The following Practice Standards and Literacy Skills will be used throughout the course:

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.

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 14 Days 16 Days 12 Days 16 Days 13 Days 12 Days 7 Days 16 Days 6 Days Unit 10 14 Days Functions, Limits, & End Behavior P.F.BF.A.2 P.F.BF.A.4 P.F.IF.A.1 P.F.BF.A.1 P.F.BF.A.3 P.F.BF.A.5.a P.F.BF.A.5.b P.F.BF.A.5.c P.F.BF.A.5.d P.F.BF.A.6 F.S.MD.A.3 P.S.MD.A.1 P.S.MD.A.2 P.S.MD.A.3 P.MCPS.6 Power, Polynomial, & Rational Functions P.F.IF.A.5 P.F.IF.A.2 P.F.IF.A.4 P.F.IF.A.6 P.F.IF.A.7 P.N.CN.B.6 P.N.CN.B.7 P.N.NE.A.4 P.N.NE.A.5 P.A.REI.A.3 P.A.REI.A.4 Exponential & Logarithmic Functions P.F.IF.A.2 P.N.NE.A.3 P.N.NE.A.2 P.N.NE.A.1 P.MCPS.2 Trigonometric Functions P.F.TF.A.1 P.G.AT.A.3 P.G.AT.A.4 P.F.TF.A.2 P.F.TF.A.3 P.F.GT.A.1 P.F.GT.A.2 P.F.GT.A.3 P.F.GT.A.4 P.F.GT.A.5 P.F.GT.A.6 P.F.GT.A.7 P.F.GT.A.8 P.G.AT.A.1 P.S.MD.A.3 P.F.TF.A.4 P.MCPS.1 Trigonometric Identities & Equations Matrices Standards (By number) P.G.TI.A.1 P.N.VM.C.7 P.G.TI.A.2 P.N.VM.C.8 P.G.AT.A.2 P.N.VM.C.9 P.G.AT.A.5 P.N.VM.C.10 P.G.AT.A.6 P.N.VM.C.11 P.N.VM.C.12 P.N.VM.C.13 P.A.REI.A.1 P.A.REI.A.2 P.MCPS.5 Conic Sections P.A.C.A.1 P.A.C.A.2 P.A.C.A.3 P.A.C.A.4 Polar Graphing & Vectors P.N.VM.A.1 P.N.VM.A.2 P.N.VM.B.3 P.N.VM.B.4.a P.N.VM.B.4.b P.N.VM.B.4.c P.N.VM.B.5.a P.N.VM.B.5.b P.N.VM.B.5.c P.N.CN.A.4 P.N.CN.A.5 P.N.VM.B.6 P.N.CN.A.1 P.N.CN.A.2 P.G.PC.A.1 P.G.PC.A.2 P.G.PC.A.3 P.N.CN.A.3 P.MCPS.4 Parametric Equations P.A.PE.A.1 P.A.PE.A.2 P.MCPS.3 Sequences, Series, & Sigma Notation P.A.S.A.1 P.A.S.A.2 P.A.S.A.3.a P.A.S.A.3.b P.A.S.A.3.c P.F.IF.A.8 P.A.S.A.4 P.A.S.A.5 Green=Major Content Blue=Supporting Content

Standards P.F.BF.A.2 Develop an understanding of functions as elements that can be operated upon to get new functions: addition, subtraction, multiplication, division, and composition of functions. P.F.BF.A.4 I can construct the difference quotient for a given function and simplify the resulting expression. P.F.IF.A.1 Determine whether a function is even, odd, or neither. P.F.BF.A.1 Understand how the algebraic properties of an equation transform the geometric properties of its graph. For example, given a function, describe the transformation of the graph resulting from the manipulation of the algebraic properties of the equation (i.e., translations, stretches, reflections and changes in periodicity and amplitude) 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 as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. P.F.BF.A.5 Find inverse functions (including exponential, logarithmic and trigonometric). Unit 1 Functions, Limits, & End Behavior 14 Days Functions I Can Statements I can create functions by adding, subtracting, multiplication, division, and composition of functions. I can construct the difference quotient for a given function and simplify the resulting expression. I can determine whether a function is even, odd, or neither algebraically and graphically. I can describe the transformation of the graph resulting from the manipulation of the algebraic properties of the equation (i.e., translations, stretches, reflections, and changes in periodicity and amplitude). I can form a composite function. I can find the domain of a composite function. I can recognize the role that domain of a function plays in the combination of functions by composition of functions. a. Calculate the inverse of a function, f(x), with respect to each of the functional operations; in other words, the additive inverse, f(x), the multiplicative inverse, 1/f(x), and the inverse with respect to composition, f- 1(x). Understand the algebraic and graphical implications of each type. b. Verify by composition that one function is the inverse of another. c. Read values of an inverse function from a graph or a table, given that the function has an inverse. 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 of one another over the line y = x. I can calculate the inverse of a function with respect to each of the functional operations. I can 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. I can find an inverse function by restricting the domain of a function that is not one-to-one. I can explain why the graph of a function and its inverse are reflections of one another over the line y = x.

I can explore the properties of a limit by analyzing sequences and series. P.MCPS.6 Develop the concept of the limit using tables, graphs, and algebraic properties. I can understand the relationship between a horizontal asymptote and the limit of a function at infinity. I can determine the limit of a function at a specified number. P.S.MD.A.1 Create scatter plots, analyze patterns and describe relationships for bivariate data (linear, polynomial, trigonometric or exponential) to model real-world phenomena and to make predictions. 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. I can analyze patterns from the scatter plots that I created. I can describe relationships in the scatter plots. P.S.MD.A.2 Determine a regression equation to model a set of bivariate data. Justify why this equation best fits the data. P.S.MD.A.3 Use a regression equation modeling bivariate data to make predictions. Identify possible considerations regarding the accuracy of predictions when interoplating or extrapolating. I can make prediction using the scatter plots. I can explain how to determine the best regression equation model that approximates a particular data set. I can find the regression equation that best fits bivariate data. I can use a regression equation modeling bivariate data to make predictions. I can identify possible considerations regarding the accuracy of predictions when interpolating or extrapolating.

Sections/Topics Activities/Resources/Materials Extra Resources www.shodor.org/interactive Pre-assessment Section 1 Functions Section 2 Analyzing Graphs of Functions Section 3 Continuity, End Behavior, and Limits Section 4 Extrema and Average Rates of Change Quiz Section 5 Parent Functions and Transformations Section 6 Function Operations and Composition of Functions Section 7 Inverse Relations and Functions Unit Review Unit 1 Test Set-builder notation Interval notation Function Vertical line test Function notation Independent variable Dependent variable Implied domain Piecewise-defined function Line symmetry Point symmetry Even function Odd function Continuous function Discontinuous function Limit Infinite discontinuity Jump discontinuity Removable discontinuity Nonremovable discontinuity Continuity test Intermediate Value Theorem End behavior Increasing Decreasing Constant Critical points Extrema Relative Extrema Absolute Extrema Vocabulary Maximum Minimum Point of inflection Average rate of change Secant line Parent function Constant function Identity function Quadratic function Cubic function Square root function Reciprocal function Absolute value function Step function Greatest integer function Transformation Translation Reflection Dilation Composition of functions Inverse relation Inverse function Horizontal line test One-to-one function

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. For example, rewrite x 2 I can extend polynomial identities to the complex numbers. + 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 division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. P.A.REI.A.3 Solve nonlinear inequalities (quadratic, trigonometric, conic, exponential, logarithmic, and rational) by graphing (solutions in interval notation if one-variable), by hand and with appropriate technology. P.A.REI.A.4 Solve systems of nonlinear inequalities by graphing. P.F.IF.A.5 Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax 2 + c. P.F.IF.A.2 Analyze qualities of exponential, polynomial, logarithmic, trigonometric, and rational functions and solve real world problems that can be modeled with these functions (by hand and with appropriate technology). 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 (exponential, polynomial, logarithmic, trigonometric, and rational). I can add, subtract, multiply, and divide rational expressions. Algebra I can solve nonlinear inequalities (quadratic and rational) by graphing (solutions in interval notation if one-variable), by using a sign chart, and with appropriate technology. I can solve systems of nonlinear inequalities by graphing. Functions I can Identify characteristics of graphs such as direction it opens, vertex based on a set of conditions or on a general equation such as y = ax 2 + 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. I can identify or analyze the following properties of polynomial, and rational functions from tables, graphs, and equations. 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. I can explain the relationship between the real zeros and the x-intercept of the graph of a function (polynomial, rational, exponential, logarithmic, and trigonometric).

P.F.IF.A.6 Visually locate critical points on the graphs of functions and determine if each critical point is a minimum, a maximum or point of inflection. Describe intervals where the function is increasing or decreasing and where different types of concavity occur. P.F.IF.A.7 Graph rational functions, identifying zeros, asymptotes (including slant), and holes (when suitable factorizations are available) and showing end-behavior. Sections/Topics I can locate critical points on the graphs of polynomial functions and determine if each critical point is a minimum or a maximum. I can describe and locate maximums, minimums, increasing and decreasing intervals, and zeroes given a sketch of the graph. I can graph rational functions, identifying zeros, asymptotes (including slant), and holes (when suitable factorizations are available) and showing endbehavior. Activities/Resources/Materials Extra Resources www.shodor.org/interactive Pre-assessment Section 1 Power and Radical Functions Section 2 Polynomial Functions Section 3 The Remainder and Factor Theorems Quiz Section 4 Zeros of Polynomial Functions Section 5 Rational Functions Section 6 Nonlinear Inequalities Unit Review Unit 2 Test Power function Monomial function Radical function Extraneous solution Polynomial function Polynomial function of degree n Leading coefficient Degree of a polynomial Leading term test Quartic function Turning points Quadratic form Repeated zero Multiplicity Polynomial long division Synthetic division Depressed polynomial Remainder theorem Factor theorem Rational zero theorem Upper bound Lower bound Upper and lower bound tests Vocabulary Descartes rule of signs Fundamental theorem of algebra Linear factorization theorem Conjugate root theorem Complex conjugate Irreducible over the reals Rational function Asymptote Vertical asymptote Horizontal asymptote Slant (oblique) asymptote Hole Polynomial inequality Sign chart Rational inequality

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. P.N.NE.A.2 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. I can change an equation from logarithmic to exponential form and back. I can solve exponential equations. I can solve logarithmic equations. P.N.NE.A.1 Use the laws of exponents and logarithms to expand or collect terms in expressions; simplify expressions or modify them in order to analyze them or compare them. P.F.IF.A.2 Analyze qualities of exponential, polynomial, logarithmic, trigonometric, and rational functions and solve real world problems that can be modeled with these functions (by hand and with appropriate technology). 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 expressions; simplify expressions or modify them in order to analyze them or compare them. I can compare exponential and logarithmic expressions. Functions I can identify or analyze the following properties of exponential, logarithmic and logistic functions: Domain, Range, Continuity, Increasing/Decreasing 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.

P.MCPS.2 Apply appropriate techniques to analyze mathematical models and functions constructed from verbal information; interpret the solution obtained in written form using appropriate units of measurement. Sections/Topics I can create and analyze mathematical models that describe situations including growth and decay and financial applications. Activities/Resources/Materials Extra Resources www.shodor.org/interactive Pre-assessment Section 1 Exponential Functions Section 2 Logarithmic Functions Section 3 Properties of Logarithms Quiz Section 4 Exponential and Logarithmic Equations Section 5 Modeling with Nonlinear Regression Unit Review Unit 3 Test Algebraic function Transcendental function Exponential function Natural base Compound interest formula Continuous compound interest formula Exponential growth function Exponential decay function Continuous exponential growth function Continuous exponential decay function Logarithmic function with base b Logarithmic form Exponential form Logarithms Properties of logarithms Common logarithm 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 Vocabulary

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. P.F.TF.A.3 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. P.F.GT.A.1 Interpret transformations of trigonometric functions. P.F.GT.A.2 Determine the difference made by choice of units for angle measurement when graphing a trigonometric function. P.F.GT.A.3 Graph the six trigonometric functions and identify characteristics such as period, amplitude, phase shift, and asymptotes. P.F.GT.A.4 Find values of inverse trigonometric expressions (including compositions), applying appropriate domain and range restrictions. P.F.GT.A.5 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. P.F.GT.A.6 Determine the appropriate domain and corresponding range for each of the inverse trigonometric functions. P.F.GT.A.7 Graph the inverse trigonometric functions and identify their key characteristics. P.F.TF.A.4 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. P.G.AT.A.3 Derive and apply the formulas for the area of sector of a circle. P.G.AT.A.4 Calculate the arc length of a circle subtended by a central angle. P.G.AT.A.1 Use the definitions of the six trigonometric ratios as ratios of sides in a right triangle to solve problems about lengths of sides and measures of angles. I can use the unit circle to explain symmetry of the six trigonometric functions. I can describe periodicity of all six trigonometric functions. I can match a trigonometric equation with its graph by recognizing the parent graph and by using transformations. I can determine the difference made by choice of units for angle measurement when graphing a trigonometric function. I can graph the six trigonometric functions (sin, cos, tan, csc, sec, cot) and identify characteristics such as period, amplitude, phase shift, and asymptotes. I can find values of inverse trigonometric functions, applying appropriate domain and range restrictions. I can understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. I can determine identify and list the appropriate domain and corresponding range for each of the inverse trigonometric functions. I can graph the inverse trigonometric functions and identify their key characteristics. I can choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Geometry I can derive and apply the formulas for the area of sector of a circle. I can calculate the arc length of a circle subtended by a central angle. I can use the definitions of the six trigonometric ratios as ratios of sides in a right triangle to solve problems about lengths of sides and measures of angles.

P.S.MD.A.3 Use a regression equation modeling bivariate data to make predictions. Identify possible considerations regarding the accuracy of predictions when interpolating or extrapolating. P.MCPS.1 Apply the arc length formula or conversion factors to real world applications. Sections/Topics Pre-assessment Section 1 Right Triangle Trigonometry Statistics and Probability I can use a regression equation modeling bivariate data to make predictions involving trigonometric functions. I can apply linear and angular velocity formulas in real world applications. Activities/Resources/Materials Extra Resources www.shodor.org/interactive Section 2 Degrees and Radians, Arc Length, Area of a Sector, Linear and Angular Speed Section 3 Trigonometric Functions on the Unit Circle Quiz Section 4 Graphing Sine and Cosine Functions Section 5 Graphing Tangent, Cosecant, and Secant Quiz Section 6 Inverse Trigonometric Functions Section 7 The Law of Sines and Law of Cosines Unit Review Unit 4 Test Trigonometric ratios Trigonometric functions Sine Cosine Tangent Cosecant Secant Cotangent Reciprocal functions Inverse trigonometric function Inverse sine Inverse cosine Inverse tangent Angle of elevation Angle of depression Solving a right triangle Vertex Initial side Terminal side Standard position of an angle Radians Degrees Coterminal angles Arc length Linear speed Angular speed Sector Vocabulary Area of a sector Quadrantal angle Reference angle Unit circle Circular functions Periodic functions Period Sinusoid Amplitude Frequency Phase shift Vertical shift Midline Damped oscillation Damped trigonometric function Damping factor Damped harmonic motion Arcsine function Arccosine function Arctangent function Oblique triangles Law of sines Law of cosines Ambiguous case Heron s formula

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 ambiguous case) and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). I can determine how many solutions are possible for the Ambiguous case of the Law of Sines. 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.

Pre-assessment Sections/Topics Activities/Resources/Materials Extra Resources www.shodor.org/interactive Section 1 Trigonometric Identities Section 2 Verifying Trigonometric Identities Quiz Section 3 Solving Trigonometric Equations Section 4 Sum and Difference Identities Section 5 Multiple-Angle and Product-to-Sum Identities Unit Review Unit 5 Test Vocabulary Identity Trigonometric identity Pythagorean identities Cofunction identities Odd-even identities Verify an identity Sum and difference identities Reduction identity Double-angle identities Power-reducing identities Half-angle identities Product-to-sum identities

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. P.N.VM.C.10 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. P.N.VM.C.11 Understand that the zero and identity matrices play a role in 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 matrix has a multiplicative inverse. P.N.VM.C.12 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. P.N.VM.C.13 Work with 2 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. P.A.REI.A.1 Represent a system of linear equations as a single matrix equation in a vector variable. P.A.REI.A.2 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 3 or greater). P.MCPS.5 Solve maximum/minimum value problems by converting the given verbal information into an appropriate mathematical model and analyzing the graph of that model graphically to answer the questions. Recognize the approximation necessary when solving graphically. I can add, subtract, and multiply matrices of appropriate dimensions. I can show that matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. I can show how the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. I can explain how the determinant of a square matrix is non-zero if and only if the matrix has a multiplicative inverse. I can multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. I can work with matrices as transformations of vectors. I can work with 2 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. Algebra I can represent a system of equations as a single matrix equation in a vector variable. I can find the inverse of a matrix if it exists and use it to solve systems of linear equations. I can use technology when solving system of equations represented my matrices of dimensions 3 3 or greater. I can solve challenging optimization problems involving three dimensional figures, i.e. boxes, cones. 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.

Pre-assessment Sections/Topics Section 1 Multivariable Linear Systems and Row Operations Section 2 Matrix Multiplication, Inverses, and Determinants Section 3 Solving Linear Systems Using Inverses and Cramer s Rule Quiz Section 4 Partial Fractions Section 5 Linear Optimization Unit Review Unit 6 Test Activities/Resources/Materials Extra Resources www.shodor.org/interactive Vocabulary Multivariable linear system Row-echelon form Gaussian elimination Augmented matrix Coefficient matrix Elementary row operations Reduced row-echelon form Gauss-Jordan elimination Properties of matrix multiplication Identity matrix Scalar Inverse matrix Invertible 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

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 and standard form. Sections/Topics Pre-assessment Section 1 Parabolas Section 2 Ellipses and Circles Quiz Section 3 Hyperbolas Section 4 Rotations of Conic Sections Unit Review Unit 7 Test I can transform equations of conic sections to convert between general and standard form. Activities/Resources/Materials Extra Resources www.shodor.org/interactive Conic section Locus Parabola Focus directrix Axis of symmetry Vertex Ellipse Foci Major axis Minor axis Center Vertices Co-vertices Eccentricity Standard form of the equation of a circle Hyperbola Transverse axis Conjugate axis Vocabulary

Standards Unit 8 Polar Graphing & Vectors 16 Days 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 direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, v, v, v). P.N.VM.A.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. P.N.VM.B.3 Solve problems involving velocity and other quantities that can 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. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. 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 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 reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy). b. Compute the magnitude of a scalar multiple cv using cv = c. 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 of complex numbers geometrically on the complex plane; use properties of this representation for computation. I can represent vectors by directed line segments and use appropriate symbols for vectors and their magnitudes. I can interpret vectors geometrically and their relationship to real life problems. I can demonstrate that vectors are determined by the coordinates of their initial and terminal points, or by their components. I can solve velocity problems with vectors. I can add and subtract vectors using a variety of methods and multiple representations. I can represent vectors and vector arithmetic graphically by creating a resultant vector. I can calculate the magnitude and direction angle of a resultant vector. I can represent vector subtraction graphically. I can multiply a vector by a scalar algebraically and by modeling them graphically. I can calculate the magnitude and the direction angle of a scalar multiple of a vector. I can represent addition, subtraction, multiplication, and division of complex numbers geometrically on the complex plane.

For example, ( 1 + 3i)3 = 8 because ( 1 + 3i) has modulus 2 and argument 120. P.N.CN.A.5 Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. P.N.VM.B.6 Calculate and interpret the dot product of two vectors. P.N.CN.A.1 Perform arithmetic operations with complex numbers expressing answers in the form a + bi. P.N.CN.A.2 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. P.N.CN.A.3 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. P.G.PC.A.1 Graph functions in polar coordinates. P.G.PC.A.2 Convert between rectangular and polar coordinates. P.G.PC.A.3 Represent situations and solve problems involving polar coordinates. P.MCPS.4 Apply De Moivre s Theorem to find powers and roots of complex numbers. 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 complex number. 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 I can use the dot product to find the angle between two vectors. I can perform arithmetic operations with complex numbers expressing answers in the form a + bi. I can find the conjugate of a complex number and use them to find moduli and quotients of complex numbers. I can represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers). I can explain why the rectangular and polar forms of a given complex number represent the same number. Geometry I can graph functions in polar coordinates. I can convert between rectangular and polar coordinates. I can represent complex numbers on the complex plane in rectangular and polar form. I can apply De Moivre s Theorem to find powers and roots of complex numbers.

Pre-assessment Sections/Topics Activities/Resources/Materials Extra Resources www.shodor.org/interactive Section 1 Introduction to Vectors Section 2 Vectors in the Coordinate Plane Section 3 Dot Products and Vector Projections Quiz Section 4 Vectors in Three-Dimensional Space Section 5 Dot Products of Vectors in Space Mid-Unit Quiz Section 6 Polar Coordinates Section 7 Graphs of Polar Equations Section 8 Polar and Rectangular Forms of Equations Quiz Section 9 Polar Forms of Conic Sections Section 10 Complex numbers and DeMoivre s Theorem Unit Review Unit 8 Test Vector Initial point Terminal point Standard position of a vector Direction of a vector Magnitude of a vector Quadrant bearing True bearing Parallel vectors Equivalent vectors Opposite vectors Resultant Triangle method Parallelogram method Zero vector Scalar of a vector Components Rectangular components Component form Unit vector Linear combination Dot product Orthogonal Vector projection Work Three-dimensional coordinate system z-axis Ordered triple Cross product Torque Parallelpiped Triple scalar product Vocabulary Polar coordinate system Pole Polar axis Polar coordinates Polar equation Polar graph Polar distance formula Limaçon Cardioid Rose Lemniscate Spiral of Archimedes Complex plane Real axis Imaginary axis Argand plane Absolute value of a complex number Polar form Trigonometric form Modulus Argument DeMoivre s Theorem p th roots of unity

Standards P.A.PE.A.1 Graph curves parametrically (by hand and with appropriate technology). P.A.PE.A.2 Eliminate parameters by rewriting parametric equations as a single equation. P.MCPS.3 Simulate motion using parametric equations. Sections/Topics Pre-assessment Section 1 Graph Parametric Equations Unit 9 Parametric Equations 6 Days Algebra I Can Statements I can graph parametrically by hand and with appropriate technology. I can eliminate parameters by rewriting parametric equations as a single equation. I can simulate motion using parametric equations. Activities/Resources/Materials Extra Resources www.shodor.org/interactive Section 2 Write Parametric Equations in Rectangular Form Unit Review Unit 9 Test Vocabulary Parametric equation Parameter Orientation Parametric curve Projectile motion Polar coordinates Rectangular coordinates

Standards P.A.S.A.1 Demonstrate an understanding of sequences by representing them recursively and explicitly. P.A.S.A.2 Use sigma notation to represent a series; expand and collect 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. a. Determine whether a given arithmetic or geometric series converges or diverges. b. Find the sum of a given geometric series (both infinite and finite). c. Find the sum of a finite arithmetic series. P.A.S.A.4 Understand that series represent the approximation of a number when truncated; estimate truncation error in specific examples. P.A.S.A.5 Know and apply the Binomial Theorem for the expansion of (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. P.F.IF.A.8 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n 1. Unit 10 Sequences, Series, & Sigma Notation 14 Days I Can Statements Algebra I can demonstrate an understanding of sequences by representing them recursively and explicitly. I can use Sigma (Σ) notation to represent a series. I can 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). I can find the sum of a finite arithmetic series. I can understand that the series represent the approximation of a number when truncated; estimate truncation error in specific examples. I can know and apply the Binomial Theorem for the expansion of (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. Functions I can analyze a variety of types of situations modeled by functions and recognize that sequences are functions, sometimes defined recursively.

Sections/Topics Activities/Resources/Materials Extra Resources www.shodor.org/interactive Pre-assessment Section 1 Sequences, Series, and Sigma Notation Section 2 Arithmetic Sequences and Series Section 3 Geometric Sequences and Series Quiz Section 4 Mathematical Induction Section 5 The Binomial Theorem Section 6 Functions as Infinite Series Unit Review Unit 10 Test Sequence Term Finite sequence Infinite sequence Explicit formula Recursive formula Fibonacci sequence Converge Diverge Series Finite series Infinite series n th partial sum Sigma notation Arithmetic sequence Common difference Arithmetic means First difference Second difference Arithmetic series Sum of a finite arithmetic series Sum of an infinite arithmetic series Geometric sequence Common ratio n th term of a geometric sequence Geometric means Geometric series Sum of a finite geometric series Sum of an infinite geometric series Vocabulary Principle of mathematical induction Anchor step Inductive hypothesis Inductive step Extended principle of mathematical induction Binomial coefficients Pascal s triangle Binomial Expansion Binomial Theorem Power series Exponential series Euler s Formula