Dominican International School PRECALCULUS

Transcription

1 Dominican International School PRECALCULUS GRADE EVEL: 11 1 Year, 1 Credit TEACHER: Yvonne Lee SY: ylee@dishs.tp.edu.tw COURSE DESCRIPTION Pre-Calculus serves as a transition between algebra and calculus. This course covers many important fundamental concepts that will prepare students for calculus and college-level mathematics. Students are expected to understand, analyze, and utilize basic functions. They are also expected to understand the relationship between exponential functions and logarithm. Trigonometric functions and identities will be included and students are expected to graph and analyze graph and prove identities. Analytic geometry in two dimension and discrete mathematics will also be covered. TEACHING STRATEGIES This course emphasizes on algebraic, numeral, graphical, and verbal methods of representing problems. Therefore, one or all of these four approaches will be applied in every section to enhance students understanding. With the use of the graphic calculator, the teacher can invite students to participate more in forming answer to a question by looking at the graph and interpreting data on the calculator. Relating real-life problems to this course is also essential to help students understand concepts because students tend to only memorize the formula for the test and then forget everything they learned after the test. When students can see the linkage between real-life situation and mathematic topics, they will be able to remember and apply for later use. STUDENT ACTIVITIES Students will participate in class activities such as discussions and presentations. Students are encouraged to answer questions orally or on the board. In every quarter, students will work in groups to present a solution to a real-life problem with poster or power point. Students will also practice questions from Khan Academy. ASSESSMENT This course will be assessed on the following three categories: class participation and homework, tests and quizzes, and the quarter exam. Each category weighs one-third of each quarter s academic grade. Students attitude and behavior during the class time will be graded and recorded in the deportment grade.

2 TEXT: PRECALCULUS Common Core (McGraw Hill 2014) FIRST QUARTER COURSE OBJECTIVES FUNCTIONS FROM A CALCULUS PERSPECTIVE Describe subsets of real numbers. Identify and evaluate functions and state their domains. Use graphs of functions to estimate function values. Identify even and odd functions. Use limits to determine the continuity of a function. Use limits to describe the end behavior of functions. Find intervals on which functions are increasing, constant, or decreasing. Determine the average rate of change of a function. Identify, graph, and describe parent functions. Identify and graph transformations of functions. Perform operations with functions. Find compositions of functions. Use the horizontal line test to determine whether a function has an inverse function. Find inverse functions algebraically and graphically. POWER, POLYNOMIAL, AND RATIONAL FUNCTIONS Graph and analyze power functions. Graph and analyze radical functions and solve radical equations. Graph polynomial functions. Model real-world data with polynomial functions. Divide polynomials using long division and synthetic division. Use the Remainder and Factor Theorems. Find real zeros of polynomial functions. Find complex zeros of polynomial functions. Analyze and graph rational functions. Solve rational equations. Solve polynomial inequalities. Solve rational inequalities.

3 FIRST QUARTER TENTATIVE WEEKLY SCHEDULE (NB: Depending on time and interest, the teacher may delete and/or add other selections.) Week / Date Week 1 Aug 3 rd to 4 th Only 1.5 Days Week 2 Aug 7 th to 11 th Only 4 Days Week 3 Aug 14 th to 18 th Topic / Projects / Assessments CHAPTER 1 FUNCTIONS FROM A CALCULUS PERSPECTIVE Introduction Functions Analyzing Graphs of Functions and Relations Continuity, End Behavior, and Limits Extrema and Average Rates of Change Week 4 Aug 21 st to 25 th Parent Functions and Transformation Function Operations and Composition of Functions Week 5 Aug 28 th to Sep 1 st Week 6 Sep 4 th to 8 th Inverse Relations and Functions Chapter 1 Test CHAPTER 2 POWER, POLYNOMIAL, AND RATIONAL FUNCTIONS Power and Rational Functions Polynomial Functions The Remainder and Factor Theorems Week 7 Zeros of polynomial Functions Rational Functions Sep 11 th to 15 th Nonlinear Inequalities Week 8 Nonlinear Inequalities Sep 18 th to 22 nd Chapter 2 Test Week 9 Sep 25 th to 27 th Only 3 Days Review Quarter Examination

4 SECOND QUARTER COURSE OBJECTIVES TRIGONOMETRIC FUNCITONS Find values of trigonometric functions for acute angles of right triangles. Solve right triangles. Convert degree measures of angles to radian measures and vice versa. Use angle measures to solve real-world problems. Find values of trigonometric functions for any angle. Find values of trigonometric functions using the unit circle. Graph transformations of the sine and cosine functions. Use sinusoidal functions to solve problems. Graph tangent and reciprocal trigonometric functions. Graph damped trigonometric functions. Evaluate and graph inverse trigonometric functions. Find compositions of trigonometric functions. Solve oblique triangles by using the Law of Sines or Law of Cosines. Find areas of oblique triangles. TRIGONOMETRIC IDENTITIES AND EQUATIONS Identify and use basic trigonometric identities to find trigonometric values. Use basic trigonometric identities to simplify and rewrite trigonometric expressions. Verify trigonometric identities. Determine whether equations are identities. Solve trigonometric equations using algebraic techniques. Use sum and difference identities to evaluate trigonometric functions. Use sum and difference identities to solve trigonometric equations. Use double-angle, power-reducing, half-angle and product-to-sum identities to evaluate trigonometric expressions and solve trigonometric equations.

5 SECOND QUARTER TENTATIVE WEEKLY SCHEDULE (NB: Depending on time and interest, the teacher may delete and/or add other selections.) Week / Date Week 1 (10) Oct 5 th to 6 th Only 2 Days Week 2 (11) Oct 11 th to 13 th Only 3 Days Topic / Projects / Assessments TRIGONOMETRIC FUNCITONS Right Triangle Trigonometry Degrees and Radians Trigonometric Functions on the Unit Circle Week 3 (12) Trigonometric Functions on the Unit Circle Oct 16 th to 20 th Week 4 (13) Graphs of Sine and Cosine Functions Oct 23 rd to 27 th Graphing Technology Lab: Sums and Differences of Sinusoids Week 5 (14) Oct 30 th to Nov 3 rd Graphing Other Trigonometric Functions Quiz (Graphing Sine and Cosine graphs) Inverse Trigonometric Functions Week 6 (15) The Law of Sines and the Law of Cosines Nov 6 th to 10 th Chapter Test Week 7 (16) Nov 13 th to 17 th ANALYTIC TRIGONOMETRY Trigonometric Identities Verifying Trigonometric Identities Week 8 (17) Solving Trigonometric Identities Nov 20 th to 24 th Sum and Differences Identities Week 9 (18) Nov 27 th to Dec 1 st Week 10 (19) Dec 4 th to 8 th Only 4 Days Week 11 (20) Dec 11 th to 15 th Only 2 Days / Exams Dec 17 th Jan 2 nd Multiple-Angle Identities Chapter Test Review Quarter Examination Christmas Break

6 THIRD QUARTER COURSE OBJECTIVES SYSTEMS OF EQUATIONS AND MATRICES Solve systems of linear equations using matrices and Gauss-Jordan Elimination. Multiply matrices. Find determinants and inverses of 2 2 and 3 3 matrices. Solve systems of linear equations using inverse matrices. Solve systems of linear equations using Cramer s Rule. Write partial fraction decompositions of rational expressions with linear factors in the denominator. Write partial fraction decompositions of rational expressions with prime quadratic factors in the denominator. Use linear programming to solve applications. Recognize situations in which there are multiple points at which a function is optimized. EXPONENTIAL AND LOGARITHMIC FUNCITONS Evaluate, analyze and graph exponential functions. Solve problems involving exponential growth and decay. Evaluate expressions involving logarithms. Sketch and analyze graphs of logarithmic functions. Apply properties of logarithms. Apply the Change of Base Formula. Apply the One-to-One Property of Exponential Functions to solve equations. Apply the One-to-One Property of Logarithmic Functions to solve equations. Model data using exponential logarithmic and logistic functions. CONIC SECTIONS AND PARAMETRIC EQUATIONS Analyze and graph equations of parabolas. Write equations of parabolas. Analyze and graph equations of ellipses and circles. Use equations to identify ellipses and circles. Analyze and graph equations of hyperbolas. Use Equations to identify types of parabolas. Graph parametric equations. Solve problems related to the motion of projectiles.

7 THIRD QUARTER TENTATIVE WEEKLY SCHEDULE (NB: Depending on time and interest, the teacher may delete and/or add other selections.) Week / Date Week 1 (21) Jan 3 rd to 5 th Only 3 Days Topic / Projects / Assessments SYSTEMS OF EQUATIONS AND MATRICES Multivariable Linear Systems and Row Operations Week 2 (22) Jan 8 th to 12 th Matrix Multiplication, Inverses, and Determinants Week 3 (23) Solving Linear Systems using Inverse and Cramer s Rule Jan 15 th to 19 th Week 4 (24) Partial Fractions Jan 22 nd to 26 th Linear Optimization Week 5 (25) Jan 29 th to Feb 2 nd Chapter Test EXPONENTIAL AND LOGARITHMIC FUNCITONS Exponential Functions Week 6 (26) Logarithmic Functions Feb 5 th to 9 th Properties of Logarithms Week 7 (27) Feb 12 th to 14 th Only 3 Days / CNY Week 8 (28) Feb 21 st to 23 rd CNY / Only 3 Days Week 9 (29) Feb 26 th to Mar 2 nd Only 4 Days Exponential and Logarithmic Equations Exponential and Logarithmic Equations Chapter Test CONIC SECTIONS AND PARAMETRIC EQUATIONS Parabola Week 10 (30) Ellipses and Circles Mar 5 th to 9 th Hyperbola Week 11 (31) Parametric Equation March 12 th to 16 th Week 12 (32) March 19 th to 23 rd Only 3 Days / Exams March 26 th to April 6 th Review Quarter Examination Easter Break

8 FOURTH QUARTER COURSE OBJECTIVES VECTORS Represent and operate with vectors geometrically. Solve vector problems and resolve vectors into their rectangular components. Represent and operate with vectors in the coordinate plane. Write vector as a linear combination of unit vectors. Find the dot product of two vectors and use the dot product to find the angle between them. Find the projection of one vector onto another. SEQUENCES AND SERIES Investigate several different types of sequences. Use sigma notation to represent and calculate sums of series. Find nth term and arithmetic mean of arithmetic sequences. Find sums of n terms of arithmetic series. Find nth term and geometric mean of geometric sequences. Find sums of n terms of geometric series and the sums of infinite geometric series. Mathematical induction to prove summation formulas and properties of divisibility involving a positive integer n. Use extended mathematical induction. Use Pascal s Triangle to write binomial expansions. Use the Binomial Theorem to write and find the coefficients of specified terms in binomial expansions. INFERENTIAL STATISTICS Identify the shapes of distributions. Use measures of position to compare to sets of data. Construct and use a probability distribution. Construct and use a binomial distribution. Find area under normal distribution curves. Find probabilities for normal distributions.

9 FOURTH QUARTER TENTATIVE WEEKLY SCHEDULE (NB: Depending on time and interest, the teacher may delete and/or add other selections.) Week / Date Topic / Projects / Assessments Week 1 (33) Apr 9 th to 13 th VECTORS Introduction to Vectors Vector in the Coordinate Plane Week 2 (34) Dot Products and Vector Projections. Apr 16 th to 20 th Week 3 (35) Apr 23 rd to 27 th Week 4 (36) Apr 30 th to May 4 th Week 5 (37) May 7 th to 11 th SEQUENCES AND SERIES Sequences, Series, and Sigma Notation Arithmetic Sequences and Series Geometric Sequences and Series Mathematical Induction The Binomial Theorem Chapter Test INFERENTIAL STATISTICS Descriptive Statistics Probability Distribution Week 6 (38) The Normal Distribution May 14 th to 18 th Review Week 7 (39) May 21 st to 25 th Only 1 Day / Exams / Graduations Quarter Examination