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Functions, Statistics and Trigonometry (FST) Course Outcome Summary Information Credits 1 Organization Hartford Union High School: Mission/Description Mission Statement: Our mathematics program is designed to enable all students to function successfully in a number related world, to give students a basis to increase their mathematical knowledge and improve their quality of life, and to develop an understanding and appreciation of mathematics and technology. Course Description: This course is designed as a college preparatory course for the student who is not necessarily majoring in a mathematics or science field. Successful completion of this course should prepare the student for Pre-Calculus. The topics will include functions, logarithms, trigonometry, probability, and statistics. The student will be required to have a graphing calculator (TI83 Plus or TI83 recommended. Cost approximately $100.) Textbooks Advanced Mathematical Concepts Units and Timelines Linear Relations and Functions - 10 days Exploring Graphs of Functions - 15 days Solving Polynomial and Rational Functions - 20 days Exploring Conic Sections - 15 days Exploring Exponential and Logarithmic Functions - 15 days Sequences and Series - 15 days The Trigonometric functions - 15 days Graphs and Inverses of the Trigonometric functions - 15 days Trigonometric Identities and Equations - 15 days Vectors and Parametric Equations - 10 days Combinatorics and Probability - 15 days Statistics and Data Analysis - 20 days Core Abilities Analyze divergent views to resolve conflicts. Assess personal goals, values, and motivations. Assume responsibility for own actions. Balance a lifestyle that is safe and healthy. Demonstrate appropriate communication skills. Devise solutions to complex problems. Initiate positive leadership skills. Integrate self awareness and attitudes appropriate in diverse social situations. Organize data into useable forms. Utilize appropriate behaviors and attitudes in the work environment. Utilize technology to improve efficiency. Competencies, Linked Standards, Objectives and Performance Standards 1. Use statistics to describe data sets. Properties Domain: Cognitive Level: Application Difficulty: Medium Importance: Important Linked External Standards WI.MA.A.12.1 Use reason and logic WI.MA.A.12.2 Communicate logical arguments and clearly show why a result does or does not make sense, why the reasoning is or is not valid, and an understanding of the difference between examples that support a conjecture and a proof of the conjecture WI.MA.A.12.3 Analyze non-routine problems and arrive at solutions by various means WI.MA.A.12.4 Develop effective oral and written presentations employing correct mathematical terminology, notation, symbols, and conventions for mathematical arguments and display of data WI.MA.A.12.5 Organize work and present mathematical procedures and results clearly, systematically, succinctly, and correctly WI.MA.A.12.6 Read and understand mathematical texts and other instructional materials, writing about mathematics (e.g., articles in journals), and mathematical ideas as they are used in other contexts WI.MA.B.12.1 Use complex counting procedures such as union and intersection of sets and arrangements (permutations and combinations) to solve problems WI.MA.E.12.1 Work with data in the context of real-world situations WI.MA.E.12.2 Organize and display data from statistical investigations WI.MA.E.12.3 Interpret and analyze information from organized and displayed data when given measures of dispersion, including standard deviation and variance; measures of reliability; and measures of correlation WI.MA.E.12.4 Analyze, evaluate, and critique the methods and conclusions of statistical experiments reported in journals, magazines, news media, advertising, etc. Performance Standards o learner calculates statistics from a data set and display the results in a graph with 75% accuracy. o learner determines the probability that a randomly selected member of a sample lies within a specified number of standard deviations from the mean. o learner determines the standard error of the mean to predict the true mean of a population with a 1% and 5% level of confidence. Learning objectives a. Calculate measures of central tendency and spread for data sets. b. Describe relations between measures of central tendency or measures of spread. c. Use sigma notation to represent a sum, mean, mean deviation, standard deviation or variance. d. Interpret data presented in a frequency distribution. e. Read and interpret histograms, stem-and-leaf plots, and box-and-whisker plots. f. Draw a histogram, frequency polygon, stem-and-leaf plot, and box-and-whisker plot, to display data. g. Use the normal distribution curve to represent data. h. Use samples to make inferences about populations. 2. Describe the nature of graphs by examining transformations, symmetry, continuity, extrema, end behavior, and asymptotes. Properties Domain: Cognitive Level: Comprehension Difficulty: Low Importance: Important Linked External Standards WI.MA.A.12.1 Use reason and logic WI.MA.A.12.4 Develop effective oral and written presentations employing correct mathematical terminology, notation, symbols, and conventions for mathematical arguments and display of data WI.MA.C.12.4 Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity WI.MA.F.12.2 Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways Performance Standards o learner describes how transformations affect important features of graphs and how those effects are represented in the changes in equations with 75% accuracy. o learner analyzes all aspects of a function using appropriate tests with 75% accuracy. Learning objectives a. Describe the symmetries of graphs. b. Identify transformations of the constant, identity, polynomial, square root, absolute value, greatest integer, and rational functions. c. Graph nonlinear inequalities. d. Solve absolute value inequalities. e. Determine the inverse of a function. f. Graph functions and their inverses. g. Determine whether a function is continuous or discontinuous. h. Identify the end behavior of functions . i. Determine whether a function is increasing or decreasing on an interval. j. Find the critical points of a function. k. Use the first and second derivative tests to determine whether a critical point is a maximum, minimum, or inflection point. l. Graph rational functions. m. Determine vertical, horizontal, and slant asymptotes of a function. 3. Solve exponential and logarithmic equations. Properties Domain: Cognitive Level: Application Difficulty: High Importance: Important Linked External Standards WI.MA.A.12.4 Develop effective oral and written presentations employing correct mathematical terminology, notation, symbols, and conventions for mathematical arguments and display of data WI.MA.A.12.5 Organize work and present mathematical procedures and results clearly, systematically, succinctly, and correctly WI.MA.B.12.3 Perform and explain operations on real numbers WI.MA.B.12.4 Select and use appropriate procedures in problem solving situations involving the application of different number systems (natural, integers, rational, and real) WI.MA.B.12.5 Create and critically evaluate numerical arguments presented in a variety of classroom and real-world situations (e.g., political, economic, scientific, social WI.MA.E.12.1 Work with data in the context of real-world situations WI.MA.F.12.1 Analyze and generalize patterns of change (e.g., direct and inverse variation) and numerical sequences, and then represent them with algebraic expressions and equations WI.MA.F.12.2 Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways WI.MA.F.12.3 Solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities WI.MA.F.12.4 Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities Performance Standards o learner applies the properties of logarithms to solve equations with 75% accuracy. Learning objectives a. Find the value of logarithmic expressions. b. Describe properties of exponential and logarithmic functions. c. Graph exponential and logarithmic functions. d. Use e and natural logarithms to solve applied problems. e. Use logarithmic and exponential functions to model data. 4. Use trigonometry to find sides or angles in triangles. Properties Domain: Cognitive Level: Application Difficulty: Medium Importance: Essential Linked External Standards WI.MA.A.12.1 Use reason and logic WI.MA.A.12.3 Analyze non-routine problems and arrive at solutions by various means WI.MA.A.12.4 Develop effective oral and written presentations employing correct mathematical terminology, notation, symbols, and conventions for mathematical arguments and display of data WI.MA.A.12.5 Organize work and present mathematical procedures and results clearly, systematically, succinctly, and correctly WI.MA.C.12.1 Identify, describe, and analyze properties of figures, relationships among figures and relationships among their parts WI.MA.C.12.2 Use geometric models to solve mathematical and real-world problems WI.MA.C.12.4 Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity WI.MA.C.12.5 Identify and demonstrate an understanding of the three ratios used in right-triangle trigonometry (sine, cosine, tangent) WI.MA.D.12.3 Determine measurements indirectly WI.MA.F.12.4 Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities Performance Standards o learner uses properties of trigonometry to solve for missing dimensions in a triangle with 75% accuracy. Learning objectives a. Convert decimal degree measures to degrees, minutes, and seconds and vice versa. b. Find sines, cosines, and tangents of acute angles using the trigonometric ratios. c. Find missing side and/or angle measures of a triangle using the trigonometric ratios. d. Solve problems involving the Law of Sines and the Law of Cosines. e. Determine the area of a triangle given the measure of two sides and the included angle, the measure of two angles and a side, or the measure of the three sides. 5. Solve problems involving circular functions and their graphs. Properties Domain: Cognitive Level: Application Difficulty: Medium Importance: Important Linked External Standards WI.MA.C.12.4 Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity WI.MA.F.12.4 Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities Performance Standards o learner solves equations involving circular functions with 75% accuracy. o learner graphs the 6 circular functions and be able to graph their image under a linear transformation with 75% accuracy. o learner uses sinusoidal functions to solve problems with 75% accuracy. Learning objectives a. Identify the amplitude, period, frequency, vertical translation, and phase shift of circular functions. b. Evaluate inverse and reciprocal circular functions. c. State properties of inverse and reciprocal circular functions. d. Graph or identify graphs of circular functions. e. Graph or identify graphs of inverse functions. f. Model real-world data using sine and cosine functions. 6. Use the unit circle to find the values of the trigonometric functions for any angle. Linked External Standards WI.MA.B.12.4 Select and use appropriate procedures in problem solving situations involving the application of different number systems (natural, integers, rational, and real) WI.MA.C.12.2 Use geometric models to solve mathematical and real-world problems WI.MA.C.12.4 Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity WI.MA.C.12.5 Identify and demonstrate an understanding of the three ratios used in right-triangle trigonometry (sine, cosine, tangent) Performance Standards o learner labels the unit circle with 100% accuracy. o learner uses properties of the unit circle to find the value of the six trigonometric ratios with 75% accuracy. Learning objectives a. Identify angles that are conterminal. b. Identify the key points on the unit circle. c. Convert between degrees and radians. d. Find the values of the six trigonometric functions of an angle in standard position given a point on its terminal side. e. Identify the number of degrees or radians in a given number of rotations. 7. Solve problems using combinatorics and probability. Properties Domain: Cognitive Level: Application Difficulty: High Importance: Essential Linked External Standards WI.MA.A.12.1 Use reason and logic WI.MA.B.12.1 Use complex counting procedures such as union and intersection of sets and arrangements (permutations and combinations) to solve problems WI.MA.E.12.1 Work with data in the context of real-world situations WI.MA.E.12.5 Determine the likelihood of occurrence of complex events Performance Standards o learner applies the properties and formulas for counting to solve probability problems with 75% accuracy. Learning objectives a. Solve problems related to the Basic Counting Principle. b. Distinguish between dependent and independent events. c. Use combinations to compute the number of ways of selecting objects. d. Solve problems involving permutations and/or combinations. e. Solve problems involving permutations with repetitions. f. Solve problems involving circular permutations. g. Find the probability of an event. h. Find the odds for an event. i. Find the probability of independent and dependent events. j. Identify mutually exclusive events. k. Find the probability of mutually exclusive and inclusive events. l. Find the probability of an event given the occurrence of another event. 8. Calculate or approximate zeros of polynomial functions. Properties Domain: Cognitive Level: Application Difficulty: Medium Importance: Essential Linked External Standards WI.MA.C.12.4 Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity WI.MA.F.12.2 Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways WI.MA.F.12.3 Solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities Performance Standards o learner uses the techniques of solving polynomials to approximate all the zeroes of a function with 75 % accuracy. Learning objectives a. Determine roots of polynomial equations. b. Apply the Fundamental Theorem of Algebra. c. Solve quadratic equations by factoring and using the Quadratic Formula. d. Describe the roots of a quadratic function using the discriminant. e. Find factors using the Remainder and Factor Theorems. f. Apply the Rational Root Theorem to identify all possible rational roots. g. Determine the number of positive and negative real roots of a function. h. Approximate the real zeros of a polynomial function. i. Solve rational equations and inequalities. j. Decompose a fraction into partial fractions. k. Solve radical equations and inequalities. l. Model real-world data using polynomial functions. m. Interpret real-world data using polynomial functions. 9. Examine the conic sections. Properties Domain: Cognitive Level: Analysis Difficulty: High Importance: Important Linked External Standards WI.MA.A.12.1 Use reason and logic WI.MA.C.12.1 Identify, describe, and analyze properties of figures, relationships among figures and relationships among their parts WI.MA.C.12.2 Use geometric models to solve mathematical and real-world problems WI.MA.C.12.4 Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity WI.MA.F.12.2 Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways WI.MA.F.12.3 Solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities Performance Standards o learner identifies a conic section from its graph or equation with 75% accuracy. o learner writes an equation to represent a graph of a conic section with 75% accuracy. o learner solves a system of second degree equations with 75% accuracy. Learning objectives a. State the properties of each of the conic sections. b. Use properties of conic sections (circles, ellipses, hyperbolas, and parabolas) to write equations describing them. c. Rewrite the general equations of conic sections in standard form. d. Identify conic sections by their equations in standard form. e. Identify conic sections by their equations in general form. f. Graph the conic sections. g. Graph systems of second degree equations and inequalities. h. Solve systems of second degree equations and inequalities. 10. Study the polar coordinate system. Properties Domain: Cognitive Level: Analysis Difficulty: Low Importance: Essential Performance Standards o learner converts between the rectangular coordinate system and the polar coordinate system by using the conversion formulas with 75% accuracy. o learner graphs in the polar coordinate system with 75% accuracy. Learning objectives a. Graph points in polar coordinates. b. Determine the distance between two points with polar coordinates. c. Graph polar equations. d. Convert between polar and rectangular coordinates. e. Write the polar from of a linear equation. f. Graph the polar form of a linear equation. 11. Calculate powers and roots of complex numbers. Properties Domain: Cognitive Level: Application Difficulty: Medium Importance: Useful Performance Standards o learner finds powers and roots of complex numbers with 75% accuracy. Learning objectives a. Add, subtract, multiply and divide complex numbers. b. Graph complex numbers. c. Represent complex numbers in different forms. d. Explore geometric relationships in the complex plane. e. Find the product and quotient of complex numbers in polar form. f. Use De Moivre's Theorem to find powers and roots of complex numbers in polar form. 12. Perform operations with and solve problems using vectors. Linked External Standards WI.MA.D.12.2 Select and use tools with appropriate degree of precision to determine measurements directly within specified degrees of accuracy and error (tolerance) WI.MA.D.12.3 Determine measurements indirectly Performance Standards o learner performs operations and solves problems using vectors with 75% accuracy. Learning objectives a. Find equal, opposite, and parallel vectors. b. Add and subtract vectors geometrically. c. Find ordered pairs that represent vectors. d. Add, subtract, multiply, and find the magnitude of vectors algebraically. e. Add, subtract,and find the magnitude of the vectors in three-dimensional space. f. Find the inner and cross products of two vectors. g. Determine whether two vectors are perpendicular. h. Solve problems using vectors and trigonometry.

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Advanced Algebra, Problem Solving, Algebra II, graphing calculator, Algebra 2, Advanced Placement, discrete mathematics, Circular Functions, coordinate geometry, UCSMP Geometry

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posted: | 4/25/2011 |

language: | English |

pages: | 11 |

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