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Precalculus Correlated to 2000 Standards Standard ID PC.1.1 PC.1.1 PC.1.1 PC.1.1 PC.1.1 PC.1.1 PC.1.1 PC.1.1 Standard Text Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators. Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators. Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators. Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators. Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators. Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators. Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators. Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators. Lesson Lesson Title 1-1 Functions 1-2 Analyzing Graphs of Functions and Relations 1-4 Extrema and Average Rates of Change 1-5 Parent Functions and Transformations 2-2 Polynomial Functions 2-3 The Remainder and Factor Theorems 2-5 Rational Functions 2-6 Nonlinear Inequalities PC.1.1 PC.1.1 PC.1.10 PC.1.10 PC.1.10 PC.1.10 PC.1.2 PC.1.2 Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators. Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators. Write the equations of conic sections in standard form (completing the square and using translations as necessary), in order to find the type of conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.). Write the equations of conic sections in standard form (completing the square and using translations as necessary), in order to find the type of conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.). Write the equations of conic sections in standard form (completing the square and using translations as necessary), in order to find the type of conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.). Write the equations of conic sections in standard form (completing the square and using translations as necessary), in order to find the type of conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.). Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions. Use paper and pencil methods and graphing calculators. Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions. Use paper and pencil methods and graphing calculators. 3-1 Exponential Functions 3-2 Logarithmic Functions 7-1 Parabolas 7-2 Ellipses and Circles 7-3 Hyperbolas 7-4 Rotations of Conic Sections 1-1 Functions 1-2 Analyzing Graphs of Functions and Relations PC.1.2 Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions. Use paper and pencil methods and graphing calculators. Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions. Use paper and pencil methods and graphing calculators. PC.1.3 Model and solve word problems using functions and equations. 10-6 Functions as Infinite Series PC.1.3 Model and solve word problems using functions and equations. 1-4 Extrema and Average Rates of Change PC.1.3 Model and solve word problems using functions and equations. 2-4 Zeros of Polynomial Functions PC.1.3 Model and solve word problems using functions and equations. 3-5 Modeling with Nonlinear Regression PC.1.3 Model and solve word problems using functions and equations. 4-5 Graphing Other Trigonometric Functions PC.1.4 Define, find, and check inverse functions. 1-7 PC.1.2 PC.1.5 Define, find, and check inverse functions. Describe the symmetry of the graph of a function. PC.1.5 Describe the symmetry of the graph of a function. PC.1.4 PC.1.5 Describe the symmetry of the graph of a function. Describe the symmetry of the graph of a function. PC.1.5 PC.1.5 PC.1.5 1-3 Continuity, End Behavior, and Limits 1-5 Parent Functions and Transformations 0-3 Inverse Relations and Functions Graphing Technology Lab: Graphing Inverses Using Parametric Equations Quadratic Functions and Equations 1-2 Analyzing Graphs of Functions and Relations Extend 1-7 2-1 Parent Functions and Transformations Power and Radical Functions Describe the symmetry of the graph of a function. 2-5 Rational Functions Describe the symmetry of the graph of a function. 7-1 Parabolas 1-5 PC.1.6 Decide if functions are even or odd. 1-2 Analyzing Graphs of Functions and Relations PC.1.6 Decide if functions are even or odd. 2-1 Power and Radical Functions PC.1.6 Decide if functions are even or odd. 2-2 PC.1.7 1-5 PC.1.8 Apply transformations to functions. Understand curves defined parametrically and draw their graphs. Polynomial Functions Parent Functions and Transformations 7-5 Parametric Equations PC.1.9 Compare relative magnitudes of functions and their rates of change. PC.1.9 Compare relative magnitudes of functions and their rates of change. Connect to AP 1 PC.1.9 Compare relative magnitudes of functions and their rates of change. Connect to AP 3 Extrema and Average Rates of Change Connect to AP Calculus: Rate of Change at a Point Connect to AP Calculus: Approximating Rates of Change PC.1.9 Compare relative magnitudes of functions and their rates of change. Connect to AP 4 Connect to AP Calculus: Related Rates Connect to AP 5 Connect to AP Calculus: Rates of Change for Sine and Cosine PC.1.9 PC.2.1 PC.2.1 PC.2.1 PC.2.1 PC.2.1 PC.2.1 PC.2.2 Compare relative magnitudes of functions and their rates of change. Solve word problems involving applications of logarithmic and exponential functions. Solve word problems involving applications of logarithmic and exponential functions. Solve word problems involving applications of logarithmic and exponential functions. Solve word problems involving applications of logarithmic and exponential functions. Solve word problems involving applications of logarithmic and exponential functions. Solve word problems involving applications of logarithmic and exponential functions. Find the domain, range, intercepts, and asymptotes of logarithmic and exponential functions. 1-4 3-1 Exponential Functions 3-2 Logarithmic Functions 3-3 Properties of Logarithms 3-4 Exponential and Logarithmic Equations Extend 3-1 Modeling with Nonlinear Regression Graphing Technology Lab: Financial Literacy: Exponential Functions 3-1 Exponential Functions 3-5 PC.2.2 Find the domain, range, intercepts, and asymptotes of logarithmic and exponential functions. 3-2 Logarithmic Functions PC.2.3 Draw and analyze graphs of logarithmic and exponential functions. 3-1 Exponential Functions PC.2.3 Draw and analyze graphs of logarithmic and exponential functions. 3-2 Logarithmic Functions PC.2.4 Define, find, and check inverse functions of logarithmic and exponential functions. 3-2 Logarithmic Functions PC.3.1 Solve word problems involving right and oblique triangles. 4-1 Right Triangle Trigonometry PC.3.3 Apply the laws of sines and cosines to solving problems. Find the area of a triangle given two sides and the angle between them. PC.4.1 Define sine and cosine using the unit circle. 4-3 The Law of Sines and the Law of Cosines The Law of Sines and the Law of Cosines Trigonometric Functions on the Unit Circle PC.4.10 Know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line. 5-4 Sum and Difference Identities PC.4.11 Make connections between right triangle ratios, trigonometric functions, and circular functions. 4-3 Trigonometric Functions on the Unit Circle 4-2 Degrees and Radians 4-2 Degrees and Radians 4-4 Graphing Sine and Cosine Functions PC.3.2 4-7 4-7 PC.4.3 Convert between degree and radian measures. Learn exact sine, cosine, and tangent values for 0, ?2, ?3, ?4, ?6, and multiples of ?. Use those values to find other trigonometric values. PC.4.4 Solve word problems involving applications of trigonometric functions. PC.4.4 Solve word problems involving applications of trigonometric functions. 4-5 Graphing Other Trigonometric Functions PC.4.4 Solve word problems involving applications of trigonometric functions. 4-6 Inverse Trigonometric Functions PC.4.2 PC.4.5 Define and graph trigonometric functions (i.e., sine, cosine, tangent, cotangent, secant, cosecant). PC.4.5 Define and graph trigonometric functions (i.e., sine, cosine, tangent, cotangent, secant, cosecant). PC.4.5 Define and graph trigonometric functions (i.e., sine, cosine, tangent, cotangent, secant, cosecant). PC.4.6 Find domain, range, intercepts, periods, amplitudes, and asymptotes of trigonometric functions. PC.4.6 Find domain, range, intercepts, periods, amplitudes, and asymptotes of trigonometric functions. PC.4.6 Find domain, range, intercepts, periods, amplitudes, and asymptotes of trigonometric functions. PC.4.7 Draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift. PC.4.7 Draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift. PC.4.7 Draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift. PC.4.8 Define and graph inverse trigonometric functions. 4-6 PC.4.9 Find values of trigonometric and inverse trigonometric functions. 4-1 PC.4.9 Find values of trigonometric and inverse trigonometric functions. 4-3 PC.4.9 Find values of trigonometric and inverse trigonometric functions. 4-4 PC.4.9 Find values of trigonometric and inverse trigonometric functions. 4-5 4-4 Graphing Sine and Cosine Functions 4-5 Graphing Other Trigonometric Functions Explore 44 Graphing Technology Lab: Graphing the Sine Function Parametrically 4-4 Graphing Sine and Cosine Functions 4-5 Graphing Other Trigonometric Functions Explore 4-4 Graphing Technology Lab: Graphing the Sine Function Parametrically 4-4 Graphing Sine and Cosine Functions 4-5 Graphing Other Trigonometric Functions Explore 4-4 Graphing Technology Lab: Graphing the Sine Function Parametrically Inverse Trigonometric Functions Right Triangle Trigonometry Trigonometric Functions on the Unit Circle Graphing Sine and Cosine Functions Graphing Other Trigonometric Functions PC.4.9 Find values of trigonometric and inverse trigonometric functions. 4-6 Inverse Trigonometric Functions 4-7 The Law of Sines and the Law of Cosines 5-1 Trigonometric Identities 5-1 Trigonometric Identities PC.5.2 Find values of trigonometric and inverse trigonometric functions. Know the basic trigonometric identity cos2x + sin2x = 1 and prove that it is equivalent to the Pythagorean Theorem. Use basic trigonometric identities to verify other identities and simplify expressions. PC.5.2 Use basic trigonometric identities to verify other identities and simplify expressions. 5-2 Verifying Trigonometric Identities PC.5.2 Use basic trigonometric identities to verify other identities and simplify expressions. 5-4 Sum and Difference Identities PC.5.2 Use basic trigonometric identities to verify other identities and simplify expressions. 5-5 Multiple-Angle and Product-to-Sum Identities PC.5.2 Use basic trigonometric identities to verify other identities and simplify expressions. PC.5.3 Understand and use the addition formulas for sines, cosines, and tangents. PC.4.9 PC.5.1 Extend 5-4 Graphing Technology Lab: Reduction Identities 5-4 Sum and Difference Identities PC.5.4 Understand and use the half-angle and double-angle formulas for sines, cosines, and tangents. 5-5 Multiple-Angle and Product-to-Sum Identities PC.5.5 Solve trigonometric equations. 5-3 Solving Trigonometric Equations PC.5.6 Solve word problems involving applications of trigonometric equations. 5-3 Solving Trigonometric Equations PC.5.6 PC.5.6 Solve word problems involving applications of trigonometric equations. Solve word problems involving applications of trigonometric equations. 5-4 5-5 Sum and Difference Identities Multiple-Angle and Product-to-Sum Identities PC.6.1 PC.6.2 PC.6.2 PC.6.2 PC.6.3 Define polar coordinates and relate polar coordinates to Cartesian coordinates. Represent equations given in rectangular coordinates in terms of polar coordinates. Represent equations given in rectangular coordinates in terms of polar coordinates. Represent equations given in rectangular coordinates in terms of polar coordinates. Graph equations in the polar coordinate plane. PC.6.4 Graph equations in the polar coordinate plane. Define complex numbers, convert complex numbers to trigonometric form, and multiply complex numbers in trigonometric form. PC.6.5 PC.7.1 PC.6.3 PC.7.3 PC.7.4 9-3 Polar and Rectangular Forms of Equations 9-4 9-2 Explore 9-2 Polar Forms of Conic Sections Graphs of Polar Equations Graphing Technology Lab: Investigate Graphs of Polar Equations 9-5 Complex Numbers and De Moivre's Theorem Understand and use summation notation. 10-1 Sequences, Series, and Sigma Notation Find sums of infinite geometric series. PC.7.3 Polar Coordinates State, prove, and use De Moivre's Theorem. PC.7.2 PC.7.3 9-1 Complex Numbers and De Moivre's Theorem PC.7.1 PC.7.2 Polar Coordinates 9-5 Understand and use summation notation. Understand and use summation notation. PC.7.1 9-1 Find sums of infinite geometric series. Prove and use the sum formulas for arithmetic series and for finite and infinite geometric series. Prove and use the sum formulas for arithmetic series and for finite and infinite geometric series. Prove and use the sum formulas for arithmetic series and for finite and infinite geometric series. Use recursion to describe a sequence. 10-3 Arithmetic Sequences and Series Geometric Sequences and Series 10-1 Sequences, Series, and Sigma Notation 10-6 Functions as Infinite Series 10-2 Arithmetic Sequences and Series 10-3 Geometric Sequences and Series 10-2 10-6 10-1 Functions as Infinite Series Sequences, Series, and Sigma Notation PC.7.5 Use recursion to describe a sequence. Use recursion to describe a sequence. Understand and use the concept of limit of a sequence or function as the independent variable approaches infinity or a number. Decide whether simple sequences converge or diverge. Understand and use the concept of limit of a sequence or function as the independent variable approaches infinity or a number. Decide whether simple sequences converge or diverge. Understand and use the concept of limit of a sequence or function as the independent variable approaches infinity or a number. Decide whether simple sequences converge or diverge. Understand and use the concept of limit of a sequence or function as the independent variable approaches infinity or a number. Decide whether simple sequences converge or diverge. Understand and use the concept of limit of a sequence or function as the independent variable approaches infinity or a number. Decide whether simple sequences converge or diverge. PC.7.6 Solve word problems involving applications of sequences and series. 10-1 Sequences, Series, and Sigma Notation PC.7.6 Solve word problems involving applications of sequences and series. 10-2 Arithmetic Sequences and Series PC.7.6 Solve word problems involving applications of sequences and series. 10-3 Geometric Sequences and Series 10-6 Functions as Infinite Series 11-7 Correlation and Linear Regression PC.7.4 PC.7.4 PC.7.5 PC.7.5 PC.7.5 PC.7.5 PC.7.6 PC.8.1 Solve word problems involving applications of sequences and series. Find linear models using the median fit and least squares regression methods. Decide which model gives a better fit. 10-3 Arithmetic Sequences and Series Geometric Sequences and Series 10-1 Sequences, Series, and Sigma Notation 10-3 Geometric Sequences and Series 10-6 Functions as Infinite Series 1-3 Continuity, End Behavior, and Limits 10-2 Extend 103 Graphing Technology Lab: Continued Fractions PC.8.2 PC.8.2 PC.8.3 PC.8.3 Calculate and interpret the correlation coefficient. Use the correlation coefficient and residuals to evaluate a "best-fit" line. Calculate and interpret the correlation coefficient. Use the correlation coefficient and residuals to evaluate a "best-fit" line. Find a quadratic, exponential, logarithmic, power, or sinusoidal function to model a data set and explain the parameters of the model. Find a quadratic, exponential, logarithmic, power, or sinusoidal function to model a data set and explain the parameters of the model. 11-7 Extend 117 Correlation and Linear Regression Graphing Technology Lab: Median-Fit Lines 3-5 Modeling with Nonlinear Regression 4-4 Graphing Sine and Cosine Functions