Pre Cal/Adv Alg & Trig Syllabus

 Subject Pre Cal/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 Graphs and Graphing Utilities   Linear and Rational Equations   Models and Applications (Optional)   Complex Numbers   Quadratic Equations   Other Equations   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   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 TASK – Exploring 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   5.3 Trigonometric Functions of Any Angle   5.4 Trigonometric Functions of Real Numbers, Periodic Functions TASK – Intro To Trig Graphs   5.5 Graphs of Sine and Cosine TASK – Graphing Sine/Cosine Worksheet for TASK – Sine/Cosine TASK – Trig 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   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 TASK – Supply 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     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   TASK – Sequences 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