Adv Alg & Trig Syllabus

Subject

Advanced Algebra & Trig

 

Nine Week

 


1st Nine weeks

Standard

 

 

 

 

 

 

N-CN Perform Arithmetic Operations with Complex Numbers

 

N-Q Reason Quantitatively and Use Units to Solve Problems

 

A-REI Solve Equations and Inequalities in One Variable

 

F-LE Construct and Compare Linear, Quadratic, and Exponential Models and Solve Problems

 

F-IF Understand the Concept of a Function and Use Function Notation

 

F-BF Build a Function that Models the Relationship Between Two Quantities

 

S-ID Interpret Linear Models

 

F-LE Construct and Compare Linear, Quadratic, and Exponential Models and Solve Problems

 

A-APR Understand the Relationship Between Zeros and Factors of Polynomials

 

Objectives

 

 

 

 

 

 

 

 

 

CLE 3124.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.

CLE 3124.1.3 Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition.

CLE 3124.3.4 Solve nonlinear inequalities (quadratic, trigonometric, conic, exponential, and logarithmic).

CLE 3124.3.5 Solve problems by converting the given verbal information into an appropriate mathematical model involving equations or systems of equations; apply appropriate techniques to analyze these mathematical models; and interpret the solution obtained in written form using appropriate units of measurement.

CLE 3124.1.6 Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.

CLE 3124.1.7 Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.

CLE 3124.2.3 Develop the arithmetic and properties of the complex numbers

CLE 3124.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.

CLE 3124.3.2 Identify or analyze the distinguishing properties of exponential, polynomial, logarithmic, trigonometric, and rational functions from tables, graphs, and equations.

CLE 3124.1.7 Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.

CLE 3124.5.1 Create scatter plots, analyze patterns and describe relationships that exist in a set of linear and non-linear paired data to make predictions.

CLE 3124.5.3 Examine all aspects of using regression equations to act as a model for a real world situation, including interpolation, extrapolation and validity of model.

CLE 3124.2.1 Understand the capabilities and the limitations of calculators and computers in solving problems.

CLE 3124.1.3 Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition.

CLE 3124.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

CLE 3124.1.4 Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.

Topics

 

 

 

 

 

  1. Graphs and Graphing Utilities

     

  2. Linear and Rational Equations

     

  3. Models and Applications (Optional)

     

  4. Complex Numbers

     

  5. Quadratic Equations

     

  6. Other Equations

     

  7. Linear and Absolute Value Inequalities

2.1 Functions and Their Graphs

Domain and Range of Common Functions

 

2.2 More Functions

TI-84 Activity: Functions & Graphs

 

2.3 Linear Functions and Slope

TI-84 Activity: Slope

 

2.4 More on Slope

 

2.5 Transformations of Functions

 

2.6 Composite Functions

Video Tutorial Using TI-84

 

2.7 Inverse Functions

 

2.8 Distance/Midpoint Formulas

 

3.1 Quadratic Functions

 

3.2 Polynomial Functions & Graphs

TI-84 Activity Lesson 3.2

TASK - Polynomial Graphs

 

3.3 Dividing Polynomials –

Remainder & Factor Theorems

 

3.4 Zeros of Polynomial Functions

TI-84 Activity Lesson 3.4

 

3.5 Rational Functions and Graphs

Sketching Graphs

TASKAsymptotes and Rational Functions

 

3.6 Polynomial and Rational Inequalities

 

3.7 Modeling Variation (Optional)

 

 

 

 

Major Assignment/s

 

 

 

 

 

 

 

 

 

Instructional Materials

 

Pearson Adv Alg & Trig, graphing calculator

Field Trip/s

 

 


Subject

Advanced Algebra & Trig

 

Nine Week

 

2nd Nine weeks

Standard

 

 

 

 

 

F-LE Construct and Compare Linear, Quadratic, and Exponential Models and Solve Problems

 

F-IF Understand the Concept of a Function and Use Function Notation

 

F-BF Build a Function that Models the Relationship Between Two Quantities

 

F-BF Build New Functions from Existing Functions

 

A-REI.11 Represent and solve equations as a process of reasoning and explain the reasoning

G-SRT Define Trigonometric Ratios and Solve Problems Involving Right Triangles

 

G-SRT Apply Trigonometry to General Triangles

 

F-TF Extend the Domain of Trigonometric Functions Using the Unit Circle

 

F-TF Model Periodic Phenomena with Trigonometric Functions

 

 

Objectives

 

 

 

 

 

 

 

 

 

CLE 3124.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.

CLE 3124.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

CLE 3124.1.5 Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.

CLE 3124.2.2 Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

CLE 3124.5.1 Create scatter plots, analyze patterns and describe relationships that exist in a set of linear and non-linear paired data to make predictions.

CLE 3124.5.2 Identify and interpret the correlation coefficient for a linear bivariate data set.

CLE 3124.5.3 Examine all aspects of using regression equations to act as a model for a real world situation, including interpolation, extrapolation and validity of model

CLE 3124.4.1 Understand basic right triangle trigonometry an use it to solve problems.

CLE 3124.4.2 Know how the trigonometric functions can be extended to the periodic functions on the real number line, derive basic formulas of these functions, and use these functions and formulas to solve problems.

CLE 3124.4.3 Solve trigonometric equations.

CLE 3124.4.6 Understand the measure of angles and the relationship to the circle;

convert between degrees and radians.

CLE 3124.4.7 Develop the measurement of arcs of circles; calculate angular and

linear velocity.

Topics

 

 

 

 

 

4.1 Exponential Functions

TASKExploring Exponentia

 

4.2 Logarithmic Functions

 

4.3 Properties of Logarithms

Examples of Properties of Logarithms

 

4.4 Exponential and Logarithmic Equations

Examples of Solving Logarithmic Equations

 

4.5 Exponential Growth and Decay

.1 Angles and Radian Measure

 

5.2 Right Triangle Trigonometry

Review of Special Right Triangles

TASKRight Triangle Trigonometry

 

5.3 Trigonometric Functions of Any Angle

 

5.4 Trigonometric Functions of Real Numbers, Periodic Functions

TASKIntro To Trig Graphs

 

5.5 Graphs of Sine and Cosine

TASKGraphing Sine/Cosine

Worksheet for TASKSine/Cosine

TASKTrig Transformations

 

5.6 Graphs of Other Trigonometric Functions

Exploration of Transformations of Trig Graphs

Summary of Properties of Trig Graphs

 

5.7 Inverse Trigonometric Functions

 

5.8 Applications of Trigonometric Functions

 

 

 

Major Assignment/s

 

 

 

 

 

 

 

 

 

Instructional Materials

 

Pearson Textbook, TI-84 graphing calculators, Promethian Board.

Field Trip/s

 

 


Subject

Advanced Algebra & Trig

 

Nine Week

 

3rd Nine weeks

Standard

 

 

 

 

 

F-LE Construct and Compare Linear, Quadratic, and Exponential Models and Solve Problems

 

F-IF Understand the Concept of a Function and Use Function Notation

 

F-BF Build a Function that Models the Relationship Between Two Quantities

 

F-BF Build New Functions from Existing Functions

 

F-TF Prove and Apply Trigonometric Identities

 

A-REI.11 Represent and solve equations as a process of reasoning and explain the reasoning

G-SRT Apply Trigonometry to General Triangles

 

N-CN Perform Arithmetic Operations with Complex Numbers

 

N-CN Represent Complex Numbers and

 

Their Operations on the Complex Plane

 

N-VM Represent and Model with Vector Quantities

 

N-VM Perform Operations on Vectors

 

A-REI Solve Systems of Equations

Objectives

 

 

 

 

 

 

 

 

 

CLE 3124.4.3 Solve trigonometric equations.

CLE 3124.4.4 Apply trigonometric identities to rewrite expressions and solve equations.

CLE 3124.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.

CLE 3124.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

CLE 3124.1.5 Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.

CLE 3124.2.2 Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

CLE 3124.5.1 Create scatter plots, analyze patterns and describe relationships that exist in a set of linear and non-linear paired data to make predictions.

CLE 3124.5.2 Identify and interpret the correlation coefficient for a linear bivariate data set.

CLE 3124.5.3 Examine all aspects of using regression equations to act as a model for a real world situation, including interpolation, extrapolation and validity of model.

CLE 3124.4.1 Understand basic right triangle trigonometry an use it to solve problems.

CLE 3124.4.2 Know how the trigonometric functions can be extended to the periodic functions on the real number line, derive basic formulas of these functions, and use these functions and formulas to solve problems.

CLE 3124.4.3 Solve trigonometric equations.

CLE 3124.4.6 Understand the measure of angles and the relationship to the circle;

convert between degrees and radians.

CLE 3124.4.7 Develop the measurement of arcs of circles; calculate angular and

linear velocity.

CLE 3124.4.5 Apply vectors to solve real world problems.

CLE 3124.3.5 Solve problems by converting the given verbal information into an appropriate mathematical model involving equations or systems of equations; apply appropriate techniques to analyze these mathematical models; and interpret the solution obtained in written form using appropriate units of measurement.

 

Topics

 

 

 

 

 

6.1 Verifying Trigonometric Identities

TASKIdentities and Equations

 

6.2 Sum and Difference Formulas

Examples of Sum and Difference Formulas

 

6.3 Double Angle/Half Angle Formulas, Power Reducing

Examples of Double and Half Angle Formulas

 

6.4 Product to Sum and Sum to Product Formulas (Optional)

Examples of Product to Sum and Sum to Product

 

6.5 Trigonometric Equations

Examples of Solving Trig Equations

 

7.1 Law of Sines

Visual Proof of Ambiguous Case

On-line Law of Sines Practice

 

7.2 Law of Cosines

On-Line Law of Cosines Practice

TASK - Law of Sines and Cosines

 

7.3 Polar Coordinates

 

7.4 Graphs of Polar Equations

 

7.5 Complex Numbers in Polar Form, DeMoivre’s Theorem

 

7.6 Vectors

Explanations of Vectors

 

7.7 Dot Product

 

8.1 Systems of Linear Equations in Two Variables

TASKSupply and Demand

 

8.2 Systems of Linear Equations in Three Variables

Using Excel to Solve Systems of Linear Equations

 

8.3 Partial Fractions

 

8.4 Systems of Non-Linear Equations in Two Variables

Examples of Non-Linear Systems

 

8.5 Systems of Inequalities

TASK -Rabbit Food

 

8.6 Linear Programming

 

 

 

 

 

Major Assignment/s

 

 

 

 

 

 

 

 

 

Instructional Materials

 

Pearson Adv Alg & Trig, graphing calculator

Field Trip/s

 

 


Subject

Advanced Algebra & Trig

 

Nine Week

 

4th Nine weeks

Standard

 

 

 

 

 

N-VM Perform Operations on Matrices and Use Matrices in Applications

 

G-GPE Translate Between the Geometric Description and the Equation for a Conic Section

 

A-SSE Derive the Formula for the Sum of a Finite Geometric Series and Use the Formula to Solve Problems

 

F-LE Construct Arithmetic and Geometric Sequences, given a Graph, a Description of a Relationship, or Two Input/Output Pairs

 

S-CP Understand Independence and Conditional Probability and Use Them to Interpret Data

 

S-CP Use the Rules of Probability to Compute Probabilities of Compound Events in a Uniform Probability Model

 

S-CP Use Probability to Evaluate Outcomes

Objectives

 

 

 

 

 

 

 

 

 

CLE 3124.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

CLE 3124.1.4 Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.

solution strategies.

CLE 3124.1.6 Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.

CLE 3124.3.3 Understand how the algebraic properties of an equation transform the geometric properties of its graph.

CLE 3124.3.4 Solve nonlinear inequalities (quadratic, trigonometric, conic, exponential, and logarithmic).

CLE 3124.3.6 Understand the properties of conic sections whether displayed in equation or graphical form.

CLE 3124.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

CLE 3124.3.1 Derive and use the formulas for the general term and summation of finite or infinite arithmetic and geometric series, if they exist.

CLE 3124.3.7 Use the binomial theorem to solve problems.

Topics

 

 

 

 

 

9.1 Matrix Solutions to Linear Systems

 

9.2 Inconsistent and Dependent Systems

 

9.3 Matrix Operations

 

9.4 Matrix Equations

 

TASKS – Unit on Solving Systems of Equations

 

9.5 Determinants and Cramer’s Rule

Video of Determinatants and Cramer’s Rule for 3 x 3

 

TASKS - Unit on Matrices

 

10.1 The Ellipse

Examples of Ellipse

 

10.2 The Hyperbola

Examples of Hyperbolas

 

10.3 The Parabola

Video on Graphing Parabolas

 

10.4 Rotation of Axes (Optional)

 

10.5 Parametric Equations

 

10.6 Conic Sections in Polar Coordinates

 

11.1 Sequences and Summation Notation

 

11.2 Arithmetic Sequences

Examples of Arithmetic

 

11.3 Geometric Sequences and Series

Examples of Geometric

 

TASKSequences and Series

 

11.4 Mathematical Induction

 

11.5 The Binomial Theorem

 

11.6 Counting Principles, Permutations, Combinations

Video on Counting Principles

 

11.7 Probability

Video on Intro to Probability

 

 

 

 

Major Assignment/s

 

 

 

 

 

 

 

 

 

Instructional Materials

 

PearsonAdv Alg & Trig, graphing calculator

Field Trip/s