0445 Credits: 1.0 Grades: 11, 12 Unweighted: Prerequisite: … · 2013. 8. 29. · Modified: 06/28/2011 and graph systems of equations and inequalities. 2.8.11.B: Evaluate and simplify

Modified: 06/28/2011

Radnor High School Course Syllabus

Advanced Algebra 3 with Trigonometry

0445

Credits: 1.0 Grades: 11, 12 Unweighted: Prerequisite: Advanced Algebra 2 or teacher rec. Length: 1 year Format: Meets Daily

Overall Description of Course

Advanced Algebra 3 is a college‐preparatory course.

Advanced Algebra 3 is a College Preparatory level which features moderate pacing and workload with teacher guidance to assist in the mastery of the material. Students enrolled on this level should be seeking to satisfy college requirements/expectations of mathematics course but not necessarily have an interest in pursuing math related college majors.

This course is designed for the students who need to strengthen their knowledge and skill sets of Advanced Algebra 2 before taking a full year course in Trigonometry. Time will be spent reviewing, strengthening and reinforcing skills and concepts involving functions, equations, inequalities and applications. Additional topics will include exponential and logarithmic functions, sequences and series and complex and imaginary numbers. Trigonometry will be introduced through the unit circle and extended to include solving triangles.

MARKING PERIOD ONE

SYSTEMS OF LINEAR EQUATIONS

POLYNOMIALS – EXPRESSIONS AND EQUATIONS

RATIONAL EXPRESSIONS AND EQUATIONS

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 systems of equations in two variables by graphing, substitution and linear combination

Solve problems by translating them to a system of equations

Determine whether a system of equations has 0, 1 or infinite number of solutions, and whether lines are parallel or perpendicular

Graph and solve systems of inequalities

Evaluate and simplify polynomial functions

Add, subtract, and multiply polynomial functions

Recognize and factor certain polynomials

Solve equations using the zero‐product property

Add, subtract, multiply, divide and simplify rational expressions

Activities, Assignments, & Assessments ACTIVITIES

Solve systems of equations in two variables by graphing and by substitution

Solve systems of equations in two or three variables by linear combinations

Solve problems by translating to a system of equations

Determine whether a system of equations has a solution and whether that solution is


unique

Determine whether a system of equations is perpendicular

Graph and solve systems of inequalities (shading)

Find the additive inverse of a number

Add, subtract and multiply rational numbers

Graph linear equations in two variables

Graph linear inequalities and absolute value inequalities in two variables

Determine whether two lines are parallel

Evaluate polynomial expressions

Use a greatest common factor to factor polynomial expressions

Use the distributive property

Remove parentheses from polynomial expressions

Simplify expressions with integer exponents

Solve equations in factored form using the zero‐product property

Evaluate and simplify polynomial functions

Add, subtract, and multiply polynomials

Recognize and factor certain polynomials

Solve equations using the zero‐product property

Add, subtract, multiply, divide, and simplify rational expressions

Add and subtract signed fractions

Multiply and divide signed fractions

Evaluate algebraic expressions

Factor a GCF

Simplify expressions using rules of exponents

Solve linear equations ASSIGNMENTS Chapter 4

0 n/a Algebra Review Quizaroo!

1 4.1 Graphing Systems of Equations Page 161 #1 ‐15odd, 18‐21 all, 25

2 4.1 Graphing Systems of Equations Page 161 #2 ‐14 evens, 22‐24 all, 26,28

3 4.2 Solving systems of equations by substitution or by linear combination

Page 166 #1 ‐4 all, 7‐19 odds, 28, 30, 33, 35

4 4.2 Solving systems of equations by substitution or by linear combination

Worksheet


5 4.3 Applications of systems of equations

Page 171 #1 ‐7 odds, 13, 17, 19, 25, 40, 42, 43

6 4.3 Applications of systems of equations

Page 171 #2 ‐ 6 evens, 14, 18, 20, 26, 41

7 4.4 Systems of equations in three variables

Page 178 #14 ‐20 all , 23

8 4.5 Applications of systems of equations in three variables

Page 181 #1 ‐ 13 odds

9 4.6 Independent/Dependent Systems Worksheet

10 4.6 Independent/Dependent Systems Page 186 #1 – 19 odds, 20

11 4.7 Systems of Linear Inequalities Page 192 #1, 5, 9, 15, 17, 23, 27, 30

12 4.7 Systems of Linear Inequalities Page 192 #3, 7, 11, 13, 19, 21, 25, 29

13 Ch 4 Chapter 4 Review Page 200 #1‐12 all Page 203 #56‐66 all

Chapter 5

HW # Section Topic Assignment

14 5.1, 5.2 Polynomials, Adding and Subtracting

Page 208 #1, 2, 9, 11, 13 Page 212 #3, 5, 7, 11, 15, 17, 19, 28

15 5.3 Multiplying Polynomials Page 218 #5, 6, 7, 8, 13, 14, 17, 18, 19, 21, 25, 27, 33, 35, 37

16 5.4 Factoring: GCF, Difference of Squares, Perfect Square Trinomials, Grouping

Page 222 #9 ‐17 odds, 19‐29 odds, 37‐43 odds, 55‐59 odds

17 5.4 Factoring: GCF, Difference of Squares, Perfect Square Trinomials, Grouping

Page 222 #8 ‐18 evens, 20‐30 evens, 36‐42 evens, 54‐58 evens

18 5.5 Factoring: Difference or Sum of Cubes, Trinomials

Page 227 #5 ‐13 odds, 23‐35 odds, 43‐53 odds, 71, 77, 83

19 5.5 Factoring: Difference or Sum of Cubes, Trinomials

Page 227 #4 ‐12 evens, 22‐34 evens, 42‐52 evens, 70, 76, 82


20 5.6 Factoring: A general strategy Page 231 #1‐7 odds, 11, 13, 19, 23,24, 25, 27, 33, 35

21 5.7 Solving Polynomials (ZPP) Page 233 #1‐33 odds, 36, 47

22 5.8 Applications of Polynomials Page 235 #1 ‐ 11 odds, 15

23 Ch 5 Chapter 5 Review Page 241 #1 – 41 odds

Chapter 6


24 6.1 Multiplying and Simplifying Rational Expressions

Page 248 #5‐31 odds

25 6.1 Multiplying and Simplifying Rational Expressions

Worksheet

26 6.2 Adding and Subtracting Rational Expressions

Page 253 #1 ‐29 odds


Page 253 #2 ‐30 evens


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 Boundary, consistent systems, constraints, dependent systems, half‐plane, inconsistent systems, linear combinations, linear inequality, method of elimination, ordered triple, perpendicular systems, substitution method, systems of equations, triangular form, unique form. (Chapter 4) Ascending order, binomial coefficients, degree of a polynomial, degree of a term, descending order, factor, greatest common factor, like terms, monomial, polynomial function, polynomial


in x, prime factors, prime polynomial, terms, trinomial, trinomial square. (Chapter 5) Rational expressions, rational equations, multiplication of rational expressions, least common multiple (LCM), least common denominator (LCD), complex rational expression, addition of rational expressions. (Chapter 6.1 – 6.3)

Materials & Texts Smith, Stanley A., Randall, Charles I., Dossey, John A., Bittinger, Marvin L. (2001). Algebra 2 with Trigonometry. Upper Saddle River, NJ: Prentice‐Hall, Inc. ISBN 0‐13‐051968‐5

Media, Technology, Web Resources

Prentice Hall Algebra 2 With Trigonometry Home Page

Teacher‐developed smart‐board documents

Calculator based documents


MARKING PERIOD TWO

RATIONAL EXPRESSIONS – SOLVING, COMPLEX AND VARIATION

POWERS, ROOTS AND COMPLEX NUMBERS

QUADRATIC FUNCTIONS AND TRANSFORMATIONS

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

F‐LE.1 F‐IF.7 F‐IF.8, 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.


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.







Student Objectives

At the end of the second marking period, students should be able to successfully manage the following skills:

How to add, subtract, multiply and divide complex rational expressions

How to factor and rationalize radical expressions

Ability to solve rational equations

Ability to solve work and motion problems using rational equations

Find the constant of variation and an equation of variation for direct and inverse variation problems given certain information, and then solve the problem

How to add, subtract, multiply, simplify (by factoring) and rationalize radical expressions

Will be able to find principal square roots and find odd/even nth roots

Will write expressions with rational exponents as radical expressions, and vice versa.

Will simplify expressions containing negative rational exponents

Will be able to use rational exponents to simplify radical expressions

Will be able to solve problems with radicals and radical equations

How to add, subtract, multiply and find the conjugate of imaginary and complex numbers

Ability to transform a graph given either coordinates or a function

Problem‐solve using quadratic functions


Solve complex rational expressions

Solve a formula for a specified variable

Solve work, motion, and variation problems


Simplify absolute value expressions

Use the product, quotient, and power rules for integer exponents

Solve linear equations and quadratic equations in factored form

Multiply binomial expressions

Add, subtract, multiply, simplify (by factoring) and rationalize radical expressions

Find principal square roots and find odd/even nth roots

Use rational exponents

Define, add, subtract, multiply and find the conjugate of imaginary and complex numbers

Solve equations using radicals, imaginary numbers, and complex numbers

Factor binomials and trinomials

Identify the graph of a function

Find x‐ and y‐intercepts of linear equations

Determine whether a function is even, odd, or neither

Sketch or graph quadratic functions

Find a standard form for a quadratic equation

Determine maximum or minimum values and x‐intercepts of the graph of a quadratic function, if they exist

Fit a quadratic function to a graph or data points

Solve problems using quadratic functions ASSIGNMENTS Chapter 6


29 6.3 Complex Rational Expressions Page 258 #1 ‐15 odds

30 6.3 Complex Rational Expressions Page 258 #2 ‐16 evens

31 6.6 Solving Rational Equations Page 269 #5‐25 odds

32 6.6 Solving Rational Equations Worksheet

33 6.6 Solving Rational Equations Worksheet

34 6.7 Applications of Rational Equations Page 273 #1,3,6,8,11,13,19

35 6.7 Applications of Rational Equations Page 273 #2, 4, 7, 9, 12,14,18

36 6.9 Variation Page 283 #1, 3, 5, 9, 11, 13, 17, 19, 21, 25, 30


37 Ch 6 Chapter 6 Review Page 289 #1‐10 all, 15‐18all, 20‐23all

Chapter 7


38 7.1‐7.4 Radicals and their Operations Worksheet

39 7.5 Rational Exponents Page 315 #1‐63 every other odd. (Ex: 1, 5, 9…)

40 7.6 Solving Radical Equations Page 319 #1 ‐31 odds

41 7.6 Solving Radical Equations Page 319 #6 ‐34 evens

42 7.7, 7.9 Complex Numbers Page 323 #1‐9 odds, 25‐33 odds, 35‐39 all Page 329 #12‐15 all, 19‐22 all

43 Ch 7 Chapter 7 Review Worksheet

Chapter 9


44 9.2 Translations Page 393 #1‐21 odds

45 9.3 Stretching and Shrinking Page 398 #1‐25 odds

46 9.3 Transformations Page 99 #27‐36 all

47 9.4 Graphs of Quadratic Functions Page 402 #5 ‐17 odds, 19‐24 all

48 9.5 Graphs of f(x)=a(x‐h)2 + k Page 406 #1 ‐21 odds

49 9.6 Standard Form of Quadratic Functions

Page 410 #1 ‐17 odds, 21, 22

50 9.7 Graphs and x‐intercepts Page 413 #1 ‐15 odds, 26‐28 all

51 9.8 Modeling with quadratic functions

Page 418 #1 ‐13 odds, 23, 25, 27

52 9.8 Modeling with quadratic functions

Page 418 #2 ‐12 evens, 22, 24, 26, 28

53 Ch 9 Chapter 9 Review Page 424 #13_38 all page 426 #10‐22 all

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 expressions, rational equations, complex rational expression, constant of variation, direct variation, graphing rational functions, inverse variation, rational equation, rational expression, reciprocal, vary directly, vary inversely, solving rational equations (Chapter 6). Complex numbers, complex conjugate, conjugate, cube root, even root, extraneous roots, imaginary axis, imaginary numbers, index, kth root, odd root, principal square root, radical equation, radical expressions, radical sign, radicand, rational exponents, rationalizing the denominator, real axis, square root. (Chapter7). Data points, maximum value of a quadratic function, minimum value of a quadratic function, odd and even functions, parabola, quadratic function, standard form, vertex form, vertex of a parabola, step sequence, ‐b/2a, line of symmetry of a quadratic (Chapter 9).







MARKING PERIOD THREE

CONIC SECTIONS

TRIGONOMETRIC FUNCTIONS

TRIGONOMETRIC GRAPHS

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.



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).



2.8.11.C Recognize, describe and generalize patterns using sequences and sries to predict long term outcomes




Student Objectives

At the end of the third marking period, students should be able to successfully manage the following skills:

How to find the length and midpoint of a segment

How to find the equation of a conic section (circle, ellipse, hyperbola, parabola) given certain characteristics

How to graph a conic section

How to identify conic sections from their equations or graphs

How to find the six trigonometric function values for an angle

How to find the reference angle of a rotation and use it to find trigonometric function values

How to convert from degrees to radian measures and back again

How to graph trigonometric functions (sin, cos, tan and cot) with transformations


Use the distance formula to find the distance between any two points in the plane

Use the midpoint formula to find the midpoint between any two points in the plane

Find the equations of a circle (given appropriate information)

Work backwards to find the radius and center of a circle

Given the equation of an ellipse, determine its vertices and foci, and graph the shape

Given the equation of a hyperbola, determine its vertices, foci and asymptotes, and graph it

Given the equation of a parabola, find its vertex, focus and directrix, then graph

Determine the type of conic from the equation

Find the six trigonometric ratios for an angle of a right triangle

Find the lengths of sides in special triangles

Use the Pythagorean theorem to solve non‐special right triangles

Using angle relationships, determine various coterminal angles, reference angles, and the like

Use the definitions of trigonometric functions to find function values

Use inverse trigonometric functions to determine angle values

Define radian measure, and convert between radians and degrees

Use radian measure to find applications of radian measure (arc measure, latitude/longitude, etc.)

Determine circular functions

Apply radian measure to solve linear and angular velocity problems

Graph sine and cosine using vertical and horizontal stretches and a vertical shift


ASSIGNMENTS Chapter 10


54 10.1 Distance, Midpoint Page 431 #1‐15 odds, 28, 29

55 10.2 Conic Sections: Circles Page 436 #1‐11 odds, 17‐22 all, 24, 39

56 10.2 Conic Sections: Circles Worksheet

57 10.3 Conic Sections: Ellipses Page 442 #1‐11 odds, 21, 23, 25

58 10.3 Conic Sections: Ellipses Worksheet

59 10.4 Conic Sections: Hyperbola Page 450 #1‐6 all, 7‐13 odds, 17‐22 all

60 10.4 Conic Sections: Hyperbola Worksheet

61 10.5 Conic Sections: Parabolas Page 456 #1 ‐8 all, 19‐27 odds

62 10.5 Conic Sections: Parabolas Worksheet


Chapter 17A


64 17.5 Right Triangle Trigonometry Page 732 #1‐21 odds

65 17.1 Right Triangle Trigonometry Page 732 #2‐18 evens, 22

66 Supp Solving Non‐Special Right Δs Worksheet

67 17.4, 18.6 Solving Non‐Special Right Δs with Degrees, Minutes, Seconds

Page 753 #23‐26 all,31‐34 all,

Page 807 #1‐13 odds, include labeled drawing of triangle

68 18.6 Applications, Solving Non‐Special Right Δs

Page 808 #17‐29 odds, include labeled drawing of triangle


69 17.2 More on Trigonometric Functions:Coterminaland Reference angles (SUPP)

Page 739 #1 ‐17 odds, 21, 22

70 Supp More on Trigonometric Functions: Function values of special angles

Worksheet

71 Supp More on Trigonometric Functions: Reciprocal Functions, Inverse Functions and Calculator Values

Page 753 #1‐21 odd, #39‐49 odd, #63‐68 all

72 17.3 Radian Measure Conversions, Reference of Special Angles

Worksheet

73 17.3 Radian Measure Conversions, Reference of Special Angles

Worksheet

74 17.3 Arc Length, Angular Velocity, Linear Speed

Page 746 #19, 21, 33‐41 odds

75 17.3 Arc Length, Angular Velocity, Linear Speed

Page 746 #20, 22, 32‐42 evens

76 Ch 17 Chapter 17 Review Page 779 #1*‐13 all

Chapter 17B


77 Supp Graphing Sine and Cosine (No Trans)

Worksheet

78 Supp Amplitude Transformations and Vertical Shifts

Worksheet

79 Supp Amplitude Transformations and Vertical Shifts

Worksheet

80 Supp Period Transformations Worksheet

81 Supp Period Transformations Worksheet

82 Supp Graphing Sine and Cosine with all transformations and working backwards

Worksheet


83 Supp Graphing Sine and Cosine with all transformations and working backwards

Worksheet

84 Supp Graphing Tangent and Cotangent (No trans)

Worksheet

85 Supp Graphing Review Worksheet

ASSESSMENTS


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 Asymptotes of a hyperbola, branches of a hyperbola, center of a circle, center of a hyperbola, center of an ellipse, circle, cone, conic section, conjugate axis, directrix, distance formula, ellipse, foci, focus, major/minor axes of an ellipse, parabola, radius of a circle, transverse axis, vertex, vertices of a hyperbola/of an ellipse. (Chapter 10). Sine, cosine, tangent, cosecant, secant, cotangent, adjacent angles, linear pair, vertical angles, opposite, adjacent, initial side, terminal side, vertex, positive angle, negative angle, degree, complementary angles, supplementary angles, minute ('), secont ("), 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. (Chapter17A). Periodic function, period, sinusoid, odd function, even function, amplitude, argument,

vertical asymptote, period 2

b

. (Chapter 17B).

Materials & Texts

Smith, Stanley A., Randall, Charles I., Dossey, John A., Bittinger, Marvin L. (2001). Algebra 2 with Trigonometry. Upper Saddle River, NJ: Prentice‐Hall, Inc. ISBN 0‐13‐051968‐5







MARKING PERIOD FOUR

TRIGONOMETRIC FUNCTIONS AND APPLICATIONS

EXPONENTIAL AND LOGARITHMIC FUNCTIONS

SEQUENCES AND SERIES

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‐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. 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.



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.







Student Objectives

At the end of the fourth marking period, students should be able to successfully manage the following skills:

Recognize and solve problems that require the Law of Sines and/or the Law of Cosines

Solve basic trigonometric equations that require a minimum of algebraic manipulation with some reference to Pythagorean identities

Take inverses of linear functions

Recognize that the exponential and logarithmic functions are inverses of each other

Take the inverse of an exponential function, and conversely take the inverse of a logarithmic function

Graph an exponential and/or a logarithmic function with various transformations

Solve exponential and logarithmic problems using the properties of exponents and the properties of logarithms

Solve specific applications of exponents and logarithms

Recognize and articulate the difference between a sequence and a series

Given a reasonable sequence, be able to write the next three terms in that sequence

Recognize sigma notation, and given specific directions, be able to write out and sum the required terms

Recognize an arithmetic sequence; be able to collect all required terms for its algorithm and be able to construct a particular term from that information.

Recognize an arithmetic series; be able to collect all required terms for its algorithm and be able to construct a particular sum from that information.

Recognize a geometric sequence; be able to collect all required terms for its algorithm and be able to construct a particular term from that information.

Recognize a geometric series; be able to collect all required terms for its partial sum algorithm and be able to construct a particular sum from that information.

Recognize an infinite convergent geometric series; be able to collect all required terms for its algorithm and be able to construct a particular sum from that information.



Find the inverse of a function

Use trigonometric identities

Use cosine, sine, and tangent identities to simplify trigonometric expressions

Use trigonometry to solve problems involving triangles

Solve problems by applying trigonometric equations

Solve equations involving trigonometric expressions

Solve triangle perimeter problems using Law of Sines/Law of Cosines methods

Graph exponential and logarithmic functions

Determine whether the graph of a relation is symmetric with respect to the line y = x

Simplify exponential and logarithmic expressions

find natural and common logarithms and antilogarithms using a calculator, a table, or linear interpolation

Solve exponential and logarithmic equations

Define sequences, define specific terms and general terms of a sequence, and find partial sums

Use sigma notation

Find the first and nth terms and the common difference of an arithmetic sequence

Find specific terms and find partial and infinite sums of a geometric series

Determine whether a geometric series has an infinite sum

Find the common ratio of a series ASSIGNMENTS Chapter 18


86 17.6, 17.8 Algebra Manipulations of Trigonometric Functions (Quotient and Pythagorean Identities)


87 17.6, 17.8 Algebra Manipulations of Trigonometric Functions (Quotient and Pythagorean Identities)

Worksheet


88 18.5 Solving Trigonometric Equations Page 802 #1‐10 all, 15,25

89 18.5 Solving Trigonometric Equations Worksheet

90 18.7 Law of Sines Page 815 #1‐19 odds

91 18.7 Law of Sines Page 815 #21‐33 odds

92 18.8 Law of Cosines Page 815 #1‐17 odds

93 18.8 Law of Cosines Page 815 #8‐24 all


Chapter 12


95 12.1 Inverse Relation and Functions Page 519 #1‐11 odds, 25‐39 odds, 48‐50 all

96 12.2 Exponential and Logarithmic Functions (Incl Natural Log)

Page 525 #1,5,11, 13, 18, 19, 21, 22, 30, 31

97 12.3 Exponential and Logarithmic Relationships (Incl Natural Log)


98 12.4 Properties of Logarithmic Functions (Incl Change of Base)

Page 532 #1‐23 odds 33‐43 odds

99 12.4 Properties of Logarithmic Functions (Incl Change of Base)

Page 532 #2‐24 evens 34‐44 evens

100 12.7 Exponential and Logarithmic Equations

Page 547 #1‐23 odds, 38, 39

101 12.7 Exponential and Logarithmic Equations

Worksheet

102 12.7, 12.8 Applications Exponential and Logarithmic Functions

Page 547 #26‐29 all Page 555 #23‐29 odds, 39


Chapter 14


104 14.1 Sequences and Series Page 615 #1‐7 odds, 13‐24 all


105 14.1 Sigma Notation Page 616 #25‐36 all

106 14.2 Arithmetic Sequences Page 622 #1‐18 all

107 14.2 Arithmetic Series Page 622 #19‐ 35 all

108 14.3 Geometric Sequences Page 628 #1‐14 all

109 14.3 Geometric Series Page 628 #15‐28 all, 31

110 14.4 Infinite Geometric Series Page 632 #1‐13 all

111 Ch 14 Chapter 14 Review Page 641 #1‐19 all

ASSESSMENTS


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 Trigonometric identities (Pythagorean), trigonometric equations, basic identities, reciprocal identities, quotient identities, law of sines, law of cosines. (Chapter 18). Common logarithm, compound interest, base e, exponential decay, exponential equation, exponential function, exponential growth, inverse equation, half life, log, logax, natural logarithm, properties of exponents, properties of logs. (Chapter12). Arithmetic means, arithmetic sequence, arithmetic series, common difference, common ratio, converge, convergent, general term, geometric means, geometric sequence, geometric series,

infinite sequence, infinite series, nth term, partial sums, sequence, series, sigma , term.

(Chapter 14).







Documents

0445 Credits: 1.0 Grades: 11, 12 Unweighted: Prerequisite: … · 2013. 8. 29. · Modified: 06/28/2011 and graph systems of equations and inequalities. 2.8.11.B: Evaluate and simplify