Honors Curriculum Pacing Guide

PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 The mathematical processes provide the framework for teaching, learning, and assessing in...
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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013

The mathematical processes provide the framework for teaching, learning, and assessing in all high school mathematics core courses. Instructional programs should be built around these processes. Standard PC-6:

The student will demonstrate through the mathematical processes an understanding of the behavior of conic sections both geometrically and algebraically.

Indicators: PC-1.1

Communicate knowledge of algebraic and trigonometric relationships by using mathematical terminology appropriately.

PC-1.2

Connect algebra and trigonometry with other branches of mathematics.

PC-1.3

Apply algebraic methods to solve problems in real-world contexts.

PC-1.4

Judge the reasonableness of mathematical solutions.

PC-1.5

Demonstrate an understanding of algebraic and trigonometric relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

PC-1.6

Understand how algebraic and trigonometric relationships can be represented in concrete models, pictorial models, and diagrams.

PC-1.7

Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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Copyright © July 1, 2012

PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 2

Copyright © July 1, 2012

PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 First Nine Weeks Duration

Day

Objective: The student will be able to…

Course Indicator SC PC-5.1 CCSS F-TF.3

Unit 1 – Introduction to Trigonometry 11 days

1

2

Draw and recognize positive and negative angles in standard position using radian measure and give the quadrant of the terminal side.

Convert radian measure to degree measure and vice versa.

Standard Understand how angles are measured in either degrees or radians. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for /3,  /4, and  /6, and use the unit circle to express the values of sine, cosine, and tangent for  – x,  + x, and 2 – 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.

SC PC-5.1

Understand how angles are measured in either degrees or radians.

SC PC-5.2

Carry out a procedure to convert between degree and radian measures.

CCSS F-TF.3

(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for /3,  /4, and  /6, and use the unit circle to express the values of sine, cosine, and tangent for  – x,  + x, and 2 – 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.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 First Nine Weeks

Unit 1 – Introduction to Trigonometry 11 days

Duration

Day

3

4-7

Objective: The student will be able to…

Course Indicator SC PC-5.1

Understand how angles are measured in either degrees or radians.

CCSS F-TF.3

(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for /3,  /4, and  /6, and use the unit circle to express the values of sine, cosine, and tangent for  – x,  + x, and 2 – 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. Apply a procedure to evaluate trigonometric expressions.

Find the length of an arc and the area of a sector of a circle

Identify the angles, in degrees & radians, on the unit circle and find the exact values of all 6 trigonometric functions for each angle.

8

Use reference angles to determine the terminal point P(x,y) on the unit circle for a given angle.

9

Use a calculator to find trigonometric values of any angle

10

Unit Review

11

Unit Test

Standard

SC PC-5.6 CCSS F-TF.3

(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for /3,  /4, and  /6, and use the unit circle to express the values of sine, cosine, and tangent for  – x,  + x, and 2 – 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.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 4

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 First Nine Weeks

Unit 2 – Applications of Trigonometric Functions on Right Triangles 7 days

Duration

Day

Objective: The student will be able to…

Course Indicator

Standard

12-13

Solve right and isosceles triangles using trigonometric ratios.

PC-5.8

Analyze given information to write a trigonometric equation that models a given problem situation involving right triangles.

14-15

Solve word problems using the angles of elevation and depression.

PC-5.8

Analyze given information to write a trigonometric equation that models a given problem situation involving right triangles.

16-17

Find the trigonometric function values of angles whose terminal side passes through a certain coordinate.

PC-5.6

Apply a procedure to evaluate trigonometric expressions.

17-18

Given a trigonometric value, find the quadrant and values of the other five trigonometric functions.

PC-5.6

Apply a procedure to evaluate trigonometric expressions.

Unit Review

Unit Test

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 First Nine Weeks

Unit 3 – Applications of Trigonometric Functions on Oblique Triangles 11 days

Duration

Day

Objective: The student will be able to…

19-21

Use the Law of Sines to solve oblique triangles. Include the ambiguous case.

22

23-24

25

26-27

Course Indicator PC-5.12

Apply the laws of sines and cosines to solve problems.

PC-5.7

Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.

PC-5.12

Apply the laws of sines and cosines to solve problems.

PC-5.12

Apply the laws of sines and cosines to solve problems.

PC-5.7

Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.

PC-5.12

Apply the laws of sines and cosines to solve problems.

PC-5.9

Carry out a procedure to calculate the area of a triangle when given the lengths of two sides and the measure of the included angle.

Use the Law of Sines to solve word problems.

Use the Law of Cosines to solve general oblique triangles.

Use the Law of Cosines to solve word problems

Find the area of triangles given various data sets.

28

Unit Review

29

Unit Test

Standard

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 First Nine Weeks

Unit 4 – Graph Trigonometric Functions 16 days

Duration

Day

30

Objective: The student will be able to…

Sketch the graphs of the sine and cosine functions and state their domain and range.

Course Indicator

Standard

SC PC-5.4

Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

CCSS F-TF.6

(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed

F-TF.7

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes.)

SC PC-5.5 CCSS F-TF.6

(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed

F-TF.7

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 First Nine Weeks

Unit 4 – Graph Trigonometric Functions 16 days

Duration

Day

31

Objective: The student will be able to…

Find the amplitude, period, and phase shifts of sine and cosine graphs to sketch the graph.

Course Indicator

Standard

SC PC-2.1

Carry out a procedure to graph parent functions (including y = sin x, y = cos x).

CCSS F-TF.6

(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed

F-TF.7

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

SC PC-5.4 CCSS F-TF.6

(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed

F-TF.7

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 First Nine Weeks

Unit 4 – Graph Trigonometric Functions 16 days

Duration

Day

32

Objective: The student will be able to…

Write equations of sine and cosine functions when given the graph.

Course Indicator

Standard

SC PC-5.4

Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

CCSS F-TF.6

(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed

F-TF.7

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes.)

SC PC-5.5 CCSS F-TF.6

(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed

F-TF.7

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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Copyright © July 1, 2012

PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 First Nine Weeks Duration

Day

Unit 4 – Graph Trigonometric Functions 16 days

33

34

Objective: The student will be able to…

Sketch the graph of secant and cosecant functions and state their domain and range.

Sketch the graph of tangent and cotangent functions and state their domain and range.

Course Indicator

Standard

SC PC-2.1

Carry out a procedure to graph parent functions (including y = sin x, y = cos x).

PC-5.4

Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

PC-5.5

Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes.)

CCSS F-TF.6

(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed

F-TF.7

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

35

Graph the inverse trigonometric functions and state their domain and range. Write the restricted ranges for all inverse trigonometric functions.

PC-5.13

Apply a procedure to graph the inverse functions of sine, cosine, and tangent.

36

Evaluate expressions using inverse trigonometric functions.

PC-5.6

Apply a procedure to evaluate trigonometric expressions.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 First Nine Weeks

Unit 4 – Graph Trigonometric Functions 16 days

Duration

Day

Objective: The student will be able to…

37

Solve problems using the inverse trigonometric functions. (ex: Arcsin(cos(5/13))

38

Unit Review

39

Unit Test

40-44

45

Course Indicator

PC-5.6

Standard

Apply a procedure to evaluate trigonometric expressions.

Exam Review 1st Nine Weeks Exam

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 First Nine Weeks

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Second Nine Weeks

Unit 5 – Trigonometric Identities 13 days

Duration

Day

Objective: The student will be able to…

SC PC-5.14

46-48

Prove identities involving reciprocal and Pythagorean identities.

49-51

Proving more difficult trigonometric identities.

52-53

Solve problems and prove identities involving addition formulas

54-56

Solve problems and prove identities involving double and half-angle formulas.

57

Unit Review

58

Unit Test

Course Indicator

CCSS F-TF.9

Standard Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities. (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Second Nine Weeks

Duration

Day

Unit 6 – Solving Trig Equations 11 days

59-60

61-63

Objective: The student will be able to…

Course Indicator

Standard

PC-5.10

Carry out a procedure to solve trigonometric equations algebraically.

PC-5.11

Carry out a procedure to solve trigonometric equations graphically.

PC-5.10

Carry out a procedure to solve trigonometric equations algebraically.

PC-5.11

Carry out a procedure to solve trigonometric equations graphically.

PC-5.14

Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities.

Solving basic trigonometric equations.

Solve trigonometric equations that involve the use of identities.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 14

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Second Nine Weeks Duration

Day

Unit 6 – Solving Trig Equations 11 days

64-66

67

Objective: The student will be able to…

Course Indicator

Standard

PC-5.10

Carry out a procedure to solve trigonometric equations algebraically.

PC-5.11

Carry out a procedure to solve trigonometric equations graphically.

PC-5.10

Carry out a procedure to solve trigonometric equations algebraically.

PC-5.11

Carry out a procedure to solve trigonometric equations graphically

Solve trigonometric equations that involve the use of the quadratic equation.

Solve trigonometric equations graphically with the graphing calculator.

68

Unit Review

69

Unit Test

70

Exam Review

71

Second Nine Weeks Exam

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Second Nine Weeks

Unit 7 – Vectors and Parametrics 9 days

Duration

Day

Objective: The student will be able to…

72

Graph parametric equations over a specified interval for the parameter.

73-74

Write “x-y” equation for the set of parametric equations by removing the parameter.

75-76

Determine the magnitude and direction of vectors.

77-78

Write vectors in both component form and as the linear combination of the standard unit vector.

79-80

Find the slope of the line given the angle of inclination.

81

Unit Review

82

Unit Test

Course Indicator

Standard

CCSS N-VM.1

(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitude (e.g., v, |v|, ||v||, v).

N-VM.2

(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

N-VM.3

(+) Solve problems involving velocity and other quantities that can be represented by vectors.

SC PC-5.15

Carry out a procedure to compute the slope of a line when given the angle of inclination of the line.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Second Nine Weeks

Duration

Day

Unit 8 – Polar Coordinates 10 days

83

84-85

Objective: The student will be able to…

Course Indicator

Standard

Plot points in the polar coordinate system. Use the polar coordinate system to draw the graphs of polar equations. PC-5.3

86-87

Change polar coordinates to rectangular coordinates and vice-versa.

88-89

Write polar equations as rectangular equations and vice-versa.

Carry out a procedure to plot points in the polar coordinate system.

Unit Review

90

Unit Test

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Second Nine Weeks

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Third Nine Weeks

Duration

Day

Unit 9 – Conic Sections 10 days

91

Objective: The student will be able to…

Write the general and standard forms of the equations of circles and graph it.

Course Indicator SC PC-6.1

Carry out a procedure to graph the circle whose equation is of the form (x-h)2 + (y-k)2 = r2.

PC-6.2

Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle.

CCSS G-GPE.3

(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

SC PC-6.4 92-93

Write the general and standard forms of the equations of ellipses and graph it.

CCSS G-GPE.3 SC PC-6.5

94-95

Write the general and standard forms of the equations of hyperbolas and graph it.

Standard

CCSS G-GPE.3

Carry out a procedure to graph the ellipse whose equation is of the form

 x  h 2   y  k 2 a2

b2

 1.

(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. Carry out a procedure to graph the hyperbola whose equation is of the form

 x  h 2   y  k 2 a2

b2

 1.

(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Third Nine Weeks Duration

Day

Unit 9 – Conic Sections 10 days

96

Objective: The student will be able to…

Write the general and standard forms of the equations of parabolas and graph it.

Course Indicator

Standard

SC PC-6.6

Carry out a procedure to graph the parabola whose

CCSS G-GPE.3

(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

equation is of the form y  k  a  x  h  . 2

SC PC-6.1

Carry out a procedure to graph the circle whose equation is of the form (x-h)2 + (y-k)2 = r2.

PC-6.4

Carry out a procedure to graph the ellipse whose equation is of the form

97

Recognize the graphs & equations of all conic sections

PC-6.5

a2

b2

 1.

Carry out a procedure to graph the hyperbola whose equation is of the form

PC-6.6

 x  h 2   y  k 2  x  h 2   y  k 2 a2

b2

 1.

Carry out a procedure to graph the parabola whose equation is of the form y  k  a  x  h  . 2

CCSS G-GPE.3

(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 20

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Third Nine Weeks

Unit 9 – Conic Sections 10 days

Duration

Day

98

Objective: The student will be able to…

Find points of intersection between quadratics, lines, and conics.

99

Unit Review

100

Unit Test

Course Indicator

Standard

SC PC-6.3

Apply a procedure to calculate the coordinates of points where a line intersects a circle.

CCSS A-REI.8

(+) Represent a system of linear equations as a single matrix equation in a vector variable.

A-REI.9

(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 x 3 or greater).

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Third Nine Weeks

Unit 10 – Linear and Quadratic Functions 10 days

Duration

Day

Objective: The student will be able to…

101

Write equations of and graph linear functions, including parallel, perpendicular, horizontal and vertical lines.

102-103

Graph quadratic functions given various forms and write a quadratic function given a graph

104

Factoring Quadratics

105

Solve Quadratics by Factoring

106

Computing and simplifying imaginary numbers.

107

Solve quadratic equations (including imaginary roots) by quadratic formula

108

Solve quadratic word problems

109

Unit Review

110

Unit Test

Course Indicator

Standard

PC-3.1

Carry out a procedure to graph quadratic and higherorder polynomial functions by analyzing intercepts and end behavior.

PC-3.6

Carry out a procedure to solve polynomial equations algebraically.

PC-3.7

Carry out a procedure to solve polynomial equations graphically.

PC-3.5

Analyze given information to write a polynomial function that models a given problem situation.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Third Nine Weeks

Duration

Day

Unit 11 – Polynomial Functions 12 days

111-113

114

115-118

Objective: The student will be able to…

Course Indicator

Standard

PC-2.1

Carry out a procedure to graph parent functions (including y = xn).

PC-3.1

Carry out a procedure to graph quadratic and higherorder polynomial functions by analyzing intercepts and end behavior.

PC-3.2

Apply the rational root theorem to determine a set of possible rational roots of a polynomial equation.

PC-3.3

Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros.

PC-3.6

Carry out a procedure to solve polynomial equations algebraically.

PC-3.7

Carry out a procedure to solve polynomial equations algebraically.

Recognize higher order polynomial functions, sketch parent graphs to show patterns of graphs of other polynomials and their end behavior.

Dividing Polynomials

Use synthetic division/substitution to find the zeros of a polynomial. Use these and patterns to sketch the polynomial. To write a polynomial function given linear factors or a graph. (Rational Root Theorem)

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 23

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Third Nine Weeks

Unit 11 – Polynomial Functions 12 days

Duration

Day

119-120

Objective: The student will be able to…

Course Indicator

Standard

PC-3.10

Carry out a procedure to solve polynomial inequalities algebraically.

PC-3.11

Carry out a procedure to solve polynomial inequalities graphically.

Solve polynomial inequalities

121

Unit Review

122

Unit Test

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Third Nine Weeks

Duration

Day 123

Laws of exponents

124

Simplifying rational exponents

125-126

13 days

127 Unit 12 - Exponents

Objective: The student will be able to…

128

Advanced simplifying – include factoring with rational exponents

Graphs of exponential equations – determine the domain & range.

Unit Review

130

Unit Test

135

Standard

PC-4.5

Apply the laws of exponents to solve problems involving rational exponents.

PC-4.8

Carry out a procedure to solve exponential equations algebraically.

PC-4.9

Carry out a procedure to sole exponential equations graphically.

PC-2.1

Carry out a procedure to graph parent functions (including y=ax and y=ex).

PC-2.5

Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y=ax and y=ex).

PC-4.3

Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).

Solve exponential equations with like bases

129

131-134

Course Indicator

Exam Review 3rd Nine Weeks Exam

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Third Nine Weeks

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Fourth Nine Weeks Duration

Day

Unit 13 – Logarithmic Functions 12 days

136

137

Objective: The student will be able to…

Find the inverse of a function, sketch and give its domain and range.

Introduce logarithmic function as the inverse of the exponential function.

Course Indicator

Standard

PC-2.1

Carry out a procedure to graph parent functions (including y  log a x , y  ln x ).

PC-2.5

Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y  log a x , y  ln x ).

PC-2.8

Carry out a procedure to determine whether the inverse of a function exists.

PC-2.1

Carry out a procedure to graph parent functions (including y=ax and y=ex).

PC-2.5

Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y=ax and y=ex).

PC-2.8

Carry out a procedure to determine whether the inverse of a function exists.

PC-4.4

Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).

CCSS F-IF.7d

(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 27

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PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Fourth Nine Weeks Duration

Day

Unit 13 – Logarithmic Functions 12 days

138

139-140

141-143

Objective: The student will be able to…

Course Indicator

Standard

PC-2.8

Carry out a procedure to determine whether the inverse of a function exists.

PC-4.5

Apply the laws of exponents to solve problems involving rational exponents.

PC-4.5

Apply the laws of exponents to solve problems involving rational exponents.

PC-4.7

Apply the laws of logarithms to solve problems.

PC-4.8

Carry out a procedure to solve exponential equations algebraically.

PC-4.9

Carry out a procedure to sole exponential equations graphically.

PC-4.10

Carry out a procedure to solve logarithmic equations algebraically.

PC-4.11

Carry out a procedure to solve logarithmic equations graphically.

Write logarithmic expressions as exponential and vice versa

Use the laws of logarithms to simplify or expand logarithmic expressions.

Solve logarithmic and exponential equations with and without calculators including natural logs.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 28

Copyright © July 1, 2012

PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Fourth Nine Weeks

Unit 13 – Logarithmic Functions 12 days

Duration

Day

144-145

Objective: The student will be able to…

Solve exponential growth/decay problems and compound interest problems.

146

Unit Review

147

Unit Test

Course Indicator

Standard

PC-4.6

Analyze given information to write an exponential function that models a given problem situation.

PC-4.8

Carry out a procedure to solve exponential equations algebraically.

PC-4.10

Carry out a procedure to solve logarithmic equations algebraically.

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 29

Copyright © July 1, 2012

PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Fourth Nine Weeks

Unit 14 – Rational Functions and Limits 15 days

Duration

Day

Objective: The student will be able to…

148

Identify and sketch graphs of transformations of absolute value and square root functions from the parent graphs and determine the domain and range of each function.

149

150

151

Identify and sketch parent graphs of transformations of the greatest integer function and determine the domain and range of the function.

Identify and sketch parent graphs of transformations of piecewise functions and determine the domain and range of each function.

Evaluate limits as x approaches infinity, describing the end behavior.

Course Indicator

Standard

PC-2.1

Carry out a procedure to graph parent functions.

PC-2.5

Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions.

PC-2.1

Carry out a procedure to graph parent functions.

PC-2.5

Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions.

PC-2.1

Carry out a procedure to graph parent functions.

PC-2.5

Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions.

PC-3.4

Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 30

Copyright © July 1, 2012

PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Fourth Nine Weeks

Unit 14 – Rational Functions and Limits 15 days

Duration

Day

Objective: The student will be able to…

152

Evaluate limits as x approaches a, describing local behavior.

153-155

Sketch the graph of rational functions using limits.

155-157

158-160

Course Indicator

Standard

PC-3.4

Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

PC-3.4

Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

PC-3.8

Carry out a procedure to solve rational equations algebraically.

PC-3.9

Carry out a procedure to solve rational equations graphically.

Solve rational equations.

Evaluate limits, use properties of limits ATP

161

Unit Review

162

Unit Test

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 31

Copyright © July 1, 2012

PreCalculus CP/Honors – Curriculum Pacing Guide – 2012-2013 Fourth Nine Weeks

Unit 15 – Sequences and Series 18 days

Duration

Day

Objective: The student will be able to…

163

Introduction to sequences and series – looking at patterns inductively

164

Work with factorials and sigma notation.

165

Find the general term of an arithmetic sequence.

166-167 168 169-170

Find the general term of a geometric Sequence. Find the partial sum of a geometric series. Include sigma notation. Find the sum of an infinite series

172

Use the Binomial Theorem or Pascal’s triangle to expand a binomial to a power and find specific terms of an expansion.

173

Unit Review

174

Unit Test

180

Standard

Find the partial sum of an arithmetic series. Include sigma notation.

171

175-179

Course Indicator

End of Course Review 4th Nine Weeks Exam

*AB Schedule needs to cover 2 daily (45 min) sections. Anderson School District Five

Page 32

Copyright © July 1, 2012