Student Name: IGCSE Algebra II/Trigonometry Mrs. Maneval manevaan@pwcs.edu COURSE DESCRIPTION: Students enrolled in IGCSE Algebra II/Trigonometry are assumed to have mastered the concepts outlined in the Algebra I and IGCSE Geometry curricula. This course is designed for advanced students who are capable of a more rigorous course at an accelerated pace. A thorough treatment of advanced algebraic concepts is provided through the study of functions, polynomials, rational expressions, complex numbers, matrices, and sequences and series. Oral and written communication concerning the language of algebra, logic of procedures, and interpretation of results will also permeate the course of study. Graphing calculators will be used as they enhance the understanding of realistic applications through mathematical modeling, and aid in the investigation and study of functions and their inverses. In addition to objectives below, supplementary vocabulary, notation, and review topics will be studied in preparation for the IGCSE Mathematics exams. IGCSE EXAMS: The IGCSE exams this year will be sometime in May 2018. THERE ARE NO MAKE-UP EXAMS FOR ANY REASON!!! If you are absent for either exam, you will be required to reimburse the school for your examination fee and will not receive the course weight. VIRGINIA STANDARDS OF LEARNING END OF COURSE ALGEBRA II TEST: The Algebra II SOL test will be administered sometime in May 2018. Passing proficient requires a score of 400+ and passing advanced requires a score of 500+. PRINCE WILLIAM COUNTY/STATE OBJECTIVES: Identify field properties, axioms of equality and inequality and properties of order that are valid for the set of complex numbers, real numbers and its subsets. Identify field properties, axioms of equality and properties of order that are valid for matrices. Add, subtract, multiply, divide, and simplify rational expressions, including complex fractions. Add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents; Write radical expressions as expressions containing rational exponents, and vice-versa. Solve absolute value equations graphically and algebraically. Use graphing calculator to find solutions and to verify algebraic solutions Solve absolute value inequalities graphically and algebraically. Use graphing calculator to find solutions and to verify algebraic solutions Identify and factor completely polynomials representing the difference of squares, perfect square trinomials, the sum and difference of cubes, and general trinomials. Select, justify, and apply graphing and algebraic techniques to solve a quadratic equation over the set of complex numbers. Model and solve real-life applications with quadratics. Solve equations containing rational expressions algebraically and graphically. Use graphics calculators for solving the equations and for confirming algebraic solutions. Solve equations containing radical expressions algebraically and graphically. Use graphics calculators for solving the equations and for confirming algebraic solutions. Recognize a linear function and convert between a graph, a table and symbolic form. Recognize a quadratic function and convert between a graph, a table and symbolic form. Recognize an absolute value convert between a graph, a table and symbolic form. Recognize an exponential function and convert between a graph, a table and symbolic form. Find the domain, range, zeros, and inverse of a linear function. The functions will include those that have domains and ranges that are limited and/or discontinuous. Find the domain, range, zeros, and inverse of a quadratic function. The functions will include those that have domains and ranges that are limited and/or discontinuous.
Find the domain, range, zeros, and inverse of a rational function. The functions will include those that have domains and ranges that are limited and/or discontinuous. Find the domain, range, and inverse of exponential and logarithmic functions. Find the composition of multiple functions. Find the value of a function for a given element in its domain. Investigate and describe through the use of graphs the relationships between the solution of an equation, zero of a function, x-intercept of a graph, and factors of a quadratic expression. Investigate and describe through the use of graphs the relationships between the solution of an equation, zero of a function, x-intercept of a graph, and factors of a polynomial expression with degree 3. Solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and graphically. The graphing calculator will be used as a tool to visualize graphs and predict the number of solutions. Recognize the general shape of polynomial, with degree 3. The graphing calculator will be used as a tool to investigate the shape and behavior of these functions. Recognize the general shape of exponential, and logarithmic functions. The graphing calculator will be used as a tool to investigate the shape and behavior of these functions. Investigate and apply the properties of arithmetic and geometric sequences to solve practical problems, including writing the first n terms, and finding the n th term, Investigate and apply the properties of arithmetic and geometric series to solve practical problems including writing the first n terms, finding the n th term, and evaluating summation formulas. Notation will include and a n. Perform operations on complex numbers and express the results in simplest form. Recognize patterns of powers of i. Collect and analyze data to make predictions, write equations, and solve practical problems. Graphing calculators will be used to investigate scatterplots to determine the equation for a curve of best fit. Models will include polynomial, exponential, and logarithmic functions. Identify, create, and solve practical problems involving inverse variation and a combination of direct and inverse variations. Solve practical problems involving permutations and combinations. The student will use the definitions of the six trigonometric functions to find the sine, cosine, tangent, cotangent, secant, and cosecant of an angle in standard position, given a point, other than the origin, on the terminal side of the angle. Circular function definitions will be connected with trigonometric function definitions. The student, given the value of one trigonometric function, will find the values of the other trigonometric functions. Properties of the unit circle and definitions of circular functions will be applied. The student will find without the aid of a calculating utility the values of the trigonometric functions of the special angles and their related angles as found in the unit circle. This will include converting radians to degrees and vice versa. The student will find with the aid of a calculator the value of any trigonometric function and inverse trigonometric functions. The student will verify basic trigonometric identities and make substitutions using the basic identities. The student, given one of the six trigonometric functions in standard form (e.g., y = A sin (Bx C) + D, where A, B, C, and D are real numbers), will: state the domain and the range of the function; determine the amplitude, period, phase shift, and vertical shift; and sketch the graph of the function by using transformations for at least a one-period interval. The graphing calculator will be used to investigate the effect of changing A, B, C, and D on the graph of a trigonometric function. The student will identify the domain and range of the inverse trigonometric functions and recognize the graph of these functions. Restrictions on the domains of the inverse trigonometric functions will be included. The student will solve trigonometric equations that include both infinite solutions and restricted domain solutions and solve basic trigonometric inequalities. Graphing utilities will be used to solve equations, to check for reasonableness of results, and to verify algebraic solutions. The student will identify, create, and solve practical problems involving triangles. Techniques will include using the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines.
ADDITIONAL IGCSE OBJECTIVES NOT COVERED BY PRINCE WILLIAM COUNTY: The student will give and obtain appropriate upper and lower bounds to solutions of simple problems given data to specified accuracy. The student will recognize a step function and convert between a graph, a table and symbolic form. The student will use current units of mass, length, area, volume, and capacity in practical situations and express quantities in terms of larger or smaller units. The student will solve practical problems using systems of linear inequalities and linear programming problems and describe results both orally and in writing. A graphing calculator will be used to facilitate solutions to linear programming problems. The student will calculate times in terms of the 24-hour and 12-hour clock and read clocks, dials and time tables. The student will calculate using money and convert from one currency to another. The student will use given data to solve problems on personal and household finance involving earnings, simple interest, discount, profit and loss and draw graphs from given data. The student will apply the idea of rate of change to easy kinematics involving distance-time and speed-time graphs, acceleration and deceleration and calculate distance traveled as area under a linear speed-time graph. The student will estimate gradients of curves by drawing tangents. The student will interpret and use three-figure bearings measured clockwise from the north. The student will calculate the determinant and inverse A -1 of a non-singular matrix A. MATERIALS: All materials must be brought to class every day, unless otherwise stated. Algebra II Text (covered at all times) IGCSE Extended Mathematics Text (covered at all times) Precalculus: Graphing and Data Analysis Text (covered at all times) 3-ring notebook/folder with loose-leaf paper and graph paper Pencil and Blue/Black Pen, Red Pen Scientific calculator (A Casio fx-115ms will be available for classroom use.) *Graphic calculator.* ***Students will need to use a calculator to complete some assignments at home. The Casio fx-9750gii, fx-9750g+, cfx-9850ga+, cfx -9850Gb+, cfx -9850Gc+ are equivalent to the calculators used in class. TI s can be used, but are different from those shown in class.*** GRADING POLICY: Grading will follow the Prince William County guidelines for high school instruction. Grades are determined by the following: Summative Assessments (Tests) 55% Formative Assessments (Quizzes) 30% Classwork 10% Homework 5% All categories may include group assignments. There will be quarter tests towards the end of each marking period, which will contain questions from all objectives covered during the marking period. QUARTER TESTS: Every student will take a quarter test towards the end of each marking period, which will contain questions from all objectives covered during that marking period. CALENDARS: Students will be given a preliminary calendar and will be able to access an updated calendar on the class webpage. It is just a guide and may need to be adjusted. HOMEWORK: Homework comprehension is essential for success in this class. The amount of effort and value students give to their independent practice greatly contributes to their learning. Students are expected to neatly SHOW ALL WORK for all assignments. Answers for most problems are in the back of the textbook or on the class website. These are used to verify answers and understanding when completing independent practice. Students should check each question as they complete the problem, not after the assignment is completed. Students should rework any wrong problems, using the textbook and their notes as guides.
ABSENCES: Students are expected to continue their learning and assignments even when they miss school. When a student is absent, it is expected that he or she will attempt to do the assignment. When the student returns to class, he or she should have a few very specific questions about the assignment. If a student is present the day prior to a quiz or test, but absent the day the class takes the assessment, the student must take the assessment upon return to class or in the CIE block. Assessments will not be returned to any students until all students have taken the test or quiz. Remember to make up any missed assignments as soon as possible! EXPECTATIONS: IGCSE Algebra II/Trig is an advanced course that moves at an accelerated pace. Student work habits and behavior should also be above average. I will enforce the PWCPS Code of Behavior and the rules and regulations of the student handbook. I will make every effort to update grades in a timely manner. I will use parent and student email addresses to contact you as necessary. CLASSROOM RULES: The 3 B s for Groupwork The 5 E s 1. Be Respectful 1. Be Respectful 1. Engage 2. Take care of materials and classroom 2. Be Productive 2. Explore 3. No bathroom breaks unless emergency 3. Be Willing 3. Explain 4. No cell phones 4. Elaborate 5. DO YOUR BEST! 5. Evaluate COURSE WEIGHT: The course is weighted and students earning grades A-B will receive an extra 0.5 in their GPA calculation. EXTRA HELP: Continuous understanding is essential for success in this class. If you are having difficulty after participating in class and studying the text, seek help as soon as possible. Students should utilize the advisory block as much as possible. I will also be available for help after school Mondays and Wednesdays until 3:00. RE-TAKE POLICY: Students will be allowed to re-take ONE test per marking period. (Quizzes, quarter tests, and finals cannot be retaken.) The student will receive the higher grade. The retake must be taken within the marking period of the original test. Parent signature required on the original test. The student is required to stay during an advisory block or after school with the teacher. The student will be assigned an Ascellus section to complete to show readiness for a retake. This can be completed at school or at home. The student must correct the original test on a separate piece of paper prior to the date of the retake. (The original work should not be erased.) The student must have taken the original test on time. The student must have made up any work for which they were absent prior to the retake. The re-test will not be the same test! CELL PHONE POLICY Students will be assigned a cell phone parking spot where they will place their cell phone at the beginning of class. They will get their cell phones out of the spot in the last few minutes of class time. Students will not have access to their cell phones during class at all. Students must have their phones in the correct spot, and be in their seats when the bell rings to begin class.
IGCSE Algebra II/Trig Mrs. Maneval Printed Student Name: Please sign your name below indicating that you have read and understood the goals and expectations of the class, and that you will agree to demonstrate: Character: Integrity: Excellence: Being open to other s strategies and input and supportive of everyone especially when mistakes are made because learning from mistakes is part of the process. I will always submit my own work. I will do my best, and ask questions when I need help. I will be persistent. Signature of student Date PLEASE PRINT: Parent and guardian information Name E-mail address Signature Relationship to student Name E-mail address Signature Relationship to student Parents, please use the space below to share with me any information you feel would be helpful to me in working with your student this year. If you prefer to email me any information, please feel free to do so.