UNIT 1 PREREQUISITES Precalculus...Textbook: Precalculus: Graphical, Numerical, & Algebraic (Common...

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UNIT 1 – PREREQUISITES

Textbook: Precalculus: Graphical, Numerical, & Algebraic (Common Core) by Demana, Foley, Kennedy, Bock, and Watts

(Approximately 6 Days ● 8/8/19 -8/15/19)

Unit 1 Overview

In this unit, students will review prior Algebra I and II skills and concepts. Specifically, students will do the following:

Solve Linear Equations and Inequalities Lines in plane Solve equations graphically, numerically, and algebraically Complex Numbers

Focus Standards LOUISIANA CONNECTORS When teaching students with significant disabilities who are eligible to take the LEAP Connect assessment, use the specific Louisiana Connectors that are aligned to the unit’s focus standards.

A-CED.1 Create equations and inequalities in one variable and use them to solve problems

A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

A-REI B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

N-CN.1 Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.

N-CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

https://www.louisianabelieves.com/docs/default-source/students-with-disabilities/k-12-louisiana-connectors-for-students-with-significant-disabilities.pdf?sfvrsn=6

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N-CN.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

A-REI.B.4 Solve quadratic equations in one variable. A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same

reasoning as in solving equations.

SMP.1 Make sense of problems and persevere in solving them. SMP.2 Reason abstractly and quantitatively. SMP.7 Look for and make use of structure. SMP.8 Look for and express regularity in repeated reasoning.

Unit Terms & Tools Spanish cognates are included (if applicable) for Tier 3 and Tier 2 vocabulary terms. Spanish cognates will be shown as follows: Vocab Term/Spanish Cognate.

New Unit Terms (Tier 3 Vocabulary)

Equations Equivalent General Form for an

equation Parallel

Linear Equations Point slope from Slope Perpendicular

Linear inequality Solution set Slope intercept form X intercept Y intercept

Familiar Terms (Tier 3 Vocabulary)

Algebra

Suggested Tools Area Models, Geoboards, graph paper, and white board

Sample Calendar Sample Calendar Please note, this calendar suggests lessons that can be combined and taught in one class period.

Week Beginning: Monday Tuesday Wednesday Thursday Friday

August 5th No school for students

No school for students

No school for students

Section: P3 Topic: Linear Equations and Inequalities

Section: P4 Topic: Lines in a plane

August 12th Section: P5 Topic: Solve equations graphically,

Section: P5 Topic: Complex Number

Review of the Prerequisite Section

Assessment Unit 2 Begins

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numerically, and algebraically

Additional Information

Additional Lessons (Optional for remediation and enrichment)

Kutasoftware Eureka Precalculus log in and go to Precalculus Section Khan academy

https://www.kutasoftware.com/freeipc.html

https://greatminds.org/

https://www.khanacademy.org/math/precalculus

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UNIT 2 – FUNCTIONS AND GRAPHS


(Approximately 6 Days ● 8/16/19 -8/23/19)

Unit 1 Overview

In this unit, we begin the study of functions that will continue throughout the book. Your previous courses have introduced you to some basic functions. These functions can be visualized using a graphing calculator, and their properties can be described using the notation and terminology that will be introduced in this chapter. A familiarity with this terminology will serve you well in later chapters when we explore properties of functions in greater depth. Specifically, students will do the following: Modeling and Equation Solving Functions and Their Properties Twelve Basic Functions Building Functions from Functions Graphical Transformations

Focus Standards LOUISIANA CONNECTORS When teaching students with significant disabilities who are eligible to take the LEAP Connect assessment, use the specific Louisiana Connectors that are aligned to the unit’s focus standards.

HSF-IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

HSF-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

. HSF-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers

HSF-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship


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MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.


New Unit Terms (Tier 3 Vocabulary)

Asymptotes Functions Composite Function

Continuity Domain End Behavior

Symmetry Range Zero Factor Property

Familiar Terms (Tier 3 Vocabulary)

Algebra


Sample Calendar Sample Calendar Please note, this calendar suggests lessons that can be combined and taught in one class period.


August 12th

Unit One Ends

Sections: Functions and graphs Topic: Modeling and Equation Solving

August 19th Sections: Functions and graphs Topic: Functions and Their Properties

Sections: Functions and graphs Topic: Twelve Basic Functions

Sections: Functions and graphs Topic: Graphical Transformations

Review Unit 2

Topics Assessment

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Kutasoftware , Eureka Precalculus log in and go to Precalculus Section, and Khan academy




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Unit 3 – Polynomial, Power, and Rational Functions


(Approximately 12 Days ● 8/26/19 - 9/12/19)

Unit 3 Overview

In this unit and the next two, we will explore the theory and applications of specific families of functions. We begin this exploration by studying three interrelated families of functions: polynomial, power, and rational functions. These three families of functions are used in the social, behavioral, and natural sciences. This chapter includes a thorough study of the theory of polynomial equations. We investigate algebraic methods for finding both real- and complex-number solutions of such equations and relate these methods to the graphical behavior of polynomial and rational functions. The chapter closes by extending these methods to inequalities in one variable. Specifically, students will do the following:

Linear and Quadratic Functions and Modeling

Power Functions with Modeling

Polynomial Functions of Higher Degree with Modeling

Real Zeros of Polynomial Functions

Solving Rational Equations

Focus Standards LOUISIANA CONNECTORS

When teaching students with significant disabilities who are eligible to take the LEAP Connect assessment, use the specific Louisiana Connectors that are aligned to the unit’s focus standards.

HSA-APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

HSA-APR.C.4 rove polynomial identities and use them to describe numerical relationships.

HSA-REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the


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assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

HSA-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.7 Look for and make use of structure.

MP.8 Look for and express regularity in repeated reasoning.


New Unit Terms

(Tier 3 Vocabulary)

Average Rate of Change

Extraneous Solutions

Polynomial Functions Rational Equations

Zero of Polynomial Functions

Familiar Terms

(Tier 3 Vocabulary)

Correlation

Linear Equations


Sample Calendar Sample Calendar

Please note, this calendar suggests lessons that can be combined and taught in one class period.


August 26th Topic: Linear and Quadratic Functions and Modeling

Topic: Linear and Quadratic Functions and Modeling

Topic: Power Function with Modeling

Topic: Power Function with Modeling

Topic: Polynomial Functions of Higher Degree modeling

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Day One Day Two Day One Day Two Day One

September 2nd

Labor Day

Topic: Polynomial Functions of Higher Degree modeling

Day Two

Topic: Real Zeros of Polynomial Functions

Day One

Topic: Real Zeros of Polynomial Functions

Day Two

Topic: Solving Rational Equations

Day One

September 9th Topic: Solving Rational Equations

Day Two

Review all topics covered

in Unit 3

FLEX/ Assessment

Unit 4 begins







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Unit 4 – Exponential, Logistic, and Logarithmic Functions



Unit 4 Overview

In this unit we study three interrelated families of functions: exponential, logistic, and logarithmic functions. Polynomial functions, rational functions, and power functions with rational exponents are algebraic functions— functions obtained by adding, subtracting, multiplying, and dividing constants and an independent variable, and raising expressions to integer powers and extracting roots. In this chapter and the next one, we explore transcendental functions, which go beyond, or transcend, these algebraic operations. Just like their algebraic cousins, exponential, logistic, and logarithmic functions have wide application. Exponential functions model growth and decay over time, such as unrestricted population growth and the decay of radioactive substances. Logistic functions model restricted population growth, certain chemical reactions, and the spread of rumors and diseases. Logarithmic functions are the basis of the Richter scale of earthquake intensity, the pH acidity scale, and the decibel measurement of sound. The chapter closes with a study of the mathematics of finance, an application of exponential and logarithmic functions often used when making investments. Specifically, students will do the following:

Exponential and Logistic Functions

Exponential and Logistic Modeling

Logarithmic Functions and Their Graphs

Properties of Logarithmic Functions



HSF-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

HSF-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).


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HSF-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context.






New Unit Terms

(Tier 3 Vocabulary)

exponential function

exponential growth function

exponential decay function

Logarithmic Functions

logistic growth function

logistic decay functions

logistic function

natural logarithms

transcendental functions,

Familiar Terms

(Tier 3 Vocabulary)

Functions Domain Range

Suggested Tools Geoboards, Graph paper, T-84 Scientific Graphing Calculator and white board




September 9th Topic: Exponential and Logistic Functions

Day One

Topic: Exponential and Logistic Functions

Day Two

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September 16th

PD Day

Topic: Exponential and Logistic Modeling

Day One

Topic: Exponential and Logistic Modeling

Day Two

Topic: Logarithmic Functions and Their Graphs

Day One

Topic: Logarithmic Functions and Their Graphs

Day Two

September 23rd Topic: Properties of Logarithmic Function

Day One

Topic: Properties of Logarithmic Function

Day Two

Topic: Properties of Logarithmic Function

Day Three

Review Unit 4

FLEX / Assessment







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Unit 5 – Trigonometric Functions



Unit 5 Overview

In this unit, trigonometric functions and the role it plays in the real world.

Specifically, students will do the following:

Angles and Their Measures

Trigonometric Functions of Acute Angles

Trigonometry Extended: The Circular Functions

Graphs of Sine and Cosine: Sinusoids

Graphs of Tangent, Cotangent, Secant, and Cosecant



HSF-TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

HSF-TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

HSF-TF.A.3 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 express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.


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HSF-TF.A.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

HSF-TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

HSF-TF.B.6 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.






New Unit Terms

(Tier 3 Vocabulary)

central angle

Circular Arc Length

Six basic Trigonometric Functions

coterminal angles

Quadrantal angles

degree

line of travel

right triangle trigonometry

standard position in the xy-plane

minutes

nautical mile

statute miles

radian

seconds

Familiar Terms

(Tier 3 Vocabulary)

30-60- 09 triangle

45-45-90 Triangle

Similarity

Domain

Range

Vertex




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September 30th Topic:


Day One

Topic:


Day Two

Topic:


Day One

Topic:


Day Two

Topic:


Day one

October 7th Topic:


Day Two

Topic:


Day One

Topic:


Day Two

Fall Break Fall Break

October 14 Topic:


Day One

Topic:


Day Two

Review Unit Five

Day One

Review Unit Five

Day Two

Assessment







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Unit 6 – Analytic Trigonometry


(Approximately 12 Days ● 10/ 21 /19 - 11/5/19) Unit 6 Overview

In this unit, although the title of this chapter suggests that we are now moving into the analytic phase of our study of trigonometric functions, the truth is that we have been in that phase for several sections already. Once the transition is made from triangle ratios to functions and their graphs, one is on analytic soil. But our primary applications of trigonometry so far have been computational; we have not made full use of the properties of the functions to study the connections among the trigonometric functions themselves. In this chapter we will shift our emphasis more toward theory and proof, exploring where the properties of these special functions lead us, often with no immediate concern for real-world relevance at all. We hope in the process to give you an appreciation for the rich and intricate tapestry of interlocking patterns that can be woven from the six basic trigonometric functions—patterns that will take on even greater beauty later on when you can view them through the lens of calculus Students will specifically learn the following;

Fundamental Identities

Proving Trigonometric Identities

Sum and Difference Identities

The Law of Sines

The Law of Cosines



HSF-TF.A.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

HSF-TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.


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HSF-TF.B.6 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

HSF-TF.C.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

HSF-TF.C.9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.






New Unit Terms

(Tier 3 Vocabulary)

Basic Trigonometric Identities

Identities Cofunction Identities Solving Trigonometric

Equation

Basic Trigonometric Identities

Pythagorean Identities

Odd-Even Identities

Simplifying Trigonometric Expressions

Solving Trigonometric Equation

Familiar Terms

(Tier 3 Vocabulary)




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October 21 Topic:


Day One

Topic:


Day Two

Topic:


Day Three

Topic: Proving Trigonometric Identities

Day One

Topic:

Proving Trigonometric Identities

Day Two

October 28 Topic:


Day One

Topic:


Day Two

Topic:

The Law of Sines

Day One

Topic: The Law of Sines

Day Two

Unit 6 Sections: Analytic Trigonometry Topic: The Law of Cosines

November 4th Review Unit 6 Assessment Unit 7 Begins







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Unit 7 – Application of Trigonometry


(Approximately 15 Days ● 11/ 6 /19 - 11/18/19)

Unit 7 Overview

In this unit, we introduce vectors in the plane, perform vector operations, and use vectors to represent quantities such as force and velocity. Vector methods are used extensively in physics, engineering, and applied mathematics. Vectors are used to plan airplane flight paths. The trigonometric form of a complex number is used to obtain De Moivre’s Theorem and find the nth roots of a complex number. Parametric equations are studied and used to simulate motion. One of the principal applications of parametric equations is the analysis of motion in space. Polar coordinates (another of Newton’s inventions, although Jakob Bernoulli usually gets the credit because he published first) are used to represent points in the coordinate plane. Planetary motion is best described with polar coordinates. We convert rectangular coordinates to polar coordinates, polar coordinates to rectangular coordinates, and study graphs of polar equations. Students will specifically the following topics:

Vectors in the Plane

Dot Product of Vectors

Polar Coordinates

Graphs of Polar Equations

De Moivre’s Theorem and nth Roots



N.VM.A.3 Solve problems using vectors analytically and geometrically


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New Unit Terms

(Tier 3 Vocabulary)

Dot product Polar Coordinates Vector

Familiar Terms

(Tier 3 Vocabulary)

Distance formula Midpoint Formula Volume





November 4th Topic:

Vectors in Plane

Day One

Topic:

Vectors in Plane

Day Two

Topic:

Vectors in Plane

Day Three

November 11th

Teacher PD day

Topic:

Dot Product of Vectors

Topic:

Polar Coordinate

Day

Topic:

Graph of Polar Coordinate

Day

Review of Unit 7

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November 18

Assessment

Unit 8 Begins

Systems and Matrices







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Unit 8 – System and Matrices



Unit 8 Overview

In this unit, many applications of mathematics in science, engineering, business, and other areas involve the use of systems of equations or inequalities in two or more variables as models for the corresponding problems. We investigate several techniques commonly used to solve such systems; and we investigate matrices, which play a central role in several of these techniques. The information age has made the use of matrices widespread because of their use in handling vast amounts of data. We decompose a rational function into a sum of simpler rational functions using the method of partial fractions. This technique can be used to analyze a rational function, and is used in calculus to integrate rational functions analytically. Finally, we introduce linear programming, a method used to solve problems concerned with decision making in management science. Students will specifically the following topics:

Solving Systems of Two and Three Equations Matrix Algebra



N.VM.C.6 Use matrices to represent and model real world situations.

N.VM.C.8 Add, subtract, and multiply matrices.

N.VM.C.11 Use matrices to perform linear transformations in the plane. N.VM.C.12 Calculate and interpret the determinant of a matrix.





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New Unit Terms

(Tier 3 Vocabulary)

Determinant Matrices Matrices System of Equation

Familiar Terms

(Tier 3 Vocabulary)

Inverse Linear Equation Linear Equation System





November 18

Topic: Solving System of Two and Three Equations Day One

Topic: Solving System of Two and Three Equations Day Two

Topic: Matrix Algebra Day One

Topic: Matrix Algebra Day Two

November 25 Thanksgiving Holiday

Thanksgiving Holiday




December 2nd Topic: Matrix Algebra

Day Three Review for Unit 8 Assessment







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Unit 9 – Analytic Geometry in Two

and Three Dimensions



Unit 9 Overview

In this unit, in Sections 8.1–8.4, we will learn that parabolas, ellipses, and hyperbolas are all conic sections and can all be expressed as second-degree equations. We will investigate their uses, including the reflective properties of parabolas and ellipses and how hyperbolas are used in long-range navigation. In Section 8.5, we will see how parabolas, ellipses, and hyperbolas are unified in the polar coordinate setting. In Section 8.6, we will move from the two-dimensional plane to revisit the concepts of point, line, midpoint, distance, and vector in three-dimensional space. Students will specifically the following topics:

Conic Sections and Parabolas Ellipses Hyperbolas



G.GPE.A.3 Derive the equations of ellipses and hyperbolas given the foci. Use these equations to model real life situations






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New Unit Terms

(Tier 3 Vocabulary)

Conic

Ellipse Parabola

Hyperbola Parabola

Familiar Terms

(Tier 3 Vocabulary)

Axis of Symmetry

Line segment

Polar coordinate

X intercept

Y intercept

Vertex





December 2nd

Assessment

Topic: Conic Sections and Parabolas Day One

Topic: Conic Sections and Parabolas Day Two

December 9th Topic: Ellipses Day One

Topic: Ellipses Day Two

Topic: Hyperbolas Day One

Topic: Hyperbolas Day Two

Review for Unit 9

December 16th Assessment Review for Exam Review for Exam Exam Exam

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Assessment Test bank and answers

https://www.wrps.org/faculty/BluellKS/testbanks.cfm


https://www.wrps.org/faculty/BluellKS/testbanks.cfm


UNIT 1 PREREQUISITES Precalculus...Textbook: Precalculus: Graphical, Numerical, & Algebraic (Common...

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