ࡱ> %` p6bjbjNN >,,L-#*N*N*N8bNO<l8NQRF^R^RvRT.TT l"l"l"l"l"l"l$mhApFlWfTfT@WWFl^RvR[l\\\Wx^RvR l\W l\\\^RBQ E3*NXl\c$ql0l\pYPp\p\hTL@U6\vU,UfTTTFlFl<\XTTTlWWWWAGdG Grade Level: 11th and 12th Title: Pre-Calculus Functions & Their Graphs Time Frame: 4 weeks Enduring Understanding: The graph of a function is a visual aid to understanding the function. Essential Questions: What is a function and what is the meaning of its domain and range? What operations may be performed on functions? How are those operations carried out? What situations can be modeled with functions? How can functions be used to model and solve problem situations? Concept/Topic IndicatorsVocabulary Development Assessment StrategiesInstructional Activities/ Extension Activities Resources Functions Graphs  PC-2.1 Carry out a procedure to graph parent functions (including y = xn, y = loga x, y = ln x, y =  EMBED Equation.3 , y = ex, y = ax, y = sinx, y = cos x, y = tan x, y =csc x, y = sec x, and y = cot x).Slope Parent function Quadratic Absolute Value Piecewise functions PC-2.2 Carry out a procedure to graph transformations (including f(x), a f(x), f(x) + d, f(x - c), f(-x), f(b x), |f(x)|, and f(|x|)) of parent functions and combinations of transformations. Transformation Reflection Combination PC-2.3 Analyze a graph to describe the transformation (including f(x), a f(x), f(x) + d, f(x - c), f(-x), f(b x), |f(x)|, and f(|x|)) of parent functions.  Domain and Range PC-2.5 Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = xn, y = loga x, y = ln x, y =  EMBED Equation.3 , y = ex, y = ax, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x). Domain Range Function Vertical Line test  Describe symmetry of even and odd functions PC-2.6 Analyze a function or the symmetry of its graph to determine whether the function is even, odd, or neither. Even Odd Inverse functionsPC-2.8 Carry out a procedure to determine whether the inverse of a function exists. Inverse Horizontal line test One-to-one PC-2.9 Carry out a procedure to write a rule for the inverse of a function, if it exists.  Title: Pre-Cal - Polynomials Time Frame: 4 weeks Enduring Understanding: Knowledge of exponents will be used to manipulate and solve polynomials. Essential Questions: How is factorability of a polynomial determined? How are polynomials divided using synthetic and long division? What are zeros of a functions and what methods are there to find them? What are the important characteristics of a polynomial graph and how are those determined? How can those important characteristics help to solve real world problem situations? Polynomial functions PC-3.1 Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior. PC2.7 Recognize and use connections among significant points of a function (including roots, maximum points, and minimum points), the graph of a function, and the algebraic representation of a function. Quadratic function Axis of symmetry Standard form Vertex form Relative Max Relative Min Absolute Max Absolute Min Root/zero Increasing Decreasing Constant http://www.mastermathmentor.com/ 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-3.5 Analyze given information to write a polynomial function that models a given problem situation. PC-3.6 Carry out a procedure to solve polynomial equations algebraically. PC-3.7 Carry out a procedure to solve polynomial equations graphically.  Polynomial inequalitiesPC-3.10 Carry out a procedure to solve polynomial inequalities algebraically. PC-3.11 Carry out a procedure to solve polynomial inequalities graphically. Test intervalsAppendix B.4 Title: Pre-Calculus Rational functions Time Frame: 2 weeks Enduring Understanding: Rational functions can be represented verbally, numerically, graphically, and analytically to understand patterns and relationships. Essential Questions: What are rational functions? What is asymptotic behavior? What situations are modeled using a rational function and how can these be used to solve problems? Rational FunctionsPC-3.4 Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities). Rational function Asymptotehttp://www.mastermathmentor.com/ PC-3.8 Carry out a procedure to solve rational equations algebraically. PC-3.9 Carry out a procedure to solve rational equations graphically. Title: Pre-Calculus Exponential and Logarithmic Functions Time Frame: 2 weeks Enduring Understanding: Exponential and logarithmic functions are inverse functions. Essential Questions: What are the characteristics of exponential and logarithmic functions? How are exponential and logarithmic functions simplified, solved and manipulated? What situations are modeled with exponential and log equations? How can these functions be used to solve problems? Exponential Functions: PC-4.1 Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior. PC-4.3 Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).Exponential functionhttp://www.mastermathmentor.com/ Logarithmic Functions: PC-4.2 Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior. PC-4.4 Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes).Logarithmic function Natural logarithm Solving exponential and log functionsPC-4.7 Apply the laws of logarithms to solve problems. 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 solve 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 graphicallyProblem situationsPC-4.6 Analyze given information to write an exponential function that models a given problem situation.  Title: Pre-Calculus Trigonometric Functions Time Frame: Time Frame: 4 weeks Enduring Understanding: Trigonometry can be used to determine indirect measurements of lengths and angles to solve a variety of problems. Essential Questions: What are the six trigonometric functions and what do their graphs look like? How are trigonometric equations used to model situations and solve problems? What are the trigonometric identities and how can they be applied to solve equations? Trigonometric FunctionsPC-5.1 Understand how angles are measured in either degrees or radians. PC-5.2 Carry out a procedure to convert between degree and radian measures. PC-5.6 Apply a procedure to evaluate trigonometric expressions. Angle Initial side Terminal side Vertex Standard position Positive angle Negative angle Central angleTrig on a Paper Plate HYPERLINK "http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet_Reduced.pdf" http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet_Reduced.pdf http://www.k12math.com/math-concepts/trigonometry/unit%20circle/part1.htm PC-5.8 Analyze given information to write a trigonometric equation that models a given problem situation involving right triangles.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).Amplitude Period Phase shift Solving Trig EquationsPC-5.10 Carry out a procedure to solve trigonometric equations algebraically. PC-5.11 Carry out a procedure to solve trigonometric equations graphically.Problem solvingPC-5.7 Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.Inverse Trig FunctionsPC-5.13 Apply a procedure to graph the inverse functions of sine, cosine, and tangentInverse trig functionPolar CoordinatesPC-5.3 Carry out a procedure to plot points in the polar coordinate system. Polar coordinate system Pole Polar axis Directed angle Directed distanceLaw of sines and cosinesPC-5.12 Apply the laws of sines and cosines to solve problems. Area of a trianglePC-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.Solve problemsPC-5.15 Carry out a procedure to compute the slope of a line when given the angle of inclination of the line.Angle of inclination Title: Conic Sections Time Frame: 2 weeks Enduring Understanding: Conic sections can be identified and graphed from their equations. Essential Questions: What are the conics? How are they formed? What are the differentiating characteristics of each conic? What are the applications of the conics in our world? CirclesPC-6.1 Carry out a procedure to graph the circle whose equation is the form  EMBED Equation.3 . 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. PC-6.3 Apply a procedure to calculate the coordinates of points where a line intersects a circle.Algebra II McDougal Littell Section 10.3EllipsePC-6.4 Carry out a procedure to graph the ellipse whose equation is the form  EMBED Equation.3 .Algebra II McDougal Littell Section 10.4HyperbolaPC-6.5 Carry out a procedure to graph the hyperbola whose equation is the form  EMBED Equation.3 .Algebra II McDougal Littell Section 10.5ParabolaPC-6.6 Carry out a procedure to graph the parabola whose equation is the form  EMBED Equation.3 .  Algebra II McDougal Littell Section 10.2Course Assessment Houghton Mifflin Test Generator V 7.0 (provided with textbook)Course Resources http://www.mastermathmentor.com/  HYPERLINK "http://college.cengage.com/mathematics/larson/precalculus/6e/students/digital_lessons.html" http://college.cengage.com/mathematics/larson/precalculus/6e/students/digital_lessons.html http://www.picrust.com/precalculus.htm  HYPERLINK "http://itech.pjc.edu/falzone/course/1105handouts.htm" http://itech.pjc.edu/falzone/course/1105handouts.htm  HYPERLINK "http://education.ti.com/educationportal/activityexchange/activity_list.do" http://education.ti.com/educationportal/activityexchange/activity_list.do  HYPERLINK "http://www.math.cornell.edu/~numb3rs/" http://www.math.cornell.edu/~numb3rs/ http://mathbits.com/      Mathematics Curriculum Map PAGE   FILENAME Precalculus 8/2/10 DATE \@ "M/d/yyyy"  300 South Catawba Street, Lancaster SC 29720   PAGE - 1 -   !%1>LQST]^fgh~$ Ǻעגׂpl^PhhJ5OJQJ^JhsJph~ 5OJQJ^Jh[u#h~ h~ 5B*OJQJ\phhh[u5>*OJQJ^JhTOh[u5>*OJQJ^JhJ5OJQJ^Jh[u5>*OJQJ^Jh[u5H*OJQJ^JhP)h[u5H*OJQJ^Jh[u5OJQJ^JhsJph[u5OJQJ^JhZh[u5>*OJQJ^JRSgh ! 7 Q f g q $$Ifa$gdlzz  gd#D  gd[ugd~ gd[uL5o6$ x   7 e f p q r s } ~ Ϳ{wogc_[_[_S_hlzzh0H6h Eoh0HhvhlzzhM:5hlzzh7'5h7'hlzzh0H5hM:hlzzh{ d5OJQJ^Jhlzzh95OJQJ^JhlzzhM:5OJQJ^Jhlzzh7x5OJQJ^Jhlzzh)5OJQJ^JhsJphsJp5hh{ d5OJQJ^JhhJ5OJQJ^Jhh[u5OJQJ^J q r s } ~ 4.%% $Ifgd0H$Ifkd$$Ifl4ֈp!x-(AIH d t0644 laytlzz~ 7 n     $If           . / 0 1 3 4 5 G I J K M N Q R S U V \ ] _ ` g h j k l ~ 辱hsJphlzzh0H6H*jhlzzh0HEHUj*5O h0HUVjh0HUh Eohlzzh0HB*phhlzzh0HH*h0Hhlzzh0HH*hlzzh0H6h7Q@     J f g A [ \ | OPSTUWX^_`acdjkmnqrͽͲ͉͠hlzzh0H6H*jhlzzh0HEHU#jSI hlzzh0HCJUVaJjh=qsh0HUhlzzh0HH*hlzzh0HH* h=qsh0Hhlzzh7'5hlzzh0H5hlzzh0H6h0Hh)hhM:h06     5////$Ifkd$$Iflֈp!x-(AIH d t0644 laytlzz f $If 88$If^8`gdlzz 5////$Ifkd$$Iflֈp!x-(AIH d t0644 laytlzz [  88$If^8`gdlzz$If 5////$Ifkd$$Iflֈp!x-(AIH d t0644 laytlzz ?3GPWXmxy~ ֽ⹵h"C5>*OJQJ^JhL< hxch Eohlzzh495hlzzh0HOJQJ^Jhlzzh0H5h0h0Hhlzzh0H6H* h=qsh0Hhlzzh0H6? 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