tn ready performance standards by unit sdc precalculus ... sdc precalculus...look for and express...

SDC Precalculus TN Ready Performance Standards by Unit

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

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.



SDC Precalculus– Curriculum Overview

Quarter 1 Quarter 2 Quarter 3 Quarter 4

Unit 1 12 Days

Unit 2 14 Days

Unit 3 12 Days

Unit 4 16 Days

Unit 5 13 Days

Unit 6 12 Days

Unit 7 16 Days

Unit 8 20 Days

Functions,

Limits, & End

Behavior

Power,

Polynomial, &

Rational

Functions

Exponential &

Logarithmic

Functions

Trigonometric

Functions

Trigonometric

Identities &

Equations

Conic Sections &

Vectors

Polar Graphing

& Vectors

SDC Exam

Review/ Wrap Up

& Short Topics

Standards (By number) 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

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

1.E.a

1.E.e

1.E.f

1.E.g

1.E.a

6.TF.a

6.TF.b

6.TF.c

7.G.T.a

7.G.T.b

7.G.T.c

8.G.C.d

1.E.a

6.TF.d

6.TF.e

6.TF.f

1.E.a

8.GC.a

8.GC.b

8.GC.c

1.E.a

7.G.T.d

8.G.C.e

Matrices

Partial Fraction

Decomposition

Elipses &

Hyperbolas

Sequences,

Series, & Sigma

Notation

Green=Major Content Blue=Supporting Content



Unit 1

Functions, Limits, and End Behavior

12 Days

Standards “I Can” Statements

Algebra

1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques.

I can add, subtract, multiply, and divide various expressions.

I can simplify various complex expressions.

I can solve various complex equations.

1e.Equations: Solve equations involving absolute values, radical, rational, exponential or logarithmic expressions.

I can identify the real zeros of the graph of a function (polynomial, rational,

exponential, logarithmic, and trigonometric) in equation or graphical form.

1f.Equations: Identify equations that can’t be solved directly and use graphical or other approximations.

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).

I can use the discriminant to determine the number and types of zeros of

quadratic functions.

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 solve nonlinear inequalities (quadratic and rational) by graphing

(solutions in interval notation if one-variable), and by using a sign chart.

Functions

3a. Properties of Functions: Express properties and transformations of

functions graphically, and can use a graph to determine function properties.

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.



I can recognize the role that domain of a function plays in the combination of

functions by composition of functions.

5b. Functions: Identify basic properties of functions (definition of function,

domain, range, odd, even, asymptotic behavior).

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).

I can construct the difference quotient for a given function and simplify the

resulting expression.

5d. Functions: Construct and evaluate inverse functions and use domain

and/or range restriction appropriately.

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.

P.MCPS.6 Develop the concept of the limit using tables, graphs, and

algebraic properties.

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.



Sections/Topics Activities/Resources/Materials

• 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

Extra Resources

• www.shodor.org/interactive

•

Vocabulary

• 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

• 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

http://www.shodor.org/interactive



Unit 2

Power, Polynomial, and Rational Functions

14 Days


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.

I know the Fundamental Theorem of Algebra and can show it is true for

quadratic polynomials.

1d. Equations: Use synthetic division and other relevant results to identify and simplify the equation.

I can use synthetic division to identify and simplify the equation.

1e.Equations: Solve equations involving absolute values, radical, rational, exponential or logarithmic expressions.

I can identify the real zeros of the graph of a function (polynomial, power,

and rational) in equation or graphical form.

1f.Equations: Identify equations that can’t be solved directly and use graphical or other approximations.


graph of a function (exponential and logarithmic).

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.

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 solve nonlinear inequalities (quadratic and rational) by graphing

(solutions in interval notation if one-variable), and by using a sign chart.



Functions

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.

I can graph functions, identifying intercepts, domain, range, asymptotes

(including slant), and holes (when suitable factorizations are available) and

showing 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.

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.

I can explain how to determine the best regression equation model that

approximates a particular data set.

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 identify possible considerations such as domain and range regarding the

accuracy of predictions when interpolating or extrapolating.




• 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

Extra Resources


•

Vocabulary

• 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

• 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 and Logarithmic Functions

12 Days


Algebra


I can add, subtract, multiply, and divide exponential and logarithmic

expressions.

I can simplify complex exponential and logarithmic expressions.

I can solve complex exponential and logarithmic equations.

1e.Equations: Solve equations involving absolute values, radical, rational,

exponential or logarithmic expressions.

I can identify the real zeros of the graph of a function (exponential and

logarithmic) in equation or graphical form.

1f.Equations: Identify equations that can’t be solved directly and use

graphical or other approximations.


graph of a function (exponential and logarithmic).

1g.Equations: Use the properties of logs and exponentials to simplify

expressions involving logs and exponentials.

I can use the properties of logarithms to solve logarithmic and exponential equations.


• 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

Extra Resources


•

Vocabulary

• 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




Unit 4

Trigonometric Functions

16 Days


Algebra

1a. Equations: Apply various techniques, as appropriate, to simplify

expressions and solve equations. This includes using exact symbolic

(algebraic), approximation and graphical techniques.

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 specific results.




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.

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.

6c. Trig Functions: Graph the six trigonometric functions and identify characteristics such as period, amplitude, phase shift, and asymptotes.

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. 30o

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-minutes-

seconds).



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.

I can find areas of triangles using the two area formulas 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 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.




• Pre-assessment

• 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

• 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

Extra Resources


•

Vocabulary

• 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

• 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 and Equations

13 Days


Algebra





Functions

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 .)

I can recognize and use the following trigonometric identities to verify

identities and solve trigonometric equations: Pythagorean, Reciprocal,

Quotient, Sum/Difference, Double Angle.

I can prove the sum and difference formulas for sine, cosine, and tangent and

apply them in solving problems.

6e. Trig Functions: Apply multiple identities to simplify expressions and

solve equations, including ones involving inverse functions.

I can use various trigonometric identities and combinations of trigonometric

identities to simplify and solve trigonometric equations.

I can use various trigonometric identities and combinations of trigonometric

identities to find inverses of trigonometric functions.

6f. Trig Functions: Solve trigonometric equations by factoring, by using

identities, and by graphing.

I can solve trigonometric equations by factoring and using trigonometric

identities.


• Pre-assessment

• 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

Extra Resources


Vocabulary

• Identity

• Trigonometric identity

• Trigonometric equation

• Pythagorean identities

• Cofunction identities

• Odd-even identities

• Verify an identity

• Sum and difference

identities

• Sum and difference

identities

• Reduction identity

• Double-angle identities

• Power-reducing identities

• Half-angle identities

• Product-to-sum identities




Unit 6

Conic Sections and Vectors

12 Days


Algebra





I can simplify complex various expressions.

I can solve complex various equations.

Geometry

8a. Circles: Work with circles as a (Cartesian) conic section and in terms of its geometric and polar properties.

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.

8b. Circles: Convert a quadratic equation into the equation of a circle or parabola using completion of squares.

I can transform equations of conic sections to convert between general and

standard form.

8c. Circles: Identify the center and radius of a circle, and can write and use the equation of a circle from its properties.

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.




• Pre-assessment

• Section 1 Parabolas

• Section 2 Circles

• Section 3 Rotations of Conic Sections

• Quiz

• Section 4 Introduction to Vectors

• Section 5 Vectors in the Coordinate Plane

• Section 6 Dot Products and Vector Projections

• Unit Review

• Unit 6 Test

Extra Resources


•

Vocabulary

• 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

• 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




Unit 7

More Vectors and Polar Graphing

15 Days


Algebra





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.



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.




• Pre-assessment

• Section 1 Vectors in Three-Dimensional Space

• Section 2 Dot Products of Vectors in Space

• 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 7 Test

Extra Resources


•

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

• pth roots of unity




Unit 8

Review for SDC Exam/Extra Topics

20 Days


Matrices (for ACT prep) 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.

I can work with 2 × 2 matrices as transformations of the plane, and interpret

the absolute value of the determinant in terms of area.

Partial Fraction Decomposition (for Calculus 2 or BC prep) 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.

Complete Conics with Ellipses and Hyperbolas I can display all of the conic sections as portions of a cone.



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.




• 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

• Quiz

• Section 6 Ellipses

• Section 7 Hyperbolas

• Quiz

• Section 8 Sequences, Series, and Sigma Notation

• Section 9 Arithmetic Sequences and Series

• Section 10 Geometric Sequences and Series

• Quiz

• Section 11 Mathematical Induction

• Section 12 The Binomial Theorem

• Section 13 Functions as Infinite Series

• Unit Review

Extra Resources


•

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

• Sequence

• Term

• Finite sequence

• Infinite sequence

• Explicit formula

• Recursive formula

• Fibonacci sequence

• Converge

• Diverge

• Series

• Finite series

• Infinite series

• nth 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

• nth term of a geometric

sequence

• Geometric means

• Geometric series

• Sum of a finite geometric

series




• 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

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