Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
MATHEMATICS DEPARTMENT HANDBOOK 2011-2012 MATHEMATICS DEPARTMENT LIST OF COURSES Algebra Concepts Algebra I-K Honors Algebra I-K Plane Geometry Honors Plane Geometry Algebra II-K Honors Algebra II-K Probability and Statistics Honors Probability and Statistics Trigonometry Honors Trigonometry Pre-Calculus Honors Pre-Calculus Calculus I Honors Calculus I Calculus II Honors Calculus II Advanced Placement Calculus Computer Science C++ Honors Computer Science MATHEMATICS DEPARTMENT PHILOSOPHY The Mathematics Department of the Hazleton Area School District has undertaken the process of curricular revision under the direction of the Superintendent of Schools in order to accomplish the following district goals: 1. To upgrade the curricular offerings of the H.A.S.D. to prepare students for life in an everchanging and complex society. 2. To coordinate instruction among all grade levels. 3. To standardize the curriculum in all schools of the district. 4. To involve teachers in the construction and implementation of curriculum. Furthermore the Mathematics Department herein sets forth its collective beliefs regarding children, its subject, and education. Mathematics at all levels gives the student an opportunity to use logical thinking in problem solving. This we consider a very important overall value to every student. We in the Mathematics Department are trying to foster the following values and attitudes among our students. A. Positive attitude towards mathematics. B. Independent and logical thinking. C. Practical application. D. Self-confidence. E. Life-long learning Mathematics is extremely important for today’s competitive and highly technical society. Our Mathematics personnel feel, therefore, that mathematics instruction is of paramount importance. Our professionals are striving to help students develop the necessary skills and attitude for success in their daily lives as well as post-secondary education. The fundamental goal of the Mathematics Department is to teach quality mathematics to all students. To attain this goal we make every effort to provide all students with a varied sequence of mathematics courses at a grade and ability level to meet their academic and career needs. These courses not only provide each student with a certain degree of success, but also stimulate growth through challenging problem solving concepts. Traditionally, our mathematics courses emphasize the basic skills and logical reasoning, as well as the development of theory and analytical thinking. Students are encouraged to develop problem-solving skills that will help them in future course work and life’s challenges. The upper level mathematics courses that are intended for post-secondary science and mathematics majors emphasize proof and structure along with basic skills which enables our students to compete successfully with students from other high schools. Our career oriented mathematics sudents are provided with appropriately challenging courses integrating mathematic skills and concepts with today technology. COURSE TITLE: ALGEBRA CONCEPTS BOOK: “Algebra I”; Author: Smith, Charles, Dossey, and Bittinger; Copyright: 2001; Publisher: Prentice Hall. OBJECTIVES: Algebra I will build on the concepts of Pre-Algebra and introduce students to the number system, solving algebraic equations and inequalities, and factoring. MATERIAL COVERED: Teachers should be giving a Chapter 1 Assessment on Page 50 of the student textbook being used. Chapter 2: Integers and Rational Numbers *This chapter should be completed during the first week of school. Section 2.1: Integers and number lines, Absolute values Section 2.2: Rational numbers (Positive and Negative) Section 2.3: Add Section 2.4: Subtract Section 2.5: Multiply Section 2.6: Divide Section 2.7: Distributive property, Factoring Section 3.1: Addition property of equations (If necessary) Section 3.2: Multiplication property of equalities (If necessary) Chapter 3: Equations Section 3.3: Using properties together Section 3.4: Expressions and equations Section 3.5: Solving equations. Whole numbers Section 3.6: Decimal numbers and fractions Section 3.9: Proportions Section 3.10: Percent, Decimal, Fraction Section 3.11: More Expressions and Equations Chapter 4: Inequalities Section 4.1: Inequalities and their graphs Section 4.3: Multiplication property Section 4.4: Using Inequalities Chapter 5: Exponents Section 5.1: Exponents Section 5.2: More with Exponents Section 5.3: Multiplying and dividing monomials Section 5.5: Polynomial types Section 5.6: More on Polynomials Section 5.7: Adding polynomials Section 5.8: Subtracting polynomials Section 5.9: Multiplying of monomials and binomials Cont’d Chapter 5: Exponents Section 5.10: Special products Section 5.11: Multiplying Polynomials Chapter 6: Polynomials and Factoring Section 6.1: Factoring Section 6.2: Difference of two squares Section 6.3: Trinomial Squares Section 6.4: Factoring x2 + bx + c Section 6.5: Factoring ax2 + bx + c Section 6.7: Factoring a general strategy Section 6.8: Solve equations by factoring Section 6.9: Word problems Chapter 7: Graphs and Linear Equations Section 7.1: Graphing ordered pairs Section 7.2: Graphing equations Section 7.3: Linear equations, intercepts, standard form Section 7.4: Slope intercept Section 7.5: Equation and slope Section 7.6: Finding an equation of a line Section 7.8: Parallel and perpendicular lines COURSE TITLE: ALGEBRA I-K BOOK: Prentice Hall, “Algebra 2 with Trigonometry”, Authors: Smith, Charles, Dossey, Bittinger; Copyright 2001 OBJECTIVES: Algebra I will continue to build upon the Algebra Concepts course. Students will delve into the study of Equations and Inequalities, Graphing, Systems of Equations, Factoring, and Simplifying Polynomials. MATERIAL COVERED: Chapter 1: Real Numbers, Algebra, and Problem Solving Section 1.1: Real Numbers and Operations Section 1.3: Algebraic Expressions and Properties of Numbers Section 1.4: The Distributive Property Section 1.5: Solving Equations Section 1.6: Writing Equations Section 1.7: Exponential Notation Section 1.8: Properties of Exponents Chapter 2: Equations and Inequalities Section 2.1: More on Solving Equations Section 2.2: Using Equations Section 2.4: Solving Inequalities Section 2.5: Using Inequalities Section 2.6: Compound Inequalities Section 2.7: Absolute Value Chapter 3: Relations, Functions, and Graphs Section 3.1: Relations and Ordered Pairs Section 3.2: Graphs Section 3.3: Functions Section 3.4: Graphs of Linear Equations Section 3.5: Slope Section 3.6: More Equations of Lines Section 3.7: Parallel and Perpendicular Lines “Best Fit” for Assessment Testing-other resource Section 3.8: Mathematical Modeling: Using Linear Functions Chapter 4: Systems of Equations and Problem Solving Section 4.1: Systems of Equations in Two Variables Section 4.2: Solving Systems of Equations Section 4.3: Using a System of Two Equations Chapter 5: Polynomial and Polynomial Equations Section 5.1: Polynomials and Functions Section 5.2: Addition and Subtraction of Polynomials Section 5.3: Multiplication of Polynomials Section 5.4: Factoring Section 5.5: More Factoring Section 5.6: Factoring: A General Strategy Chapter 6: Rational Expressions and Equations Section 6.1: Multiplying and Simplifying Section 6.2: Addition and Subtraction Section 6.3: Complex Rational Expressions Section 6.4: Division of Polynomials Chapter 7: Powers, Roots, and Complex Numbers Section 7.1: Radical Expressions Section 7.2: Multiplying and Simplifying Section 7.3: Operations with Radical Expressions Section 7.4: More Operations with Radical Expressions Chapter 15: Counting and Probability Section 15.5: Probability Section 15.6: Compound Probability Chapter 16: Statistics and Data Analysis Section 16.1: Statistics: Organizing Data Section 16.2: Using Measures of Central Tendency Section 16.3: Measures of Variation COURSE TITLE: HONORS ALGEBRA I BOOK: Holt, Algebra with Trigonometry, Authors: Nichols, Edwards, Garland, Hoffman, Mamary, Palmer, Copyright 1992 OBJECTIVES: Algebra I will continue to build upon the Algebra Concepts course. Students will delve into the study of Equations and Inequalities, Graphing, Systems of Equations, Factoring, and Simplifying Polynomials. MATERIAL COVERED: Chapter 1: Linear Equations Section 1.1: Operations with Real Numbers Section 1.3: Algebraic Expressions Section 1.4: Linear Equations Section 1.6: Problem Solving: One or More Numbers Section 1.7: Problem Solving: Perimeter and Area Chapter 2: Linear Inequalities Section 2.1: Linear Inequalities Section 2.2: Compound Inequalities Section 2.3: Sentences with Absolute Value Section 2.4: Problem Solving: Using Inequalities Chapter 3: Relations, Functions: Graphing Linear Functions Section 3.1: Relations and Functions Section 3.2: Graphs of Functions Section 3.3: Slope Section 3.4: Equation of a Line Section 3.5: Graphing Linear Relations Section 3.6: Linear Models Section 3.7: Parallel and Perpendicular Lines Chapter 4: Linear Systems in Two Variables Section 4.1: Graphing Linear Systems Section 4.2: The Substitution Method Section 4.3: The Linear Combination Method Chapter 5: Polynomials Section 5.1: Positive Integral Exponents Section 5.2: Zero and Negative Exponents Section 5.3: Polynomials Section 5.4: Factoring Section 5.5: Special Products Section 5.6: Special Factors Section 5.7: Combined Types of Factoring Section 5.8: Dividing Polynomials Chapter 7: Rational Expressions Section 7.1: Rational Expressions Section 7.2: Products and Quotients of Rational Expressions Section 7.4: Sums and Differences of Rational Expressions Section 7.5: Complex Rational Expressions Chapter 8: Radicals and Rational Expressions Section 8.1: Square Roots and Functions Section 8.2: Simplifying Square Roots Section 8.3: Sums, Differences, and Products of Square Roots Section 8.4: Quotients of Square Roots Section 8.5: Simplifying Radicals with Indices Greater Than 2 Chapter 14: Permutations, Combinations, and Probability Section 14.7: Probability Section 14.8: Adding and Multiplying Probability Section 14.9: Selecting More Than One Object at Random Section 14.10: Frequency Distributions Course Name: Book: PLANE GEOMETRY Prentice Hall, “Geometry” Authors: Bass, Charles, Johnson, Kennedy Copyright 2004 Objectives: Plane Geometry is for all college bound and career oriented students. It includes the study of the properties of physical shapes such as angles, triangles, polygons, and circles with emphasis on theory, problem solving and practical applications. Integrated into problem solving is the deductive reasoning approach and the use of algebraic concepts to arrive at solutions. MATERIAL COVERED: Teachers must give a Chapter 1 Assessment on Page 64 of the student text book being used. Chapter 1: Tools of Geometry Section 1-6: Midpoint and distance Section 1-7 Perimeters, Circumference and Areas Chapter 2: Reasoning and Proofs Section 2-5: Proving Angles Congruent Chapter 3: Parallel and Perpendicular Lines Section 3-1: Properties of Parallel Lines Section 3-2: Proving Lines Parallel Section 3-4: The Polygon-Angle Sum Theorems Section 3-6 Slopes of Parallel and perpendicular lines Chapter 4: Congruent Triangles Section 4-1: Congruent Figures Section 4-2: Triangle Congruence by SSS and SAS Section 4-3: Triangle Congruence by ASA and AAS Section 4-4: Using Congruent Triangles:CPCTC Section 4-5: Isosceles and Equilateral Triangles Section 4-6: Congruence in Right Triangles Chapter 5: Relationships Within Triangles Section 5-1: Midsegments of a Triangle Section 5-2: Bisectors in Triangles Section 5-3: Concurrent Lines (Medians,Altitudes, Perpendicular Bisectors, Angle Bisectors) Section 5-5: Inequalities in Triangles Chapter 6: Quadrilaterals Section 6-1: Classifying Quadrilaterals Section 6-2: Properties of Parallelograms Section 6-3: Proving that a Quadrilateral is a Parallelogram Section 6-4: Special Parallelogram Section 6-5: Trapezoids and Kites Section 6.6: Placing figures in the coordinate plane Section 6.7: Proofs using coordinate geometry Chapter 7: Area Section 7-1: Section 7-2: Section 7-3: Section 7-4: Section 7-5: Section 7-6: Section 7-7: Section 7.8: Areas of Parallelograms and Triangles The Pythagorean Theorem and its Converse Special Right Triangles Areas of Trapezoids, Rhombuses and Kites Areas of Regular Polygons Circles and Arcs Areas of Circles and Sectors Geometric Probability Chapter 8: Similarity Section 8-2 Similar Polygons Section 8-3 Proving Triangles Similar Section 8-4 Similarity in Right Triangles Section 8-5: Proportions in Triangles Section 8-6: Perimeters and Areas of Similar Figures Chapter 9: Right Triangle Trigonometry Section 9.1: Tangent Ratio Section 9.2: Sine & cosine Ratios Section 9.3 Angles of Elevation & Depression Chapter 10: Surface Area and Volume Section 10-3: Surface Areas of Prisms and Cylinders Section 10-4: Surface Areas of Pyramids and Cones Section 10-5: Volumes of Prisms and Cylinders Section 10-6: Volumes of Pyramids and Cones Section 10-7: Surface Area and Volume of Spheres Section 10-8: Areas and Volumes of Similar Solids Chapter 11: Circles Section 11-1: Tangent Lines Section 11-2: Chords and Arcs Section 11-4: Angle Measures and Segment Lengths COURSE TITLE: HONORS PLANE GEOMETRY BOOK: Addison-Wesley, “Geometry”, Authors: Clemens, O’Daffer, Cooney, and Dossey; Copyright: 1994 OBJECTIVE: Honors Plane Geometry includes covering all the topics of Plane Geometry, but in greater depth. Greater emphasis is placed on the application of algebraic solutions in problem solving. Also included is the formal method of the deductive proof to develop the topics in sequential manner, and to theoretically apply the definitions, axioms and theorems. Chapter 1: Basic Ideas of Geometry Section 1-1: Points, Lines, Plane and Space Section 1-2: Distance and Segment Measure Section 1-3: Rays, Angles, and Angle Measure Section 1-4: Congruent Segments and Angles Section 1-5: Triangles Section 1-6: Conditional Statements Section 1-7: Drawing and Supporting Conclusions Section 1-8: Deductive Reasoning – Using Algebraic Properties Chapter 2: Introduction to Proof Section 2-1: Two-Column Proofs Section 2-2: Complementary, Supplementary, and Vertical Angles Section 2-3: Perpendicular Lines Section 2-4: Drawing and Using Diagrams Section 2-5: Planning and Writing a Proof Section 2-6: Proving Theorems: Segments and Lines Section 2-7: Proving Theorems: Angles Chapter 3: Parallel Lines and Planes Section 3-1: Parallel Lines, Lines, and Transversals Section 3-2: Properties of Parallel Lines Section 3-3: Proving Lines Parallel Section 3-4: Angles of a Triangle Section 3-5: Theorems Related to the Angle Sum Theorem for Triangles Section 3-6: Angles of a Polygon Chapter 4: Congruent Triangles Section 4-1: Congruent Triangles Section 4-2: Congruence Postulates Section 4-3: Proofs: Using Congruence Postulates Section 4-4: Proving Angles and Segments Congruent Section 4-5: Proofs: Overlapping Triangles Section 4-6: Isosceles Triangles Section 4-7: AAS Congruence and Right Triangle Congruence Section 4-8: Medians, Altitudes, and Perpendicular Bisectors Chapter 5: Using Congruent Triangles and Parallel Lines Section 5-1: Properties of Parallel Lines Section 5-2: Proving Quadrilaterals and Parallelograms Section 5-3: Rectangles, Rhombuses, and Squares Section 5-4: Trapezoids Section 5-5: The Midsegment Theorem Section 5-6: Indirect Proof Section 5-7: Inequalities in One Triangle Section 5-8: Inequalities in Two Triangles Chapter 6: Similarity Section 6-1: Section 6-2: Section 6-3: Section 6-4: Section 6-5: Section 6-6: Ratio and Proportion Properties of Proportions Similarity Polygons AA Similarity Postulate SAS and SSS Similarity Theorems Segments Divided Proportionally Right Triangles Section 7-1: Section 7-2: Section 7-3: Section 7-4: Section 7-5: Section 7-6: Section 7-7: Right Triangles Properties The Pythagorean Theorem The Converse of the Pythagorean Theorem Special Right Triangles The Tangent Ratio The Sine and Cosine Ratios Angles of Elevation and Depression Chapter 7: Chapter 8: Circles Section 8-1: Section 8-2: Section 8-3: Section 8-4: Section 8-5: Section 8-6: Section 8-7: Section 8-8: Basic Terms Tangent Lines Common Tangents and Tangent Circles Arcs and Their Measures Chords and Circles Inscribed Angles Angles of Chords, Secants, Tangents Segments of Chords, Secants, Tangents Chapter 10: Area and Perimeters of Polygons Section 10-1: Perimeter and Area of Rectangles Section 10-2: Areas of Parallelograms and Triangles Section 10-3: Areas of Trapezoids and Other Quadrilaterals Section 10-4: Areas of Regular Polygons Section 10-5: Ratios of Areas and Perimeters of Similar Polygons Section 10-6: Circumference and Arc Length Section 10-7: Areas of Circles, Sectors, and Segments COURSE NAME: Book: ALGEBRA II-K Title: “College Algebra”; Authors: R. David Gustafson and Peter D. Frisk; Publisher: Thomson/ Brooks/ Cole; Copyright: 2004 OBJECTIVES: The Algebra II-K course is the second level in the study of algebra. The concepts learned in Algebra I are reviewed and expanded into the study of products and factors of polynomials, operations on rational expressions, the complex number system, and quadratic equations and inequalities. Higher order polynomial equations and selected analytical geometric concepts are introduced as the students expand their algebraic skills and knowledge to prepare for higher-level mathematics. Material Covered: Chapter 0: Basic Algebra Section 0.2 Integer exponents and scientific notation Section 0.3 Rational exponents and radicals Section 0.5 Factoring polynomials Section 0.6 Algebraic Functions Chapter 1: Equations and Inequalities Section 1.1 Solving equations Section 1.2 Applications of linear equations Section 1.3 Solving quadratic equations Section 1.4 Applications of quadratic equations Section 1.5 The Complex number system Section 1.6 Polynomial and radical equations Chapter 2: Graphs of Equations Section 2.3 Writing of linear equations (Unit 5 Lesson 4 – PSSA Finish Line) Section 2.5 Proportion and variation (supplemental material) Chapter 3: Functions Section 3.1 Functions and function notation Section 3.2 Quadratic functions Section 3.3 Polynomials and Other Functions (supplemental material) Section 3.4 Translating and Stretching Graphs Section 3.5 Rational Functions Section 3.7 Inverse functions Chapter 4 Section 4.1 Exponential Functions and Their Graphs Section 4.2 Applications of Exponential Functions Section 4.3 Logarithmic Functions and Their Graphs Section 4.4 Applications of Logarithmic Functions Section 4.5 Properties of Logarithms Section 4.6 Exponential and Logarithmic Equations Chapter 8: Probability Section 8.2 Sequences, Series, and Summation Notation Section 8.3 Arithmetic Sequences Section 8.4 Geometric Sequences Section 8.6 Permutations and Combinations Section 8.7 Probability Section 8.8 Computation of Compound Probabilities Section 8.9 Odds and Mathematical Expectation COURSE NAME: Book: HONORS ALGEBRA II-K Title: “Structure and Method Book 2”; Authors: Brown, Dolciani, Sorgenfrey, Kane Publisher: Houghton Mifflin; Copyright: 1994 OBJECTIVES: The Honors Algebra II-K course is the second level in the study of algebra. The concepts learned in Algebra I are reviewed and expanded into the study of products and factors of polynomials, operations on rational expressions, the complex number system, and quadratic equations and inequalities. Higher order polynomial equations and selected analytical geometric concepts are introduced as the students expand their algebraic skills and knowledge to prepare for higher-level mathematics. Material Covered: Chapter 1: Basic Concepts of Algebra Section 1.7 Solving Equations in One Variable Chapter 3: Linear Equations and Functions Section 3.10 Relations Chapter 4: Products and Factors of Polynomials Section 4.5 Factoring Polynomials Section 4.6 Factoring Quadratic Polynomials Section 4.7 Solving Polynomial Equations Chapter 5: Rational Expressions Section 5.1 Quotients of Monomials Section 5.2 Zero and Negative Exponents Section 5.4 Rational Algebraic Expressions Section 5.9 Fractional Equations Chapter 6: Irrational and Complex Numbers Section 6.5 Equations Containing Radicals Section 6.7 The Imaginary Number i Section 6.8 The Complex Numbers Chapter 7: Quadratic Equations and Functions Section 7.1 Completing the Square Section 7.2 The Quadratic Formula Section 7.5 (xh )2 Graphing yka Section 7.6 Quadratic Functions Chapter 8: Variation and Polynomial Equations Section 8.1 Direct Variation and Proportion Section 8.2 Inverse and Joint Variation Chapter 10: Exponential and Logarithmic Functions Section 10.1 Rational Exponents Section 10.2 Real Number Exponents Section 10.3 Composition and inverses of Functions Section 10.4 Definition of Logarithms Section 10.5 Laws of Logarithms Section 10.6 Applications of Logarithms Section 10.7 Problem Solving: Exponential Growth and Decay Section 10.8 The Natural Logarithm Function Chapter 11: Sequences and Series Section 11.1 Types of Sequences Section 11.2 Arithmetic Sequences Section 11.3 Geometric Sequences Chapter 15: Statistics and Probability Section 15.4 Correlation Section 15.5 Fundamental Counting Principles Section 15.6 Permutations Section 15.7 Combinations Section 15.9 Sample Spaces and Events Section 15.10 Mutually Exclusive and independent Events Chapter 9: Analytic Geometry Section 9.2 Circles Section 9.3 Parabolas Section 9.4 Ellipses Section 9.5 Hyperbolas Course Name: Probability and Statistics (Honors and Regular) Syllabus and PSSA Anchors Book: The Basic Practice of Statistics 2nd Edition ; Autohor: David S. Moore; Copyright: 1995, 2000 Publisher: WH Freeman and Company; ISBN # : 0-7167-3627-6 Objectives: Prob and stat is intended for college-bound students who anticipate needing this background for their individual course study. Students with an interest in business or the social sciences (physiology, sociology, etc). should strongly consider taking this elective course. Probability and both descriptive and inferential statistics will be discussed at length. The honors course covers the material in more depth, at a more rigorous pace, with more mataerial both in text and supplementary. Material Covered: Chapter 1: 1.1 Displaying Distributions with Graphs 1.2 Describing Distributions with Numbers 1.3 The Normal Distributions Chapter 2: 2.1 Scatterplots 2.2 Correlation 2.3 Least-Squares Regression 2.4 Cautions about Correlations and Regression Chapter 3: 3.1 Designing Samples 3.2 Designing Experiments Chapter 4: 4.1 Randomness 4.2 Probabilty Models 4.3 Sampling Distributions Chapter 5: 5.1 General Probablity Rules 5.2 Conditional Probablity Probability Packet Chapter 6: 6.1 Estimating with Confidence 6.2 Tests of Significance 6.3 Making Sense of Statistical Significance 6.4 Error Probabilities and Power Chapter 7: 7.1 Inference for the Mean of a Population 7.2 Comparing Two Means Chapter 8: 8.1 Inference for a Population Proportion 8.2 Comparing Two Proportions Chapter 9: 9.1 Two-Way Tables 9.2 The Chi-Square Test *P and S = Probability and Statistics Anchors COURSE TITLE: TRIGONOMETRY BOOK: Addison Wesley Longman; “Trigonometry” 7th Edition; Authors: Lial, Hornsby, Schneider Copyright 2001 OBJECTIVES: Trigonometry places emphasis on the understanding of definitions and principles of trigonometry and their applications to problems solving. It includes the circular function concepts, identities, radian measure, and triangle solutions. Use of the right triangle and its properties and applications are shown through construction and formula solution. Scientific calculators are used heavily throughout this course. MATERIAL COVERED: Entire Course uses anchor M11.C.1.4.1 Chapter 1: The Trigonometric Functions Section 1.1: Basic concepts Section 1.2: Angles Section 1.3: Angle Relationships and similar triangles Section 1.4: Definitions of the trigonometric functions Section 1.5: Using the definitions of the trigonometric functions Chapter 2: Acute Angles and Right Angles Section 2.1: Trigonometric functions of acute angles Section 2.2: Trigonometric functions of non-acute angles Section 2.3: Finding trigonometric function values using a calculator Section 2.4: Solving right triangles Section 2.5: Further applications of right triangles Chapter 3: Radian Measure and the Circular Functions Section 3.1: Radian measure Section 3.2: Applications of radian measure Section 3.3: Circular functions of real numbers Section 3.4: Linear and angular velocity Chapter 4: Graphs of the Circular Functions Section 4.1: Graphs of the sine and cosine functions Section 4.2: Translations of the graphs of the sine and cosine functions Section 4.3: Graphs of the other circular functions Chapter 5: Trigonometric Identities Section 5.1: Fundamental identities Section 5.2: Verifying trigonometric identities Section 5.3: Sum and difference identities for cosine Section 5.4: Sum and difference identities for sine and tangent Section 5.5: Double-angle identities Section 5.6: Half-angle identities Chapter 6: Inverse Trigonometric Functions and Trigonometric Equations Section 6.1: Inverse trigonometric functions Section 6.2: Trigonometric equations I Section 6.3: Trigonometric equations II Section 6.4: Equations involving inverse trigonometric functions Chapter 7: Applications of Trigonometry and Vectors Section 7.1: Oblique triangles and the law of sines Section 7.2: The ambiguous case of the law of sines Section 7.3: The law of cosines COURSE TITLE: HONORS TRIGONOMETRY BOOK: Addison Wesley Longman; “Trigonometry” 7th Edition; Authors: Lial, Hornsby, Schneider Copyright 2001 OBJECTIVES: Honors Trigonometry is designed for students with a strong background in previous math courses. This course places emphasis on the understanding of definitions and principles of trigonometry and their applications to problems solving. It includes the circular function concepts, identities, radian measure, and triangle solutions. Use of the right triangle and its properties and applications are shown through construction and formula solution. This course will cover polar coordinates and polar graphing. Scientific calculators are used heavily throughout this course. MATERIAL COVERED: Chapter 1: The Trigonometric Functions Section 1.1: Basic concepts Section 1.2: Angles Section 1.3: Angle Relationships and similar triangles Section 1.4: Definitions of the trigonometric functions Section 1.5: Using the definitions of the trigonometric functions Chapter 2: Acute Angles and Right Angles Section 2.1: Trigonometric functions of acute angles Section 2.2: Trigonometric functions of non-acute angles Section 2.3: Finding trigonometric function values using a calculator Section 2.4: Solving right triangles Section 2.5: Further applications of right triangles Chapter 3: Radian Measure and the Circular Functions Section 3.1: Radian measure Section 3.2: Applications of radian measure Section 3.3: Circular functions of real numbers Section 3.4: Linear and angular velocity Chapter 4: Graphs of the Circular Functions Section 4.1: Graphs of the sine and cosine functions Section 4.2: Translations of the graphs of the sine and cosine functions Section 4.3: Graphs of the other circular functions Chapter 5: Trigonometric Identities Section 5.1: Fundamental identities Section 5.2: Verifying trigonometric identities Section 5.3: Sum and difference identities for cosine Section 5.4: Sum and difference identities for sine and tangent Section 5.5: Double-angle identities Section 5.6: Half-angle identities Chapter 6: Inverse Trigonometric Functions and Trigonometric Equations Section 6.1: Inverse trigonometric functions Section 6.2: Trigonometric equations I Section 6.3: Trigonometric equations II Section 6.4: Equations involving inverse trigonometric functions Chapter 7: Applications of Trigonometry and Vectors Section 7.1: Oblique triangles and the law of sines Section 7.2: The ambiguous case of the law of sines Section 7.3: The law of cosines Section 7.4: Vectors and the dot product Section 7.5: Applications of vectors As time allows, Chapter 8: Complex Numbers, Polar Equations, and Parametric Equations Section 8.1: Complex numbers Section 8.2: Trigonometric (polar) form of complex numbers Section 8.3: The product and quotient theorems Section 8.4: Powers and roots of complex numbers Section 8.5: Polar equations and graphs Section 8.6: Parametric equations, graphs, and applications Chapter 9: Exponential and Logarithmic Functions Section 9.1: Exponential functions Section 9.2: Logarithmic functions Section 9.3: Evaluating logarithms and the change-of-base theorem Section 9.4: Exponential and logarithmic equations COURSE TITLE: Pre-Calculus BOOK: Title: “Blitzer PRECALCULUS Third Edition” Copyright: 2007; Publisher: Pearson Prentice Hall OBJECTIVES: Pre-calculus is recommended for students who have done well in previous math courses and who have college ambitions where mat is utilized. This course provides a rich background for calculus, analytic geometry, linear algebra, as well as a course in functional analysis. Graphing is used to incorporate many of the concepts taught. MATERIAL COVERED: Chapter P: Prerequisites: Fundamental Concepts of Algebra Sections P.1 to P. 9 (These sections are to be used at most for two days of a review before beginning chapter 1) Chapter 1: Functions and Graphs Section 1.1: Graphs and Graphing Utilities Section 1.2: Basics of Functions and Their Graphs Section 1.3: More on Functions and Their Graphs Section 1.6: Transformations of Functions Section 1.8: Inverse Functions Section 1.10: Modeling with Functions Chapter 2: Polynomial and Rational Functions Section 2.2: Quadratic Functions Section 2.3: Polynomial Functions and Their Graphs Section 2.6: Rational Functions and Their Graphs Section 2.7: Polynomial and Rational Inequalities Section 2.8: Modeling Using Variation Chapter 3: Exponential and Logarithmic Functions Section 3.1: Exponential Functions Section 3.2: Logarithmic Functions Section 3.3: Properties of Logarithms Section 3.4: Exponential and Logarithmic Equations Section 3.5: Exponential Growth and Decay Chapter 7: Systems of Equations and Inequalities Section 7.1: Systems of Linear Equations in Two Variables Section 7.2: Systems of Linear Equations in Three Variables Section 7.3: Partial Fractions Chapter 8: Matrices and Determinants Section 8.1: Matrix Solutions to Linear Systems Section 8.2: Inconsistent and Dependent Systems Section 8.3: Matrix Operations Section 8.4: Inverses and Matrix Equations Section 8.5: Determinants and Cramer’s Rule Chapter 10: Sequences, Induction and Probability Section 10.1: Sequences and Summation Notation Section 10.2: Arithmetic Sequences Section 10.3: Geometric Sequences and Series COURSE TITLE: Honors Pre-Calculus BOOK: Title: “Blitzer PRECALCULUS Third Edition”; Copyright: 2007; Publisher: Pearson Prentice Hall OBJECTIVES: Honors Pre-calculus is for students whose previous math background is strong. This course offers an excellent background in Pre-Calculus, linear algebra, functions and a complete foundation for calculus. This particular course will also cover some analytical geometry and the use of equations and inequalities as mathematical models. MATERIAL COVERED: Chapter P: Prerequisites: Fundamental Concepts of Algebra Sections P.1 to P. 9 (These sections are to be used for one day of a review before beginning chapter 1) Chapter 1: Functions and Graphs Section 1.1: Graphs and Graphing Utilities Section 1.2: Basics of Functions and Their Graphs Section 1.3: More on Functions and Their Graphs Section 1.6: Transformations of Functions Section 1.8: Inverse Functions Section 1.10: Modeling with Functions Chapter 2: Polynomial and Rational Functions Section 2.2: Quadratic Functions Section 2.3: Polynomial Functions and Their Graphs Section 2.6: Rational Functions and Their Graphs Section 2.7: Polynomial and Rational Inequalities Section 2.8: Modeling Using Variation Chapter 3: Exponential and Logarithmic Functions Section 3.1: Exponential Functions Section 3.2: Logarithmic Functions Section 3.3: Properties of Logarithms Section 3.4: Exponential and Logarithmic Equations Section 3.5: Exponential Growth and Decay Chapter 7: Systems of Equations and Inequalities Section 7.1: Systems of Linear Equations in Two Variables Section 7.2: Systems of Linear Equations in Three Variables Section 7.3: Partial Fractions Chapter 8: Matrices and Determinants Section 8.1: Matrix Solutions to Linear Systems Section 8.2: Inconsistent and Dependent Systems Section 8.3: Matrix Operations Section 8.4: Inverses and Matrix Equations Section 8.5: Determinants and Cramer’s Rule Chapter 10: Sequences, Induction and Probability Section 10.1: Sequences and Summation Notation Section 10.2: Arithmetic Sequences Section 10.3: Geometric Sequences and Series Section 10.4: Mathematical Induction Section 10.5: The Binomial Theorem Section 10.6: Permutations and Combinations Section 10.7: Probability As time allows, Chapter 9: Conic Sections and Analytic Geometry Section 9.1: The Ellipse Section 9.2: The Hyperbola Section 9.3: The Parabola Section 9.4: Rotation of Axes Section 9.5: Parametric Equations Section 9.6: Conic Sections in Polar Coordinates COURSE TITLE: CALCULUS I BOOK; Title: Calculus of a Single Variable (eighth edition); Author: Larson, Hostetler, Edwards; Copyright: 2006; Publisher: Houghton Mifflin Company OBJECTIVES: Calculus I uses a non-trigonometric approach to learning calculus. It includes both derivatives and integrals of polynomials, exponential functions as well as logarithmic functions with their applications. A strong foundation in Algebra and graphing functions is essential. MATERIAL COVERED: Chapter P: Preparation for Claculus P.I Graphs and Models P.2 Linear Models and Rates of Change P.3 Functions and Their Graphs Chapter 1: Limits and Their Properties 1.1 A Preview of Calculus 1.2 Finding Limits Graphically and Numerically 1.3 Evaluating Limits Analytically 1.4 Continuity and One-Sided Limits 1.5 Infinite Limits Chapter 2: Differentiation 2.1 The derivative and the Tangent Line Problem 2.2 Basic Differentiation Rules and Rates of Change 2.3 Product and Quotient Rules and Higher-Order Derivatives 2.4 The Chain Rule 2.5 Implicit Differentiation 2.6 Related Rates Chapter 3: Applications of the Differentiation 3.1 Extrema on an Interval 3.2 Rolle's Theorem and the Mean Value Theorem 3.3 Increasing and Decreasing Functions and the First Derivative Test 3.4 Concavity and the Second Derivative Test 3.5 Limits at Infinity 3.6 A Summary of Curve Sketching 3.7 Optimization Problems 3.9 Differentials Chapter 4: Integration 4.1 Anti-Derivatives and Indefinite Integration 4.2 Area 4.3 Reimann Sums and Definite Integrals 4.4 The Fundamental Theorem of Calculus 4.5 Integration by Substitution 4.6 Numerical Integration Chapter 5: Logarithmic And Exponential Functions 5.1 The Natural Logarithmic Function: Differentiation 5.2 The Natural Logarithmic Function; Integration 5.4 Exponential Functions: Differentiation and Integration Chapter 7: Applications of Integration 7.1 Area of a region Between Two Curves 7.2 Volume: The Disk Method 7.3 Volume: The Shell Method COURSE TITLE: BOOK: HONORS CALCULUS I Title: Elements of Calculus and Analytical Geometry; Author: Thomas and Finney; Copyright: 1989; Publisher: Addison-Wesley Publishing Company OBJECTIVES: Honors Calculus I is a college level calculus course designed for those Honor students entering mathematics or science related fields. The main objective of this course is to teach the mathematics of calculus and to provide the training students will need to use calculus effectively in their later academic and professional work. Major topics include differential and integral calculus along with their applications. MATERIAL COVERED: Chapter 1: Find the Rate of Change of a Function 1.1Plot coordinates for a plane 1.2 Find the slope of a line 1.3 Write equations for lines 1.4 Graph functions 1.5 Solve absolute values 1.6 Find tangent lines and slopes of quadratic and cubic curves 1.7 Find the derivatives of y = f(x) 1.8 Find the velocity and other rates of change 1.9 Solve for limits 1.10 Solve using infinity as a limit 1.11 Work with continuous functions Chapter 2: Find Derivatives 2.1 Find derivatives of polynomial functions 2.2 Find derivatives of products, powers, and quotients 2.3 Derive functions implicitly/Derive functions with fractional powers 2.4 Solve linear approximations and differentials 2.5 Use the chain rule 2.6 Review concepts of trigonometry 2.7 Derivatives of trigonometric functions 2.8 Solving parametric equations 2.10 Using derivative formulas Chapter 3: Use Applications of Derivatives 3.1 Sketch curves with the first derivative 3.2 Find concavity and points of inflection 3.3 Find asymptotes and symmetry 3.4 Use maxima and minima theory to solve problems 3.5 Applications of maxima and minima 3.6 Solve related rates of change 3.7 Use the mean-value theorem 3.8 Solve indeterminate forms and L’Hopital’s Rule Chapter 4: Integration 4.1 Solve for the indefinitie integral 4.2 Select the values for the constant of integration 4.3 Use the substitution method of integration 4.4 Find integrals of trigonometric functions 4.5 Find the definite integral: the area under a curve 4.6 Calculate definite integrals by summation 4.7 Use the fundamental theorems of integral calculus 4.8 Use substitution of definite integrals 4.9 Use rules for approximating definite integrals Chapter 5: Applications of Definite Integrals 5.1 Find the net change in position and distance traveled by a moving body 5.2 Find areas between curves 5.3 Calculate volumes by slicing: volumes of revolution\ 5.4 Find the volumes modeled with washers and cylindrical shells COURSE TITLE: BOOK: CALCULUS II Title: Calculus of a Single Variable (eighth edition); Author: Larson, Hostetler, Edwards; Copyright: 2006; Publisher: Houghton Mifflin Company OBJECTIVES: Calculus II is a course designed for those students who wish to increase their knowledge base in calculus. Major topics will include the various methods of integration, transcendential functions, elementary differential equations, and application problems related to these topics. MATERIAL COVERED: Calculus II I. Chapter 2: Differentiation (Quick Review) 2.2 Basic Differentiation Rules and Rates of Change 2.3 Product and Quotient Rules and Higher Order Derivatives 2.4 The Chain Rule 2.5 Implicit Differentiation II. Chapter 4: Integration (Quick Review) 4.1 Antiderivatives and Indefinite Integration 4.4 The Fundamental Theorem of Calculus 4.5 Integration by Substitution III. Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions 5.1 The Natural Logarithmic Function: Differentiation 5.2 The Natural Logarithmic Function: Integration 5.3 Inverse Functions 5.4 Exponential Functions: Differentiation and Integration 5.5 Bases other than e and Applications 5.6 Inverse Trigonometric Functions: Differentiation 5.7 Inverse Trigonometric Functions: Integration 5.8 Hyperbolic Functions IV. Chapter 6: Differential Equations 6.1 Slope Fields and Euler's Method 6.2 Differential Equations: Growth and Decay 6.3 Separation of Variables and The Logistic Equation 6.4 First-Order Linear Differential Equations V. Chapter 7: Applications of Integration (Quick Review) 7.1 Area of a Region Between Two Curves 7.2 Volume: The Disk Method 7.4 Arc Length and Surfaces of Revolution VI. Chapter 8: Integration Techniques and Improper Integrals 8.1 Basic Integration Rules 8.2 Integration by Parts 8.3 Trigonometric Integrals 8.4 Trigonometric Substitution 8.5 Partial Fractions 8.6 Integration by Tables and Other Integration Techniques 8.7 Indeterminate Forms and L'Hopital's Rule 8.8 Improper Integrals COURSE TITLE: BOOK: HONORS CALCULUS II Title: Elements of Calculus and Analytical Geometry; Author: Thomas and Finney; Copyright: 1989; Publisher: Addison-Wesley Publishing Company OBJECTIVES: Honors Calculus II is a course designed for those students who wish to increase their knowledge base in calculus. Major topics will include the various methods of integration, transcendential functions, elementary differential equations, and application problems related to these topics. Honors Calculus II is slightly more rigorous than Regular Calculus II. MATERIAL COVERED: I. Honors Calculus II Chapter 2: Derivatives a. Section 6: A brief review of trigonometry b. Section 7: Derivatives of trigonometric functions c. Section 8: Parametric equations II. Chapter 4: Integration a. Section 4: Integrals of trigonometric functions b. Section 5: The area under the curve involving trigonometric functions III. Chapter 5: Application of Definite Integrals a. Section 3: Calculating volumes by slicing volumes of revolution b. Section 4: Volumes modeled with washers and cylindrical shells c. Section 5: Lengths of plane curves d. Section 7: The average value of a function IV. Chapter 6: Transcendential Functions a. Section 1: Inverse functions b. Section 2: The inverse trigonometric functions c. Section 3: Derivatives of the inverse trigonometric Functions: Related integrals d. Review 1. Section 4,5: The natural logarithm y = ln x 2. Section 6,7: The exponential function ex 3. Section 8: The functions ax, au, y = log u V. Chapter 7: Methods of Integration a. Section 1: Basic integration formulas b. Section 2: Integration by parts c. Section 3: Products and powers of trigonometric functions d. Section 4: Even powers of sines and cosines e. Section 5: Trigonometric substitutions that replace a² - u², a² + u², and u² - a² by single squared term f. Section 6: Integrals involving ax² + bx + c g. Section 7: The integration of rational functions--partial fractions h. Section 8: Improper integrals i. Section 9: Using integral tables VI. Chapter 14: Differential Equations a. Section 1: First order differential equations of first degree 1. Separable equations 2. Homogenous equations 3. Linear equations b. Reference Books: Reference and Review Formulas COURSE TITLE: BOOK: ADVANCED PLACEMENT CALCULUS A and B Title: Calculus Graphical, Numerical, Algebraic; Authors: Finney, Demana, Waits, Kennedy; Copyright: 2007; Publisher: Pearson Prentice Hall Note: The textbook titled: Elements of Calculus and Analytical Geometry; Authors: Thomas and Finney; Copyright 1989; Publisher: Addison - Wesley can be used as a supplement. Sections from this textbook that correspond to the Finney textbook (where applicable) can be found in parentheses. OBJECTIVES: The Advanced Placement Calculus IA contains the selection of topics that is designed to meet the requirements set forth hi the syllabus of the College Entrance Examination Board for the AB examination. Major topics include differential and integral calculus along with their applications. The A.P. students are required to take the AB level of the Advanced Placement Examination upon completion of the course. A.P. students are required to take Calculus for both semesters. MATERIAL COVERED: AP Calculus A and B I. Chapter 1: Prerequisites for Calculus 1.1 Lines (1.1-1.3) 1.2 Functions and Graphs (1.4) 1.3 Exponential Functions 1.4 Parametric Equations (2.8 problems 1-29) 1.5 Functions and Logarithms 1.6 Trigonometric Functions (2.6) II. Chapter 2: Limits and Continuity 2.1 Rates of Change and Limits (1.9) 2.2 Limits Involving Infinity (1.10) 2.3 Continuity (1.11) 2.4 Rates of Change and tangent Lines (1.7, 1.8) III. Chapter 3: Derivatives 3.1 Derivative (2.1) 3.2 Differentiability 3.3 Rules for Differentiation (3.3) 3.4 Velocity and Other Rates of Change (2.1, 1.8) 3.5 Derivatives of Trigonometric Functions (2.7) 3.6 Chain Rule (2.5) 3.7 Implicit Differentiation (2.3) 3.8 Derivatives of Inverse Trigonometric Functions (6.3) 3.9 Derivatives of Exponential and Logarithmic Functions (6.4-6.6) IV. Chapter 4: Applications of Derivatives 4.1 Extreme Value of functions (3.4) 4.2 Mean Value Theorem (3.7) 4.3 Connecting f and f' with the Graph of / (3.1) 4.4 Modeling and Optimization (3.5) 4.6 Related Rates (3.6) Go to Chapter 8 and do Section 8.2 L'Hopital's Rule (3.8) V. Chapter 5: The Definite Integral 5.1 Estimating with Finite Sums (4.5) 5.2 Definite Integrals (4.5) 5.3 Definite Integrals and Antiderivadves (4.5) 5.4 Fundamental Theorem of Calculus (4.7) 5.5 Trapezoidal Rule (4.9) VI. Chapter 6: Differential Equations and Mathematical Modeling 6.1 Slope Fields and Euler's Method (14.9) 6.2 Antidifferentiation by Substitution (4.1-4.2) 6.3 Exponential Growth and Decay (6.9) VII. Chapter 7: Applications of Definite Integrals 7.1 Integral as Net Change (5.1) 7.2 Areas in a Plane (5.2) 7.3 Volumes (5.3-5.4) Thomas book Chapter 5 Section 5.7 VIII. Review for Advanced Placement Calculus Examination 1. Reference and review formulas 2. Advanced placement examinations in calculus (materials can be obtained from the website www.apcentral.collegeboard.com/ 3. Review calculator use for the AP Exam IX. After Advanced Placement Exam 7.4 Lengths of Curves (5.5) 8.4 Improper Integrals (7.8) 6.4 Integration by Parts (7.2) Thomas Text Chapter 7 Sections 7.3 to 7.10 COURSE TITLE: Computer Science (C++) BOOK: Lawrenceville Press; “A Guide to Programming in C++” Authors: Corica, Brown, Presley Copyright 1997 OBJECTIVES: This is a powerful programming language which uses object-oriented programming. Topics include programming skills in C++, functions, classes, and loops. Students will learn to program in C++. MATERIAL COVERD: I. Beginning C++ A. The C++ language B. C++ program C. C++ program Structure D. Running a program E. Syntax errors and warnings F. Variations on cout G. Displaying special characters H. Using help I. Program style II. Variables and constants A. Using variables B. Obtaining a value from the user C. Using constants built-in data variable definitions expressions and operators D. String library E. Ignore() function F. Formatting III. Controlling program flow A. If statements; if-else statements B. Compound statements nested and ladders C. Logical operators looping: do-while, while, for D. Debugging E. Counting and summing F. Bool library G. Break H. Random numbers I. Conio library IV. Functions A. The function B. Parameters and overloading and default C. Return statement and reference parameters D. Documentation E. Building a library V. Classes and objects (Time permitted) A. Classes and objects B. String C. Ios D. Constructors E. Object VI. Math, recursion and enum (Time permitted) A. Math library B. Trig functions C. Log and exponential functions D. Other math.h functions E. Precision F. Recursion G. Data storage COURSE TITLE: Honors Computer Science (C++) BOOK: Lawrenceville Press; “A Guide to Programming in C++” Authors: Corica, Brown, Presley Copyright 1997 OBJECTIVES: This is a powerful programming language which uses object-oriented programming. Topics include programming skills in C++, functions, classes, chains, and loops. Students will learn to program in C++. MATERIAL COVERD: I. Beginning C++ a. The C++ language b. C++ program c. C++ program Structure d. Running a program e. Syntax errors and warnings f. Variations on cout g. Displaying special characters h. Using help i. Program style II. Variables and constants a. Using variables b. Obtaining a value from the user c. Using constants built-in data variable definitions expressions and operators d. String library e. Formatting III. Controlling program flow a. If statements; if-else statements b. Compound statements nested and ladders c. Logical operators looping: do-while, while, for d. Debugging e. Counting and summing f. Bool library g. Break h. Random numbers IV. Functions a. The function b. Parameters and overloading and default c. Return statement and reference parameters d. Documentation e. Building a library V. Classes and objects a. Classes and objects b. String c. Ios d. Constructors e. Object VI. Math, recursion and enum a. Math library b. Trig functions c. Log and exponential functions d. Other math.h functions e. Precision f. Recursion g. Data storage