* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Algebra 3
Survey
Document related concepts
Big O notation wikipedia , lookup
History of the function concept wikipedia , lookup
History of mathematical notation wikipedia , lookup
Elementary mathematics wikipedia , lookup
Recurrence relation wikipedia , lookup
List of important publications in mathematics wikipedia , lookup
Elementary algebra wikipedia , lookup
Factorization wikipedia , lookup
History of trigonometry wikipedia , lookup
Partial differential equation wikipedia , lookup
Signal-flow graph wikipedia , lookup
System of linear equations wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Transcript
Radnor High School Course Syllabus Algebra 3 and Trigonometry 0446 General Information Credits: 1.0 Credits Weighted: Unweighted Prerequisite: Algebra 2 Length: Full Year Format: Meets Daily Grade: 11, 12 Course Description Algebra 3 is intended to complete the topics of Algebra not developed in Algebra 2. In addition, the course will review, reinforce and strengthen the concepts and skills studied in Algebra 2 with emphasis on equation and inequality solving. The new topics will include but not be limited to complex numbers, exponential and logarithmic functions, and sequences and series. Trigonometry will be introduced through right triangles and extended to include the circular functions. MARKING PERIOD ONE LINEAR EQUATIONS AND INEQUALITIES IN 1 AND 2 VARIABLES, WITH GRAPHING EXPONENTS, POLYNOMIALS AND POLYNOMIAL FUNCTIONS FACTORING Common Core Standards A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. A-APR.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. A-APR.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/ b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. A-APR.7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. A-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A-CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. A-CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. A-REI.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A-REI.2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. A-REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A-REI.7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line F-LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). F-LE.5. Interpret the parameters in a linear or exponential function in terms of a context. A-REI.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A-REI.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ A-REI.12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Keystone Connections 2.8.A2.B: Evaluate and simplify algebraic expressions, for example: products/quotients of polynomials, logarithmic expressions and complex fractions; and solve and graph linear, quadratic, exponential and logarithmic equations and inequalities, and solve and graph systems of equations and inequalities. 2.8.11.B: Evaluate and simplify algebraic expressions and solve and graph linear, quadratic, exponential and logarithmic equations and inequalities, and solve and graphic systems of equations and inequalities. 2.8.A2.D: Demonstrate an understanding and apply properties of functions (domain, range, inverses) and characteristics of families of functions (linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8.A2.E: Use combinations of symbols and numbers to create expressions, equations and inequalities in two or more variables, systems of equations and inequalities, and functional relationships that model problem situations. 2.8.A2.F: Interpret the results of solving equations, inequalities, systems of equations and inequalities in the context of the situation that motivated the model. 2.5.11.A: Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts. 2.5.11.B: Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results. Student Objectives At the end of the first marking period, students should be able to successfully manage the following skills: Solve linear equations by using the addition and/or multiplication properties of equality Solve linear equations by using the distributive property Solve linear inequalities by using the addition and/or multiplication properties of equality Solve linear inequalities by using the distributive property Solve linear inequality a x b Solve application problems with inequalities Define absolute value Solve various absolute value problems, including special cases of absolute value and inequalities Distinguish between independent and dependent variables Define and identify relations and functions Find domain and range for specific functions and/or relations Use function notation, and identify functions defined by graphs and equations Solve 2 equation linear systems by graphing, substitution and elimination Solve special systems (dependent and inconsistent) Use a graphing calculator to assist in solving systems of equations Define and use the rules of exponents for products & quotients and the power rule Define and use negative exponents and the zero power Simplify exponential expression Define polynomials Find the degree of a polynomial Add, subtract and multiply polynomials Divide polynomials, through both long division and synthetic division Evaluate polynomial functions through function notation Define and use composite functions Factor using GCF; by grouping; factoring trinomials; factoring differences of squares; factoring perfect square trinomials Using the zero product property Quadratic Formula Materials & Texts Lial, Margaret L., Hornsby, John, (2011). Algebra and trigonometry for college readiness. Boston, MA: Pearson Education, Inc. ISBN 0-13-136626-2 Activities, Assignments, & Assessments ACTIVITIES Use properties of equality to solve linear equations Use the distributive property to solve linear equations Solve linear equations with fractions and decimals Use properties of equality to solve linear inequalities Use the distributive property to solve linear inequalities Use all properties to solve a x b Use all properties to solve applications problems with inequalities Define absolute value Solve an absolute value equation Solve one-way absolute value inequalities, such as 2 x 1 7 and/or 2 x 1 7 Solve an absolute value equation that requires rewriting Solve an equation with 2 absolute values, such as ax b cx d Define and use the definitions of relation and function Determine whether relations are functions Find domain and range of relations and functions from various sources Use the 'vertical line test' Identify functions from their equations Write equations using function notation Graph linear and constant functions, using function notation to express the graphs Decide whether an ordered pair is a solution to a system of equations Solve a system of equations by graphing, substitution and elimination Determine the number of solutions a system of equations has Define Dependent and Inconsistent systems, and solve those types of systems Use the product rule, the quotient rule and the power rule for exponents Use the negative exponent rule and the zero exponent rule Add and subtract polynomials; use descending powers rule and combine like terms Define and use function compositions; define new domain and range Use synthetic division and or long division to divide polynomials Factoring techniques o GCF; Binomial factor; Negative common factor; Grouping; Rearrange Terms, then Factor; Factor Trinomials; Difference of Squares; Perfect Square Trinomials; Difference of Cubes; Sum of Cubes Solve Quadratic Equations by Factoriong and Using the ZPP Review the Quadratic Equation ASSIGNMENTS CHAPTERS 2, 3, 4 HW # Section Topic Assignment 1 2.1` Solving Equations Pg 50-51: 11, 13, 17, 21, 23, 33, 35 2 2.4 Solving Inequalities (graphs required Pg. 80-81: 11, 15, 17, 21, 27, 31, 33 3 2.6 Absolute value equations Pg 96-98: 5-13odd, 59, 63, 65, 85 4 2.6 Absolute value inequalities Pg 96-98: 21-25odd, 29, 31, 35-45 odd 5 Ch. 2 Review Pg. 102-105: 1, 5, 7, 27, 28, 51, 53, 55, 59, 61, 62 6 3.5 Functions Pg. 157-158: 1, 2, 5, 7, 1121odd 7 3.5 F(x) notation Pg. 158-159: 41, 43, 49, 51, 53, 61, 63, 65 8 Ch. 3 Review Worksheet 9 4.1 2 variable systems Pg. 179: 1, 7-13 10 4.1 Solve systems by graphing (on calc) Worksheet 11 4.1 Solve systems by substitution 179-180: 17-25 odd, 29, 33 12 4.1 Solve systems by elimination 180: 35-47odd 13 Ch. 4 Chapter 4 reveiw Pg 180: 58-62 Pg 230-231 2, 3, 5, 14 CHAPTER 5 HW # Section Topic Assignment 14 5.1 Exponents Pg246: 19-39odd 15 5.1 Rules of exponents Pg 246-248: 7-15odd, 6377odd, 89, 105 16 5.1 Rules of exponents 247-248: 79-87odd, 93, 95, 99, 101 17 5.2 Standard form and degree Pg 253: 1-25odd 18 5.2 Add/subtract polynomials Pg. 253-254: 29, 31, 39, 43, 51, 57, 63-69odd 19 5.3 Add/subtract polynomial functions Pg 262-263: 1, 3, 7, 13, 15, 17, 18, 25, 27 20 5.3 Composition of functions Pg. 263: 35-47odd 21 5.3 Add/subtract/compositions Worksheet 22 5.4 Multiply polynomials Pg. 270-271: 1, 3, 5, 11, 3339o, 47, 59, 15(do last) 23 5.4 Multiply polynomials Pg 270-271: 7, 9, 16, 19, 49, 51, 55, 61, 63, 85 24 5.4 Multiply polynomial functions Pg 271: 93-105odd 25 5.5 Polynomial division Pg 277: 5-19odd 26 5.5 Polynomial division 277: 21-31 odd 27 Ch.5 Review 281-283: 3, 9, 11, 13, 23, 39, 40, 47, 53, 59, 71 CHAPTER 6 HW # Section Topic Assignment 28 6.1 Factoring (GCF only) Pg. 290: 1-19odd 29 6.1 GCF’s 290: 2-20even 30 6.2 Factoring trinomials 297: 5-19odd 31 6.2 Factoring trinomials 297: 33-39odd, 45, 46, 47 32 6.2 Factoring trinomials Worksheet 33 6.3 Special cases (factoring) 302: 7-23odd 34 6.3 Special cases Worksheet 35 6.5 Factoring to solve equations (ZPP) 312: 3-15odd 36 6.5 Factoring, including GCF 312: 19, 23, 29, 31, 39, 41 37 9.2 Quadratic formula pg 450: 5-13 odd 38 Ch. 6 Review Pg 315: 1, 3, 11, 13, 15, 25, 28, 37, 41, 45 ASSESSMENTS Assignment sheets will be distributed periodically throughout the school year. Homework will be assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics Department page of Radnor High School’s web site. Grades will be based on quizzes, tests, homework, group activities and projects. The Radnor High School grading system and scale will be used to determine letter grades. Terminology Linear equations, solution, solution set, equivalent equations, identity, inequality, linear inequality, absolute value, absolute value inequality, independent and dependent variables, relation, function, domain, range, function notation, linear function, constant function, systems of equations, system of linear equations, solution set of a linear system, consistent system, independent equations, inconsistent system, dependent equations, elimination method, substitution method (Chapters 2, 3, 4) Term, coefficient, algebraic expression, polynomial, descending powers, trinomial, binomial, monomial, degree of a term, degree of a polynomial, negative of a polynomial, polynomial function, composition of functions, identity function, squaring function, cubing function (Chapter 5). Factoring, greatest common factor (GCF), prime polynomial, difference of squares, perfect square trinomial, difference of cubes, sum of cubes, quadratic equation, standard form of a quadratic equation (Chapter 6). Media, Technology, Web Resources Teacher-developed documents Calculator based documents MathXLforSchool.com MARKING PERIOD TWO RATIONAL EXPRESSIONS AND FUNCTIONS ROOTS, RADICALS AND ROOT FUNCTIONS Common Core Standards A-APR.7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. A-APR.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial N-CN.1. Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real. N-CN.2. Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. N-CN.3. (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. N-CN.5. (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°. N-CN.7. Solve quadratic equations with real coefficients that have complex solutions. N-CN.8. (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i). N-CN.9. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. A-REI.4. Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Keystone Connections 2.8.A2.B: Evaluate and simplify algebraic expressions, for example: products/quotients of polynomials, logarithmic expressions and complex fractions; and solve and graph linear, quadratic, exponential and logarithmic equations and inequalities, and solve and graph systems of equations and inequalities. 2.8.11.B: Evaluate and simplify algebraic expressions and solve and graph linear, quadratic, exponential and logarithmic equations and inequalities, and solve and graphic systems of equations and inequalities. 2.8.A2.D: Demonstrate an understanding and apply properties of functions (domain, range, inverses) and characteristics of families of functions (linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8.A2.E: Use combinations of symbols and numbers to create expressions, equations and inequalities in two or more variables, systems of equations and inequalities, and functional relationships that model problem situations. 2.8.A2.F: Interpret the results of solving equations, inequalities, systems of equations and inequalities in the context of the situation that motivated the model. 2.5.11.A: Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts. 2.5.11.B: Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results. Student Objectives At the end of the second marking period, students should be able to successfully manage the following skills: Define rational functions and describe their domains Write rational expressions is lowest terms Find a least common denominator Perform standard operations with rational expressions Determine the domain of the variable in a rational equation Solve rational equations Recognize the graph of a rational function Find roots of numbers Solve radical equations Simplify the square root of negative numbers Manipulate and use “i” Materials & Texts Lial, Margaret L., Hornsby, John, (2011). Algebra and trigonometry for college readiness. Boston, MA: Pearson Education, Inc. ISBN 0-13-136626-2 Activities, Assignments, & Assessments ACTIVITIES Find numbers that are not in the domains of rational functions Write rational expressions in lowest terms Use multiplication and division to combine rational expressions Add and subtract rational expressions that have common denominators Find least common denominators Add and subtract rational expressions that have different denominators Use the distributive property when subtracting rational expressions Determine the domains of the variables in rational equations Solve rational equations Find square roots Identify the graph of a radical function Use the power rule to solve radical equations Use the power rule to square a binomial Simplify square roots of negative numbers Perform operations using “i” Use “i” when raised to a power ASSIGNMENTS Chapter 7 HW # Section Topic Assignment 39 7.1 Simplify rational expressions pg 328: 9, 11, 17, 25, 27, 35, 37, 39 40 7.1 Multiply/divide rational expressions 329: 61-64, 67-71 41 7.1 Multiply/divide rational expressions (w/factoring 329: 71-75, 79-83 42 7.2 Add/subtract rational expressions 336: 1-12 43 7.2 Add/subtract rational expressions (unlike denoms) 336-337: 21-29odd, 39, 49, 53, 55 44 7.4 Solving rational equations 348-349: 1, 3, 9, 11, 15-23odd 45 7.4 Solving rational equations 348-349: 25-33odd 46 7.4 Solving rational equations 348-349: 2, 4, 6, 16, 18, 22, 26, 28 47 Ch. 7 Review Pg 375-377: 3, 5, 9, 17, 18, 25, 27 HW # Section Topic Assignment 48 8.1 Simplify square roots Worksheet 49 8.1 Other roots Pg 384: 13-27odd 50 8.6 Radical equations 418-419: 1, 7-17odd, 37,38 Chapter 8 51 8.6 Radical equations 418-419: 23-31odd, 43,45 52 8.7 Square roots of negative numbers 425: 1-12 53 8.7 Square roots of negative numbers 425: 15, 17, 23, 39, 41, 43, 45 54 Ch. 8 Review Pg430-433: 3, 5, 103, 105, 107, 110, 120, 121, 126, plus worksheet. ASSESSMENTS Assignment sheets will be distributed periodically throughout the school year. Homework will be assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics Department page of Radnor High School’s web site. Grades will be based on quizzes, tests, homework, group activities and projects. The Radnor High School grading system and scale will be used to determine letter grades. Terminology Rational expression, rational function, least common denominator (LCD), rational equation, domain of the variable, asymptote, radicand, index, radical, root, radical expression, radical equation, extraneous solution, imaginary numbers, “i” Media, Technology, Web Resources Teacher-developed documents Calculator based documents MathXLforSchool.com MARKING PERIOD THREE EXPONENTIAL AND LOGARITHMIC FUNCTIONS SEQUENCES AND SERIES RIGHT TRIANGLE TRIGONOMETRY Common Core Standards F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F-IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. F-IF.9. Compare properties of two functions each represented in a different way (either algebraically, graphically, numerically in tables, or by verbal descriptions). F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. F-LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). F-LE.3. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. F-LE.4. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. F-LE.5. Interpret the parameters in a linear or exponential function in terms of a context. F-TF.1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. F-TF.2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. F-TF.3. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number. F-TF.4. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. F-TF.5. Choose trigonometric functions to model periodic phenomena with specified amplitude, period, and sinusoidal axis. A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. A-SSE.4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. Keystone Connections 2.8.A2.B: Evaluate and simplify algebraic expressions, for example: products/quotients of polynomials, logarithmic expressions and complex fractions; and solve and graph linear, quadratic, exponential and logarithmic equations and inequalities, and solve and graph systems of equations and inequalities. 2.8.11.B: Evaluate and simplify algebraic expressions and solve and graph linear, quadratic, exponential and logarithmic equations and inequalities, and solve and graphic systems of equations and inequalities. 2.8.A2.D: Demonstrate an understanding and apply properties of functions (domain, range, inverses) and characteristics of families of functions (linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8.A2.E: Use combinations of symbols and numbers to create expressions, equations and inequalities in two or more variables, systems of equations and inequalities, and functional relationships that model problem situations. 2.8.A2.F: Interpret the results of solving equations, inequalities, systems of equations and inequalities in the context of the situation that motivated the model. 2.5.11.A: Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts. 2.5.11.B: Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results. Student Objectives At the end of the third marking period, students should be able to successfully manage the following skills: Define an exponential function Graph an exponential function Solve exponential equations Use exponential functions with growth and decay Define a logarithm Convert between exponential and logarithmic forms Evaluate logarithms Solve logarithmic equations Identify sequences Evaluate sequences Recognize and use sigma notation Identify arithmetic and geometric sequences and series Understand the basic terminology of angles Find measures of complementary and supplementary angles Calculate with degrees, minutes, and seconds Find the measures of coterminal angles Classify triangles Find the unknown angles and side lengths in similar triangles Find the values of the six trigonometric functions of a triangle Solve right triangles with Pythagorean theorem Materials & Texts Lial, Margaret L., Hornsby, John, (2011). Algebra and trigonometry for college readiness. Boston, MA: Pearson Education, Inc. ISBN 0-13-136626-2 Activities, Assignments, & Assessments ACTIVITIES Graph an exponential function with a > 1 Graph an exponential function with 0 < a < 1 Solve exponential equations Explore the difference between growth and decay Apply growth and decay to real world problems Graph logarithmic functions both by hand and on the calculator Explore how and why the graphs shift Solve logarithmic functions Write equations in both logarithmic form and exponential form Identify which form will provide the solution in the simplest way Identify patterns and sequences Explore the difference between an arithmetic sequence and a geometric sequence Solve series’ in sigma notation Explore the difference between an arithmetic series and a geometric series Identify an infinite geometric series Find the complement and supplement of an angle Calculate with degrees minutes and seconds Find measures of coterminal angles Find angle measures based on relationships Apple the angle sum of a triangle property Find angle measures in similar triangles Find side lengths in similar triangles Find the six trigonometric values given a right triangle Solve right triangles both with Pythagorean theorem and trigonometry Solve right triangles given an angle and a side Solve right triangles given two sides Find angles of elevation and depression ASSIGNMENTS Chapter 11 and sequence/series assignments HW # Section Topic Assignment 55 11.2 Exponential function graphs (by hand) Pg 545: 1,3, 5-9 56 11.2 Exponential function graphs (by hand) Worksheet 57 11.2 Exponential equations Pg 546: 15-31odd, 37 58 11.3 Logarithmic function graphs (by hand) Worksheet 59 11.3 Logarithmic function graphs (by hand) Worksheet 60 11.3 Explore log/exponential relationship Pg 552-553: 1-19odd 61 11.3 Evaluate logs Worksheet 62 11.3 Solve exponential equations Worksheet 63 11.3 Solve log equations Worksheet 64 Add Evaluate sequences Worksheet 65 Add Arithmetic sequences Worksheet 66 Add Sigma notation Worksheet 67 Add Arithmetic series Worksheet 68 Add Geometric sequences Worksheet 69 Add Geometric series Worksheet 70 Add Infinite geometric series worksheet .Chapter 14 (part one) assignments HW # Section Topic Assignment 71 14.1 Comp/Supp. Angles pg 665: 1-21odd 72 14.1 Degree subunits (calc only) 666: 33, 35, 39, 41, 45, 47, 53, 57, 59, 63 73 14.1 Angles in standard position (coterminal values) 666-667: 69, 73, 75, 77, 83, 103, 105, 109 74 14.1 Angles in standard position (coterminal values) Worksheet 75 14.2 Angle relationships from geometry 673: 3-15odd 76 14.2 Triangle similarity 674-675: 25-39odd, 43, 49, 51, 53 77 14.3 Right triangles/Pythagorean thm. Worksheet 78 14.3 Right triangle trigonometry (6 definitions) Worksheet 79 14.3 Right triangle trig Worksheet 80 15.4 Solving right triangles 724-725: 9-15odd, 21, 23, 27, 33 81 15.4 Solving right triangles 724-725: 10-16even,25, 31, 35 82 15.4 Solving right triangles (word problems) 725-727: 39,41,42,45 83 15.4 Solving right triangles (elevation/depression) 726-727: 49-53 ASSESSMENTS Assignment sheets will be distributed periodically throughout the school year. Homework will be assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics Department page of Radnor High School’s web site. Grades will be based on quizzes, tests, homework, group activities and projects. The Radnor High School grading system and scale will be used to determine letter grades. Terminology Exponential function, asymptote, exponential equation, logarithm, logarithmic equation, sequence, series, arithmetic sequence, arithmetic series, geometric sequence, geometric series, infinite geometric series, sigma notation, angle, side of an angle, vertex of an angle, initial side of an angle, terminal side of an angle, right angle, acute angle, obtuse angle, complements, supplements, degrees, minutes, seconds, vertical angles, similar triangles, sine, cosine, tangent, cotangent, secant, cosecant, coterminal Media, Technology, Web Resources Teacher-developed documents Calculator based documents MathXLforSchool.com MARKING PERIOD FOUR RIGHT TRIANGLE TRIGONOMETRY TRIGONOMETRIC FUNCTIONS TRIGONOMETRIC APPLICATIONS Common Core Standards F-TF.1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. F-TF.2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. F-TF.3. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number. F-TF.4. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. F-TF.5. Choose trigonometric functions to model periodic phenomena with specified amplitude, period, and sinusoidal axis. F-TF.1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. F-TF.2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. F-TF.3. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number. F-TF.4. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. F-TF.5. Choose trigonometric functions to model periodic phenomena with specified amplitude, period, and sinusoidal axis. Keystone Connections 2.10.11.A Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. 2.10.11.B Graph periodic and circular functions; describe properties of the graphs. 2.8.A2.D: Demonstrate an understanding and apply properties of functions (domain, range, inverses) and characteristics of families of functions (linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8.A2.E: Use combinations of symbols and numbers to create expressions, equations and inequalities in two or more variables, systems of equations and inequalities, and functional relationships that model problem situations. 2.8.A2.F: Interpret the results of solving equations, inequalities, systems of equations and inequalities in the context of the situation that motivated the model. 2.8.11.C Recognize, describe and generalize patterns using sequences and sries to predict long term outcomes 2.5.11.A: Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts. 2.5.11.B: Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results. Student Objectives At the end of the fourth marking period, students should be able to successfully manage the following skills: Define and find the six trigonometric function values for an angle, including quadrantal angles Ability to use the definitions of the trigonometric functions to find both special angles and points on the unit circle. Use the Pythagorean and quotient identities to find function values Identify and use reciprocal identities to find function values Define and use cofunction identities Use special right triangles to identify points on the unit circle for 300, 450, 600 angles Identify reference angles and positive/negative angles Identify coterminal angles Use trigonometric applications Convert from degrees to radians and from radians to degrees Use the Law of Sines/Law of Cosines to solve triangle perimeter problems Materials & Texts Lial, Margaret L., Hornsby, John, (2011). Algebra and trigonometry for college readiness. Boston, MA: Pearson Education, Inc. ISBN 0-13-136626-2 Activities, Assignments, & Assessments ACTIVITIES Find the function values of an acute angle using trigonometric ratios Find the function values of an angle using quadrantal angles given specific values Use reciprocal identities to find function values Determine the signs of the trigonometric functions of nonquadrantal angles Find all function values given one value and the quadrant Define quotient and reciprocal identities Use the Pythagorean and quotient identities to find function values Find trigonometric function values of an acute angle Writing functions in terms of cofunctions Solving equations using the cofunction identities Comparing function values fo acute angles Finding function values for special right triangles Finding reference angles in all quadrants Use reference angles, quotient and reciprocal identities plus trigonometric functions to solve application problems Convert from radians to degrees and from degrees to radians Solve triangle perimeter problems using Law of Sines/Law of Cosines methods ASSIGNMENTS CHAPTER 14 HW # Section Topic Assignment 84 14.3 Right triangles in standard position Worksheet 85 14.3 Intro to the unit circle Pg 681: 1-8, 25-33odd 86 14.3 Intro to the unit circle 681: 26-34even, 37-43odd 87 14.4 Unit circle definitions (quadrantal values) 681: 55-63odd, 73-79odd 88 14.4 Reciprocal functions 689: 1-11odd, 19, 21, 25, 29 89 14.4 Locations 690: 23, 26, 30, 31-41odd 90 14.4 Using “p of theta” 690-691: 61-65odd, 69-77odd 91 14.4 Using “p of theta” 690-691: 45,62-66even, 7278even 92 Ch.14 Review 694-697: 1, 5, 9, 12, 13, 17, 19, 21, 23, 25, 29, 37, 41, 43 CHAPTERS 15, 16 AND 20 HW # Section Topic Assignment 93 15.1 Reference angles and families Worksheet 94 15.1 Reference angles and families Worksheet 95 15.2 Intro to special angles on the unit circle Worksheet 96 15.2 Intro to special angles on the unit circle Worksheet 97 15.2 Intro to special angles on the unit circle Pg 713-714: 1, 3, 5, 11, 13, 15, 19, 21, 30 98 15.3 Evaluating trig functions (on calc) 718: 5-21odd 99 15.3 Evaluating trig functions (on calc) 718-719: 37-51odd 100 15.3 Determine the value of theta (on calc) 718: 23-31 101 Ch.15 Review 730-732: 1, 7, 12, 14, 23, 2937odd, 47, 53, 54 102 16.1 Radians/degrees 740-741: 7-15odd, 25-37odd 103 16.1 Radians/degrees 740-741: 8-16even, 2638even 104 20.1 Law of sines 886-887: 1-11odd 105 20.1 Law of sines 887: 13-19odd, 25 106 20.2 Law of cosines 899: 1-17odd 107 20.2 Law of cosines 900-901: 19, 21, 23, 27, 37, 39 ASSESSMENTS Assignment sheets will be distributed periodically throughout the school year. Homework will be assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics Department page of Radnor High School’s web site. Grades will be based on quizzes, tests, homework, group activities and projects. The Radnor High School grading system and scale will be used to determine letter grades. Terminology Sine, cosine, tangent, cotangent, secant, cosecant, reciprocal, adjacent angles, linear pair, vertical angles, opposite, adjacent, initial side, terminal side, vertex, positive angle, negative angle, degree, complementary angles, supplementary angles, minute ('), second ("), standard position, quadrantal angle, coterminal angle, identify, quadrants, reference angle, angle of elevation, angle of depression, radian measure, sector of a circle, unit circle, linear velocity, angular velocity, Trigonometric identities (Pythagorean), trigonometric equations, basic identities, reciprocal identities, quotient identities, law of sines, law of cosines. Media, Technology, Web Resources Teacher-developed documents Calculator based documents MathXLforSchool.com