Radnor High School - Radnor Township School District

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Radnor High School

Course Syllabus

Algebra 3 and Trigonometry

0446

|General Information |

|Credits: 1.0 Credits Length: Full Year |

|Weighted: Unweighted Format: Meets Daily |

|Prerequisite: Algebra 2 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 [pic] |

|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 [pic] |

|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 [pic] |

|Solve an absolute value equation that requires rewriting |

|Solve an equation with 2 absolute values, such as [pic] |

|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 |

|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, 11-21odd |

| |

|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, 63-77odd, 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, 33-39o, 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 |

| |

| |

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 |

| |

| |

|Chapter 8 |

|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 |

| |

|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 |

| |

| |

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 |

| |

| |

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, 72-78even |

| |

|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, 29-37odd, 47, 53, 54 |

| |

|102 |

|16.1 |

|Radians/degrees |

|740-741: 7-15odd, 25-37odd |

| |

|103 |

|16.1 |

|Radians/degrees |

|740-741: 8-16even, 26-38even |

| |

|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 |

| |

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