Algebra 2 (College Prep B) Curriculum Guide Number: 323 Level: College Prep B Textbook: Algebra 2 with Trigonometry, Prentice Hall, 2006 Workbook: Preparing for the New Jersey HSPA, Glatzer and Glatzer, AMSCO, 2001 Credits: 5 Written: July, 2005 Revised: January 2012 Midterm Exam Revised: January 2012 Final Exam Revised: June 2011 Prerequisite: Students must have successfully completed Algebra 1 (CP B). Students who received lower than a C in Algebra 1 (CP A) should also schedule this course. Course Description: This course is the third year of mathematics at the College Prep B level. It meets college entrance requirements and prepares students for a liberal arts college mathematics course. It is designed for students who have demonstrated some difficulty mastering mathematical concepts. This course meets the Common Core State Standards for Mathematics. During this course, topics from Algebra 1 such as solving equations in one or two variables, graphing and operations with polynomials and factoring will be reviewed and extended. Other topics studied are relations and functions, rational equations, negative and rational exponents, radicals, complex numbers, the Quadratic Formula and logarithms. Time will also be allocated to review for the High School Proficiency Assessment in March. Note to Teachers: Unit 6 is the review for the HSPA. It is planned for 20 days and should begin about a month before the HSPA is given in March. Units 1 5 should be completed before the mid-term exam. 1
District Policy: ACADEMIC INTEGRITY Pupils are expected to be honest in all of their academic work. This means that the students in this course will not engage in any of the following acts: Cheating on examinations or other school assignments, including but not limited to, the non-authorized use of books or notes, the use of crib sheets, copying from other students papers, exchanging information with other students orally, in writing, or by signals, obtaining copies of the examination illegally and other similar activities. Cheating through the use of technology to exchange information on any school assignment, examination, etc. is prohibited. Technology is defined as, but not limited to, computers, telephones, text messaging, palm pilots, calculators, cameras or any other hand held device. Plagiarism is not permitted in term papers, themes, essays, reports, images, take-home examinations, and other academic work. Plagiarism is defined as stealing or use without acknowledgment of the ideas, words, formulas, textual materials, on-line services, computer programs, etc. of another person, or in any way presenting the work of another person as one s own. Falsifications, including forging signatures, altering answers after they have been graded, inserting answers after the fact, erasing of grader s markings, and other acts that allow for falsely taking credit. A pupil found guilty of academic dishonesty may be subjected to a full range of penalties including, but not limited to reprimand and loss of credit for all of the work that is plagiarized. Disciplinary action may also be a consequence of such behavior. Additional consequences may apply as defined in specific department policies and guidelines. A teacher who believes that a pupil has been academically dishonest in his/her class should resolve the matter in the following manner: Reprimand the student orally and/or in writing. The teacher is also authorized to withhold credit in the work due to academic dishonesty. If warranted, the teacher shall file a written complaint against the student with the Administration, requesting a more stringent form of discipline. The complaint must describe in detail the academic dishonesty that is alleged to have taken place, and must request that the matter be reviewed by the Administration. The Administration will determine if further discipline of the pupil is appropriate, and will determine the nature of the discipline on a case-by-case basis. If the pupil is not in agreement with the disciplinary action of the Administration, he/she may appeal the action first to the Principal and secondly to the Superintendent. If the pupil is dissatisfied with the Superintendent s disposition of the case, he/she may grieve the action in accordance with Policy No. 5710, Pupil Grievance. 2
District Policy: Equal Opportunity High Point Regional High School s curriculum and instruction are aligned to the State s Core Curriculum Content Standards and address the elimination of discrimination by narrowing the achievement gap, by providing equity in educational programs and by providing opportunities for students to interact positively with others regardless of race, creed, color, national origin, ancestry, age, marital status, affectional or sexual orientation, gender, religion, disability or socio-economic status. Course 1. evaluate and simplify algebraic expressions. 2. select and use appropriate methods to solve equations and inequalities. 3. identify relations and functions and their graphs and transformations and explain their properties. 4. use various representations for functions, including equations or inequalities, tables, charts and graphs and convert among them. 5. use all concepts to model problems. Course Policies: Homework will usually be assigned daily and is an important part of the course, providing students with the opportunity to apply skills learned in class, strengthen conceptual understanding and identify areas of weakness. It is imperative that students do homework regularly and conscientiously. Assignments will be reviewed in class and it is the student s responsibility to ask questions about problems he/she may not understand, to identify specific mistakes and to take notes on any further explanations concerning these problems. Students are responsible to make up any missed class work (quizzes, tests, homework) in a timely manner and according to teacher established policies, which will be discussed in class. It is the student s responsibility to obtain material (notes, homework) for any extended absence and meet with the teacher upon return to class. The teacher will be available to meet with students for extra help and to help students make up work from absences. This class will use graphing calculators (TI-83, 83+, or 84+). Students who do not have a calculator will be issued one by the school. The student will sign that he/she has received the calculator and is expected to return the calculator in the condition they received it or pay the full purchase price of the calculator. Students may not substitute a calculator for a lost or damaged calculator. Students are expected to bring their textbook, homework, calculator and a pen/pencil to class. They are expected to take notes during class and to keep these notes, along with homework, quizzes and tests, in an organized manner. A three ring binder is strongly recommended. 3
Student Evaluation: Quizzes, based on the course proficiencies, will be given about once a week, with a major test, based on the proficiencies, given at the end of each unit. An exam covering the semester s work will be given at the end of each semester. Homework will be checked daily. All work must be shown neatly. Homework will usually not be graded, but will be considered satisfactory if the work shown indicates the student has made a conscientious effort to complete the assignment. If a student is not able to complete an assignment because he/she does not understand the work, he/she may be asked to complete it after the assignment is reviewed in class and/or the student has come for extra help in order to receive credit for the assignment. Sometimes an assignment given for homework may be collected and graded as a quiz. This will only occur when the concepts have been thoroughly reviewed. Class work/group work may also be graded. Each teacher will explain his/her homework policy to the class. Grades will be calculated according to the school grading policy and the following guidelines: A. Marking Period Grade: 1. Tests and Quizzes 70 80 % 2. Homework and class work 20 30 % (Each teacher will explain his/her policy to the class.) B. Final Grade 1. Each Marking Period 20 % 2. Midterm Exam 10 % 3. Final Exam 10 % Proficiencies Unit 1 Real Numbers, Linear Equations and Exponents Time: 18 Days Goals: Students will be able to solve basic linear equations, evaluate expressions using properties of exponents and use these skills to solve problems. 1. identify rational and irrational numbers. 2. perform operations with integers. 4
3. use properties of real numbers to evaluate expressions. 4. use properties of equality and real numbers to solve linear equations. 5. use properties of integer exponents to evaluate expressions. 6. write and evaluate expressions using scientific notation. 7. use the concepts above to solve problems. Common Core State Standards (CCSS) addressed: (The CCSS are attached at the end of this curriculum guide.) A-CED 1, 2; A-REI 1; A-SSE 1a, b; N-RN 3. 1. Textbook, Chapter 1 (omit section 1-10) Unit 2 Equations and Inequalities Time: 12 Days Goals: Students will be able to solve linear equations and inequalities, including those containing fractions and decimals, and absolute value equations and use them to solve problems. 1. solve linear equations containing fraction, decimals and parentheses, both by clearing of fractions or decimals and by using a calculator. 2. solve a formula for a given variable. 3. determine whether a given number is a solution of an inequality. 4. solve linear inequalities. 5. solve absolute value equations. 6. use these concepts to solve problems. CCSS Addressed: A-CED 1, 2; A-REI 1 1. Textbook, Chapter 2 (Solve only linear equations and absolute value equations; omit zero product principle; omit 2-6; omit absolute value inequalities; omit 2-8) 5
Unit 3 Relations, Functions and Graphs Time: 18 Days Goals: Students will be able to graph relations and functions, write equations of lines, determine composite functions and use these skills to solve problems. 1. use graphing terminology and graph points on a coordinate plane. 2. identify the domain and range from a set of points or a graph. 3. determine the domain of a rational function from the equation. 4. determine whether an ordered pair is a solution of an equation. 5. determine whether a given set of points or a graph is a function. 6. use function notation. 7. graph linear equations by plotting points, determining the x and y intercept, using the slope intercept form of the equation. 8. write the equation of a line given the slope and y-intercept or given two points. 9. use these concepts to solve problems. CCSS Addressed: A-REI 10, 11; F-BF 1a, b, c; F-IF 1, 2, 5, 6; F-LE 1, 5; S-ID 5-9. 1. Textbook, Chapter 3 (omit 3.9) Unit 4 Systems of Equations Time: 16 Days Goals: Students will be able to solve systems of linear equations and inequalities and use this skill to solve problems. 1. use a graphing calculator to graph equations, selecting an appropriate window, and use the I-Sect feature to determine the intersection of two lines. 2. solve a system of two linear equations algebraically by graphing, substitution, and linear combinations. 6
3. determine whether a system of linear equations is consistent, dependent or inconsistent. 4. graph linear inequalities and systems of linear inequalities with and without a graphing calculator. 5. use the concepts above to solve problems. CCSS Addressed: A-CED 3; A-REI 5, 6, 12. 1. Textbook, Chapter 4 (omit4.4, 4.5, 4.8) Unit 5 Polynomials and Polynomial Equations Time: 18 Days Goals: Students will be able to perform operations with polynomials, use the zero product principle to solve problems and use these concepts to solve problems. 1. use the terminology associated with polynomials and evaluate polynomial functions. 2. add, subtract, multiply and combine like terms of polynomial functions. 3. factor polynomial functions using the following methods: greatest common factor, guess method, difference of two squares, sum and difference of two cubes. 4. use the zero product property to solve polynomial equations. 5. use the concepts above to solve problems. CCSS: A-APR 1, 2, 3; A-REI 4a, b; A-SSE 3a, b; F-IF 5, 8a. 1. Textbook, Chapter 5 7
Unit 6 Review for HSPA Time: 20 days Goals: Students will be able to pass the March administration of the HSPA 1. classify numbers and use them to solve problems. 2. use exponential and scientific notation. 3. identify prime numbers, factors and multiples of numbers and use them to solve problems. 4. use ratios, proportions and percents to solve real world problems. 5. recognize and apply geometric properties to real world problems. 6. use coordinate geometry in problem solving situations. 7. apply the principles of congruence, similarity, tessellations, vectors and transformations. 8. apply the principles of measurement and geometry to solve problems involving direct and indirect measurement. 9. recognize, create and extend patterns and use inductive reasoning to represent mathematical situations and real world phenomena. 10. use various functions to model mathematical and real world situations. 11. use algebraic concepts and processes to express and model real world situations. 12. determine, interpret and use probabilities of simple and compound events. 13. interpret statistical distributions and apply to real world situations. 14. collect, organize, represent, analyze and interpret data. 15. apply the concepts and methods of discrete mathematics to model and explore a variety of practical situations. 16. use iteration and recursive patterns and processes to model a variety of situations. CCSS: A-ARP 1; A-CED 1-3; A-REI 1-6; 10-12; A-SSE 1-5; F-BFa, b, 3; F-IF 1-6, 7a, 8; G-C 2; G-CO 1-6; G-GMD 1, 3; G-GPE 4-7; G-MG 1, 2; G-SRT 1-3, 8; N-RN 1-3; N- Q 1-3; S-ID 1-9; S-CP 1, 2, 5-7. 1. Workbook, Preparing for the New Jersey HSPA, Glatzer, AMSCO, 2001 2. Workbook, HSPA, A Collection of Activities, Walton and Klein, CEO Solutions 3. Teacher Prepared Materials Unit 7 Rational Expressions and Equations Time: 20 Days Goals: Students will know how to perform operations with rational expressions, graph 8
and analyze rational functions, solve rational equations and use these skills to solve problems. 1. simplify, multiply, divide, add and subtract rational expressions. 2. use a graphing calculator to graph rational functions and identify the asymptotes. 3. divide polynomials by monomials; divide a polynomial by another polynomial. 4. use synthetic division to divide polynomials. 5. solve rational equations with and without a calculator. 6. use formulas containing rational expressions to solve problems. 7. find the constant of variation and an equation of variation for direct variation problems. 8. use the concepts above to solve problems. CCSS Addressed: A-SSE 2, 3c; A-CED 2. 1. Textbook, Chapter 6 (omit 6.3) Unit 8 Powers, Roots and Complex Numbers Time: 16 days Goals: Students will be able to perform operations with radicals and imaginary and complex numbers, use rational exponents, solve equations involving radicals and use these concepts to solve problems. 1. use the terminology associated with radicals. 2. find the principal square root and the nth roots of numbers with and without a calculator. 3. simplify, multiply, divide, add and subtract radical expressions. 4. use the conjugate to simplify radical expressions. 5. evaluate expressions with rational exponents with and without a calculator. 6. write expressions with rational exponents in radical form and vice versa. 7. use the laws of exponents to perform operations with expressions with rational exponents. 9
8. solve radical equations with and without a graphing calculator. 9. express the square root of negative numbers and their products in terms of i. 10. add and subtract complex numbers. CCSS Addressed: A-CED 2; F-IF 8b; F-LE 1-4; N-CN 1-3; N-RN 1, 2. 1. Textbook, Chapter 7 (omit 7-8, 7-9, 7-10) Unit 9 Quadratic Equations Time: 10 Days Goals: Students will be able to solve quadratic equations and use this skill to solve problems. 1. identify a quadratic equation. 2. use the Quadratic Formula to solve a quadratic equation. 3. use the Quadratic Formula to identify the types of roots of a quadratic equation. 4. use the concepts above to solve problems. CCSS: A REI 4a, b, 11; F-IF 5, 8a; N-CN 7, 8. 1. Textbook, Chapter 8.3, 8.4, 8.2, 8.6 Unit 10 Transformations of Functions Time: 15 Days Goals: Students will be able to perform transformations on functions and use quadratic 10
functions to model problems. 1. identify horizontal and vertical translations and vertical stretching and shrinking from equations and sketch the graph. 2. identify and sketch the graph of the parent equation for a parabola, y = x 2, and recognize and perform transformations of that graph. 3. use a graphing calculator to identify maximum or minimum points and the x and y intercepts of a parabola. 4. use quadratic functions to model problems. CCCS: A-REI 11; F-IF 4, 5, 7a, b, c; F-LE 9 1. Textbook, Chapter 9 (omit 9-1) 11