Precalculus TN Ready Performance Standards by Unit Precalculus

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Precalculus TN Ready Performance Standards by Unit Precalculus – Curriculum Overview

The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency 1. Make sense of problems and persevere in solving them. 1. Use multiple reading strategies. 2. Reason abstractly and quantitatively. 2. Understand and use correct mathematical vocabulary. 3. Construct viable arguments and critique the reasoning of others. 3. Discuss and articulate mathematical ideas. 4. Model with mathematics. 4. Write mathematical arguments. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

*Unless otherwise noted, all resources are from Glencoe Precalculus.

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Precalculus – Curriculum Overview

Quarter 1 Quarter 2 Quarter 3 Quarter 4 Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 14 Days 16 Days 12 Days 16 Days 13 Days 12 Days 7 Days 16 Days 6 Days 14 Days

Functions, Power, Exponential Trigonometric Trigonometric Matrices Conic Polar Parametric Sequences, Limits, & Polynomial, & Functions Identities & Sections Graphing & Equations Series, & End & Rational Logarithmic Equations Vectors Sigma Behavior Functions Functions Notation Standards (By number) P.F.BF.A.2 P.F.IF.A.5 P.F.IF.A.2 P.F.TF.A.1 P.G.TI.A.1 P.N.VM.C.7 P.A.C.A.1 P.N.VM.A.1 P.A.PE.A.1 P.A.S.A.1 P.F.BF.A.4 P.F.IF.A.2 P.N.NE.A.3 P.G.AT.A.3 P.G.TI.A.2 P.N.VM.C.8 P.A.C.A.2 P.N.VM.A.2 P.A.PE.A.2 P.A.S.A.2 P.F.IF.A.1 P.F.IF.A.4 P.N.NE.A.2 P.G.AT.A.4 P.G.AT.A.2 P.N.VM.C.9 P.A.C.A.3 P.N.VM.B.3 P.MCPS.3 P.A.S.A.3.a P.F.BF.A.1 P.F.IF.A.6 P.N.NE.A.1 P.F.TF.A.2 P.G.AT.A.5 P.N.VM.C.10 P.A.C.A.4 P.N.VM.B.4.a P.A.S.A.3.b P.F.BF.A.3 P.F.IF.A.7 P.MCPS.2 P.F.TF.A.3 P.G.AT.A.6 P.N.VM.C.11 P.N.VM.B.4.b P.A.S.A.3.c P.F.BF.A.5.a P.N.CN.B.6 P.F.GT.A.1 P.N.VM.C.12 P.N.VM.B.4.c P.F.IF.A.8 P.F.BF.A.5.b P.N.CN.B.7 P.F.GT.A.2 P.N.VM.C.13 P.N.VM.B.5.a P.A.S.A.4 P.F.BF.A.5.c P.N.NE.A.4 P.F.GT.A.3 P.A.REI.A.1 P.N.VM.B.5.b P.A.S.A.5 P.F.BF.A.5.d P.N.NE.A.5 P.F.GT.A.4 P.A.REI.A.2 P.N.VM.B.5.c P.F.BF.A.6 P.A.REI.A.3 P.F.GT.A.5 P.MCPS.5 P.N.CN.A.4 F.S.MD.A.3 P.A.REI.A.4 P.F.GT.A.6 P.N.CN.A.5 P.S.MD.A.1 P.F.GT.A.7 P.N.VM.B.6 P.S.MD.A.2 P.F.GT.A.8 P.N.CN.A.1 P.S.MD.A.3 P.G.AT.A.1 P.N.CN.A.2 P.MCPS.6 P.S.MD.A.3 P.G.PC.A.1 P.F.TF.A.4 P.G.PC.A.2 P.MCPS.1 P.G.PC.A.3 P.N.CN.A.3 P.MCPS.4

Green=Major Content Blue=Supporting Content

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Unit 1 Functions, Limits, & End Behavior 14 Days Standards “I Can” Statements Functions P.F.BF.A.2 Develop an understanding of functions as elements that can be I can create functions by adding, subtracting, multiplication, division, and operated upon to get new functions: addition, subtraction, multiplication, composition of functions. division, and composition of functions. P.F.BF.A.4 I can construct the difference quotient for a given function and I can construct the difference quotient for a given function and simplify the simplify the resulting expression. resulting expression. I can determine whether a function is even, odd, or neither algebraically and P.F.IF.A.1 Determine whether a function is even, odd, or neither. graphically. P.F.BF.A.1 Understand how the algebraic properties of an equation transform the geometric properties of its graph. For example, given a I can describe the transformation of the graph resulting from the manipulation function, describe the transformation of the graph resulting from the of the algebraic properties of the equation (i.e., translations, stretches, manipulation of the algebraic properties of the equation (i.e., translations, reflections, and changes in periodicity and amplitude). stretches, reflections and changes in periodicity and amplitude) I can form a composite function. P.F.BF.A.3 Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon I can find the domain of a composite function. as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. I can recognize the role that domain of a function plays in the combination of functions by composition of functions. P.F.BF.A.5 Find inverse functions (including exponential, logarithmic and trigonometric).

a. Calculate the inverse of a function, f(x), with respect to each of the I can calculate the inverse of a function with respect to each of the functional functional operations; in other words, the additive inverse, − f(x), the operations. multiplicative inverse, 1/f(x), and the inverse with respect to composition, f- 1(x). Understand the algebraic and graphical implications of each type. I can verify by composition that one function is the inverse of another.

b. Verify by composition that one function is the inverse of another. I can identify whether a function has an inverse with respect to composition and when functions are inverses of each other with respect to composition. c. Read values of an inverse function from a graph or a table, given that the function has an inverse. I can find an inverse function by restricting the domain of a function that is not one-to-one. d. Recognize a function is invertible if and only if it is one-to-one. Produce an invertible function from a non-invertible function by restricting the domain. P.F.BF.A.6 Explain why the graph of a function and its inverse are reflections I can explain why the graph of a function and its inverse are reflections of one of one another over the line y = x. another over the line y = x.

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit I can explore the properties of a limit by analyzing sequences and series.

I can understand the relationship between a horizontal asymptote and the P.MCPS.6 Develop the concept of the limit using tables, graphs, and limit of a function at infinity. algebraic properties. I can determine the limit of a function at a specified number.

I can find the limit of a function at a number using algebra. Statistics and Probability I can create scatter plots for bivariate data (linear, polynomial, trigonometric or exponential) to model real-world phenomena.

P.S.MD.A.1 ★ Create scatter plots, analyze patterns and describe I can analyze patterns from the scatter plots that I created. relationships for bivariate data (linear, polynomial, trigonometric or exponential) to model real-world phenomena and to make predictions. I can describe relationships in the scatter plots.

I can make prediction using the scatter plots. P.S.MD.A.2 ★Determine a regression equation to model a set of bivariate I can explain how to determine the best regression equation model that data. Justify why this equation best fits the data. approximates a particular data set. I can find the regression equation that best fits bivariate data.

P.S.MD.A.3 ★Use a regression equation modeling bivariate data to make I can use a regression equation modeling bivariate data to make predictions. predictions. Identify possible considerations regarding the accuracy of predictions when interoplating or extrapolating. I can identify possible considerations regarding the accuracy of predictions when interpolating or extrapolating.

Vocabulary • Pre-assessment • Set-builder notation • Maximum • Interval notation • Minimum Point of • Section 1 Functions • Function inflection

• Vertical line test • Average rate of change • Section 2 Analyzing Graphs of Functions • Function notation • Secant line • Independent variable • Parent function • Section 3 Continuity, End Behavior, and Limits • Dependent variable • Constant function • Implied domain • Identity function • Section 4 Extrema and Average Rates of Change • Piecewise-defined function • Quadratic function • Line symmetry • Cubic function • Quiz • Point symmetry • Square root function • Even function • Reciprocal function • Section 5 Parent Functions and Transformations • Odd function • Absolute value function • Continuous function • Step function • Greatest integer function • Section 6 Function Operations and Composition of Functions • Discontinuous function • Limit • Transformation

• Infinite discontinuity • Translation • Section 7 Inverse Relations and Functions • Jump discontinuity • Reflection

• Removable discontinuity • Dilation • Unit Review • Nonremovable discontinuity • Composition of functions • Continuity test • Inverse relation • Unit 1 Test • Intermediate Value • Inverse function Theorem • Horizontal line test • End behavior • One-to-one function • Increasing • Decreasing • Constant • Critical points • Extrema • Relative Extrema • Absolute Extrema

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Unit 2 Power, Polynomial, & Rational Functions 16 Days Standards “I Can” Statements Number and Quantity P.N.CN.B.6 Extend polynomial identities to the complex numbers. I can extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i). P.N.CN.B.7 Know the Fundamental Theorem of Algebra; show that it is true I know the Fundamental Theorem of Algebra and can show it is true for for quadratic polynomials. quadratic polynomials. P.N.NE.A.4 Simplify complex radical and rational expressions; discuss and display understanding that rational numbers are dense in the real numbers I can simplify complex radical and rational expressions. and the integers are not. P.N.NE.A.5 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and I can add, subtract, multiply, and divide rational expressions. division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. Algebra P.A.REI.A.3 Solve nonlinear inequalities (quadratic, trigonometric, conic, I can solve nonlinear inequalities (quadratic and rational) by graphing exponential, logarithmic, and rational) by graphing (solutions in interval (solutions in interval notation if one-variable), by using a sign chart, and with notation if one-variable), by hand and with appropriate technology. appropriate technology. P.A.REI.A.4 Solve systems of nonlinear inequalities by graphing. I can solve systems of nonlinear inequalities by graphing. Functions P.F.IF.A.5 I can Identify characteristics of graphs such as direction it opens, vertex based Identify characteristics of graphs based on a set of conditions or on a general on a set of conditions or on a general equation equation such as y = ax2 + c. such as y = ax2 + c I can analyze qualities of exponential, polynomial, logarithmic, trigonometric, and rational functions and solve real world problems that can be modeled with these functions.

P.F.IF.A.2 ★Analyze qualities of exponential, polynomial, logarithmic, I can identify or analyze the following properties of polynomial, and rational trigonometric, and rational functions and solve real world problems that can functions from tables, graphs, and equations. be modeled with these functions (by hand and with appropriate technology). I can describe the following of a given function: Domain, Range, Continuity, Increasing/decreasing Behavior, Symmetry, Boundedness, Extrema, Asymptotes, Intercepts, Holes, End Behavior with Limit Notation, Concavity. I can identify the real zeros of the graph of a function (polynomial, rational, exponential, logarithmic, and trigonometric) in equation or graphical form. P.F.IF.A.4 Identify the real zeros of a function and explain the relationship

between the real zeros and the x-intercepts of the graph of a function I can explain the relationship between the real zeros and the x-intercept of the (exponential, polynomial, logarithmic, trigonometric, and rational). graph of a function (polynomial, rational, exponential, logarithmic, and trigonometric).

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit I can locate critical points on the graphs of polynomial functions and P.F.IF.A.6 Visually locate critical points on the graphs of functions and determine if each critical point is a minimum or a maximum. determine if each critical point is a minimum, a maximum or point of

inflection. Describe intervals where the function is increasing or decreasing I can describe and locate maximums, minimums, increasing and decreasing and where different types of concavity occur. intervals, and zeroes given a sketch of the graph. P.F.IF.A.7 Graph rational functions, identifying zeros, asymptotes (including I can graph rational functions, identifying zeros, asymptotes (including slant), slant), and holes (when suitable factorizations are available) and showing and holes (when suitable factorizations are available) and showing end- end-behavior. behavior. Sections/Topics Activities/Resources/Materials Extra Resources • www.shodor.org/interactive •

• Pre-assessment Vocabulary • Section 1 Power and Radical Functions • Power function • Descartes’ rule of signs • Monomial function • Fundamental theorem of • Section 2 Polynomial Functions • Radical function algebra • Extraneous solution • Linear factorization theorem • Section 3 The Remainder and Factor Theorems • Polynomial function • Conjugate root theorem • Complex conjugate • Polynomial function of degree n • Irreducible over the reals • Quiz • Leading coefficient • Rational function

• Degree of a polynomial • Asymptote • Section 4 Zeros of Polynomial Functions • Leading term test • Vertical asymptote • Quartic function • Horizontal asymptote • Section 5 Rational Functions • Turning points • Slant (oblique) asymptote • Quadratic form • Hole • Section 6 Nonlinear Inequalities • Repeated zero • Polynomial inequality • Multiplicity • Sign chart • Unit Review • Polynomial long division • Rational inequality • Synthetic division • Unit 2 Test • Depressed polynomial • Remainder theorem • Factor theorem • Rational zero theorem • Upper bound • Lower bound • Upper and lower bound tests

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Unit 3 Exponential & Logarithmic Functions 12 Days Standards “I Can” Statements Number and Quantity P. N.NE.A.3 Classify real numbers and order real numbers that include I can classify real numbers and order real numbers that include transcendental transcendental expressions, including roots and fractions of π and e. expressions, including roots and fractions of π and e. I can demonstrate understanding of the inverse relationship between exponents and logarithms.

I can solve problems containing logarithms and exponents.

I can change an equation from logarithmic to exponential form and back. P.N.NE.A.2 ★Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms I can solve exponential equations. and exponents. I can solve logarithmic equations.

I can prove basic properties of a logarithm using properties of its inverse and apply those properties to solve problems.

I can find the inverse of an exponential or a logarithmic function. I can use the laws of exponents and logarithms to expand or collect terms in P.N.NE.A.1 Use the laws of exponents and logarithms to expand or collect expressions; simplify expressions or modify them in order to analyze them or terms in expressions; simplify expressions or modify them in order to analyze compare them. them or compare them. I can compare exponential and logarithmic expressions. Functions P.F.IF.A.2 ★ Analyze qualities of exponential, polynomial, logarithmic, trigonometric, and rational functions and solve real world problems that I can identify or analyze the following properties of exponential, logarithmic can be modeled with these functions (by hand and with appropriate and logistic functions: Domain, Range, Continuity, Increasing/Decreasing technology). Behavior, Symmetry, Boundedness, Extrema, Asymptotes, Intercepts, Holes, End Behavior with Limit Notation, Concavity.

I can solve real world problems that can be modeled using quadratic, exponential, or logarithmic functions (by hand and with appropriate technology).

I can determine what function should be used to model a real-world situation.

I can apply the appropriate function to a real-world situation and then find its solution.

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit

P.MCPS.2 Apply appropriate techniques to analyze mathematical models and functions constructed from verbal information; interpret the I can create and analyze mathematical models that describe situations solution obtained in written form using appropriate units of including growth and decay and financial applications. measurement. Sections/Topics Activities/Resources/Materials Extra Resources • www.shodor.org/interactive •

Vocabulary • Algebraic function • Transcendental function • Pre-assessment • Exponential function • Natural base • Section 1 Exponential Functions • Compound interest formula • Continuous compound • Section 2 Logarithmic Functions interest formula • Exponential growth function • Exponential decay function • Section 3 Properties of Logarithms • Continuous exponential

growth function • Quiz • Continuous exponential decay function • Section 4 Exponential and Logarithmic Equations • Logarithmic function with base b • Section 5 Modeling with Nonlinear Regression • Logarithmic form • Exponential form • Unit Review • Logarithms • Properties of logarithms • Common logarithm • Unit 3 Test • Natural logarithm

• Change of base formula

• One-to-one property of exponential functions • One-to-one property of logarithmic functions • Logistic growth function • Linearizing data

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Unit 4 Trigonometric Functions 16 Days Standards “I Can” Statements Functions P.F.TF.A.1 Convert from radians to degrees and from degrees to radians. I can convert from radians to degrees and from degrees to radians. P.F.TF.A.2 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to I can find the reference angle of any angle on the unit circle. I can evaluate express the values of sine, cosine, and tangent for π – x, π + x, and 2π – x the trig functions of any angle of the unit circle using reference angles. in terms of their values for x, where x is any real number. I can use the unit circle to explain symmetry of the six trigonometric P.F.TF.A.3 Use the unit circle to explain symmetry (odd and even) and functions. periodicity of trigonometric functions. I can describe periodicity of all six trigonometric functions. I can match a trigonometric equation with its graph by recognizing the parent P.F.GT.A.1★ Interpret transformations of trigonometric functions. graph and by using transformations. P.F.GT.A.2★ Determine the difference made by choice of units for angle I can determine the difference made by choice of units for angle measurement measurement when graphing a trigonometric function. when graphing a trigonometric function. I can graph the six trigonometric functions (sin, cos, tan, csc, sec, cot) and P.F.GT.A.3★ Graph the six trigonometric functions and identify identify characteristics such as period, amplitude, phase shift, and characteristics such as period, amplitude, phase shift, and asymptotes. asymptotes. P.F.GT.A.4★ Find values of inverse trigonometric expressions (including I can find values of inverse trigonometric functions, applying appropriate compositions), applying appropriate domain and range restrictions. domain and range restrictions. P.F.GT.A.5★ Understand that restricting a trigonometric function to a I can understand that restricting a trigonometric function to a domain on domain on which it is always increasing or always decreasing allows its which it is always increasing or always decreasing allows its inverse to be inverse to be constructed. constructed. P.F.GT.A.6★ Determine the appropriate domain and corresponding I can determine identify and list the appropriate domain and corresponding range for each of the inverse trigonometric functions. range for each of the inverse trigonometric functions. P.F.GT.A.7★ Graph the inverse trigonometric functions and identify their I can graph the inverse trigonometric functions and identify their key key characteristics. characteristics. P.F.TF.A.4 Choose trigonometric functions to model periodic phenomena I can choose trigonometric functions to model periodic phenomena with with specified amplitude, frequency, and midline. specified amplitude, frequency, and midline. Geometry P.G.AT.A.3 Derive and apply the formulas for the area of sector of a I can derive and apply the formulas for the area of sector of a circle. circle. P.G.AT.A.4 Calculate the arc length of a circle subtended by a central I can calculate the arc length of a circle subtended by a central angle. angle. P.G.AT.A.1 ★Use the definitions of the six trigonometric ratios as ratios I can use the definitions of the six trigonometric ratios as ratios of sides in a of sides in a right triangle to solve problems about lengths of sides and right triangle to solve problems about lengths of sides and measures of measures of angles. angles.

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Statistics and Probability P.S.MD.A.3★ Use a regression equation modeling bivariate data to make I can use a regression equation modeling bivariate data to make predictions predictions. Identify possible considerations regarding the accuracy of involving trigonometric functions. predictions when interpolating or extrapolating. P.MCPS.1 Apply the arc length formula or conversion factors to real I can apply linear and angular velocity formulas in real world applications. world applications. Sections/Topics Activities/Resources/Materials • Pre-assessment Extra Resources • www.shodor.org/interactive • Section 1 Right Triangle Trigonometry •

• Section 2 Degrees and Radians, Arc Length, Area of a Sector, Linear Vocabulary and Angular Speed • Trigonometric ratios • Area of a sector • Trigonometric functions • Quadrantal angle • Section 3 Trigonometric Functions on the Unit Circle • Sine • Reference angle • Cosine • Unit circle • Quiz • Tangent • Circular functions • Cosecant • Periodic functions • Section 4 Graphing Sine and Cosine Functions • Secant • Period • Cotangent • Sinusoid • Reciprocal functions • Amplitude • Section 5 Graphing Tangent, Cosecant, and Secant • Inverse trigonometric • Frequency function • Phase shift • Quiz • Inverse sine • Vertical shift • Inverse cosine • Midline • Section 6 Inverse Trigonometric Functions • Inverse tangent • Damped oscillation • Angle of elevation • Damped trigonometric • Section 7 The Law of Sines and Law of Cosines • Angle of depression function • Solving a right triangle • Damping factor • Unit Review • Vertex • Damped harmonic motion • Initial side • Arcsine function • Unit 4 Test • Terminal side • Arccosine function • Standard position of an • Arctangent function angle • Oblique triangles • Radians • Law of sines • Degrees • Law of cosines • Coterminal angles • Ambiguous case • Arc length • Heron’s formula • Linear speed • Angular speed • Sector

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Unit 5 Trigonometric Identities & Equations 13 Days Standards “I Can” Statements Geometry P.G.TI.A.1 ★Apply trigonometric identities to verify identities and solve I can recognize and use the following trigonometric identities to verify equations. Identities include: Pythagorean, reciprocal, quotient, identities and solve trigonometric equations: Pythagorean, Reciprocal, sum/difference, double-angle, and half-angle. Quotient, Sum/Difference, Double Angle. P.G.TI.A.2 ★ Prove the addition and subtraction formulas for sine, cosine, I can prove the sum and difference formulas for sine, cosine, and tangent and and tangent and use them to solve problems. apply them in solving problems. P.G.AT.A.2 ★Derive the formula A = ½ ab sin C for the area of a triangle by I can derive the area of triangle formula A = ½ ab sin C by constructing a drawing an auxiliary line from a vertex perpendicular to the opposite side. drawing to model the situation P.G.AT.A.5 ★Prove the Laws of Sines and Cosines and use them to solve I can prove the Law of Sines and Cosines and apply them to solve problems. problems. I can apply the Law of Sines (including the ambiguous case) and Cosines in order to solve right and oblique triangles.

I can solve real work problems (e.g. surveying, navigation.)

P.G.AT.A.6 ★Understand and apply the Law of Sines (including the I can determine how many solutions are possible for the Ambiguous case of ambiguous case) and the Law of Cosines to find unknown measurements in the Law of Sines. right and non-right triangles (e.g., surveying problems, resultant forces). I can determine when it is appropriate to use A = ½ ab sin C and Heron’s Law.

I can find areas of triangles using the two area formulas A = ½ ab sin C and Heron’s Law.

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Sections/Topics Activities/Resources/Materials Extra Resources • Pre-assessment • www.shodor.org/interactive

• Section 1 Trigonometric Identities Vocabulary

• Identity • Section 2 Verifying Trigonometric Identities • Trigonometric identity

• Pythagorean identities • Quiz • Cofunction identities

• Odd-even identities • Section 3 Solving Trigonometric Equations • Verify an identity • Sum and difference • Section 4 Sum and Difference Identities identities

• Section 5 Multiple-Angle and Product-to-Sum Identities • Reduction identity • Double-angle identities • Unit Review • Power-reducing identities • Half-angle identities • Unit 5 Test • Product-to-sum identities

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Unit 6 Matrices 12 Days Standards “I Can” Statements Number and Quantity P.N.VM.C.7 Use matrices to represent and manipulate data, e.g., to represent I can use matrices to represent and manipulate data, e.g., to represent payoffs payoffs or incidence relationships in a network. or incidence relationships in a network. P.N.VM.C.8 Multiply matrices by scalars to produce new matrices, e.g., as I can multiply matrices by scalars to produce new matrices, e.g., as when all when all of the payoffs in a game are doubled. of the payoffs in a game are doubled. I can determine if matrices may be added, subtracted or multiplied by using their dimensions. P.N.VM.C.9 Add, subtract, and multiply matrices of appropriate dimensions.

I can add, subtract, and multiply matrices of appropriate dimensions. P.N.VM.C.10 Understand that, unlike multiplication of numbers, matrix I can show that matrix multiplication for square matrices is not a multiplication for square matrices is not a commutative operation, but still commutative operation, but still satisfies the associative and distributive satisfies the associative and distributive properties. properties. I can show how the zero and identity matrices play a role in matrix addition P.N.VM.C.11 Understand that the zero and identity matrices play a role in and multiplication similar to the role of 0 and 1 in the real numbers. matrix addition and multiplication similar to the role of 0 and 1 in the real

numbers. The determinant of a square matrix is nonzero if and only if the I can explain how the determinant of a square matrix is non-zero if and only if matrix has a multiplicative inverse. the matrix has a multiplicative inverse. I can multiply a vector (regarded as a matrix with one column) by a matrix of P.N.VM.C.12 Multiply a vector (regarded as a matrix with one column) by a suitable dimensions to produce another vector. matrix of suitable dimensions to produce another vector. Work with

matrices as transformations of vectors. I can work with matrices as transformations of vectors. P.N.VM.C.13 Work with 2 × 2 matrices as transformations of the plane, and I can work with 2 × 2 matrices as transformations of the plane, and interpret interpret the absolute value of the determinant in terms of area. the absolute value of the determinant in terms of area. Algebra P.A.REI.A.1 Represent a system of linear equations as a single matrix I can represent a system of equations as a single matrix equation in a vector equation in a vector variable. variable. P.A.REI.A.2 Find the inverse of a matrix if it exists and use it to solve I can find the inverse of a matrix if it exists and use it to solve systems of systems of linear equations (using technology for matrices of dimension 3 × 3 linear equations. I can use technology when solving system of equations or greater). represented my matrices of dimensions 3 × 3 or greater. P.MCPS.5 Solve maximum/minimum value problems by converting the given verbal information into an appropriate mathematical model and I can solve challenging optimization problems involving three dimensional analyzing the graph of that model graphically to answer the questions. figures, i.e. boxes, cones. Recognize the approximation necessary when solving graphically. I can describe the solution process by analyzing the graph and constructing arguments to explain this reasoning.

I can use precise language to write solutions to max/min problems.

• Multivariable linear system • Section 2 Matrix Multiplication, Inverses, and Determinants • Row-echelon form • Gaussian elimination • Section 3 Solving Linear Systems Using Inverses and Cramer’s Rule • Augmented matrix • Coefficient matrix • Quiz • Elementary row operations • Reduced row-echelon form • Section 4 Partial Fractions • Gauss-Jordan elimination • Properties of matrix multiplication • Section 5 Linear Optimization • Identity matrix

• Scalar • Unit Review • Inverse matrix • Invertible • Unit 6 Test • Singular matrix • Square matrix • Determinant • Expansion by minors • Square system • Invertible square linear system

• Cramer’s Rule

• Partial fraction

• Partial fraction decomposition • Optimization • Linear programming • Objective function • Constraints • Feasible region • Feasible solutions • Multiple optimal solutions • Unbounded • Unbounded region

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Unit 7 Conic Sections 7 Days Standards “I Can” Statements Algebra P.A.C.A.1 Display all of the conic sections as portions of a cone. I can display all of the conic sections as portions of a cone. P.A.C.A.2 Derive the equations of ellipses and hyperbolas given the foci, I can derive the equations of ellipses and hyperbolas given the foci, using the using the fact that the sum or difference of distances from the foci is constant. fact that the sum or difference of distances from the foci is constant. P.A.C.A.3 From an equation in standard form, graph the appropriate conic I can graph ellipses and hyperbolas and demonstrate understanding of the section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an relationship between their standard algebraic form and the graphical understanding of the relationship between their standard algebraic form and characteristics. the graphical characteristics. P.A.C.A.4 Transform equations of conic sections to convert between general I can transform equations of conic sections to convert between general and and standard form. standard form. Sections/Topics Activities/Resources/Materials Extra Resources • www.shodor.org/interactive • • Pre-assessment Vocabulary • Section 1 Parabolas • Conic section • Locus • Section 2 Ellipses and Circles • Parabola • Focus directrix • Quiz • Axis of symmetry • Vertex • Section 3 Hyperbolas • Ellipse • Foci • Major axis • Section 4 Rotations of Conic Sections • Minor axis

• Center • Unit Review • Vertices • Co-vertices • Unit 7 Test • Eccentricity • Standard form of the equation of a circle • Hyperbola • Transverse axis • Conjugate axis

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Unit 8 Polar Graphing & Vectors 16 Days Standards “I Can” Statements Number and Quantity I can represent vectors graphically with both magnitude and direction.

P.N.VM.A.1 Recognize vector quantities as having both magnitude and I can represent vectors by directed line segments and use appropriate symbols direction. Represent vector quantities by directed line segments, and use for vectors and their magnitudes. appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v). I can interpret vectors geometrically and their relationship to real life problems. P.N.VM.A.2 Find the components of a vector by subtracting the coordinates I can demonstrate that vectors are determined by the coordinates of their of an initial point from the coordinates of a terminal point. initial and terminal points, or by their components. P.N.VM.B.3 Solve problems involving velocity and other quantities that can I can solve velocity problems with vectors. be represented by vectors. P.N.VM.B.4 Add and subtract vectors.

a. Add vectors end-to-end, component-wise, and by the parallelogram rule. I can add and subtract vectors using a variety of methods and multiple Understand that the magnitude of a sum of two vectors is typically not the representations. sum of the magnitudes. I can represent vectors and vector arithmetic graphically by creating a b. Given two vectors in magnitude and direction form, determine the resultant vector. magnitude and direction of their sum. I can calculate the magnitude and direction angle of a resultant vector. c. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite I can represent vector subtraction graphically. direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. P.N.VM.B.5 Multiply a vector by a scalar.

a. Represent scalar multiplication graphically by scaling vectors and possibly I can multiply a vector by a scalar algebraically and by modeling them reversing their direction; perform scalar multiplication component-wise, e.g., graphically. as c(vx, vy) = (cvx, cvy).

I can calculate the magnitude and the direction angle of a scalar multiple of a b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|. vector.

c. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). P.N.CN.A.4 Represent addition, subtraction, multiplication, and conjugation I can represent addition, subtraction, multiplication, and division of complex of complex numbers geometrically on the complex plane; use properties of numbers geometrically on the complex plane. this representation for computation.

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit For example, (–1 + 3i)3 = 8 because (–1 + 3i) has modulus 2 and argument 120°. I can calculate the distance between numbers in the complex plane as the magnitude or modulus of the difference by finding the absolute value of the P.N.CN.A.5 Calculate the distance between numbers in the complex plane as complex number. the modulus of the difference, and the midpoint of a segment as the average

of the numbers at its endpoints. I can calculate the midpoint of a segment as the average of the numbers at its endpoints. I can interpret the dot product of two vectors P.N.VM.B.6 Calculate and interpret the dot product of two vectors. I can use the dot product to find the angle between two vectors. P.N.CN.A.1 Perform arithmetic operations with complex numbers expressing I can perform arithmetic operations with complex numbers expressing answers in the form a + bi. answers in the form a + bi. P.N.CN.A.2 Find the conjugate of a complex number; use conjugates to find I can find the conjugate of a complex number and use them to find moduli moduli and quotients of complex numbers. and quotients of complex numbers. I can represent complex numbers on the complex plane in rectangular and P.N.CN.A.3 Represent complex numbers on the complex plane in rectangular polar form (including real and imaginary numbers). and polar form (including real and imaginary numbers), and explain why the

rectangular and polar forms of a given complex number represent the same I can explain why the rectangular and polar forms of a given complex number number. represent the same number. Geometry P.G.PC.A.1 Graph functions in polar coordinates. I can graph functions in polar coordinates. P.G.PC.A.2 Convert between rectangular and polar coordinates. I can convert between rectangular and polar coordinates. P.G.PC.A.3 ★ Represent situations and solve problems involving polar I can represent complex numbers on the complex plane in rectangular and coordinates. polar form. P.MCPS.4 Apply De Moivre’s Theorem to find powers and roots of complex I can apply De Moivre’s Theorem to find powers and roots of complex numbers. numbers.

• Section 1 Introduction to Vectors Vocabulary • Vector • Polar coordinate system • Section 2 Vectors in the Coordinate Plane • Initial point • Pole • Terminal point • Polar axis

• Standard position of a • Polar coordinates • Section 3 Dot Products and Vector Projections vector • Polar equation • Direction of a vector • Polar graph • Quiz • Magnitude of a vector • Polar distance formula • Quadrant bearing • Limaçon • Section 4 Vectors in Three-Dimensional Space • True bearing • Cardioid • Parallel vectors • Rose • Section 5 Dot Products of Vectors in Space • Equivalent vectors • Lemniscate • Opposite vectors • Spiral of Archimedes • Mid-Unit Quiz • Resultant • Complex plane • Triangle method • Real axis • Section 6 Polar Coordinates • Parallelogram method • Imaginary axis • Zero vector • Argand plane • Scalar of a vector • Section 7 Graphs of Polar Equations • Absolute value of a complex • Components number

• Rectangular components • Polar form • Section 8 Polar and Rectangular Forms of Equations • Component form • Trigonometric form • Unit vector • Modulus • Quiz • Linear combination • Argument • Dot product • DeMoivre’s Theorem • Section 9 Polar Forms of Conic Sections • Orthogonal • pth roots of unity • Vector projection • Section 10 Complex numbers and DeMoivre’s Theorem • Work • Three-dimensional • Unit Review coordinate system • z-axis • Unit 8 Test • Ordered triple • Cross product • Torque • Parallelpiped • Triple scalar product

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Unit 9 Parametric Equations 6 Days Standards “I Can” Statements Algebra P.A.PE.A.1 ★Graph curves parametrically (by hand and with appropriate I can graph parametrically by hand and with appropriate technology. technology). P.A.PE.A.2 ★Eliminate parameters by rewriting parametric equations as a I can eliminate parameters by rewriting parametric equations as a single single equation. equation. P.MCPS.3 Simulate motion using parametric equations. I can simulate motion using parametric equations. Sections/Topics Activities/Resources/Materials • Pre-assessment Extra Resources • www.shodor.org/interactive • Section 1 Graph Parametric Equations •

Vocabulary • Section 2 Write Parametric Equations in Rectangular Form • Parametric equation

• Unit Review • Parameter • Orientation • Unit 9 Test • Parametric curve

• Projectile motion • Polar coordinates

• Rectangular coordinates

Maury County Public Schools 5/8/18 Office of Instruction Pk-12 Precalculus TN Ready Performance Standards by Unit Unit 10 Sequences, Series, & Sigma Notation 14 Days Standards “I Can” Statements Algebra P.A.S.A.1 Demonstrate an understanding of sequences by representing them I can demonstrate an understanding of sequences by representing them recursively and explicitly. recursively and explicitly. P.A.S.A.2 Use sigma notation to represent a series; expand and collect I can use Sigma (Σ) notation to represent a series. expressions in both finite and infinite settings. P.A.S.A.3 Derive and use the formulas for the general term and summation of finite or infinite arithmetic and geometric series, if they exist. I can determine whether a given arithmetic or geometric series converges or

diverges. a. Determine whether a given arithmetic or geometric series converges or

diverges. I can find the sum of a given geometric series (both infinite and finite).

b. Find the sum of a given geometric series (both infinite and finite). I can find the sum of a finite arithmetic series.

c. Find the sum of a finite arithmetic series. P.A.S.A.4 Understand that series represent the approximation of a number I can understand that the series represent the approximation of a number when truncated; estimate truncation error in specific examples. when truncated; estimate truncation error in specific examples. P.A.S.A.5 Know and apply the Binomial Theorem for the expansion of (x + I can know and apply the Binomial Theorem for the expansion of y)n in powers of x and y for a positive integer n, where x and y are any (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. numbers, with coefficients determined, for example, by Pascal’s Triangle. Functions P.F.IF.A.8 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. I can analyze a variety of types of situations modeled by functions and For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, recognize that sequences are functions, sometimes defined recursively. f(n+1) = f(n) + f(n-1) for n ≥ 1.

Vocabulary • Sequence • Principle of mathematical • Term induction • Finite sequence • Anchor step • Infinite sequence • Inductive hypothesis • Pre-assessment • Explicit formula • Inductive step

• Recursive formula • Extended principle of • Section 1 Sequences, Series, and Sigma Notation • Fibonacci sequence mathematical induction • Converge • Binomial coefficients • Section 2 Arithmetic Sequences and Series • Diverge • Pascal’s triangle • Series • Binomial Expansion • Section 3 Geometric Sequences and Series • Finite series • Binomial Theorem • Infinite series • Power series • Quiz • nth partial sum • Exponential series • Sigma notation • Euler’s Formula • Section 4 Mathematical Induction • Arithmetic sequence • Common difference

• Arithmetic means • Section 5 The Binomial Theorem • First difference • Second difference • Section 6 Functions as Infinite Series • Arithmetic series • Sum of a finite arithmetic • Unit Review series • Sum of an infinite • Unit 10 Test arithmetic series • Geometric sequence • Common ratio • nth term of a geometric sequence • Geometric means • Geometric series • Sum of a finite geometric series • Sum of an infinite geometric series

Maury County Public Schools 5/8/18 Office of Instruction Pk-12