COURSE OF STUDYIntermediate algebra, analytic geometry, and trigonometry are integrated with other...

COURSE OF STUDY MATHEMATICS

Name of Course: Pre-Calculus Length of Course: 180 Days Course Number: 340 Type of Offering: Academic/Elective Grade Level: 12 Credit Value: 1 credit Prerequisite/s: Algebra 1, Geometry and Algebra 2 Minutes: 7200 COURSE DESCRIPTION: Intermediate algebra, analytic geometry, and trigonometry are integrated with other precalculus topics to prepare the student for college mathematics. This course is intended for the student who has successfully completed two years of algebra and one year of plane geometry. TEXBOOK/S (if applicable) Title: Precalculus, 5th Edition

Publisher: McDougal Littell Company

Copyright: 2001 OTHER RESOURCES: Textbook Ancillary Materials

Teacher Generated Materials

Calculator Applications

Computer Software Applications

Internet-Based Applications

12/13/10

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Prerequisites Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Content Teaching Method(s) Materials & Resources Assessment

Standard: 2.2.11.A. Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations. Anchor: M11.A.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, exponents and scientific notation). Standard: 2.1.11.A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms). Anchor: M11.A.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots,

Real Numbers Exponents and Radicals

-Lecture/Demonstration -Question/Answer -Brainstorming -Discussion -Journaling -Cooperative Learning -Exercises -Practice/Application

-Textbook- Larson, Hostetler, Precaculus, fifth edition, Houghton Mifflin, 2001 -Teacher Generated Materials -Calculator Applications -Computer Applications -Internet-Based Applications

-Homework -Tests -Quizzes -Projects -Teacher observation/student participation

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Prerequisites Instructional Time: 800 minutes exponents and scientific notation). Standard: 2. 2.8.11.D Formulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and non-routine problem situations. Anchor: M11.D.2.2.2 Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is not equal to 0). Standard: 2.2.11A Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations. Anchor: M11.D.2.2.2 Factor

Polynomials and Factoring Rational Expressions

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Prerequisites Instructional Time: 800 minutes algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is not equal to 0). Standard: 2.8.11.N Solve linear, quadratic and exponential equations both symbolically and graphically. Anchor: M11.D.2.1.3 Write, solve and/or apply a linear equation (including problem situations). Standard: 2.8.11.N Solve linear, quadratic and exponential equations both symbolically and graphically. Anchor: M11.D.2.1.1 Solve compound inequalities and/or graph their solution sets on a number line (may

Solving Equations Solving Inequalities

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Prerequisites Instructional Time: 800 minutes include absolute value inequalities). Standard: 2.10.11.B Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. Anchor: M11.C.3.1.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane (formula provided on the reference sheet).

Graphical Representations of Data

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Functions and Their Graphs Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Standard: 2.8.11K Select, justify and apply an appropriate technique to graph a linear function in two variables, including slope-intercept, x- and y-intercepts, graphing by transformations and the use of a graphing calculator. Anchor: M11.D1-Demonstrate an understanding of patterns, relations & functions (2.8.11Q, 2.8.11A, 2.8.11O) M11.D2-Represent and/or analyze mathematical situations using numbers, symbols, words, tables and or graphs (2.8.8F, 2.8.11D,H, J, N, L, K) Standard: 2.8.11L Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a point on the line.

Graphs of Equations Linear Equations in Two Variables

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Functions and Their Graphs Instructional Time: 800 minutes Anchor: M11.D.3 Analyze change in various contexts. Standard: 2.8.11O Determine the domain and range of a relation, given a graph or set of ordered pairs. 2.8.11R Create and interpret functional models. Anchor: M11.D.4 Describe or use models to represent quantitative relationships. Standard: 2.8.11S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). Anchor: M11.D.4 Describe or use models to represent quantitative relationships.

Functions Analyzing Graphs of Functions

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Functions and Their Graphs Instructional Time: 800 minutes Standard: 2.8.11A Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically. Anchor: M11.D.1 Demonstrate an understanding of patterns, relations and functions. Standard: 2.8.11P Analyze a relation to determine whether a direct or inverse variation exists and represent it algebraically and graphically. Anchor: M11.D.3 Analyze change in various contexts.

Combinations of Functions Inverse Functions

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Polynomial and Rational Functions Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Standard: 2.8.11 Q Represent functional relationships in tables, charts and graphs. 2.8.11 R Create and interpret functional models. 2.8.11 S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). Anchor: M11.D.4.1 Interpret and/or use linear, quadratic and/or exponential functions and their equations, graphs or tables.

Standard: 2.8.11 Q Represent functional relationships in tables, charts and graphs. 2.8.11 R Create and interpret functional models. 2.8.11 S Analyze properties and relationships of functions (e.g., linear,

Quadratic Equations Polynomial Functions of Higher Degree

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Polynomial and Rational Functions Instructional Time: 800 minutes polynomial, rational, trigonometric, exponential, logarithmic). Standard: 2.8.11 N Solve linear, quadratic and exponential equations both symbolically and graphically. 2.8.11 S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). Anchor: M11.D.4.1 Interpret and/or use linear, quadratic and/or exponential functions and their equations, graphs or tables. Standard: 2.8.11 N Solve linear, quadratic and exponential equations both symbolically and graphically. Anchor:

Polynomial and Synthetic Division Complex Numbers

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Polynomial and Rational Functions Instructional Time: 800 minutes

M11.D.4.1 Interpret and/or use linear, quadratic and/or exponential functions and their equations, graphs or tables. Standard: 2.8.11 N Solve linear, quadratic and exponential equations both symbolically and graphically. 2.8.11 S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). Anchor: M11.D.4.1 Interpret and/or use linear, quadratic and/or exponential functions and their equations, graphs or tables. Standard: 2.8.11 S Analyze properties and relationships of functions (e.g., linear, polynomial, rational,

Zeros of Polynomial Functions Rational Functions

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Polynomial and Rational Functions Instructional Time: 800 minutes trigonometric, exponential, logarithmic). Anchor: M11.D.4.1 Interpret and/or use linear, quadratic and/or exponential functions and their equations, graphs or tables.

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Exponential & Logarithmic Equations Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Standard: 2.1.11A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms). 2.8.11S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic. Standard: 2.1.11A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms). 2.8.11S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic.

Exponential Functions and Their Graphs Logarithmic Functions and Their Graphs

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Exponential & Logarithmic Equations Instructional Time: 800 minutes Standard: 2.1.11A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms) 2.8.11 S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). Standard: 2.8.11N Solve linear, quadratic and exponential equations both symbolically and graphically. Standard: 2.8.11N Solve linear, quadratic and exponential equations both symbolically and graphically 2.11.11C Graph and interpret rates of growth/decay.

Properties of Logarithms Exponential and Logarithmic Functions Exponential and Logarithmic Models

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Trigonometry Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Standard: 2.3.11 A Select and use appropriate units and tools to measure to the degree of accuracy required in particular measurement situations. 2.3.11 B Measure and compare angles in degrees and radians. Standard: 2.10.11 A Use graphing calculators to display periodic and circular functions; describe properties of the graphs. 2.10.11 B Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. Standard: 2.10.11 A Use graphing calculators to display periodic and circular

Radian and Degree Measure Trigonometric Functions: The Unit Circle Right Triangle Trigonometry

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Trigonometry Instructional Time: 800 minutes functions; describe properties of the graphs. 2.10.11 B Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. Standard: 2.10.11 A Use graphing calculators to display periodic and circular functions; describe properties of the graphs. 2.10.11 B Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. Standard: 2.10.11 A Use graphing calculators to display periodic and circular functions; describe properties of the graphs

Trigonometric Functions of Any Angle Graphs of Sine and Cosine Functions

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Trigonometry Instructional Time: 800 minutes Standard: 2.10.11 A Use graphing calculators to display periodic and circular functions; describe properties of the graphs Standard: 2.10.11 A Use graphing calculators to display periodic and circular functions; describe properties of the graphs. 2.10.11 B Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem.

Graphs of Other Trigonometric Functions Inverse Trigonometric Functions

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Trigonometry Instructional Time: 800 minutes Standard: 2.10.11 A Use graphing calculators to display periodic and circular functions; describe properties of the graphs. 2.10.11 B Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem.

Applications and Models

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Analytic Trigonometry Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Standard: 2.8.11 S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8.11 T Analyze and categorize functions by their characteristics. Standard: 2.8.11 S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.4.11 A Use direct proofs, indirect proofs or proof by contradiction to validate conjectures. Standard: 2.8.11 S Analyze properties and relationships of functions (e.g., linear, polynomial, rational,

Using Fundamental Identities Verifying Trigonometric Identities Solving Trigonometric Identities

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Analytic Trigonometry Instructional Time: 800 minutes trigonometric, exponential, logarithmic). 2.8.11 T Analyze and categorize functions by their characteristics. Standard: 2.8.11 S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8.11 T Analyze and categorize functions by their characteristics. Standard: 2.8.11 S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8.11 T Analyze and categorize functions by their characteristics.

Sum and Difference Formulas Multiple-Angle and Product-to-Sum Formulas

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Additional Topics in Trigonometry Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Stanard: 2.9.11 G Solve problems using analytic geometry. Stanard: 2.9.11 G Solve problems using analytic geometry. Stanard: 2.9.11 G Solve problems using analytic geometry. Stanard: 2.9.11 G Solve problems using analytic geometry. Stanard: 2.9.11 G Solve problems using analytic geometry.

Law of Sines Law of Cosines Vectors in the Plane Vectors and Dot Products Trigonometric Form of a Complex Number

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Systems of Equations and Inequalities Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Standard: 2.8.11 H Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets and other software. Anchor: M11.D.2.1.4 Write and/or solve systems of equations using graphing, substitution and/or elimination (limit systems to 2 equations). Standard: 2.8.11 H Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets and other software. Anchor: M11.D.2.1.4 Write and/or solve systems of equations using graphing, substitution and/or elimination (limit

Solving Systems of Equations Two-Variable Linear Systems

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Systems of Equations and Inequalities Instructional Time: 800 minutes systems to 2 equations). Standard: 2.8.11 H Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets and other software. Standard: 2.8.11 H Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets and other software. Standard: 2.8.11 H Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets and other software.

Multivariable Linear Systems Systems of Inequalities Linear Programming

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Matrices and Determinants Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Standard: 2.8.11 I Use matrices to organize and manipulate data, including matrix addition, subtraction, multiplication and scalar multiplication. 2.8.11 H Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets and other software. Standard: 2.8.11 I Use matrices to organize and manipulate data, including matrix addition, subtraction, multiplication and scalar multiplication. Standard: 2.8.11 I Use matrices to organize and manipulate data, including matrix addition, subtraction,

Matrices and Systems of Equations Operations with Matrices The Inverse of a Square Matrix

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Matrices and Determinants Instructional Time: 800 minutes multiplication and scalar multiplication. Standard: 2.8.11 I Use matrices to organize and manipulate data, including matrix addition, subtraction, multiplication and scalar multiplication. Standard: 2.8.11 D Formulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and non-routine problem situations. 2.8.11 I Use matrices to organize and manipulate data, including matrix addition, subtraction, multiplication and scalar multiplication.

The Determinant of a Square Matrix Applications of Matrices and Determinants

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Matrices and Determinants Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Standard: 2.8.11 E Use equations to represent curves (e.g., lines, circles, ellipses, parabolas, hyperbolas). 2.8.11 J Demonstrate the connection between algebraic equations and inequalities and the geometry of relations in the coordinate plane. Standard: 2.8.11 E Use equations to represent curves (e.g., lines, circles, ellipses, parabolas, hyperbolas). 2.8.11 J Demonstrate the connection between algebraic equations and inequalities and the geometry of relations in the coordinate plane. Standard: 2.8.11 E Use equations to represent curves (e.g., lines, circles, ellipses, parabolas,

Lines Introduction to Conics: Parabolas Ellipses

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Matrices and Determinants Instructional Time: 800 minutes hyperbolas). 2.8.11 J Demonstrate the connection between algebraic equations and inequalities and the geometry of relations in the coordinate plane. Standard: 2.8.11 E Use equations to represent curves (e.g., lines, circles, ellipses, parabolas, hyperbolas). 2.8.11 J Demonstrate the connection between algebraic equations and inequalities and the geometry of relations in the coordinate plane. Standard: 2.8.11 J Demonstrate the connection between algebraic equations and inequalities and the geometry of relations in the coordinate plane. Standard: 2.8.11 S Analyze properties

Hyperbolas Rotation of Conics Parametric Equations

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Matrices and Determinants Instructional Time: 800 minutes and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8.11 T Analyze and categorize functions by their characteristics. Standard: 2.8.11 J Demonstrate the connection between algebraic equations and inequalities and the geometry of relations 2.8.11 Q Represent functional relationships in tables, charts and graphs. Standard: 2.8.11 Q Represent functional relationships in tables, charts and graphs Standard: 2.8.11 Q Represent functional relationships in tables, charts and graphs

Polar Coordinates Graphs of Polar Equations Polar Equations of Conics

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Sequences, Series, and Probability Instructional Time: 800 minutes Anchor & Academic Standard (Eligible Content)

Standards: 2.11.11.D Determine sums of finite sequences of numbers and infinite geometric series. Standards: 2.11.11.D Determine sums of finite sequences of numbers and infinite geometric series. Standards: 2.11.11.D Determine sums of finite sequences of numbers and infinite geometric series. Standards: 2.11.11.D Determine sums of finite sequences of numbers and infinite geometric series. Standards: 2.8.11 T. Analyze and categorize functions by their characteristics.

Sequences and Series Arithmetic Sequences and Partial Sums Geometric Sequences and Series Mathematical Induction The Binomial Theorem

TUNKHANNOCK AREA SCHOOL DISTRICT Course: Precalculus Mathematics Grade Level: 11-12 Unit of Study: Sequences, Series, and Probability Instructional Time: 800 minutes Standards: 2.7.11 A Compare odds and probability. 2.7.11 B Apply probability and statistics to perform an experiment involving a sample and generalize its results to the entire population. 2.7.11 C. Draw and justify a conclusion regarding the validity of a probability or statistical argument Standards: 2.7.11 A Compare odds and probability. 2.7.11 B Apply probability and statistics to perform an experiment involving a sample and generalize its results to the entire population. 2.7.11 C. Draw and justify a conclusion regarding the validity of a probability or statistical argument

Counting Principles Probability

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