Honors Pre-Calculus/Pre-Calculus Credits: 6
Text: Pre-Calculus: Graphical, Numerical, Algebraic (Demana, Waits, Foley, Kennedy)
Mathematics 21st Century Expectation for Student Learning:
Every Hull High School student will be a competent problem solver.
Course Overview:
This course is designed for students with a high interest and ability in mathematics. Topics include a survey of functions, graphing, trigonometry, analytical geometry, exponential and logarithmic functions and equations, vectors, matrices, polar coordinates, and sequences and series. Earning a grade of B or better in this course is a prerequisite for admission to AP Calculus.
A graphing calculator is required for this course.
Course Objectives:
- Students will find the zeros of a polynomial function.
- Students will understand the properties of the graphs of rational functions
- Students will explore exponential and logarithmic functions.
- Students will explore natural logarithms.
- Students will plot complex numbers using both rectangular and polar coordinate systems.
- Students will represent complex numbers using polar coordinates.
- Students will relate the number of roots of a polynomial to its degree.
- Students will solve quadratic equations with complex coefficients.
- Students will demonstrate an understanding of the trigonometric functions.
- Students will prove trigonometric identities.
- Students will demonstrate an understanding of the laws of sines and cosines.
- Students will use the laws to solve for the unknown sides or angles of triangles.
- Students will use the notion of vectors to solve problems.
- Students will identify and discuss features of conic sections.
- Students will convert between different algebraic representations of conic sections.
- Students will describe the relationship between degree and radian measures.
- Students will solve problems related to angular motion.
- Students will apply regression results and curve fitting to make predictions from data.
- Students will relate the slope of a tangent line at a specific point on a curve to the instantaneous rate of change.
Course Content:
- Zeros of polynomial functions.
- Find horizontal, vertical, and oblique asymptotes of rational functions
- Complex zeros.
- Exponential and logarithmic functions.
- Natural logs.
- Convert a complex number from rectangular form to polar form, and vice versa.
- Plot points in the complex plane.
- Find complex roots.
- Write a sequence in summation notation.
- Graph the six trigonometric functions.
- Unit circle trigonometry.
- Polar coordinates to rectangular coordinates, and vice versa.
- Solve trigonometric equations.
- Prove trigonometric identities.
- Identify the names and parts of conics.
- Explore parabolas, ellipses, and hyperbolas.
- Identify an equation of the tangent line to the graph of a function at a certain point.
- Use the Law of Sines to solve SAA, ASA, or SSA triangles.
- Use the Law of Cosines to solve SAS or SSS triangles.
- Graph vectors.
- Add and subtract vectors; find a scalar product and the magnitude of a vector.
- Convert between radians and degrees.
- Solve problems in orbital and rotary motion.
- Use scatter plots to form "lines of best fit" to make predictions.
- Use graphing calculators to plot functions, find zeros of functions, visualize solutions of equations, and calculate regression equations and tables.
Course Evaluation Criteria
· Tests 40%
· Quizzes 30%
· Homework 20%
· Class participation/preparation 10%
Course Policies
· Students are expected to follow the attendance, tardiness, behavioral, academic honesty, and make-up of missing work policies as outline in the Hull High School Student Handbook.
· Students are expected to be on time.
· Students are expected to be respectful and courteous and use appropriate language at all times.
· Students are expected to behave in a responsible manner.
· Students are expected to bring the textbook, math binder, pens/pencils, and a daily planner or agenda book to each class period. Being properly prepared for class will be counted as part of the class participation evaluation.
· Students are expected to take part in class on a daily basis. Students will be called on to answer questions and to do problems on the board.
· Homework is an integral part of this course. Homework will be given each class period, as an aid in understanding the concepts and skills presented in class.
· Homework will be checked at the beginning of class each day. Also, homework assignments may be collected and graded for a quiz grade.
Extra Help
Extra help will be available after school Monday through Thursday, except when faculty commitments conflict, or by appointment for other times. Since much of this course builds on that which the student has learned earlier, it is important that students seek help as soon as s/he encounters difficulty with the material. It is a sign of a responsible student to seek help promptly when it is needed.
Communication
I can be reached by:
· Telephone 925-3000 ext.2202
Follow the prompts to Schools…High School…Faculty…Math…Mrs. Canniff at any time if you feel that your student needs my attention. I will contact you if I feel that there are problems that we should discuss.
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