MATHEMATICSDEPARTMENT

HANDBOOK2009-2010

MATHEMATICS DEPARTMENT LIST OF COURSES

Refresher Math

Pre-AlgebraAlgebra IAlgebra II

Honors Algebra IIPlane Geometry

Honors Plane GeometryCollege Algebra

Honors College AlgebraProbability and Statistics

Honors Probability and StatisticsTrigonometry

Honors TrigonometryPre-Calculus

Honors Pre-CalculusCalculus I

Honors Calculus ICalculus II

Honors Calculus IIAdvanced 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: REFRESHER MATH

BOOK: “Refresher Mathematics”; Prentice Hall; Authors Edwin Stein; Copyright 1989OBJECTIVES: Refresher Math will provide solid basic skills involving whole numbers, decimals, fractions, and percents with emphasis on problem solving techniques. An introduction to calculators and their use in solving mathematical problems.

MATERIAL COVERED:CHAPTER 1: Whole Numbers

A. Introduction to Problem Solving (1-1)1. Planning (1-2)2. Solving (1-3)3 Checking (1-4)

B. Reading and Writing Whole Numbers (1-5, 1-6)C. Rounding (1-7)D. Adding and Subtracting (1-8, 1-9)E. Multiplying and Dividing (1-10, 1-11, 1-12, 1-13)F. Prime and Composite (1-14)G. Factors (1-14)

1. Prime Factorization2. Greatest Common Factor

CHAPTER 2: DecimalsA. Reading and Writing Decimals (2-1, 2-2)B. Rounding and Comparing Decimals (2-3, 2-4)C. Adding and Subtracting (2-5, 2-6)D. Multiplying and Dividing (2-7, 2-8, 2-9)E. Decimal Part of a Number (2-10, 2-11)F. Multiplying by Powers of Ten (2-12)G. Dividing by Powers of Ten (2-13)

CHAPTER 3: FractionsA. Lowest Terms (3-1)B. Improper Fractions and Mixed Numbers (3-2)C. Equivalent Fractions (3-3, 3-4)D. Multiples (3-5)E. Comparing and Rounding (3-6)F. Adding and Subtracting (3-7, 3-8, 3-9)G. Multiplying and Dividing (3-10, 3-11, 3-12)H. Fractions to Decimals (3-15)I. Writing Decimals to Fractions (3-16)J. Ratio (3-18)K Proportion (3-19)

CHAPTER 4: PercentA. Meaning of Percent (4-1)B. Percents as Decimals (4-2)C. Decimals as Percents (4-3)D. Percents as Fractions (4-4)E. Fractions and Mixed Numbers as Percents (4-5)F. Percent of a Number (4-6)G. What Percent One Number is of Another (4-7)H. Percent of Increase or Decrease (4-8)I. A Number When a Percent is Known (4-9)

MEASUREMENTChapter 8 A. Metric (8-1 to 8-5)Chapter 9 B. Customary (9-1 to 9-7)Chapter 10 C. Graphing (10-1 to 10-3)

COURSE TITLE: PRE-ALGEBRA I

BOOK: “Pre-Algebra”, Prentice Hall Authors: Charles, Davison, Landau, McCracken, Thompson; Copyright 2004

OBJECTIVES: Pre-Algebra I prepare students for Algebra I with an introduction to equation and problem solving. It includes a review of operations of real numbers with a concentration on fractions, decimals, and percents.

MATERIAL COVERED:CHAPTER 1: Algebraic Expressions and Integers

1.1 Variables and Expressions1.2 The Order of Operations1.3 Evaluating Expressions1.4 Integers and Absolute Value1.5 Adding Integers1.6 Subtracting Integers1.7 Inductive Reasoning1.8 Look for a Pattern1.9 Multiplying and Dividing Integers1.10 The Coordinate Plane

CHAPTER 2: Solving One-Step Equations and Inequalities2.1 Properties of Numbers2.2 The Distributive Property2.3 Simplifying Variable Expressions2.4 Variables and Equations2.5 Solving Equations by Adding or Subtracting2.6 Solving Equations by Multiplying or Dividing2.7 Try, Test, Revise2.8 Inequalities and Their Graphs2.9 Solving Inequalities by Adding or Subtracting2.10 Solving Inequalities by Multiplying or Dividing

CHAPTER 3: Decimals and Equations3.1 Rounding and Estimating3.3 Mean, Median, Mode3.4 Using Formulas3.5 Solving Equations by Adding or Subtracting Decimals3.6 Solving Equations by Multiplying or Dividing Decimals3.7 Using the Metric System

CHAPTER 4 Factors, Fractions, and Exponents4.1 Divisibility and Factors4.2 Exponents4.3 Prime Factorization and GCF4.4 Simplifying Fractions4.5 Problem Solving: Account for all Possibilities4.6 Rational Numbers4.7 Exponents and Multiplication4.8 Exponents and Division4.9 Scientific Notation

CHAPTER 5: Operations with Fractions5.1 Comparing and Ordering Fractions5.2 Fractions and Decimals5.3 Adding and Subtracting Fractions5.4 Multiplying and Dividing Fractions5.5 Customary Units of Measure5.6 Problem Solving: Working Backward5.7 Solving Equations by Adding or Subtracting Fractions5.8 Solving Equations by Multiplying Fractions5.9 Powers of Products and Quotients

CHAPTER 6 Ratios, Proportions, and Percents6.1 Ratios and Unit Rates6.2 Proportions6.3 Similar Figures and Scale Drawings6.4 Probability6.5 Fractions, Decimals, and Percents6.6 Proportions and Percents6.7 Percents and Equations6.8 Percent of Change6.9 Markup and Discount6.10 Problem Solving: Make a Table

CHAPTER 10 Area and Volume10.1 Area: Parallelogram10.2 Area: Triangles and Trapezoids10.3 Area: Circles10.4 Space Figures

If there is additional time or you have a more advance class, continue with:Chapter 10 Complete sections 10.5 to 10.9 (Surface Area and Volume)Chapter 11 Complete sections 11.1 and 11.2 (Square Roots, Irrational Numbers,

Pythagorean Theorem)Chapter 12 Complete sections 12.1, 12.2, 12.4-12.6 (Line plots, box and whisker,

permutations, and combinations)

COURSE TITLE: ALGEBRA I

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:

Chapter 1: Introduction to AlgebraSection 1.1: Symbols and expressions, Variables, Algebraic expressions, Evaluate, Simplify, Natural (Counting), Whole numbers, Order of operation M11.A.3.1.1 Section 1.2: Commutative property, Identity property M11.D.1.1.1; M11.A.2.1.1Section 1.3: Exponential notations M11.A.2.2.1Section 1.4: Associative property M11.D.1.1.1; M11.A.2.1.1Section 1.5: Distributive property M11.D.1.1.1; M11.A.2.1.1Section 1.6-1.7: Writing expressions and solving word problems M11.D.1.1.1Section 1.9: Using formulas M11.D.2.1.3; M11.B.2.2.1; M11.B.2.2.2; M11.B.2.2.3;

M11.B.2.2.4

Chapter 2: Integers and Rational NumbersSection 2.1: Integers and number lines, Absolute values M11.A.1.3.2; M11.A.2.2.1Section 2.2: Rational numbers (Positive and Negative) M11.A.1.3.2Section 2.3: Add M11.A.2.1.1Section 2.4: Subtract M11.A.2.1.1Section 2.5: Multiply M11.A.2.1.1Section 2.6: Divide M11.A.2.1.1Section 2.7: Distributive property, Factoring M11.A.3.1.1; M11.A.2.1.1; M11.D.2.2.2 Section 2.8: Inverse M11.A.2.1.1Section 2.9: Writing equations M11.D.2.1.3

Chapter 3: EquationsSection 3.1: Addition property of equations M11.D.2.1.3Section 3.2: Multiplication property of equalities M11.D.2.1.3Section 3.3: Using properties together M11.D.2.1.3Section 3.4: Expressions and equations M11.D.2.1.3Section 3.5: Solving equations. Whole numbers M11.D.2.1.3Section 3.6: Decimal numbers and fractions M11.D.2.1.3; M11.D.2.2.3Section 3.7: Formulas M11.D.2.1.3Section 3.8: Absolute value equations M11.D.2.1.3 Section 3.9: Proportions M11.A.2.1.3Section 3.10: Percent, Decimal, Fraction M11.A.2.1.1Section 3.11: More Expressions and Equations M11.D.2.1.3

Chapter 4: Inequalities Section 4.1: Inequalities and their graphs M11.D.2.1.1; M11.D.2.1.2;M11.D.2.1.3Section 4.2: Addition property M11.D.2.1.1; M11.D.2.1.2; M11.D.2.1.3Section 4.3: Multiplication property M11.D.2.1.1; M11.D.2.1.2; M11.D.2.1.3Section 4.4: Using Inequalities M11.D.2.1.1; M11.D.2.1.2; M11.D2.1.3; M11.D2.1.4

Chapter 5: ExponentsSection 5.1: Exponents M11.A.2.2.2Section 5.2: More with Exponents M11.A.2.2.2Section 5.3: Multiplying and dividing monomials M11.D.2.2.1Section 5.4: Scientific notation M11.A.1.1.2Section 5.5: Polynomial types M11.D.2.2.1Section 5.6: More on Polynomials M11.D.2.2.1Section 5.7: Adding polynomials M11.D.2.2.1Section 5.8: Subtracting polynomials M11.D.2.2.1Section 5.9: Multiplying of monomials and binomials M11.D.2.2.1Section 5.10:Special products M11.D.2.2.1Section 5.11: Multiplying Polynomials M11.D.2.2.1

Chapter 6: Polynomials and FactoringSection 6.1: Factoring M11.D.2.2.2Section 6.2: Difference of two squares M11.D.2.2.2Section 6.3: Trinomial Squares M11.D.2.2.2Section 6.4: Factoring x2 + bx + c M11.D.2.2.2Section 6.5: Factoring ax2 + bx + c M11.D.2.2.2Section 6.6: Factoring by grouping M11.D.2.2.2Section 6.7: Factoring a general strategy M11.D.2.2.2Section 6.8: Solve equations by factoring M11.D.2.1.5Section 6.9: Word problems M11.D.2.2.1; M11.D.2.2.2

APPENDIX B – PROBABILITYB-1 Probability M11.E.3.1.1; M11.E.3.1.2; M11.E.3.1.4B-2 More on Probability M11.E.3.1.1; M11.E.3.1.2; M11.E.4.1.2B-3 Probability Experimental and Simulation M11.E.3.2.1; M11.E.4.1.2B-4 Statistics Organizing Data M11.E.4.2.1; M11.E.4.2.2B-5 Graphs M11.E.4.1.1B-6 Measures of Central Tendency M11.E.2.1.1; M11.E.2.1.2; M11.E.2.1.3B-7 Scatter Plots and Data Relationships M11.E.1.1.1; M11.E.1.1.2

Chapter 7: Graphs and Linear EquationsSection 7.1: Graphing ordered pairs M11.D.2.1.2Section 7.2: Graphing equations M11.D.2.1.2Section 7.3: Linear equations, intercepts, standard form M11.D.3.2.2Section 7.4: Slope intercept M11.D.3.2.3Section 7.5: Equation and slope M11.C.3.1.2; M11.D.3.2.1Section 7.6: Finding an equation of a line M11.D.3.2.2Section 7.8: Parallel and perpendicular lines M11.C.3.1.2

Math Grade 11 Assessment Anchors and Eligible Content

Eligible ContentM11.A.1.1.1M11.A.1.1.2Alg.1 5.4M11.A.1.1.3

M11.A.1.2.1

M11.A.1.3.1M11.A.1.3.2Alg.1 2.1, 2.2

M11.A.2.1.1Alg.1 1.2, 1.4, 1.5, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 3.10M11.A.2.1.2M11.A.2.1.3Alg.1 3.9

M11.A.2.2.1Alg.1 1.3, 2.1M11.A.2.2.2Alg.1 5.1, 5.2

M11.A.3.1.1Alg.1 1.1, 2.7?

M11.A.3.2.1

M11B.2.1.1

M11.B.2.2.1Alg.1 1.9M11.B.2.2.2Alg.1 1.9M11.B.2.2.3Alg.1 1.9M11.B.2.2.4Alg.1 1.9

M11.B.2.3.1

M11.C.1.1.1M11.C.1.1.2

M11.C.1.2.1M11.C.1.2.2M11.C.1.2.3

M11.C.1.4.1

M11.C.3.1.1M11.C.3.1.2Alg.1 7.5, 7.8

M11.D.1.1.1Alg.1 1.2, 1.4, 1.5?, 1.6, 6.9?M11.D.1.1.2M11.D.1.1.3

M11.D.2.1.1Alg.1 4.1, 4.2, 4.3M11.D.2.1.2Alg.1 1.9, 4.1, 4.2, 4.3, 7.1, 7.2M11.D.2.1.3Alg.1 2.9, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.11,

4.1, 4.2, 4.3M11.D.2.1.4Alg.1 4.1, 4.2, 4.3, 4.4M11.D.2.1.5Alg.1 6.8

M11.D.2.2.1Alg.1 5.3, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10, 5.11, 6.9M11.D.2.2.2Alg.1 2.7, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.9M11.D.2.2.3Alg.1 3.6

M11.D.3.1.1M11.D.3.1.2

M11.D.3.2.1Alg.1 7.5M11.D.3.2.2Alg.1 7.3, 7.6M11.D.3.2.3Alg.1 7.4

M11.D.4.1.1

M11.E.1.1.1 Alg.1 B.7M11.E.1.1.2 Alg.1 B.7

M11.E.2.1.1 Alg.1 B.6M11.E.2.1.2 Alg.1 B.6M11.E.2.1.3 Alg.1 B.6

M11.E.3.1.1 Alg.1 B.1, B.2M11.E.3.1.2 Alg.1 B.1, B.2

M11.E.3.2.1 Alg.1 B.3

M11.E.4.1.1 Alg.1 B.5M11.E.4.1.2 Alg.1 B.1, B.2, B.3

M11.E.4.2.1 Alg.1 B.4M11.E.4.2.2 Alg.1 B.4

COURSE TITLE: ALGEBRA II/H.ALGEBRA II

BOOK: Prentice Hall, “Algebra 2 with Trigonometry”, Authors: Smith, Charles, Dossey, Bittinger; Copyright 2001

OBJECTIVES: Algebra II will continue to build upon the concepts of Algebra I. 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 SolvingSection 1.1: Real Numbers and Operations M11.A.1.3.2 N/O *Section 1.2: Multiplication and Division of Real Numbers M11.A.3.1.1 N/OSection 1.3: Algebraic Expressions and Properties of Numbers M11.9.3.1.1 N/OSection 1.4: The Distributive Property M11.A.3.1.1 N/OSection 1.5: Solving Equations M11.A.3.1.1 ALG CON **Section 1.6: Writing Equations M11.D.2.1.3 ALG CONSection 1.7: Exponential Notation M11.A.2.2.1 N/OSection 1.8: Properties of Exponents M11.A.2.2.2 N/OSection 1.9: Scientific Notation M11.A.2.2.2 N/O

Chapter 2: Equations and InequalitiesSection 2.1: More on Solving Equations M11.A.3.1.1 N/OSection 2.2: Using Equations M11.D.2.1.3 ALG CONSection 2.3: Solving FormulasSection 2.4: Solving Inequalities M11.D.2.1.4 ALG CONSection 2.5: Using Inequalities M11.D.2.1.4 ALG CONSection 2.6: Compound Inequalities M11.D.2.1.4 ALG CONSection 2.7: Absolute Value M11.A.3.1.1 N/O

Chapter 3: Relations, Functions, and GraphsSection 3.1: Relations and Ordered Pairs M11.D.3.2.1 ALG CONSection 3.2: Graphs M11.C.3.1.2 ALG CONSection 3.3: Functions M11.D.1.1.2 ALG CONSection 3.4: Graphs of Linear Equations M11.C.3.1.2 ALG CONSection 3.5: Slope M11.D.3.2.1 ALG CONSection 3.6: More Equations of Lines M11.D.3.2.2 ALG CONSection 3.7: Parallel and Perpendicular Lines M11.C.3.1.2 ALG CON

“Best Fit” for Assessment Testing-other resourceSection 3.8: Mathematical Modeling: M11.D.2.1.3 ALG CONUsing Linear Functions (Optional)Section 3.9: More about Functions (Optional) M11.D.1.1.2 ALG CON

Chapter 4: Systems of Equations and Problem SolvingSection 4.1: Systems of Equations in Two Variables M11.D.2.1.4 ALG CONSection 4.2: Solving Systems of Equations M11.D.2.1.4 ALG CONSection 4.3: Using a System of Two Equations M11.D.2.1.4 ALG CONSection 4.4: Systems of Equations in Three Variables M11.D.2.1.4 ALG CONSection 4.5: Using Systems of Three Equations (optional) M11.D.2.1.4 ALG CONSection 4.6: Consistent and Dependent Systems M11.D.2.1.4 ALG CONSection 4.7: Systems of Inequalities M11.D.2.1.1 ALG CON

Chapter 5: Polynomial and Polynomial EquationsSection 5.1: Polynomials and Functions M11.D.1.1.2; D.2.2.1 ALG CONSection 5.2: Addition and Subtraction of Polynomials M211.D.2.2.1 ALG CONSection 5.3: Multiplication of Polynomials M11.D.2.2.1 ALG CONSection 5.4: Factoring M11.D.2.2.2 ALG CONSection 5.5: More Factoring M11.D.2.2.2 ALG CONSection 5.6: Factoring: A General Strategy M11.D.2.2.2 ALG CONSection 5.7: Solving Equations by Factoring M11.D.2.1.5 ALG CONSection 5.8: Using Equations M11.D.2.1.3 ALG CON

Chapter 6: Rational Expressions and EquationsSection 6.1: Multiplying and Simplifying M11.D.2.2.3 ALG CONSection 6.2: Addition and Subtraction M11.D.2.2.3 ALG CONSection 6.3: Complex Rational Expressions M11.D.2.2.3 ALG CONSection 6.4: Division of Polynomials M11.D.2.2.3 ALG CONSection 6.5: Synthetic Division (Optional) M11.D.2.2.3 ALG CONSection 6.6: Solving Rational Equations M11.D.2.1.3 ALG CONSection 6.7: Using Rational Expressions M11.D.2.1.3 ALG CONSection 6.8: Formulas M11.D.2.2.3 ALG CONSection 6.9: Variation and Problem Solving M11.D.3.1.1 ALG CON

Chapter 7: Powers, Roots, and Complex NumbersSection 7.1: Radical Expressions M11.A.1.1.3 N/OSection 7.2: Multiplying and Simplifying M11.A.1.1.3 N/OSection 7.3: Operations with Radical Expressions M11.A.1.1.3 N/OSection 7.4: More Operations with Radical Expressions M11.A.1.1.3 N/OSection 7.5-7.10: Optional

Chapter 8: Optional

*N/O: Numbers and Operations Anchors **ALG/CON: Algebra Concepts

Course Name: Plane Geometry

Book: Prentice Hall, “Geometry”Authors: Bass, Charles, Johnson, KennedyCopyright 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.

Chapter 1: Tools of GeometrySection 1-2, Section 1-3 Points,Lines Planes, M11.B.2.1

Segments,Rays,Parallel Lines, and Planes (one day) M11.B.2.1.1Section 1-4, Section 1-7 Measuring Segments and M11.B.2.1

Angles,Perimeters, Circumference and M11.B.2.1.1Areas (one day)

Section 1-6: Midpoint and distance M11.C.3.1.1

Chapter 2: Reasoning and ProofsSection 2-1, Section 2-2 Conditional StatementsBiconditionals and Definitions (one day)Section 2-5: Proving Angles Congruent M11.B.2.1

Chapter 3: Parallel and Perpendicular LinesSection 3-1:Section 3-2: Properties of Parallel Lines;Proving Lines Parallel (one day) M11.B.2.1Section 3-3: Parallel Lines and Triangle Sum Theorem M11.B.2.1Section 3-4: The Polygon-Angle Sum Theorems M11.B.2.1Section 3-5, Section 3-6 Parallel and perpendicular lines M11C.3.1.2

Chapter 4: Congruent TrianglesSection 4-1: Congruent Figures M11.C.1.2.1Section 4-2: Triangle Congruence by SSS and SAS M11.C.1.2.1Section 4-3: Triangle Congruence by ASA and AAS M11.C.1.2.1Section 4-4: Using Congruent Triangles:CPCTC M11.C.1.2.1Section 4-5, Section 4-6 Isosceles and Equilateral Triangles; Congruence M11.C.1.2.3

in Right Triangles (one day) Section 4-7: Using Corresponding Parts of Congruent Triangles M11.C.1.3.1

Chapter 5: Relationships Within TrianglesSection 5-1: Midsegments of a Triangle M11.C.1.2.1Section 5-2; Section 5-3 Bisectors in Triangles Concurrent Lines M11.C.1.2.1

(Medians,Altitudes, Perpendicular Bisectors, Angle Bisectors)(one day)

Section 5-5: Inequalities in Triangles

Chapter 6: QuadrilateralsSection 6-1: Classifying Quadrilaterals M11.C.1.1.2Section 6-2; Section 6-3: Properties of Parallelograms; Proving that a M11.C.1.2.2

Quadrilateral is a Parallelogram (one day)Section 6-4: Special Quadrilaterals M11.C.1.2.2Section 6-5: Trapezoids and Kites M11.C.1.2.2

Chapter 7: AreaSection 7-1; Section 7-2: Areas of Parallelograms and Triangles M11.C.1.4.1

The Pythagorean Theorem and its Converse (one day)Section 7-3: Special Right Triangles M11.C.1.4.1Section 7-4: Areas of Trapezoids, Rhombuses and Kites M11.C.1.4.1Section 7-5: Areas of Regular Polygons M11.C.1.4.1Section 7-6; Section 7-7: Circles and Arcs; Areas of Circles and Sectors M11.C.1.1.2

(one day)

Chapter 8: SimilaritySection 8-1; Section 8-2 Ratio and Proportion; Similar Polygons (one day) M11.C.1.3Section 8-3; Section 8-4 Proving Triangles Similar; Similarity in Right M11.C.1.3.1

Triangles (one day)Section 8-5: Proportions in Triangles M11.C.1.3.1Section 8-6: Perimeters and Areas of Similar Figures M11.C.1.3.1

Chapter 10: Surface Area and VolumeSection 10-3: Surface Areas of Prisms and CylindersSection 10-4: Surface Areas of Pyramids and ConesSection 10-5: Volumes of Prisms and CylindersSection 10-6: Volumes of Pyramids and ConesSection 10-7: Surface Area and Volume of SpheresSection 10-8: Areas and Volumes of Similar Solids

Chapter 11: Circles Section 11-1: Tangent Lines M11.C.1Section 11-2: Chords and Arcs M11.C.1Section 11-3: Inscribes Angles M11.C.1Section 11-4: Angle Measures and Segment Lengths M11.C.1

M11.B.2.2.1 M11.B.2.2.2M11.B.2.2.3

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 GeometrySection 1-1: Points, Lines, Plane and SpaceSection 1-2: Distance and Segment MeasureSection 1-3: Rays, Angles, and Angle MeasureSection 1-4: Congruent Segments and AnglesSection 1-5: TrianglesSection 1-6: Conditional StatementsSection 1-7: Drawing and Supporting ConclusionsSection 1-8: Deductive Reasoning – Using Algebraic Properties

Chapter 2: Introduction to ProofSection 2-1: Two-Column ProofsSection 2-2: Complementary, Supplementary, and Vertical AnglesSection 2-3: Perpendicular LinesSection 2-4: Drawing and Using DiagramsSection 2-5: Planning and Writing a ProofSection 2-6: Proving Theorems: Segments and LinesSection 2-7: Proving Theorems: Angles

Chapter 3: Parallel Lines and PlanesSection 3-1: Parallel Lines, Lines, and TransversalsSection 3-2: Properties of Parallel LinesSection 3-3: Proving Lines ParallelSection 3-4: Angles of a TriangleSection 3-5: Theorems Related to the Angle Sum Theorem for TrianglesSection 3-6: Angles of a Polygon

Chapter 4: Congruent TrianglesSection 4-1: Congruent TrianglesSection 4-2: Congruence PostulatesSection 4-3: Proofs: Using Congruence PostulatesSection 4-4: Proving Angles and Segments CongruentSection 4-5: Proofs: Overlapping TrianglesSection 4-6: Isosceles TrianglesSection 4-7: AAS Congruence and Right Triangle CongruenceSection 4-8: Medians, Altitudes, and Perpendicular Bisectors

Chapter 5: Using Congruent Triangles and Parallel LinesSection 5-1: Properties of Parallel LinesSection 5-2: Proving Quadrilaterals and ParallelogramsSection 5-3: Rectangles, Rhombuses, and SquaresSection 5-4: TrapezoidsSection 5-5: The Midsegment TheoremSection 5-6: Indirect ProofSection 5-7: Inequalities in One TriangleSection 5-8: Inequalities in Two Triangles

Chapter 6: SimilaritySection 6-1: Ratio and ProportionSection 6-2: Properties of ProportionsSection 6-3: Similarity PolygonsSection 6-4: AA Similarity PostulateSection 6-5: SAS and SSS Similarity TheoremsSection 6-6: Segments Divided Proportionally

Chapter 7: Right TrianglesSection 7-1: Right Triangles PropertiesSection 7-2: The Pythagorean TheoremSection 7-3: The Converse of the Pythagorean TheoremSection 7-4: Special Right TrianglesSection 7-5: The Tangent RatioSection 7-6: The Sine and Cosine RatiosSection 7-7: Angles of Elevation and Depression

Chapter 8: CirclesSection 8-1: Basic TermsSection 8-2: Tangent LinesSection 8-3: Common Tangents and Tangent CirclesSection 8-4: Arcs and Their MeasuresSection 8-5: Chords and CirclesSection 8-6: Inscribed AnglesSection 8-7: Angles of Chords, Secants, TangentsSection 8-8: Segments of Chords, Secants, Tangents

Chapter 10: Area and Perimeters of PolygonsSection 10-1: Perimeter and Area of RectanglesSection 10-2: Areas of Parallelograms and TrianglesSection 10-3: Areas of Trapezoids and Other QuadrilateralsSection 10-4: Areas of Regular PolygonsSection 10-5: Ratios of Areas and Perimeters of Similar PolygonsSection 10-6: Circumference and Arc LengthSection 10-7: Areas of Circles, Sectors, and Segments

COURSE NAME: COLLEGE ALGEBRA

Book: Title: “College Algebra”; Authors: R. David Gustafson and Peter D. Frisk;Publisher: Thomson/ Brooks/ Cole; Copyright: 2004

OBJECTIVES: The College Algebra course is the third level in the study of algebra. The concepts

learned in Algebra II 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 AlgebraSection 0.1 Sets of real numbers N/O M11.A.1.3.2, M11A.1.3.1

Section 0.2 Integer exponents and scientific notation N/O M11.A.1.1.2, M11A.2.2.1,

M11A.2.2.2

Section 0.3 Rational exponents and radicals N/0 M11.A.1.1.1, M11.A.1.1.3

Section 0.4 Operations on polynomials ALG CONC M11.D.2.2.1, M11.A.1.2.1

Section 0.5 Factoring polynomials ALG CONC M11D.2.2.2

Section 0.6 Algebraic Functions ALG CONC M11D.2.2.3

Chapter 1: Equations and Inequalities

Section 1.1 Solving equations ALG CONC M11D.2.1.3

Section 1.2 Applications of linear equations N/O M11A.2.1.1, ALG CONC M11D.2.1.2

Section 1.3 Solving quadratic equations ALG CONC M11D.2.1.5

Section 1.4 Applications of quadratic equations N/0 M11A.2.1.1

Section 1.5 The Complex number system N/O M11A.1.1.3, M11A.1.3.1

Section 1.6 Polynomial and radical equations ALG CONC M11.D.2.2.1

Section 1.7 Solving linear and quadratic inequalities ALG CONC M11D.2.1.1,

M11D.2.1.2, M11D.2.1.3

Section 1.8 Solving equations and inequalities containing absolute values M11.D.2.1.2

Chapter 2: Graphs of Equations

Section 2.1 Rectangular coordinate system ALG CONC M11.D.1.1.1

Section 2.2 Slope of lines ALG CONC M11..D.3.2.1, M11.D.3.2.3

Section 2.3 Writing of linear equations ALG CONC M11.D.2.1.3

Section 2.4 Graphs of equations. ALG CONC M11.D.4.1.1, M11.D.2.1.2, M11.D.3.2.2

Section 2.5 Proportion and variation N/O M.11.A.2.1.2, M.11.A.2.1.3

Chapter 3: Functions

Section 3.1 Functions and function notation ALG CONC M11.D.1.1.2, M11.D.1.1.3

Section 3.2 Quadratic functions ALG CONC M11.D.2.1.5,

Section 3.6 Operations on functions ALG CONC M11.D.4.1

Section 3.7 Inverse functions (Introduction) ALC CONC M11.D.1.1.3

Chapter 7: Conic Sections

Section 7.1 The Circle and the Parabola ALG CONC M11.D.2.1.2; M11.D.2.1.5;

M11.D.4.1.1

Section 7.2 The Ellipse ALG CONC M11.D.2.1.2; M11.D.2.1.5; M11.D.4.1.1

Section 7.3 The Hyperbola ALG CONC M11.D.2.1.2; M11.D.2.1.5;

M11.D.4.1.1

Chapter 6: Linear Systems

Section 6.1 Systems of Linear Equations (Two variables; Review and Applications)

ALG CONC M11.D.2.1.4

Chapter 8: Probability (Intoduction to various topics)

Section 8.6 Permutations and Combinations DATA PROB M11.E.3.2.1

Section 8.7 Probability DATA PROB M11.E.3.1.1; M11.E.3.1.2

Section 8.8 Computation of Compound Probabilities DATA PROB M11.E.3.1.1;

M11.E.3.1.2

Section 8.9 Odds and Mathematical Expectation DATA PROB M11.E.3.1.1;

M11.E.3.1.2

Chapter 5: Solving Polynomial Equations (Optional)

Section 5.1 The Remainder and factor theorems. Synthetic division

Section 5.2 Descartes’ Rule of Signs

Section 5.3 Rational roots of polynomial equations

COURSE NAME: HONORS COLLEGE ALGEBRA

Book: Title: “Structure and Method  Book 2”; Authors: Brown, Dolciani, Sorgenfrey, Kane

Publisher: Houghton Mifflin; Copyright: 1994

OBJECTIVES: The Honors College Algebra course is the third level in the study of algebra. The

concepts learned in Algebra II 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 4 : Products and Factors of Polynomials

Section 4.1 Polynomials M.11.A.1.2.1

Section 4.2 Using Laws of Exponents M.11.A.1.1.1

Section 4.3 Multiplying Polynomials M.11.A.1.2.1 M.11.D.2.2.1

Section 4.4 Using Prime Factorization M.11.D.2.2.2

Section 4.5 Factoring Polynomials M.11.D.2.2.2

Section 4.6 Factoring Quadratic Polynomials M.11.D.2.2.2

Section 4.7 Solving Polynomial Equations M.11.D.2.1.5

Section 4.8 Problem Solving Using Polynomial Equations M.11.A.2.1.1

Section 4.9 Solving Polynomial Inequalities M.11.D.2.1.2 M.11.D.2.1.3

Chapter 5: Rational Expressions

Section 5.1 Quotients of Monomials M11.A.1.2.1

Section 5.2 Zero and Negative Exponents M11.A.2.2.2

Section 5.3 Scientific Notation and Significant Digits M11.A.1.1.2

Section 5.4 Rational Algebraic Expressions M11.A.3.1.1

Section 5.5 Products and Quotients of Rational Expressions M11.A.3.1.1

Section 5.6 Sums and Differences of Rational Expressions M11.A.3.1.1

Section 5.7 Complex Fractions

Section 5.8 Fractional Coefficients

Section 5.9 Fractional Equations

Chapter 6: Irrational and Complex Numbers

Section 6.1 Roots of Real Numbers N/O: M11.A.1.1.1, M11.A.1.1.3

Section 6.2 Properties of Radicals N/O: M11.A.1.1.1, M11.A.1.1.3

Section 6.3 Sums of Radicals N/O: M11.A.1.1.1, M11.A.1.1.3, M11.D.2.2.1

Section 6.4 Binomials Containing Radicals N/O: M11.A.1.1.1, M11.A.1.1.3, Alge

Concepts: M11.D.2.2.1

Section 6.5 Equations Containing Radicals N/O: M11.A.1.1.1, M11.A.1.1.3,

Alge Concepts: M11.D.2.1

Section 6.6 Rational and Irrational Numbers N/O: M11.A.1.3,

Section 6.7 The Imaginary Number i N/O: M11.A.1.1.1, M11.A.1.1.3

Section 6.8 The Complex Numbers N/O: M11.A.1.1.1, M11.A.1.1.3

Chapter 7: Quadratic Equations and Functions

Section 7.1 Completing the Square M11.D.2.1.5

Section 7.2 The Quadratic Formula M11.D.2.1.5

Section 7.3 The Discriminant M11.D.2.1.5

Section 7.4 Equations in Quadratic Form M11.D.2.1.5

Section 7.5 Graphing M11.D.4.1.1

Section 7.6 Quadratic Functions M11.D.4.1.1

Section 7.7 Writing Quadratic Equations and Functions M11.D.4.1

Chapter 8: Variation and Polynomial Equations

Section 8.1 Direct Variation and Proportion M11.A.1.1.1

Section 8.2 Inverse and Joint Variation M11.A.1.1.1

Section 8.3 Dividing Polynomials M11.A.3.1.1

Section 8.4 Synthetic Division M11.A.3.1.1

Section 8.5 The Remainder and Factor Theorems M11.A.1.1.1, M11.A.1.1.3

Section 8.6 Some Useful Theorems M11.A.1.1.1, M11.A.1.1.3

Section 8.7 Finding Rational Roots M11.A.1.1.1, M11.A.1.1.3

Chapter 9: Analytic Geometry

Section 9.1 Distance and Midpoint Formulas M11.C.3.1.1

Section 9.2 Circles M11.C.3.1.1

Section 9.3 Parabolas M11.C.3.1.1

Section 9.4 Ellipses M11.C.3.1.1

Section 9.5 Hyperbolas M11.C.3.1.1

Chapter 15: Statistics and Probability (Optional)

Section 15.1 Presenting Statistical Data M11.E.1.1.1

Section 15.2 Analyzing Statistical Data M11.E.1.1.2

Section 15.3 The Normal Distribution M11.E.1.1.2

Section 15.4 Correlation M11.E.1.1.2

Section 15.5 Fundamental Counting Principles M11.E.3.2.1

Section 15.6 Permutations M11.E.3.2.1

Section 15.7 Combinations M11.E.3.2.1

Section 15.9 Sample Spaces and Events M11.E.3.1.1

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 M11.E.1.1.1, M11.E.1.1.2, M11.E.4.1.1 P and S*1.2 Describing Distributions with Numbers M11.E.2.1.1, M11.E.2.1.2, M11.E.2.1.3 P and S1.3 The Normal Distributions

Chapter 2:2.1 Scatterplots M11.E.1.1.2 P and S2.2 Correlation2.3 Least-Squares Regression M11.E.4.2.1, M11.E.4.2.2 P and S2.4 Cautions about Correlations and Regression

Chapter 3: 3.1 Designing Samples3.2 Designing Experiments

Chapter 4:4.1 Randomness4.2 Probabilty Models M11.E.4.1.2 P and S 4.3 Sampling Distributions

Chapter 5:5.1 General Probablity Rules M11.I.3.1.1 P and S5.2 Conditional ProbablityProbability Packet M11.E.3.1.1, M11.E.3.1.2, M11.E.3.2.1 P and S

Chapter 6:6.1 Estimating with Confidence6.2 Tests of Significance6.3 Making Sense of Statistical Significance6.4 Error Probabilities and Power

Chapter 7:7.1 Inference for the Mean of a Population7.2 Comparing Two Means

Chapter 8:8.1 Inference for a Population Proportion8.2 Comparing Two Proportions

Chapter 9:9.1 Two-Way Tables9.2 The Chi-Square Test

*P and S = Probability and Statistics Anchors

COURSE TITLE: TRIGONOMETRY

BOOK: Addison Wesley Longman; “Trigonometry” 7th Edition;Authors: Lial, Hornsby, SchneiderCopyright 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 FunctionsSection 1.1: Basic concepts M11.C.3.1.1Section 1.2: Angles M11.B.2.1.1Section 1.3: Angle Relationships and similar trianglesSection 1.4: Definitions of the trigonometric functions M11A.1.1.1, M11.A.1.1.3Section 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 anglesSection 2.3: Finding trigonometric function values using a calculatorSection 2.4: Solving right triangles M11.A.1.1.1, M11.A.1.1.3, M11.C.1.2.1,

M11.C.1.2.2Section 2.5: Further applications of right triangles M11.A.2.1.2, M11.A.2.1.3

Chapter 3: Radian Measure and the Circular Functions M11.A.2.1.1, M11.C.1.1.1, M11.C.1.1.2

Section 3.1: Radian measureSection 3.2: Applications of radian measure M11.B.2.3.1Section 3.3: Circular functions of real numbersSection 3.4: Linear and angular velocity

Chapter 4: Graphs of the Circular Functions M11.A.1.3.1, M11.A.1.3.2, M11.D.1.1.3, M11.D.2.1.1, M11.D.2.1.2, M11.D.4.1.1

Section 4.1: Graphs of the sine and cosine functions Section 4.2: Translations of the graphs of the sine and cosine functionsSection 4.3: Graphs of the other circular functions

Chapter 5: Trigonometric IdentitiesSection 5.1: Fundamental identities Section 5.2: Verifying trigonometric identitiesSection 5.3: Sum and difference identities for cosineSection 5.4: Sum and difference identities for sine and tangentSection 5.5: Double-angle identitiesSection 5.6: Half-angle identities

Chapter 6: Inverse Trigonometric Functions and Trigonometric EquationsSection 6.1: Inverse trigonometric functions M11.D.1.1.2Section 6.2: Trigonometric equations ISection 6.3: Trigonometric equations IISection 6.4: Equations involving inverse trigonometric functions

Chapter 7: Applications of Trigonometry and VectorsSection 7.1: Oblique triangles and the law of sines Section 7.2: The ambiguous case of the law of sinesSection 7.3: The law of cosines

COURSE TITLE: HONORS TRIGONOMETRY

BOOK: Addison Wesley Longman; “Trigonometry” 7th Edition;Authors: Lial, Hornsby, SchneiderCopyright 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:

Entire Course uses anchor M11.C.1.4.1

Chapter 1: The Trigonometric FunctionsSection 1.1: Basic concepts M11.C.3.1.1Section 1.2: Angles M11.B.2.1.1Section 1.3: Angle Relationships and similar trianglesSection 1.4: Definitions of the trigonometric functions M11A.1.1.1, M11.A.1.1.3Section 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 anglesSection 2.3: Finding trigonometric function values using a calculatorSection 2.4: Solving right triangles M11.A.1.1.1, M11.A.1.1.3, M11.C.1.2.1,

M11.C.1.2.2Section 2.5: Further applications of right triangles M11.A.2.1.2, M11.A.2.1.3

Chapter 3: Radian Measure and the Circular Functions M11.A.2.1.1, M11.C.1.1.1, M11.C.1.1.2

Section 3.1: Radian measureSection 3.2: Applications of radian measure M11.B.2.3.1Section 3.3: Circular functions of real numbersSection 3.4: Linear and angular velocity

Chapter 4: Graphs of the Circular Functions M11.A.1.3.1, M11.A.1.3.2, M11.D.1.1.3, M11.D.2.1.1, M11.D.2.1.2, M11.D.4.1.1

Section 4.1: Graphs of the sine and cosine functions Section 4.2: Translations of the graphs of the sine and cosine functionsSection 4.3: Graphs of the other circular functions

Chapter 5: Trigonometric IdentitiesSection 5.1: Fundamental identities Section 5.2: Verifying trigonometric identitiesSection 5.3: Sum and difference identities for cosineSection 5.4: Sum and difference identities for sine and tangentSection 5.5: Double-angle identitiesSection 5.6: Half-angle identities

Chapter 6: Inverse Trigonometric Functions and Trigonometric EquationsSection 6.1: Inverse trigonometric functions M11.D.1.1.2 Section 6.2: Trigonometric equations I M11.D.2.1.3Section 6.3: Trigonometric equations II M11.D.2.1.5Section 6.4: Equations involving inverse trigonometric functions

Chapter 7: Applications of Trigonometry and VectorsSection 7.1: Oblique triangles and the law of sines M11.C.1.2.3Section 7.2: The ambiguous case of the law of sines M11.C.1.2.3Section 7.3: The law of cosines M11.C.1.2.3Section 7.4: Vectors and the dot product Section 7.5: Applications of vectors

As time allows,

Chapter 8: Complex Numbers, Polar Equations, and Parametric EquationsSection 8.1: Complex numbersSection 8.2: Trigonometric (polar) form of complex numbersSection 8.3: The product and quotient theoremsSection 8.4: Powers and roots of complex numbersSection 8.5: Polar equations and graphs M11.D.4.1.1Section 8.6: Parametric equations, graphs, and applications M11.D.4.1.1

Chapter 9: Exponential and Logarithmic FunctionsSection 9.1: Exponential functions M11.D.2.1.2Section 9.2: Logarithmic functions M11.D.2.1.2Section 9.3: Evaluating logarithms and the change-of-base theoremSection 9.4: Exponential and logarithmic equations

Revised 2007-2008

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)

M.11.A.1.3.2 (N & O); M.11.A.1.1.2 ( N&O); M.11.A.2.2.1 (N&O); M.11.A.2.2.2 (N&O); M.11.A.1.1.3 (N&O); M.11.D.2.2.1 (AC); M.11.A.1.2.1 (N&O); M.11.D.2.2.2. (AC); M.11.A.3.1.1. (N&O); M.11.D.2.2.3 (AC); M.11.A.2.2.2 (N&O); M.11.D.2.1.5 (AC); M.11.A.2.1.1.(N&O); M.11.D.2.1.3.(AC); M.11.C.1.4.1 (G); M.11.D.2.1.1 (AC)

Chapter 1: Functions and Graphs Section 1.1: Graphs and Graphing Utilities M.11.D.4.1.1. (AC)Section 1.2: Basics of Functions and Their Graphs M.11.D.1.1.2 (AC)/M.11.D.1.1.3 (AC)Section 1.3: More on Functions and Their GraphsSection 1.6: Transformations of FunctionsSection 1.8: Inverse Functions M.11.D.1.1.3 (AC)Section 1.10: Modeling with FunctionsM.11.A.2.2.1 (N&O)/M.11.B.2.2.1 (M)/M.11.B.2.2.2 (M)

Chapter 2: Polynomial and Rational FunctionsSection 2.2: Quadratic FunctionsSection 2.3: Polynomial Functions and Their Graphs M.11.D.2.1.2 (AC)Section 2.6: Rational Functions and Their Graphs M.11.D.4.1.1. (AC)Section 2.7: Polynomial and Rational Inequalities Section 2.8: Modeling Using Variation M.11.A.2.1.2 (N&O)/M.11.A.2.1.3 (N&O)

Chapter 3: Exponential and Logarithmic FunctionsSection 3.1: Exponential Functions M.11.D.3.1.2 (AC)Section 3.2: Logarithmic FunctionsSection 3.3: Properties of LogarithmsSection 3.4: Exponential and Logarithmic Equations M.11.D.3.1Section 3.5: Exponential Growth and Decay M.11.D.3.5

Chapter 7: Systems of Equations and InequalitiesSection 7.1: Systems of Linear Equations in Two Variables M.11.D.2.1.4 (AC) Section 7.2: Systems of Linear Equations in Three VariablesSection 7.3: Partial Fractions

Chapter 8: Matrices and DeterminantsSection 8.1: Matrix Solutions to Linear Systems Section 8.2: Inconsistent and Dependent Systems Section 8.3: Matrix OperationsSection 8.4: Inverses and Matrix EquationsSection 8.5: Determinants and Cramer’s Rule

Chapter 10: Sequences, Induction and ProbabilitySection 10.1: Sequences and Summation Notation Section 10.2: Arithmetic Sequences M.11.D.1.1 (AC)Section 10.3: Geometric Sequences and Series M.11.D.1.1 (AC)

Pre-Calc Syllabus Mapping

Eligible Content Mapped to Pre-Calculus (Blitzer)

Numbers and Operations

M.11.A.1.1.2 PC P-2M.11.A.1.1.3 PC P-3

M.11.A.1.2.1 PC P-5

M.11.A.1.3.2 PC P-1

M.11.A.2.1.1 PC P-8M.11.A.2.1.2 PC 2-8M.11.A.2.1.3 PC 2-8

M.11.A.2.2.1 PC P-2M.11.A.2.2.2 PC P-2

M.11.A.3.1.1 PC P-6

Measurement

M.11.B.2.1.1 PC 1-10M.11.B.2.2.2 PC 1-10

Geometry

M.11.C.1.4.1 PC P-8

Algebraic Concepts

M.11.D.1.1 PC 10-1; 10-2M.11.D.1.1.2 PC 1-2M.11.D.1.1.3 PC 1-2; 1-8

M.11.D.2.1.1 PC P-9M.11.D.2.1.2 PC 1-1; 1-2; 1-3 M.11.D.2.1.3 PC P-7M.11.D.2.1.4 PC 7-1 M.11.D.2.1.5 PC P-7

M.11.D.2.2.2 PC P-4 M.11.D.2.2.2 PC P-5M.11.D.2.2.3 PC P-6

M.11.D.3.1 PC 3-4; 3-5 M.11.D.3.5 PC 3-4M.11.D.3.1.2 PC 3-1

M.11.D.4.1.1 PC 1-1

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 UtilitiesSection 1.2: Basics of Functions and Their Graphs Section 1.3: More on Functions and Their Graphs

Section 1.6: Transformations of FunctionsSection 1.8: Inverse FunctionsSection 1.10: Modeling with Functions

Chapter 2: Polynomial and Rational FunctionsSection 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 FunctionsSection 3.1: Exponential FunctionsSection 3.2: Logarithmic Functions Section 3.3: Properties of LogarithmsSection 3.4: Exponential and Logarithmic EquationsSection 3.5: Exponential Growth and Decay

Chapter 7: Systems of Equations and InequalitiesSection 7.1: Systems of Linear Equations in Two Variables Section 7.2: Systems of Linear Equations in Three VariablesSection 7.3: Partial Fractions

Chapter 8: Matrices and DeterminantsSection 8.1: Matrix Solutions to Linear Systems Section 8.2: Inconsistent and Dependent Systems Section 8.3: Matrix OperationsSection 8.4: Inverses and Matrix EquationsSection 8.5: Determinants and Cramer’s Rule

Chapter 10: Sequences, Induction and ProbabilitySection 10.1: Sequences and Summation Notation Section 10.2: Arithmetic SequencesSection 10.3: Geometric Sequences and SeriesSection 10.4: Mathematical InductionSection 10.5: The Binomial TheoremSection 10.6: Permutations and Combinations Section 10.7: Probability

As time allows,

Chapter 9: Conic Sections and Analytic GeometrySection 9.1: The EllipseSection 9.2: The HyperbolaSection 9.3: The ParabolaSection 9.4: Rotation of AxesSection 9.5: Parametric EquationsSection 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 ModelsP.2 Linear Models and Rates of ChangeP.3 Functions and Their Graphs

Chapter 1: Limits and Their Properties1.1A Preview of Calculus1.2Finding Limits Graphically and Numerically1.3Evaluating Limits Analytically1.4Continuity and One-Sided Limits1.5Infinite Limits

Chapter 2: Differentiation2.1The derivative and the Tangent Line Problem2.2Basic Differentiation Rules and Rates of Change2.3Product and Quotient Rules and Higher-Order Derivatives2.4The Chain Rule2.5Implicit Differentiation2.6Related Rates

Chapter 3: Applications of the Differentiation3.1Extrema on an Interval3.2Rolle's Theorem and the Mean Value Theorem3.3Increasing and Decreasing Functions and the First Derivative Test3.4Concavity and the Second Derivative Test3.5Limits at Infinity3.6A Summary of Curve Sketching3.7Optimization Problems3.9 Differentials

Chapter 4: Integration4.1Anti-Derivatives and Indefinite Integration4.2Area4.3Reimann Sums and Definite Integrals4.4The Fundamental Theorem of Calculus4.5 Integration by Substitution4.6 Numerical Integration

Chapter 5: Logarithmic And Exponential Functions5.1 The Natural Logarithmic Function: Differentiation5.2 The Natural Logarithmic Function; Integration5.4Exponential Functions: Differentiation and Integration

Chapter 7: Applications of Integration7.1 Area of a region Between Two Curves7.2 Volume: The Disk Method7.3 Volume: The Shell Method

COURSE TITLE: HONORS CALCULUS I

BOOK: 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 thoseHonor 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 plane1.2 Find the slope of a line1.3 Write equations for lines1.4 Graph functions1.5 Solve absolute values1.6 Find tangent lines and slopes of quadratic and cubic curves1.7 Find the derivatives of y = f(x)1.8 Find the velocity and other rates of change1.9 Solve for limits1.10 Solve using infinity as a limit1.11 Work with continuous functions

Chapter 2: Find Derivatives2.1 Find derivatives of polynomial functions2.2 Find derivatives of products, powers, and quotients2.3 Derive functions implicitly/Derive functions with fractional powers2.4 Solve linear approximations and differentials2.5 Use the chain rule2.6 Review concepts of trigonometry2.7 Derivatives of trigonometric functions2.8 Solving parametric equations

2.10 Using derivative formulas

Chapter 3: Use Applications of Derivatives 3.1 Sketch curves with the first derivative3.2 Find concavity and points of inflection3.3 Find asymptotes and symmetry3.4 Use maxima and minima theory to solve problems3.5 Applications of maxima and minima3.6 Solve related rates of change 3.7 Use the mean-value theorem3.8 Solve indeterminate forms and L’Hopital’s Rule

Chapter 4: Integration4.1 Solve for the indefinitie integral4.2 Select the values for the constant of integration4.3 Use the substitution method of integration4.4 Find integrals of trigonometric functions4.5 Find the definite integral: the area under a curve4.6 Calculate definite integrals by summation4.7 Use the fundamental theorems of integral calculus4.8 Use substitution of definite integrals4.9 Use rules for approximating definite integrals

Chapter 5: Applications of Definite Integrals5.1 Find the net change in position and distance traveled by a moving body5.2 Find areas between curves5.3 Calculate volumes by slicing: volumes of revolution\5.4 Find the volumes modeled with washers and cylindrical shells

COURSE TITLE: CALCULUS II

BOOK: 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 toincrease 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 Change2.3 Product and Quotient Rules and Higher Order Derivatives2.4 The Chain Rule2.5 Implicit Differentiation

II. Chapter 4: Integration (Quick Review)4.1 Antiderivatives and Indefinite Integration4.4 The Fundamental Theorem of Calculus4.5 Integration by Substitution

III. Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions5.1 The Natural Logarithmic Function: Differentiation5.2 The Natural Logarithmic Function: Integration5.3 Inverse Functions5.4 Exponential Functions: Differentiation and Integration5.5 Bases other than e and Applications5.6 Inverse Trigonometric Functions: Differentiation5.7 Inverse Trigonometric Functions: Integration5.8 Hyperbolic Functions

IV. Chapter 6: Differential Equations6.1 Slope Fields and Euler's Method6.2 Differential Equations: Growth and Decay6.3 Separation of Variables and The Logistic Equation6.4 First-Order Linear Differential Equations

V. Chapter 7: Applications of Integration (Quick Review)7.1 Area of a Region Between Two Curves7.2 Volume: The Disk Method7.4Arc Length and Surfaces of Revolution

VI. Chapter 8: Integration Techniques and Improper Integrals8.1 Basic Integration Rules8.2 Integration by Parts8.3 Trigonometric Integrals8.4 Trigonometric Substitution8.5 Partial Fractions8.6 Integration by Tables and Other Integration Techniques8.7 Indeterminate Forms and L'Hopital's Rule8.8 Improper Integrals

COURSE TITLE: HONORS CALCULUS II

BOOK: 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:

Honors Calculus III. Chapter 2: Derivatives

a. Section 6: A brief review of trigonometryb. Section 7: Derivatives of trigonometric functionsc. Section 8: Parametric equations

II. Chapter 4: Integrationa. Section 4: Integrals of trigonometric functionsb. 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

revolutionb. Section 4: Volumes modeled with washers and cylindrical

shellsc. Section 5: Lengths of plane curvesd. Section 7: The average value of a function

IV. Chapter 6: Transcendential Functions a. Section 1: Inverse functionsb. Section 2: The inverse trigonometric functionsc. Section 3: Derivatives of the inverse trigonometric

Functions: Related integralsd. Review

1. Section 4,5: The natural logarithm y = ln x2. Section 6,7: The exponential function ex

3. Section 8: The functions ax, au, y = log u

V. Chapter 7: Methods of Integrationa. Section 1: Basic integration formulasb. Section 2: Integration by partsc. Section 3: Products and powers of trigonometric functionsd. Section 4: Even powers of sines and cosinese. Section 5: Trigonometric substitutions that replace a² - u², a² +

u², and u² - a² by single squared termf. Section 6: Integrals involving ax² + bx + cg. Section 7: The integration of rational functions--partial

fractionsh. Section 8: Improper integrals i. Section 9: Using integral tables

VI. Chapter 14: Differential Equationsa. Section 1: First order differential equations of first

degree1. Separable equations2. Homogenous equations3. Linear equations

b. Reference Books: Reference and Review Formulas

COURSE TITLE: ADVANCED PLACEMENT CALCULUS A and B

BOOK: 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 Calculus1.1 Lines (1.1-1.3)1.2 Functions and Graphs (1.4)1.3 Exponential Functions1.4 Parametric Equations (2.8 problems 1-29)1.5 Functions and Logarithms1.6 Trigonometric Functions (2.6)

II. Chapter 2: Limits and Continuity2.1 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: Derivatives3.1 Derivative (2.1)3.2 Differentiability3.3 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 Derivatives4.1 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 Integral5.1 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 Modeling6.1 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 Integrals7.1 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 Examination1. Reference and review formulas2. 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 Exam7.4 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, PresleyCopyright 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++ languageB. C++ programC. C++ program StructureD. Running a programE. Syntax errors and warningsF. Variations on coutG. Displaying special charactersH. Using helpI. Program style

II. Variables and constantsA. Using variables B. Obtaining a value from the userC. Using constants built-in data variable definitions expressions and operatorsD. String libraryE. Ignore() functionF. Formatting

III. Controlling program flowA. If statements; if-else statementsB. Compound statements nested and laddersC. Logical operators looping: do-while, while, forD. DebuggingE. Counting and summingF. Bool libraryG. BreakH. Random numbersI. Conio library

IV. FunctionsA. The functionB. Parameters and overloading and defaultC. Return statement and reference parametersD. DocumentationE. Building a library

V. Classes and objects (Time permitted)A. Classes and objectsB. StringC. IosD. ConstructorsE. Object

VI. Math, recursion and enum (Time permitted)A. Math libraryB. Trig functionsC. Log and exponential functionsD. Other math.h functionsE. PrecisionF. RecursionG. Data storage

COURSE TITLE: Honors Computer Science (C++)BOOK: Lawrenceville Press; “A Guide to Programming in C++”

Authors: Corica, Brown, PresleyCopyright 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++ languageb. C++ programc. C++ program Structured. Running a programe. Syntax errors and warningsf. Variations on coutg. Displaying special charactersh. Using helpi. Program style

II. Variables and constantsa. Using variables b. Obtaining a value from the userc. Using constants built-in data variable definitions expressions and operatorsd. String librarye. Formatting

III. Controlling program flowa. If statements; if-else statementsb. Compound statements nested and laddersc. Logical operators looping: do-while, while, ford. Debugginge. Counting and summingf. Bool libraryg. Breakh. Random numbers

IV. Functionsa. The functionb. Parameters and overloading and defaultc. Return statement and reference parametersd. Documentatione. Building a library

V. Classes and objectsa. Classes and objectsb. Stringc. Iosd. Constructorse. Object

VI. Math, recursion and enuma. Math libraryb. Trig functionsc. Log and exponential functionsd. Other math.h functionse. Precisionf. Recursiong. Data storage