits of sequences.

Topics covered in analytic geometry if time allows include work with conic sections and equations in rectangular forms. The distinguishing features of the circle, parabola, ellipse, and hyperbola in both the general forms and the standard forms of their equations are used to create graphs and solve problems involving conic sections will be examined as will polar coordinates and graphs of polar equations.