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Lana’i High and Elementary School 2015- 2016 Classroom Rules / Syllabus: Ms. Michelle Fujie Classroom: U-1 Phone: 808-563-0458 Email: [email protected] Website: http://msfujie.weebly.com Classroom Procedures: Class begins as you walk through the classroom door. You will receive assigned seating upon the second week of class. Please do not move desks or chairs unless instructed. Bring your math journal daily! At the beginning of each class, students must have a notebook or a piece of paper and a writing utensil available. “Warm Up Question” o You will have 5 minutes to respond. o There are no right or wrong answers. Take out your homework and have it readily available BEFORE you start your reflection. Your homework will NOT be graded point for point, it is your responsibility to do your homework so that you will receive adequate practice. You will receive CREDIT or NO credit for homework. o ALL calculations must be shown to receive FULL credit, No calculations, NO Credit! o Incomplete/Late homework assignments will receive HALF credit only, with all work shown. We will go over and correct selected homework problems in class. All students must BE prepared to participate in class discussions. Students should always be attentive and taking notes. Students will have daily exit tickets and bi-weekly quizzes. When possible we will do Breakout Discussions– Students will be Paired or Grouped Randomly to discuss and solve problems with their peers. “Brain Checks”- Weekly Random Quiz typically 5 questions worth 2 points each Homework Assignments will be written on whiteboard according to period, ALL students must Write in Student Planner/Math Journal and get teacher initials before leaving. Classroom expectations: Be respectful of yourself, your teacher, and your peers. If you do not understand something or have a question, ASK! Be prepared, Do your homework! It helps you practice what we learn in class. Learning is “collaborative” – when we work together everyone succeeds Absences: It is YOUR responsibility to retrieve class notes and homework. You may find assignments and notes on my website at http://msfujie.weebly.com Please present your excused note at the beginning of class. Classroom Rules: NO eating FOOD OR chewing GUM in class. Remove hats, hoods, sunglasses. Raise your hand and wait to be recognized before saying anything. Respect EVERYONE/THING, Respect the space, property and feelings of others. Do not leave your seat unless you receive instructions and or permission first. Do your homework assignments before coming to the next class. ALL STUDENTS will be responsible for bringing their own book, paper, pencil, eraser, 3-ring binder, assignments, calculator, straight edge, and index cards (Borrowing is not allowed!) ASK to sharpen your pencil / staple your work, or use any classroom supplies. Missed tests/assignments due to excused absences must be made up within a reasonable amount of time, please see teacher to discuss. Read all instructions, stay focused, and apply yourself. Practice TORCH at all times! Grading: A 100-90% B 89-80% C 79-70% D 69-60% F 59-50% Daily assessments include Exit Tickets Weekly assessments include Brain Checks (Quizzes) Homework assignments will be CREDIT / NO CREDIT. Student Participation and Explanation of Concepts Homework assignments will be posted on the board according to class period and on my website. Students are responsible for accurately recording and turning in all homework assignments as assigned in *STUDENT PLANNER/Journal*. Tests may include True/False, Multiple Choice, Application Problems, and Written Responses. (100 points). Final Exams include cumulative benchmarks / standards, typically given at end of each quarter. (100 points). Students may JUSTIFY/DEFEND their wrong answers on TESTS ONLY using complete sentences and showing all math work on Application and Written Reponses ONLY and turn in on the next class for ½ partial points per question to bring up their grade. Only students who receive less than a 90% can submit corrections. I will not accept late submissions. Student behaviors that are unacceptable in the classroom are: Vandalism, fighting, retaliating, foul language, throwing things, eating, drinking, chewing gum, copying, cheating, shouting, talking back, whistling, entering the teacher’s area, desk, and or cabinets without permission and anything else considered to be inappropriate behavior in the classroom. All Lana’i High and Elementary High School rules are in effect at all times. Classroom Management: *Raised Hand Count Down 5-4-3-2-1 Students who are not quiet with their hands raised by the time I count to 5 silently with my hand will have their names written on the board. Additional violations will face the following consequences. Students will sign in and out of classroom for bathroom/water breaks and take appropriate pass. Consequences: Name on board (warning), Deduction of 5 points per check mark, after class/school detention with me in classroom/administration, Admin Referral, Call home to parents. Course GOALS: To provide a rigorous learning environment to prepare students for college level math. To reinforce fundamental concepts learned in previous math courses. To prepare students for Calculus. To build new mathematical knowledge through problem solving that involves a variety of strategies. 5. To master the language of mathematics by expressing mathematical ideas precisely using correct mathematical notation. 6. To use graphing calculators to analyze, solve, visualize, and clarify mathematical concepts. 1. 2. 3. 4. CONTENT OF COURSE: FIRST SEMESTER Unit 1: Review Topics from Algebra II 1. Operations on monomials and polynomials 2. The real number systems 3. Union and intersection of sets Unit 2: Relations and Functions 1. Introduction to families of functions 2. Four ways to represent functions 3. Domain and range 4. Rational expressions and complex fractions 5. Arithmetic operations on functions 6. Composition of functions 7. Inverses of functions 8. Vertical and horizontal line tests Unit 3: Constant and Linear Functions 1. Domain and Range 2. Degree, coefficients, end behavior 3. Graphs of constant and linear functions 4. Slope, distance, and midpoint calculations 5. x- and y- intercept points 6. Point-slope, slope-intercept, and standard forms of equations 7. Parallel and perpendicular lines, perpendicular bisector 8. Systems of linear equations 9. Modeling with linear functions 10. Graphical analysis; determine domain interval where f x 0 , f x 0 , f x 0 . Unit 4: Quadratic Functions 1. Quadratic function, expression, equation, and the quadratic formula 2. Domain and range 3. Graphing quadratic functions - 5 key parts of a parabola 4. Roots/zeros of quadratic functions 5. Factoring 6. Completing the square 7. Modeling with quadratic functions 8. Intersection of two functions (linear and quadratic; quadratic and quadratic) Unit 5: Complex Numbers, Quadratic Inequalities, and Circles 1. Complex numbers 2. The discriminant 3. Quadratic inequalities 4. Analysis of the domain and range 5. Circles SECOND SEMESTER Unit 6: Trigonometric Functions of Angles 1. Right triangle trigonometry and its application 2. 30-60-90 and 45-45-90 triangles 3. Six trigonometric functions 4. Degree measure and radian measure 5. Coterminal, reference, and quadrantal angles 6. “All Students Take Calculus” rule 7. Law of sines and cosines 8. Fundamental trigonometric identities Unit 7: Trigonometric Functions of Real Numbers 1. 17 special angles used to graph the trigonometric functions 2. Terminal point of an arc and its coordinates 3. Graphs of the six trigonometric functions 4. Domain, range, period, amplitude, and phase-shift Unit 8: Analytic Trigonometry 1. Trigonometric identities 2. The addition and subtraction formulas 3. Inverse sine and cosine functions 4. Analyzing the graphs of the inverse sine and cosine functions Unit 9: Exponential and Logarithmic Functions 1. Graphs of exponential and logarithmic functions 2. Inverse of an exponential function and logarithmic function 3. Evaluating logarithmic expressions 4. Change of base formula 5. Expanding and condensing logarithmic expressions 6. Exponential and logarithmic equations 7. Applications of logarithms in problem solving Unit 10: Polynomial Functions of Degree 3 or Higher 1. Graphs of polynomial functions 2. Local maxima and minima, and end behavior 3. Synthetic division 4. Factoring higher degree polynomials 5. Remainder and factor theorems 6. Rational zeros theorem 7. Finding zeros of polynomials Pre-calculus / Trigonometry Unit Proficiencies Students will be able to… FIRST SEMESTER Unit 1: Review Topics from Algebra II 1. Add, subtract, multiply, and divide monomials and polynomials. 2. Identify rational, irrational, natural, whole numbers, and integers. 3. Find and graph intersection and union of sets. 4. Write sets in set-builder notation and interval notation. Unit 2: Relations and Functions 1. Determine whether a relation is a function. 2. Describe the four ways to represent a function – verbal, table of values, graphic, and algebraic. 3. Identify families of functions. 4. Find the domain and range of a given function, including restrictions on radical and rational functions. 5. Graph piecewise defined functions. 6. Add and subtract rational expressions with unlike denominators and simplify complex fractions. 7. Add, subtract, multiply, divide, and evaluate functions. 8. Compose functions and apply to real-life problems. 9. Differentiate the purposes of vertical and horizontal line tests 10. Identify a function as one-to-one and its implications on inverse functions. 11. Find the inverse of a function and verify two functions are inverses by using the property of inverse functions. 12. Graph a function and its inverse (reflections across the identity). Unit 3: Constant and Linear Functions 1. Classify a polynomial function by its degree and write its coefficients. 2. Graph a linear function, analyze the graph and separate the domain into intervals that makes a function positive, negative, and zero, noticing the intercepts. 3. Describe the end behavior of a graph, using function and infinity notations. 4. Given two end points of a line segment, find the slope, distance, and midpoint. 5. Distinguish the point-slope form, slope-intercept form, and standard form. 6. Write equations of lines given different conditions, including parallel/perpendicular lines and perpendicular bisector. 7. Solve systems of linear equations by graphing, substitution, and elimination. 8. Use a calculator to confirm the solution(intersecting point) of a linear system. 9. Apply linear systems in solving real life problems. Unit 4: Quadratic Functions 1. Distinguish between a quadratic function, expression, equation, and the quadratic formula. 2. Identify the domain and range of a quadratic function. 3. Find x- and y-intercepts, axis of symmetry, vertex, and point symmetric to y-intercept of a quadratic function, and graph the function. 4. Describe the end behavior of the function. 5. Factor polynomials, including sum and difference of two cubes and factor by grouping. 6. Find zeros of a quadratic function by factoring, completing the square, using the quadratic formula. 7. Solve maximum/minimum problems by modeling a quadratic function. 8. Utilize the maximum, minimum, and zero features of the calculator in problem solving. 9. Find intersecting point(s) of a quadratic function and a linear function by solving the system. 10. Find intersecting point(s) of two quadratic functions. Unit 5: Complex Numbers, Quadratic Inequalities, and Circles 1. Add, subtract, multiply, divide complex numbers, then simplify them - including FOIL, powers of i , and rationalizing the denominator. 2. Determine the nature of the roots by the value of the discriminant, stating the number and type of solutions. 3. Solve and graph quadratic inequalities in one variable. 4. Determine the part of the domain that makes the value of the function positive, zero, or negative. 5. Graph circles given equations in standard form. 6. Write an equation of a circle in standard form given the center and radius. 7. Convert an equation of a circle from general form to standard form. SECOND SEMESTER Unit 6: Trigonometric Functions of Angles 1. Find the trigonometric ratios of 30-60-90 triangle and 45-45-90 triangle without a calculator. 2. Find the exact value of a trigonometric function of an angle associated with the special triangles and quadrantal angles. 3. Identify quadrantal angles and their trigonometric values. 4. Find trigonometric functions of any angle. 5. Solve right triangles and apply these skills in problem solving. 6. Find the other five trigonometric ratios if given one trigonometric ratio. 7. Convert degree measure into radian measure and vice versa. 8. Find coterminal angles and reference angle of a given angle. 9. Identify positive and negative trigonometric values in all quadrants. 10. Apply the Law of Sines and Law of Cosines in solving triangles and word problems. 11. Find the six trigonometric values of an angle if a point is known on the terminal side. 12. Express a trigonometric function in terms of another by manipulating the fundamental identities. Unit 7: Trigonometric Functions of Real Numbers 1. Determine whether a point is on the unit circle. 2. Find the point on the unit circle if given one of the coordinates. 3. Find the x and y-coordinates of the 17 major points (0, / 6, / 4, / 3, / 2 .......... 2 ) on the unit circle and relate them to the six trigonometric ratios. 4. Identify the quadrant which contains the terminal point of an arc whose length is given in terms of . 5. Find the terminal point ( x , y ) on the unit circle determined by a real number. 6. Find the reference number and the terminal point determined by a real number. 7. Find all trigonometric functions from one given terminal point. 8. Find the exact value of the trigonometric function of a given number associated with the 17 major points on the unit circle. 9. Evaluate trigonometric functions with or without a calculator. 10. Write from memory the reciprocal and Pythagorean identities. 11. Graph the six trigonometric functions by incorporating the amplitude, period and phase shift. Unit 8: Analytic Trigonometry 1. Simplify trigonometric expressions and verify trigonometric identities. 2. Find the exact value of a trigonometric expression by using the addition and subtraction formulas. 3. Prove identities by using the addition and subtraction formulas. 4. Analyze and graph the inverse sine and cosine functions. 5. Evaluate the inverse sine and cosine functions. Unit 9: Exponential and Logarithmic Functions 1. Identify whether the function represents exponential growth or decay. 2. Graph exponential and logarithmic functions by incorporating the domain, range, intercepts, asymptote, and translations. 3. Find the inverse of an exponential function and logarithmic function. 4. Convert exponential form into logarithmic form and vice versa. 5. Evaluate logarithmic expressions with or without a calculator. 6. Apply the change of base formula to calculate logarithmic expressions. 7. Expand and condense logarithmic expressions by using the properties of logarithms. 8. Solve exponential and logarithmic equations. 9. Solve compound interest problems by applying logarithms. Unit 10: Polynomial Functions of Degree 3 or Higher 1. Graph and analyze polynomial functions by incorporating intercepts, end behavior, local maxima and minima, and translations. 2. Apply synthetic division to divide polynomials. 3. Apply the remainder theorem to evaluate polynomials. 4. Make the connection between the remainder theorem and factor theorem. 5. List the possible rational zeros of a polynomial function by using the rational zeros theorem. 6. Find all zeros of a polynomial function by utilizing the remainder, factor, and rational zeros theorems. 7. Find all zeros by factoring if possible. 8. Write a polynomial function if given its zeros. -----------------------------------------Detach page and turn in-------------------------------------I have read and I understand the class procedures, class rules and know what is expected of me in this class during this school year. Print the following information below: Name: ___________________________________ Date: ____________ Period: _________ Name of Parents/Guardian: ______________________________________________________ Street address: ____________________________________ Parent/Guardian phone numbers: P. O. Box: ________________ Home: ______________________________________ Work: _________________________________ Mobile _____________________Text ok? Y / N Student mobile phone? Y / N If yes, Cell Number ________________________ Text ok? Y / N IG Follow @ _________________________ Sports?______________________________________ Do you have internet access outside of school? Y / N Parent’s e-mail: ___________________________________________ Student’s email: ___________________________________________ Students Signature: _________________________________Date: ________________________ My child has shared this information with me and I understand that if I have any questions or concerns about math class and/or my child I should contact the teacher via phone, email or in person. The contact information provided above will be used by my child’s teacher to contact me as necessary. Parents Signature: ___________________________________Date: _________________________