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

Transcription

1 SDC 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 Precaclulus.

2 Unit 1 12 Days SDC Precalculus Curriculum Overview Quarter 1 Quarter 2 Quarter 3 Quarter 4 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 14 Days 12 Days 16 Days 13 Days 12 Days 16 Days Unit 8 20 Days Functions, Limits, & End Behavior 1.E.a 1.E.e 1.E.f 2.I.a 3.F.a 3.PF.a 3.PF.b 3.PF.d 5.F.a 5.F.b 5.F.c 5.F.d P.MCPS.6 Power, Polynomial, & Rational Functions 1.E.a 1.E.c 1.E.d 1.E.e 1.E.f 2.I.a 3.PF.c 3.PF.d 4.M.a 4.M.b 4.M.c Exponential & Logarithmic Functions 1.E.a 1.E.e 1.E.f 1.E.g Trigonometric Functions Trigonometric Identities & Equations Standards (By number) 1.E.a 1.E.a 6.TF.a 6.TF.d 6.TF.b 6.TF.e 6.TF.c 6.TF.f 7.G.T.a 7.G.T.b 7.G.T.c 8.G.C.d Conic Sections & Vectors 1.E.a 8.GC.a 8.GC.b 8.GC.c Polar Graphing & Vectors 1.E.a 7.G.T.d 8.G.C.e SDC Exam Review/ Wrap Up & Short Topics Matrices Partial Fraction Decomposition Elipses & Hyperbolas Sequences, Series, & Sigma Notation Green=Major Content Blue=Supporting Content

3 Standards 1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques. Unit 1 Functions, Limits, and End Behavior 12 Days I Can Statements Algebra I can add, subtract, multiply, and divide various expressions. I can simplify various complex expressions. 1e.Equations: Solve equations involving absolute values, radical, rational, exponential or logarithmic expressions. 1f.Equations: Identify equations that can t be solved directly and use graphical or other approximations. I can solve various complex equations. 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). 2a.Inequalities: Apply various techniques (algebraic and graphical) to solve inequalities involving polynomials (including degree >2), and absolute values, and can express answers using interval notation. 3a. Properties of Functions: Express properties and transformations of functions graphically, and can use a graph to determine function properties. Functions I can use the discriminant to determine the number and types of zeros of quadratic functions. I can solve nonlinear inequalities (quadratic and rational) by graphing (solutions in interval notation if one-variable), and by using a sign chart. 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). 3b. Properties of Functions: On both the graph and the function can apply and identify the basic transformations: f(x-a), f(x+a), f(x)+a, f(x)-a, f(ax), a*f(x). I can create functions by adding, subtracting, multiplication, division, and composition of functions. 3d. Properties of Functions: From the graph can locate critical points and identify if each is a minimum, maximum or point of inflection, and locate intervals of increasing/ decreasing. 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. 5a. Functions: Manipulate functions and identify their properties. I can form a composite function. I can create functions by adding, subtracting, multiplication, division, and composition of functions.

4 5b. Functions: Identify basic properties of functions (definition of function, domain, range, odd, even, asymptotic behavior). I can recognize the role that domain of a function plays in the combination of functions by composition of functions. I can find the domain of a composite function. I can determine whether a function is even, odd, or neither algebraically and graphically. 5c. Functions: Manipulate functions as elements to get new functions via addition, subtraction, multiplication, division, and composition and can simplify the resulting expression (e.g. difference quotient). 5d. Functions: Construct and evaluate inverse functions and use domain and/or range restriction appropriately. I can construct the difference quotient for a given function and simplify the resulting expression. 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. P.MCPS.6 Develop the concept of the limit using tables, graphs, and algebraic properties. 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. 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. I can find the limit of a function at a number using algebra.

5 Pre-assessment Section 1 Functions Sections/Topics Section 2 Analyzing Graphs of Functions Section 3 Continuity, End Behavior, and Limits Section 4 Extrema and Average Rates of Change 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 Activities/Resources/Materials Extra Resources 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 Difference Quotient 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

6 Standards 1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques. Unit 2 Power, Polynomial, and Rational Functions 14 Days I Can Statements Algebra I can add, subtract, multiply, and divide polynomial, power, and rational expressions. I can simplify complex polynomial, power, radical, and rational expressions. I can solve complex polynomial, power, radical, and rational equations. 1c.Equations: Solve polynomial equations of degree > 2 for both real and complex roots. 1d. Equations: Use synthetic division and other relevant results to identify and simplify the equation. 1e.Equations: Solve equations involving absolute values, radical, rational, exponential or logarithmic expressions. 1f.Equations: Identify equations that can t be solved directly and use graphical or other approximations. I know the Fundamental Theorem of Algebra and can show it is true for quadratic polynomials. I can use synthetic division to identify and simplify the equation. I can identify the real zeros of the graph of a function (polynomial, power, and rational) in equation or graphical form. I can explain the relationship between the real zeros and the x-intercept of the graph of a function (exponential and logarithmic). 2a.Inequalities: Apply various techniques (algebraic and graphical) to solve inequalities involving polynomials (including degree >2), and absolute values, and can express answers using interval notation. I can use the Remainder Theorem to determine roots of polynomials. I can use the Rational Zero Theorem to determine roots of polynomials. I can use the Upper and Lower Bound Tests to help determine roots of polynomials. I can use Descartes Rule of Signs to help find positive and negative roots of polynomials. I can use the Rational Root Theorem and the Irrational Root Theorem to determine roots of polynomials. I can solve nonlinear inequalities (quadratic and rational) by graphing (solutions in interval notation if one-variable), and by using a sign chart.

7 3c. Properties of Functions: From the function can identify graphical functional properties and vice versa: intercepts, asymptotes (vertical, horizontal, slant), domain, range, and end behavior. 3d. Properties of Functions: From the graph can locate critical points and identify if each is a minimum, maximum or point of inflection, and locate intervals of increasing/ decreasing. Functions I can graph functions, identifying intercepts, domain, range, asymptotes (including slant), and holes (when suitable factorizations are available) and showing end-behavior. 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. Statistics and Probability 4a. Models: Use functions to model behavior described by words and/or data. I can find the regression equation that best fits bivariate data. 4b. Models: Identify and make appropriate models for situations involving for example, direct and inverse proportionality, average rate of change, exponential growth and decay, logarithmic relations, and periodic behavior. 4c. Models: Use appropriate units and function properties, like domain, as needed in function models. c) Interpret the solutions in terms of the original problem. I can explain how to determine the best regression equation model that approximates a particular data set. I can identify possible considerations such as domain and range regarding the accuracy of predictions when interpolating or extrapolating.

8 Pre-assessment Sections/Topics Section 1 Power and Radical Functions Section 2 Polynomial Functions Section 3 The Remainder and Factor Theorems Section 4 Zeros of Polynomial Functions Section 5 Rational Functions Section 6 Nonlinear Inequalities Unit Review Unit 2 Test Activities/Resources/Materials Extra Resources 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

9 Standards 1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques. Unit 3 Exponential and Logarithmic Functions 12 Days I Can Statements Algebra I can add, subtract, multiply, and divide exponential and logarithmic expressions. I can simplify complex exponential and logarithmic expressions. 1e.Equations: Solve equations involving absolute values, radical, rational, exponential or logarithmic expressions. 1f.Equations: Identify equations that can t be solved directly and use graphical or other approximations. 1g.Equations: Use the properties of logs and exponentials to simplify expressions involving logs and exponentials. Sections/Topics Pre-assessment Section 1 Exponential Functions Section 2 Logarithmic Functions Section 3 Properties of Logarithms Section 4 Exponential and Logarithmic Equations Section 5 Modeling with Nonlinear Regression Unit Review Unit 3 Test I can solve complex exponential and logarithmic equations. I can identify the real zeros of the graph of a function (exponential and logarithmic) in equation or graphical form. I can explain the relationship between the real zeros and the x-intercept of the graph of a function (exponential and logarithmic). I can use the properties of logarithms to solve logarithmic and exponential equations. Activities/Resources/Materials Extra Resources 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 Vocabulary 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

10 Standards 1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques. Unit 4 Trigonometric Functions 16 Days I Can Statements Algebra I can add, subtract, multiply, and divide trigonometric expressions. I can simplify complex trigonometric expressions. I can solve complex trigonometric equations. Functions 6a. Trig Functions: Use trigonometric functions and identities to find I can add, subtract, multiply, and divide trigonometric expressions. specific results. I can simplify complex trigonometric expressions. 6b. Trig Functions: Relate values on the unit circle to trig function values, and vice-versa, with numerical values at specific angles (0, π/6, π/4, π/3, π/2) and their periodic extensions. 6c. Trig Functions: Graph the six trigonometric functions and identify characteristics such as period, amplitude, phase shift, and asymptotes. I can solve complex trigonometric equations. I can find the reference angle of any angle on the unit circle. I can evaluate the trig functions of any angle of the unit circle using reference angles. 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 determine the difference made by choice of units for angle measurement when graphing a trigonometric function. 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. Geometry 7a. Triangles: Solve right triangle problems including applications. 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. 7b. Triangles: Solve right triangle problems involving angles of elevation and depression and angles using compass notation (e.g. 30 o North) using trigonometric identities and rules. I can solve right triangle problems involving angles of elevation and depression. I can convert from degree measure to compass notation (i.e. degree-minutesseconds).

11 7c. Triangles: Use the Law of Cosines and Sines for all triangle types. I can prove the Law of Sines and Cosines and apply them to solve 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.) 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. 8d. Circles: Calculate basic geometric properties like area of a sector, arc length, and the relation between the area of a sector and the inscribed triangle. I can find areas of triangles using the two area formulas A = ½ ab sin C and Heron s Law. 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 apply linear and angular velocity formulas in real world applications.

12 Pre-assessment Sections/Topics Section 1 Right Triangle Trigonometry Section 2 Degrees and Radians, Arc Length, Area of a Sector, Linear and Angular Speed Section 3 Trigonometric Functions on the Unit Circle Section 4 Graphing Sine and Cosine Functions Section 5 Graphing Tangent, Cosecant, and Secant Section 6 Inverse Trigonometric Functions Section 7 The Law of Sines and Law of Cosines Unit Review Unit 4 Test Activities/Resources/Materials Extra Resources 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

13 Standards 1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques. 6d. Trig Functions: Use trigonometric identities to evaluate numerical values, simplify expressions and solve equations. (E.g. use sum/difference identities to evaluate sin (π/12), simplify (sin(x) + cos(x))2.) Unit 5 Trigonometric Identities and Equations 13 Days I Can Statements Algebra I can add, subtract, multiply, and divide trigonometric expressions. I can simplify complex trigonometric expressions. I can solve complex trigonometric equations. Functions I can recognize and use the following trigonometric identities to verify identities and solve trigonometric equations: Pythagorean, Reciprocal, Quotient, Sum/Difference, Double Angle. 6e. Trig Functions: Apply multiple identities to simplify expressions and solve equations, including ones involving inverse functions. I can prove the sum and difference formulas for sine, cosine, and tangent and apply them in solving problems. I can use various trigonometric identities and combinations of trigonometric identities to simplify and solve trigonometric equations. 6f. Trig Functions: Solve trigonometric equations by factoring, by using identities, and by graphing. Pre-assessment Sections/Topics Section 1 Trigonometric Identities Section 2 Verifying Trigonometric Identities 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 I can use various trigonometric identities and combinations of trigonometric identities to find inverses of trigonometric functions. I can solve trigonometric equations by factoring and using trigonometric identities. Activities/Resources/Materials Extra Resources Identity Trigonometric identity Trigonometric equation Pythagorean identities Cofunction identities Odd-even identities Verify an identity Sum and difference identities Vocabulary Sum and difference identities Reduction identity Double-angle identities Power-reducing identities Half-angle identities Product-to-sum identities

14 Standards 1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques. 8a. Circles: Work with circles as a (Cartesian) conic section and in terms of its geometric and polar properties. 8b. Circles: Convert a quadratic equation into the equation of a circle or parabola using completion of squares. 8c. Circles: Identify the center and radius of a circle, and can write and use the equation of a circle from its properties. Unit 6 Conic Sections and Vectors 12 Days I Can Statements Algebra I can add, subtract, multiply, and divide various expressions. I can simplify complex various expressions. I can solve complex various equations. Geometry I can display all of the conic sections as portions of a cone. I can graph circles and demonstrate understanding of the relationship between the standard algebraic form and the graphical characteristics. I can transform equations of conic sections to convert between general and standard form. I can derive the equation of a circle given the center and radius. I can graph the equation of a circle given the center and radius.

15 Pre-assessment Section 1 Parabolas Section 2 Circles Sections/Topics Section 3 Rotations of Conic Sections Section 4 Introduction to Vectors Section 5 Vectors in the Coordinate Plane Section 6 Dot Products and Vector Projections Unit Review Unit 6 Test Activities/Resources/Materials Extra Resources 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 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

16 Standards 1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques. Unit 7 More Vectors and Polar Graphing 15 Days I Can Statements Algebra I can add, subtract, multiply, and divide various expressions. I can simplify complex various expressions. I can solve complex various equations. Geometry 7d. Triangles: Use vector concepts of magnitude and direction. I can represent vectors graphically with both magnitude and direction. 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 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 solve velocity problems with vectors. 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.

17 8e. Circles: Relate, through the unit circle, polar coordinates to Cartesian coordinates and vice versa. 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. I can represent addition, subtraction, multiplication, and division of complex numbers geometrically on the complex plane. 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.

18 Pre-assessment Sections/Topics Section 1 Vectors in Three-Dimensional Space Activities/Resources/Materials Extra Resources Section 2 Dot Products of Vectors in Space Section 6 Polar Coordinates Section 7 Graphs of Polar Equations Section 8 Polar and Rectangular Forms of Equations Section 9 Polar Forms of Conic Sections Section 10 Complex numbers and DeMoivre s Theorem Unit Review Unit 7 Test Vocabulary Three-dimensional coordinate system z-axis Ordered triple Cross product Torque Parallelpiped Triple scalar product 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

19 Matrices (for ACT prep) Standards Unit 8 Review for SDC Exam/Extra Topics 20 Days I Can Statements I can use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. I can multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. I can determine if matrices may be added, subtracted or multiplied by using their dimensions. 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. Partial Fraction Decomposition (for Calculus 2 or BC prep) Complete Conics with Ellipses and Hyperbolas I can work with 2 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. I can write partial fraction decompositions of rational expressions with linear factors in the denominator. I can write partial fraction decompositions of rational expression with prime quadratic factors. I can display all of the conic sections as portions of a cone.

20 I can derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. I can graph ellipses and hyperbolas and demonstrate understanding of the relationship between their standard algebraic form and the graphical characteristics. I can transform equations of conic sections to convert between general and standard form. Sequence, Series, and Sigma Notation (for Calculus 2 or BC prep) 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.

21 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 Section 4 Partial Fractions Section 5 Linear Optimization Section 6 Ellipses Section 7 Hyperbolas Section 8 Sequences, Series, and Sigma Notation Section 9 Arithmetic Sequences and Series Section 10 Geometric Sequences and Series Section 11 Mathematical Induction Section 12 The Binomial Theorem Section 13 Functions as Infinite Series Unit Review Activities/Resources/Materials Extra Resources 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 Vocabulary 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

22 Unit 8 Test Unbounded region Ellipse Foci Major axis Minor axis Center Vertices Co-vertices Eccentricity Standard form of the equation of a circle Hyperbola Transverse axis Conjugate axis Sum of an infinite geometric series 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