precalculus cp/honors curriculum pacing guide 2012 … · precalculus cp/honors – curriculum...

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

*AB Schedule needs to cover 2 daily (45 min) sections.

Anderson School District Five Copyright © July 1, 2012

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).


First Nine Weeks



Duration Day Objective: The student will be able to… Course

Indicator Standard

Un

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

SC PC-5.1

CCSS F-TF.3

F-TF.4

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. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

2 Convert radian measure to degree measure and vice versa.

SC PC-5.1

SC

PC-5.2

CCSS F-TF.3

F-TF.4

Understand how angles are measured in either degrees or radians. Carry out a procedure to convert between degree and radian measures. (+) Use special triangles to determine geometrically

the values of sine, cosine, tangent for /3, /4, and





First Nine Weeks




Indicator Standard

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ntr

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

SC PC-5.1

CCSS F-TF.3

F-TF.4

Understand how angles are measured in either degrees or radians. (+) Use special triangles to determine geometrically




2 – x in terms of their values for x, where x is any

real number. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

4 - 7 Identify the angles, in degrees & radians, on the unit circle and find the exact values of all 6 trigonometric functions for each angle.

SC PC-5.6

CCSS F-TF.3

F-TF.4

Apply a procedure to evaluate trigonometric expressions. (+) Use special triangles to determine geometrically





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


First Nine Weeks




Indicator Standard

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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.


Unit Review

Unit Test


First Nine Weeks




Indicator Standard

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pp

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11

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19-21 Use the Law of Sines to solve oblique triangles. Include the ambiguous case.

PC-5.12 Apply the laws of sines and cosines to solve problems.

22 Use the Law of Sines to solve word problems.

PC-5.7 Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.


23-24 Use the Law of Cosines to solve general oblique triangles.


25 Use the Law of Cosines to solve word problems

PC-5.7 Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.


26-27 Find the area of triangles given various data sets. 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.

28 Unit Review

29 Unit Test


First Nine Weeks




Indicator Standard

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

SC PC-5.4

CCSS F-TF.6

F-TF.7

Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions. (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed (+) 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.

SC PC-5.5

CCSS F-TF.6

F-TF.7

Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes.) (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed (+) 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.


First Nine Weeks




Indicator Standard

Un

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rap

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rig

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om

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

SC PC-2.1

CCSS F-TF.6

F-TF.7

Carry out a procedure to graph parent functions (including y = sin x, y = cos x). (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed (+) 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.

SC PC-5.4

CCSS F-TF.6

F-TF.7



First Nine Weeks




Indicator Standard

Un

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rap

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

SC PC-5.4

CCSS F-TF.6

F-TF.7


SC PC-5.5

CCSS F-TF.6

F-TF.7

Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes.) (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed (+) 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.


First Nine Weeks




Indicator Standard

Un

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rap

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

SC PC-2.1

PC-5.4

PC-5.5

CCSS F-TF.6

F-TF.7

Carry out a procedure to graph parent functions (including y = sin x, y = cos x). Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions. Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes.) (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows it inverse to be constructed (+) 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.

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

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.



First Nine Weeks




Indicator Standard

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


38 Unit Review

39 Unit Test

40-44 Exam Review

45 1st Nine Weeks Exam


First Nine Weeks




Second Nine Weeks




Indicator Standard

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46-48 Prove identities involving reciprocal and Pythagorean identities.

SC PC-5.14

CCSS F-TF.9

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

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


Second Nine Weeks




Indicator Standard

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59-60 Solving basic trigonometric equations.

PC-5.10 Carry out a procedure to solve trigonometric equations algebraically.

PC-5.11 Carry out a procedure to solve trigonometric equations graphically.

61-63 Solve trigonometric equations that involve the use of identities.



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.


Second Nine Weeks




Indicator Standard

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64-66 Solve trigonometric equations that involve the use of the quadratic equation.



67 Solve trigonometric equations graphically with the graphing calculator.


PC-5.11 Carry out a procedure to solve trigonometric equations graphically

68 Unit Review

69 Unit Test

70 Exam Review

71 Second Nine Weeks Exam


Second Nine Weeks




Indicator Standard

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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.

CCSS N-VM.1

N-VM.2

N-VM.3

(+) 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).

(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. (+) Solve problems involving velocity and other quantities that can be represented by 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.

SC PC-5.15

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

81 Unit Review

82 Unit Test


Second Nine Weeks




Indicator Standard

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83 Plot points in the polar coordinate system.

PC-5.3 Carry out a procedure to plot points in the polar coordinate system.

84-85 Use the polar coordinate system to draw the graphs of polar equations.

86-87 Change polar coordinates to rectangular coordinates and vice-versa.

88-89 Write polar equations as rectangular equations and vice-versa.

Unit Review

90 Unit Test


Second Nine Weeks




Third Nine Weeks




Indicator Standard

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

SC PC-6.1

PC-6.2

CCSS G-GPE.3

Carry out a procedure to graph the circle whose equation is of the form (x-h)2 + (y-k)2 = r2. Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle. (+) 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.

92-93 Write the general and standard forms of the equations of ellipses and graph it.

SC PC-6.4

CCSS G-GPE.3

Carry out a procedure to graph the ellipse whose

equation is of the form

2 2

2 21

x h y k

a b

.

(+) 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.

94-95 Write the general and standard forms of the equations of hyperbolas and graph it.

SC PC-6.5

CCSS G-GPE.3

Carry out a procedure to graph the hyperbola whose


2 2

2 21

x h y k

a b

.



Third Nine Weeks




Indicator Standard

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

SC

PC-6.6

CCSS G-GPE.3

Carry out a procedure to graph the parabola whose

equation is of the form 2

y k a x h .


97 Recognize the graphs & equations of all conic sections

SC

PC-6.1

PC-6.4

PC-6.5

PC-6.6

CCSS G-GPE.3

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

Carry out a procedure to graph the ellipse whose


2 2

2 21

x h y k

a b

.

Carry out a procedure to graph the hyperbola whose


2 2

2 21

x h y k

a b

.

Carry out a procedure to graph the parabola whose

equation is of the form 2

y k a x h .



Third Nine Weeks




Indicator Standard

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

SC PC-6.3

CCSS

A-REI.8

A-REI.9

Apply a procedure to calculate the coordinates of points where a line intersects a circle. (+) Represent a system of linear equations as a single matrix equation in a vector variable. (+) 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).

99 Unit Review

100 Unit Test


Third Nine Weeks




Indicator Standard

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Lin

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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

PC-3.1 Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior.

104 Factoring Quadratics

105 Solve Quadratics by Factoring

106 Computing and simplifying imaginary numbers.

107 Solve quadratic equations (including imaginary roots) by quadratic formula

PC-3.6 Carry out a procedure to solve polynomial equations algebraically.

PC-3.7 Carry out a procedure to solve polynomial equations graphically.

108 Solve quadratic word problems PC-3.5 Analyze given information to write a polynomial function that models a given problem situation.

109 Unit Review

110 Unit Test


Third Nine Weeks




Indicator Standard

Un

it 1

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Po

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111-113 Recognize higher order polynomial functions, sketch parent graphs to show patterns of graphs of other polynomials and their end behavior.

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 higher-order polynomial functions by analyzing intercepts and end behavior.

114 Dividing Polynomials

115-118

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)

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.




Third Nine Weeks




Indicator Standard

Un

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119-120 Solve polynomial inequalities

PC-3.10 Carry out a procedure to solve polynomial inequalities algebraically.

PC-3.11 Carry out a procedure to solve polynomial inequalities graphically.

121 Unit Review

122 Unit Test


Third Nine Weeks




Indicator Standard

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Ex

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123 Laws of exponents

124 Simplifying rational exponents

PC-4.5 Apply the laws of exponents to solve problems involving rational exponents. 125-126

Advanced simplifying – include factoring with rational exponents

127 Solve exponential equations with like bases

PC-4.8 Carry out a procedure to solve exponential equations algebraically.

PC-4.9 Carry out a procedure to sole exponential equations graphically.

128 Graphs of exponential equations – determine the domain & range.

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).

129 Unit Review

130 Unit Test

131-134 Exam Review

135 3rd Nine Weeks Exam


Third Nine Weeks




Fourth Nine Weeks




Indicator Standard

Un

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3 –

Lo

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

PC-2.1 Carry out a procedure to graph parent functions

(including logay x , lny x ).

PC-2.5

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

logay x , lny x ).

PC-2.8 Carry out a procedure to determine whether the inverse of a function exists.

137 Introduce logarithmic function as the inverse of the exponential function.

PC-2.1

PC-2.5

PC-2.8

PC-4.4

CCSS F-IF.7d

Carry out a procedure to graph parent functions (including y=ax and y=ex). 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). Carry out a procedure to determine whether the inverse of a function exists. Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes). (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.


Fourth Nine Weeks




Indicator Standard

Un

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138 Write logarithmic expressions as exponential and vice versa

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.

139-140 Use the laws of logarithms to simplify or expand logarithmic expressions.

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.

141-143 Solve logarithmic and exponential equations with and without calculators including natural logs.


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.


Fourth Nine Weeks




Indicator Standard

Un

it 1

3 –

Lo

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rith

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Fu

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144-145 Solve exponential growth/decay problems and compound interest problems.

PC-4.6 Analyze given information to write an exponential function that models a given problem situation.


PC-4.10 Carry out a procedure to solve logarithmic equations algebraically.

146 Unit Review

147 Unit Test


Fourth Nine Weeks




Indicator Standard

Un

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Ra

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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.

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.

149

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



150

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



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

PC-3.4 Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).


Fourth Nine Weeks




Indicator Standard

152 Evaluate limits as x approaches a, describing local behavior.


Un

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Lim

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15

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153-155 Sketch the graph of rational functions using limits.


155-157 Solve rational equations.

PC-3.8 Carry out a procedure to solve rational equations algebraically.

PC-3.9 Carry out a procedure to solve rational equations graphically.

158-160 Evaluate limits, use properties of limits ATP

161 Unit Review

162 Unit Test


Fourth Nine Weeks




Indicator Standard

Un

it 1

5 –

Se

qu

en

ce

s a

nd

Se

rie

s

18

da

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

168 Find the general term of a geometric Sequence.

169-170 Find the partial sum of a geometric series. Include sigma notation.

171 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

175-179 End of Course Review

180 4th Nine Weeks Exam

precalculus cp/honors curriculum pacing guide 2012 … · precalculus cp/honors – curriculum...

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