Pre-Calculus Room 114

Transcription

1 Pre-Calculus Room 114 Ms. Johansen COURSE DESCRIPTION Course Description: This is a full year rigorous course designed as a college level Pre-Calculus course. Topics studied include: Functions, Algebra, Applications, Complex Numbers and Polar Coordinates, Vectors, Matrices, Linear, Polynomial and Rational Functions, Introduction to Calculus, and Probability. The course will end with a final exam in June 2016 and will count for 20% of your final average. Text Book: All lessons and homework may be found on my website. Class Supplies: Each day you are required to bring a pen or pencil, TI-83/84 calculator, and a spiral or loose-leaf notebook. An organized notebook with readable notes including attached handouts is essential to this class. Grading Policy: Each quarter the average is calculated a points system (raw score). The amount of points for each quarter depends on the number of assignments/tests/quizzes given. At the end of each quarter all points earned by each student are added. The number of points earned is then divided by the total number of points for the quarter. This percentage represents each student s quarter average. Homework and class participation will account for approximately 10% of the total points for each quarter. Attendance: Student absences will be dealt with according to the district attendance policy. In a full year course 20 absences may result in denial of credit. Homework Policy: Homework will be assigned on a daily basis and will be checked daily. Failure to complete assignments will greatly impact your quiz and test grades. Homework assignments will account for approximately 10% of your quarter average. Make-Up Policy: Work missed due to student absence will be made up according to the district attendance policy. Any tests/quizzes missed due to a legal absence must be made up within 5 class days or will result in a zero. Extra Help: Sessions will be posted in the classroom or are available by appointment.

2 YEAR AT A GLANCE: Pre-Calculus UNIT 1 UNIT 2 UNIT 3 UNIT 4 UNIT 5 Title Functions Algebra Applications Complex Numbers and Polar Coordinates Vectors Unit Length (weeks taught) Sept. Oct. Nov. Dec. Jan. Performance Task (e.g., Persuasive Essay, DBQ, Nutritional Analysis, etc.) Sinusoidal Modeling Project Identities and Equations Law of Sines and Cosines Project Polar Coordinates Graphing Project Vectors Enduring Understanding (The big ideas, the why we include these ideas able to use s to solve right triangles, find values of s of any angle, and graph s. able to understand our world is periodic. The amount of sunlight a city receives on a given day, high and low tides are all real life instances where sinusoids explain and model real life phenomena. able to verify identities and solve equations. able to use the Law of Sines and the Law of Cosines to solve general triangles, find the area of oblique triangles, and solve various application problems. able to use properties of difference of two squares to find the modulus. able to relate the modulus visually vectors. able to graph numbers and identify the magnitude of the number, the distance of the number from the origin, and the direction of the number from the origin. able to express recognize that the addition of numbers is connected to the addition of vectors. understand that vectors could be used to represent and manipulate data, e.g. to represent payoffs or incidence relationships in a network. see that vectors and polar coordinates are useful in

3 numbers in polar coordinate form and in rectangular form. solving realworld problems. be able to represent and operate with vectors algebraically in two and threedimensions, find vector projections, cross products, and dot products of vectors. Essential Questions (What do we want students to think about) How is the unit circle used to describe s? How do you graph the basic s on the coordinate plane? How do transformations affect the graphs of each Such as, how do you determine the period and amplitude of a without looking at the graph of the What are periodic s? Why is modeling them so important? What are the relationships between the Pythagorean Identities for Trigonometry? How does the algebraic solution to a equation relate to the graphic solution? difference between sine and the restricted sine and why is it important when working with the inverse sine How is proving or verifying a identity different then solving a equation? When is it necessary to use the Law of Sines to solve a triangle? How does trigonometry allow us to calculate distances that can t be measured directly, and to model periodic phenomena? How is a number converted to polar form? How can you graph a number in rectangular and polar form? relationship between rectangular and polar form of a number? importance of knowing the conjugate of a number? Why are s represented by polar equations? How is number addition connected to vector addition? Why are s and relations represented by vectors? How is the law of sines learned in Unit 3 connected to the law of sines derived vectors in 3- space?

4 UNIT 6 UNIT 7 UNIT 8 UNIT 9 UNIT 10 Title Matrices Linear Polynomial/Rational Functions Intro to Calculus Probability Unit Length (weeks taught) Feb. After Feb break March End of April May+ Performance Task (e.g., Persuasive Essay, DBQ, Nutritional Analysis, etc.) Encoding/Decoding Matrix Project Linear Project Polynomial and Rational Functions Class projects calculator weekly review Class projects calculator weekly review Linear Partner Test Enduring Understanding (The big ideas, the why we include these ideas -find the inverse of a matrix -determine how data can be represented as a matrix - determine if the inverse of a matrix exists. -use matrices to solve real-world problems involving system of linear equations - transform linear equations into a single matrix -connect their understanding of solving systems of inequalities to realworld situations -use problemsolving and communication skills to maximize/minimize an objective -define and divide polynomials. -apply the Remainder and Factor Theorems and make connections between remainders and factors. - determine the maximum number of polynomial. -find all rational polynomial. -factor a polynomial completely. -recognize and describe the graphs of various be - expand a power of a binomials the Binomial Theorem. - find the coefficient of a given term of a binomial expansion -find the derivative of a polynomial limits and the difference quotient -find the derivative of be -calculate permutations and combinations -use Bernoulli s theorem to find the probability of an event

5 polynomial s. -identify the properties of general polynomial find the domain of a rational. a polynomial derivative rules -find intercepts, asymptotes, and holes. -describe the end behavior of a. -write and perform arithmetic operations on numbers. -find the number of polynomial. -give the complete factorization of polynomial expressions. s Essential Questions (What do we want students to think about) procedure that is used to verify two matrices are inverses of each other? a formula to find the inverses of 2x2 matrices? inverse matrices to solve systems of linear equations? systems of inequalities in two variables to model and solve real-life problems? linear programming to model and solve real-life problems? procedure that is used to find real polynomial How can you use the Binomial Theorem to expand binomials? How does the derivative of a relate to its graph? What is important about permutation, combination, tree diagrams and other methods of counting?