Pre Calculus Curriculum Guide Grade 11
Objectives	Core Curr. Content Standards	Instructional Activities	Assessment (Cross-curricular) (Multi-cultural)	Resources	GEPA HSPA Terra Nova
PREREQUISITES (10-15 days) The student will be able to:				Pre Calculus-4th Edition, Larson, Ronald E and Robert P. Hostetler, New York, Houghton Mifflin Co, 1997
Review real numbers.	4.2 4.5 4.6 4.11	Pretest to determine weaknesses. Review real numbers. Go over concepts of addressing real numbers, absolute value and distance, algebraic expressions, and basic rules of Algebra. Introduce the graphic calculator.	PP. 10-12 Problems including Budget Variance and Federal Deficit Do "think about it" questions	Pre Calculus: A Graphing Approach 4th Edition Demana, et al, NY, Addison-Wesley, 1997	M. I M. V
Do Exponents and Radicals.	4.3 4.5 4.8 4.11	Review all rules and calculations for exponents, scientific notation, simplifying radicals, and rational exponents. Review rationalizing denominators and numerators. Teach calculator procedure for radicals and calculations.	PP. 22 Group Activity - Johannes Kepler PP. 23-26 with emphasis on "practical" problems #103-110	Study Guide Pre Calculus, Demana, et al, NY, Addison-Wesley, 1997	M. III M. V
Do Polynomials and Factoring.	4.3 4.4 4.11	Define polynomial. Review procedures for operations with polynomials. Demonstrate special types of multiplication and inverse operation of factoring.	P. 35 Group Activity - Three Dimensional View of Special Product PP. 36-40 multiple problems with emphasis on #57-62, 147	Graphing Calculator Resource Manual, Demana, et al, NY, Addison-Wesley, 1997	M. II M. V
				Pre Calculus-Tests Pre-Calculus-Quizzes Pre Calculus Warm Up Masters, Demana, et al, NY, Addison Wesley, 1997
				Pre Calculus with Limits - A Graphing Approach, Larson, Ronald E, Robert P. Hostetler and Bruce H Edwards, NY, Houghton Mifflin Co., 1997 Additional Source Materials
Do fractional expressions.	4.1 4.5 4.11	Discuss and demonstrate finding the domain of an Algebraic Expression, simplifying rational expressions, and operations with rational expressions and compound fractions. Note, problems with certain aspects of the domain when using a Graphing Calculator.	P. 47, Group Activity - Comparing Domains PP. 48-51, Word problems from 81-92		M. V
Solve equations.	4.1 4.3 4.5 4.11	Discuss various type of equations and solutions. Demonstrate solutions for linear equations, quadratic equations, radical equations and absolute value equations. Discuss common types of errors.	Ancient Papyrus - p. 52 Group Activity, p. 60 - Solving Equations PP. 61-64, All word problems		M. III M. V
Do Solving Inequalities.	4.3 4.5 4.6 4.13	Review properties of inequalities. Discuss and demonstrate solutions of linear, quadratic and absolute value inequalities. Use technology to demonstrate absolute value solutions.	Group Activity p. 72, Communicating Mathematically PP. 73-76, Do word problems on topics such as break-even Analysis and Resistors		M. V
Do Errors of Algebra and Calculus.	4.3 4.13 4.15	Demonstrate algebraic errors to avoid. Discuss how these types of errors would impact on calculus problems.	Have students demonstrate solutions to problems and show where there are errors in thinking. Individual project, pp. 83-84		M. I M. V
Do graphical Representation of Data.	4.2 4.12 4.13	Review the cartesian plane including the distance formula midpoint formula and applications of the coordinate plane. Discuss a scatter plot.	Student Activity - Locate a set of real data that can be coincided as ordered pairs - additional project PP. 91-94, multiple problems including word problems		M. IV
Review.		Review all concepts using review exercises, pp. 95-99 - Discuss modeling the volume of a box.	Test Chapter P - Materials from test booklet and other sources		M. I M. III M. V
CHAPTER 1 Functions and Their Graphs
Do Graphs and use Graphing Calculators.	4.2 4.5 4.13	Discuss graphing equations through the use of intercepts and symmetry. Show parallel solutions on graphing calculator. Show graphs of circles.	Technology, p. 106 - Creating of Viewing Rectangle P. 108, Zooming in to find Intercepts; Group Activity, p. 113 PP. 114-117, problems including Data Analysis		M. I M. V
Do lines in the Plane & Slope.	4.3 4.5 4.13 4.17	Define slope parallel and perpendicular lines. Review procedure for finding slope of line and writing linear equations. Discuss appropriate applications. Use technology where appropriate.	P. 126, Group Activity-Modeling Linear Data PP. 127-132, do all application problems. Including Data Analysis		M. I M. II
Do functions.	4.3 4.13 4.15	Review definition of a function. Describe function notation and the domain of a function. Have student pay special attention to concepts of function domain and range for use in Calculus.	Leohand Euler, p. 135 Group Activity, p. 140 PP. 141-146, problems including all practical types such as Cost Analysis		M. II M. V
Analyze the Graphs of Functions.	4.3 4.5 4.13 4.16	Discuss the graph of a function including increasing and decreasing functions, step functions, even and odd functions, and other common functions. Use technology for graphing.	Group Activity, p. 153 and alternate Group Activity, p. 154 (T.E.) PP. 154-158, multiple problems including fluid flow, comparing models and costs of overnight delivery		M. III M. V
Do translations and combinations of functions.	4.3 4.5 4.15 4.17	Using both graphing calculators and pen and paper develop concepts of shifting, reflecting, and stretching of graphs. Discuss arithmetic combinations of functions and compositions of functions.	Group Activity-Analyzing Combinations of Functions, p. 167 PP. 168-172, Word problems concerning graphical reasoning, stopping distance and sales		M. II M. III M. V
Do Inverse Function.	4.3 4.5 4.13 4.16	Define the inverse of a function. Demonstrate the methods for finding the inverse. Show graphically both with and without calculator - the graph of the inverse of a function.	Technology, P. 177-Program for T.E. 8-3 Group Activity-Error Analysis,   p. 179 PP. 180-183, miscellaneous problems and word problems or diesel engine, average miles per gallon and wages		M. III M. V
Do Mathematical Modeling.	4.3 4.5 4.6 4.12	Discuss various technique for fitting models to date. Do direct, inverse and joint variation. Introduce least squares regression.	Hooke’s Law-T.E, p. 185 Technology, p. 189 Group Activity, p. 190 PP. 191-197, Scatter Plots, Regression and other problems		M. I M. IV
Review chapter.	4.2 4.17 4.18	Review all concepts. Focus on Concepts, p 198 Review Exercise pp. 199-201	Chapter Project, pp. 202-203 Test Chapter 1-Test Book, Test Booklet, and other sources		M. I M. II M. V
CHAPTER 2 Polynomial & Rational Functions
Do Quadratic Functions.	4.2 4.5 4.13 4.15	Describe the graph of a quadratic function. Present the standard form of the quadratic function. Show how it conforms to same procedure as functions in chapter. Explain concept of maximums and minimums.	Group Activity-Quadratic Modeling, p. 213 PP. 213-217, Algebraic solutions and problems concerning numerical, graphical, and analytical analysis		M. III M. V
Do Polynomial Functions of higher degree.	4.2 4.5 4.13 4.16	Analyze the graphs of polynomial functions with regard to the leading coefficient test, zero of the function and the intermediate value theorem. Include all types of transformations.	Technology, pp. 224-225 Group Activity, p. 226-Creating Polynomial Functions PP. 227-228, Point of diminishing returns and graphical reasoning		M. III M. V
Do Polynomial and Synthetic Division.	4.3 4.6 4.8 4.13	Review arithmetic long division. Show parallels to polynomial long divisions. Demonstrate synthetic division and its facility in solving equations. Explain the remainder and fact or theorem.	Group Activity - Analyzing a Slant Asymptote PP. 239-241, Graphical Analysis, Data Analysis, and Power of an Engine		M. III M. V
Do Real Zeros of a Polynomial Function.	4.1 4.5 4.13 4.16	Define real zeros. Show how Descartes’ Rule of Signs indicates possible solution. Perform the rational zero test and bounds for the real zeros of a function.	Group Activity - Comparing Real Zeros and Rational Zeros, p. 247 PP. 248-251, Perform indicated tests. Do a graphical analysis		M. II M. III M. V
Do Complex Numbers.	4.1 4.6 4.13	Review the Imaging Unit, Perform operations of add, subtract, and multiplication with Complex Numbers. Demonstrate Complex Conjugate & Division and the Complex Solution of Quadratic Equations.	Show computation on TE 8-3 Group Activity, p. 257 PP. 258-259, Essay Problem 77 Mixture Problems & Average Speed		M. V
Do the Fundamental Theorem of Algebra.	4.3 4.10 4.13 4.18	Technology, p. 261 Define and discuss the fundamental Theorem of Algebra. Existence’s Theorems. Review conjugate pairs and how to factor higher order polynomials.	Group Activity-Factoring, p. 265 PP. 266-268-Factoring, graphical reasoning, Essay #60		M. II M. V
Do Rational Function.	4.3 4.10 4.13 4.16	Introduce concept of rational functions Horizontal, Vertical, and Slant Asymptote. Using all information, sketch the graph of a rational function.	Technology, p. 272 & 277 Group Activity-Analyzing Data, p. 277 PP. 278-281, Page design, concentration of a mixture and date analysis		M. II M. V
Do Partial Fractions.	4.3 4.4 4.13 4.16	Introduce concept of partial fractions. Show how to decompose into a sum from a single fraction. Look at linear decomposition only.	Technology, p. 283 John Bernoulli, p. 285 Group Activity, p. 287 PP. 288-289, Exhaust Temperature		M. I M. V
Review Chapter.	4.2 4.18	Focus on concepts. Review exercise, pp. 291-293 Chapter Project-Graphical approach to funding zeros, p. 295	Test Chapter 2 - Multiple Choice Open Ended Questions		M. I M. II M. III M. IV M. V
CHAPTER 3 Exponential and Logarithmic Functions
Do Exponential Functions and their graphs.	4.3 4.5 4.13 4.16	Define and discuss exponential functions once the Natural Base e. Do graphs of Exponential Functions. Use calculators to evaluate problems.	Exploration, p. 300 Activities, p. 303 TE Group Activity, p. 305 PP. 306-309, Use concepts for graphical analysis, depreciation, once inflation		M. I M. V
Do Logarithmic Functions and their graphs.	4.3 4.5 4.12 4.13	Define a logarithm and discuss the differences between logarithms, common logarithms and the natural logarithm. Show graphs of all functions and practical applications.	Group Activity, p. 316 PP. 317-320, Multiple Problems with emphasis on Modeling- World Population growth ventilation rates and sound density		M. I M. V
Do Properties of Logarithms.	4.3 4.5 4.11	Discuss Change of Base Formula, properties of logarithms and the rewriting of logarithms expressions. Show common errors which may occur. Look at mathematical models.	John Napier, p. 321 Group Activity-Kepler’s Law, p. 324 PP. 325-327, Look at Human Memory Model		M. I M. V
CHAPTER 3 Exponential and Logarithmic Functions
Do Exponential and Logarithmic equations.	4.3, 4.5 4.11, 4.13 4.17	Review the log properties and exponential properties. Show examples of solutions of both types. Use technology to check answers. Show applications using interest.	Group Activity-Comparing Mathematics Model, p. 334 PP. 335-338, To multiple problems Graded assignment #94, p. 338		M. I M. V
Do Exponential and Logarithmic Models.	4.2 4.5 4.11 4.16	Introduce concepts of exponential growth and decay. Go over Gaussian Models and Logistic Growth Models. Investigate Logarithmic Model-All application stressed for calculus.	Group Activity-Comparing Population Models, p. 345 PP. 346-351, As many applications as possible, Essays on p. 351, #72 & 73		M. I M. III M. V
Review Chapter 3.	4.1 4.2 4.18	Do focus on concepts, Review Exercises pp. 353-356 Chapter Test 1-3	Test Chapter 3, Questions from multiple sources Chapter project, pp. 356-357 due in 3 days		M. I M. II M. III M. IV M. V
CHAPTER 4 Trigonometry
Do Radian and Degree Measure.	4.3 4.7 4.9 4.11	Define angle, co-terminal, initial and terminal. What exactly are radians ® relation to degrees - application including arc length. Show calculator change.	Project from, p. 359 (p. 370, #98-99) Group Activity-Degree and Radian Measure PP. 367-370, Problem including all word problems		M. I M. II M. III
Do Trigonometric Functions: The Unit Circle.	4.2 4.5 4.9 4.16	Discuss unit circle. Define trigonometric functions in terms of the unit circle. Evaluate trigonometric with a calculator and develop the concept of domain and period of sine and cosine.	Group Activity-Error Analysis, p. 376 PP. 377-379, Emphasis on problem #55-58, Electrical Circuits		M. II M. V
Do Right Triangle Trigonometry.	4.1 4.3 4.5 4.7 4.13	Define the six trigonometric for right triangles (same as geometry). Develop the Pythagorean Identities from the Pythagorean theorem and definitions of functions. Evaluate trigonometric functions with a calculator.	Group Activity-Evaluating Trigonometry Functions, p. 386 PP. 387-391, All word problems		M. II M. V
Do Trigonometric functions of any angle.	4.3 4.5 4.11 4.13	Review the Cartesian Plane. Define reference angle. Show relationship between angles in first quadrant and angle in other form quadrants.	Group Activity-Patterns in Trigonometric Functions, p. 398 PP. 399-401, Essay question #84		M. II M. V
Do graphs of Sine and Cosine Functions.	4.3 4.5 4.13 4.16	Graph the basic sine and cosine curves. Define the period and amplitude. Using the graphing calculator show translations and shifts of both functions. Show how they are used in Mathematical Modeling.	Group Activity-A sine show (program for TE 83) PP. 410-414, Exploration, p. 414 #91 Data Analysis #93		M. II M. V
Do Graphs of Other Trigonometric Functions.	4.5 4.9 4.11 4.15 4.16	With graphing calculator graph the tangent, cotangent, secant, and cosecant functions. Review domain, range, and period. Show transformation. Discuss damped trigonometric graphs.	Group Activity-Combining Trigonometric Functions, p. 421 PP. 422-426, Essay problems 47-48 #68 Television Coverage #71 Harmonic Motion #374 Approximation		M. II M. V
Do Inverse Trigonometric Functions.	4.3 4.5 4.9 4.16	Define inverse functions-remember one-to-one concept. Emphasize domain and range restrictions used in defining inverse functions. Review compositions of functions. Remind students answers are in radians.	Group Activity-Inverse Functions, p. 433; PP. 434-437, Photography, #84 and 85; Angle of Elevation #87 and Security Patrol #88		M. III M. V
Do Applications and Models.	4.1 4.5 4.7 4.16	Review angle of elevation and depression Problems: involving right triangles, trigonometry and bearings, and harmonic motion.	Group Activity-Radio Waves, p. 443; PP. 444-449, Do all word problems-special emphasis on Harmonic Motion Problems, pp. 49-59		M. II M. III
Review Chapter.	4.2, 4.3 4.5, 4.18	Focus on concepts, p. 450 Review Exercises, pp. 451-453	Chapter Project-Analyzing a graph, pp. 454-455 Test Chapter 4		M. I M. II M. III M. IV M. V
CHAPTER 5 Analytic Trigonometry
Use Fundamental Identities.	4.3 4.13 4.16	Demonstrate how to use the fundamental identities to evaluate trigonometric functions and to simplify trigonometric expressions. Use calculations to check problems.	Daylight House, p. 457-ex. 73-74, p. 473 Group Activity-Remembering Trig Identities, p. 462 PP. 463-465, Do almost all problems		M. II M. V
Verify Trigonometric Identities.	4.3 4.13 4.16	Review the distinctions among expressions, equations, and identities. Review algebraic identities and conditional equations. Verify trigonometric identities.	Group Activity-alternative, p. 470 T.E. PP. 471-473, Do all identities 1-56, 61-64, Rate of Change 73-74		M. II M. V
Solve Trigonometric Equations.	4.3 4.5 4.13 4.15	Review algebraic equations involving quadratics. Solve trigonometric equations in quadratic form, using inverse functions, and involving multiple angles. Remind students to give exact answers instead of decimal approximations.	Group Activity-Equations with no solutions, p. 480 PP. 481-484, Problems 11-56 #57-58 Calculus based #61-62 Graphical Reasoning		M. I M. II M. V
Do Sum and Difference Formulas.	4.3 4.5 4.16	Show that sin (u+v) = sinu + sinv Proof of cos (u+v) - Using formulas to evaluate trigonometric functions Calculus Application and Trig Equations	Hipparchus, p. 486 Group Activity, p. 489 PP. 490-492, representative problems 1-58		M. II M. III M. V
Do Multiple Angles and Product-to-Sum Formulas.	4.3 4.15 4.16	Have students prove double angle formulas. Derive power reducing and half angles. Discuss product-to-sum formulas. Use solution in identities and equations.	Group Activity-deriving an area formula PP. 501-504, Do all problems #80 selected problems-#112 Exploration
Review Chapter.	4.2 4.17 4.18	Focus on concepts, p. 505 Review Exercises, pp. 506-507	Chapter Project, pp. 508-509 Test Chapter 5		M. I M. II M. III M. IV M. V
CHAPTER 6 Additional Topics In Trigonometry
Do Law of Sine.	4.3 4.5 4.7 4.9	Relate to geometry congruence theorems S.A.S., S.S.S., A.S.A., A.A.S. and Ambiguous Case (SSA) find the area of an oblique triangle and other applications with Law of Sines (A.S.A., A.A.S., S.S.A.)	Civil Engineering, p. 511 Alternative Group Activity, p. 517 T.E. Group Activity-Using Law of Sine, p. 517 PP. 518-521, Word problems 25-36		M. II M. IV
Do Law of Cosines.	4.3 4.5 4.7 4.16	Discuss way to solve a triangle given SSS and SAS-Introduce Law of Cosines (Pythagorean Theorem with an addition for oblique triangle) Standard and Alternative Form. To find the area of triangle given three sides by Heron’s Formula.	Group Activity-The Area of a Triangle, p. 526 PP. 527-530, Word problems 21-38 Heron’s Area Formula 41-48		M. I M. II
Do Vectors in the Plane.	4.3 4.11 4.16	Define a vector. Show component form. Representation by directed line segments. Discuss Unit Vectors, vector operations, and applications of vector. Explain direction angles.	William Rowan Hamilton, p. 535 Group Activity, p. 539 PP. 540-544 Word problems Chapter open #89, 90		M. II M. V
Do Vectors and Dot Products.	4.1 4.3 4.5 4.11	Define the dot product of two vectors. Explain the properties of the dot product. Find the angle between two vectors and find vector components omit work	P. 552 Group Activity-the sign of the dot product PP. 553-554 Problems up to 44		M. II M. V
Do DeMoore’s Theorem.	4.3 4.5 4.11 4.13	Review the complex plan. Show the trigonometric form of a complex number. Discuss Multiplication, division, powers and routs of complex numbers. Show how Demorore’s Theorem can be used to solve a polynomial equation.	Group Activity-Euler’s Formula PP. 563-565 as many as necessary in each section-Omit word problems		M. II M. III M. V
Review Chapter.	4.2 4.5 4.17 4.18	Focus on Concepts, p. 566 Review Exercise, pp. 567-570	Chapter Project pp. 570-571 Test Chapter 6		M. I M. II M. III M. IV M. V
CHAPTER 9 Sequences and Probability
Do Sequences and Summation Notation.	4.1 4.4 4.6 4.8	Define a sequence and finding the terms. Define a factorial and evaluating expressions. Define Summation Notation.	Group Activity, p. 715 PP. 716-718 A few of each type		M. III M. V
Do Arithmetic Sequence.	4.1 4.5 4.6	Define an arithmetic series. Common difference-formula for the nth term. Find the sum of a finite arithmetic sequence.	P. 725 Group Activity-Numerical Relationships PP. 726-728-3 or 4 problems each section and word problems 79-84		M. III M. V
Do Geometric Sequence.	4.1 4.5 4.8	Define a geometric sequence. Common ratio. Find the nth term of a geometric sequence. Find the sums of finite and infinite geometric series.	P. 734 Group Activity-An Experiment PP. 735-738 Some of each type		M. I M. III M. V
Do the Binomial Theorem.	4.3 4.5 4.12 4.13	Redo Pascal’s Triangle. Expand for binomial coefficients and binomial expansions-Do the Binomial Theorem Combinations	Group Analysis-Alternate p. 754 TE PP. 755-756 1-48 approximately 2 Exercises 65-68 probability		M. III M. V
Review 4 Selections of Chapter.	4.2, 4.5 4.17, 4.18	Review Exercises, pp. 783-785	Chapter Project 786-787 Test Chapter 9		M. I M. II M. III M. IV M. V
CHAPTER 10 Topics in Analytic Geometry
Ellipses.	4.3 4.5 4.16	Define an Ellipse-face and directrix-major and minor axis. Do standard equation of an Ellipse Application of Elliptical Orbit. Define eccentricity	Solar System, p. 789 Ex. 53-54 p. 816 Group Activity-Graphing Ellipses, p. 812 PP. 813-816 problems-fireplace arch and mountain tunnel		M. V
Do Hyperbolas.	4.3 4.5 4.16	Define hyperbolas. Standard form of equation. Using asymptotes to graph a hyperbole. Do eccentricity of a hyperbola. Classify a comic from its general equation.	Caroline Herschel, p. 823 Group Activity-Sketching Comics, p. 823 PP. 824-825, 1-43 some		M. II M. III M. V
Do Parametric Equations.	4.3 4.5 4.15 4.16	Explain what parametric equations are and their uses. Sketch a plane curve. Eliminate the parameter and find parametric equations for a graph.	Group Activity-Changing the orientation of a curve, p. 841 P. 842, 3-32		M. I M. V
Review Chapter.	4.2 4.5 4.18	Review selections of Chapter 10	Test Chapter 10		M. I M. II M. III M. IV M. V