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MATHEMATICS GRADE 7This two-semester course, taken by all seventh graders, covers a wide range of topics designed to provide each student with a strong

mathematical foundation. Problem solving is stressed throughout the course, and students are encouraged to discover mathematical patterns and relationships. The topics included are:

Semester 1 Semester 2

Key Concepts and

Content

Elementary set theory, properties of divisibility of whole numbers, numerical and algebraic expressions, solving algebraic equations and inequalities, solving verbal problems algebraically

Investigating Rational and Irrational numbers, the Pythagorean Theorem, scientific notation, elementary algebraic operations with polynomials – addition, subtraction, multiplication and division.

Skills

General skills: Start developing skills for interpreting more advanced mathematics texts Continue developing organizational and note taking skills. Continue improving/developing good work habits, for example:

Review class notes with a color highlighter Do HW nightly and keep it for future reference Fully correct each HW after it is reviewed in class Do not wait for the last minute to study for quizzes and tests Ask for assistance – Math Resource Center, peer-tutoring, classroom teacher

Content specific skillsCreate, read and apply Venn diagrams to finite and infinite sets, subsets, universal, complement, etc setsBe able to find prime factors, greatest common factor, recognize relative prime factors, apply properties of divisibilitySet and solve algebraic equations and inequalities with variables on one side, both sides, etc.

Understand and applying the properties of the Rational and Irrational numbers, e.g. determining which of two rational numbers is larger decimal equivalents of rational numbers; terminating vs. non-terminating

decimals adding, subtracting, and multiplying with repeating decimals converting a repeating decimal to fractional form multiplying, dividing, adding and subtracting numbers in scientific notation solving verbal problems involving proportions approximating a square root to the nearest tenth proof that is irrational simplifying radicals with index >2 adding, subtracting, multiplying, and dividing monomial radicals

Assessments

Formative assessment.The goal of formative assessment is to gain an understanding of what students know (and don't know) in order to make responsive changes in teaching and learning.Examples of formative assessment: students discuss their thinking, students write their understanding of vocabulary or concepts before and after instruction, summarize the main ideas, interview students individually or while working in groups – the entire groupEvaluative assessmentUnit tests, quizzes, midyear and final examinations, possibly – assigning projects

MATHEMATICS GRADE 8HThis two-semester course. Most topics are extended beyond the scope of the texts designed for Course I. A variety of verbal problems serve as applications and are stressed in many areas. Most topics are extended beyond the scope of the texts designed for Course I. A variety of verbal

problems serve as applications and are stressed in many areas. This course includes aspects of:Semester 1 Semester 2

Key Concepts and

Content

Symbolic logic, probability and combinatorics, operations on polynomial expressions, solving linear and quadratic equations, solving linear inequalities, literal equations

Functions, factoring, quadratic equations, radicals (operations and simple equations), fractional equations, area problems

Skills

General skills:See 7th grade General skills Content specific skills Understand the terminology of and apply laws of

Symbolic logic and be able to work with: Truth Tables Conjunction, Disjuntion, and Negations Conditionals and Biconditionals Tautologies and Contradictions

Apply basic laws of combinatorics and theory of probability

Multiplying Binomials Solve Equations and Inequalities Involving Absolute

Value Solve Verbal Problems: motion problems Work with Negative Exponents

Understand and apply functions and be able to: Graph Linear Functions; Vertical and Horizontal Lines Determine Rate of Change of a Linear Function Apply the Formula for Slope

Be able to represent an equation of line in Slope-Intercept Form Point-Slope Form

Be able to find an Equation of a Line Solve fractional equations and area problems

Assessments

Formative assessment.The goal of formative assessment is to gain an understanding of what students know (and don't know) in order to make responsive changes in teaching and learning.Examples of formative assessment: students discuss their thinking, students write their understanding of vocabulary or concepts before and after instruction, summarize the main ideas, interview students individually or while working in groups – the entire groupEvaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects

MATHEMATICS GRADE 8EThis two-semester course. This is the first course in our "E" or "Extended Honors" sequence of studies, a sequence generally characterized by a

faster pace, greater depth and a higher level of abstraction than our “Honors” program. The students are expected to be capable of doing a greater amount of work independently. The concept and methods of proof are emphasized, as is the ability to apply previously learned material

to new situations. The major units of study include:Semester 1 Semester 2

Key Concepts and

Content

Symbolic logic, algebra (functions/linear equations) with verbal problem applications throughout

Algebra (factoring, quadratic equations, radicals, and rational expressions), probability and combinations

Skills

General skills:See 7th grade General skillsContent specific skills Understand the terminology of and apply laws of

Symbolic logic and be able to work with: Conjunction, Disjuntion, and Negations Conditionals and Biconditionals Tautologies and Contradictions Disjunctive addition Simplification Chain rule/syllogism

Be able to do Deductive proofs in statement-reason format Indirect proofs/using RAA Conditional proof rule/in conjunction with proofs

Solve Equations and Inequalities Involving Absolute Value

Solve Verbal Problems: motion problems Work with Negative Exponents Define and discuss – relation, function, 1-1 function Apply vertical and horizontal line tests

Polynomials – be able to Multiply polynomials Find monomial common factors Square of a binomial and difference of two squares Factor trinomials of the form (including those with ) Divide of polynomials (long division)

Solve quadratic equations by factoring, completing the square, quadratic formula

Solve Verbal problems Determine the nature of roots/based on discriminant and graphs Radicals – simplifying, performing operations involving radicals – additions,

subtraction, multiplication Rational expressions - simplifying, and determining when undefined,

multiplying and dividing Simplify complex fractions Solve fractional equations Apply basic laws of combinatorics and theory of probability

Assessments


MATHEMATICS GRADE 9HFull Year, Credits – 1.0, Prerequisites: Math 8H, This course meets five times a week.

The first half of this course focuses on two-column proof: first in logic and then in Euclidean geometry. The nature of Euclidean geometry as a postulational system is stressed, as is deductive reasoning. The second half of the course reviews and extends many algebraic topics from the 8th grade, including: factoring, rational expressions, fractional equations, word problems, linear equations and inequalities in two variables, work with radicals, and quadratic equations. Graphing is extended to a unit on analytic geometry, parabolas, and linear-quadratic systems. Statistics are introduced. A comprehensive final examination is given in June and is a course requirement. This course includes aspects of:

Semester 1 Semester 2Concepts and

Content Logic and Euclidean Geometry. Solid Geometry Coordinate Geometry, Algebra of Polynomials and Quadratic Equations, Intro to Statistics

Skills

General skills:See 7th grade General skills Content specific skillsI. LOGIC

Review truth tables Proofs applying the Laws of Double Negation,

Disjunctive Inference, Detachment, Modus Tollens, Syllogism, De Morgan’s Laws, Material Implication, Non-Contradiction

Optional topic – Conditional Proof RuleII. EUCLIDEAN GEOMETRY

Axioms about line, planes, and segments, angles Mini-proofs using all of the above Parallel and Perpendicular Lines, Theorems Congruent Triangles Inequalities in triangles – angles, sides Pythagorean test for acute, right, obtuse triangle Quadrilaterals – definitions, theorems, areas

III. SOLID GEOMETRY Volume and Surface Area of: right rectangular

prism, pyramid, right cylinder, right cone.

IV. COORDINATE GEOMETRY Formulas - distance, midpoint, slope. Slopes - parallel and perpendicular

lines Coordinate geometry proofs – both numerical and variable Finding the equation of a line: slope-intercept; point-slope; general Solving a system of equations. Lin inequalities. Systems of lin inequalities

V. ALGEBRA Factoring Trinomials, Long division of polynomials. Rational expressions. Simplifying complex fractions. Equations with

rational expressions; application to word problems. Quadratic Equations

VI. STATISTICS Central tendency, Spread, Quartiles and percentiles Distributions of data – histograms; stem-and-leaf plots; box plots Empirical normal distribution (68-95-99.7 rule) Optional topic – Identify skewness of data; estimate mean and median on

graphical data

Assessments

Formative assessment.The goal of formative assessment is to gain an understanding of what students know (and don't know) in order to make responsive changes in teaching and learning. Examples of formative assessment: students discuss their thinking, students write their understanding of vocabulary or concepts before and after instruction, summarize the main ideas, interview students individually or while working in groups – the entire groupEvaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects

MATHEMATICS GRADE 9EFull Year, Credits – 1.0, Prerequisites: Math 8E, This course meets five times a week.

Algebraic topics - solving “hidden” quadratic equations, exponential equations, and equations with rational exponents. The set of real numbers is extended to the set of complex numbers. Function notation is introduced with inverse functions and composition of functions. Linear programming is presented as a high point in the discussion of linear functions. Linear functions are expanded into quadratic functions and conic sections. A major part of the course is the study of Euclidean geometry as an axiomatic system, and an introduction to geometric proof. Trigonometry of the right triangle is introduced. In addition, matrices, their determinants, scalar multiplication and matrix multiplication are introduced. A comprehensive final examination is given in June and is a course requirement. The major units of study include:


ContentExponents, Complex Numbers, Coordinate Geometry, Axioms in Theorems in Euclidean Geometry Euclidean Geometry – cont., Right Angle Trigonometry, Statistics

Skills

General skills:See 7th grade General skillsContent specific skills1. EXPONENTS

Rational exponents, Radical & Exponential equations2. COMPLEX NUMBERS

Introduction of "i," consecutive powers of i, Simplifying expressions involving complex numbers, Solving equations with complex roots

3. COORDINATE GEOMETRY Relation, function, domain and range Composition of functions and inverse functions; Midpoint and a distance formulae; Derivation of equations from their locus definitions

for circle, parabola, ellipse, and hyperbola4. EUCLIDEAN GEOMETRY

Introduction to an axiomatic system, postulates versus theorems.

Relationships between angles

4. EUCLIDEAN GEOMETRY – cont. Congruency of triangles and discuss the ambiguity of SSA Properties of isosceles and equilateral triangles Geometric inequalities involving one triangle Parallel Lines Postulates and Theorems Sum of all interior angles in a triangle and in any polygon, sum of the

exterior angles of a polygon Quadrilaterals. Areas of a parallelogram, a triangle, a trapezoid Similarity. Mean Proportional & Pythagorean Theorem. Areas/volumes.

5. RIGHT TRIANGLE TRIGONOMETRY6. STATISTICS

Central tendency, Spread, Quartiles and percentiles Distributions of data graphically & Normal distribution. Skewness of data; estimate mean and median an graphical data

Assessments



In this course, the study of Euclidean Geometry is extended to similarity and right triangle trigonometry. Algebra is taught along with geometry, where it is directly related to specific geometric concepts. Analytic geometry is introduced, and applied to proofs and other geometric problems. Also included are classic constructions, circles and transformational geometry. Exponential functions and logarithmic functions are introduced. Probability is extended to problems involving permutations and combinations. A comprehensive final examination is given in June and is a course requirement. The major units of study include:


ContentEuclidean geometry: similarity, constructions, circlesComplex numbers

Analytic Geometry, Transformations, Exponents and logs, Theory of Probability

Skills

General skills:See 7th grade General skillsContent specific skillsI. Euclidean Geometry

1) Ratio and Proportion, Similar figures and theorems, incl. area, volumes

2) Right triangle trig - elevation/depressionII. ConstructionsIII. Circles

1) Circle, radius, chord, diameter, secant, tangent 2) Circumference, Area of a circle, sectors and

segments3) Chords, arcs, tangents, secants and their theorems4) Angles in a circle and their relationship to arcs

IV. Complex Numbers1) Definition of i2 = -1 and complex numbers, a + bi2) Powers of i, computations with complex numbers3) Roots and factors

V. Analytic Geometry1) Proofs with points in the plane regarding figures. Area of a polygon.2) Locus, equation of a circle and parabola

VI. Transformational Geometry1) Functions, relations - domain, range, composition, inverse2) Transformations, composition of transformations

VII. Exponential and Logarithmic Functions1) Rational exponents, Exponential functions and equations2) Definition of logarithm, graphing exp and log functions3) Properties of logarithms, incl. change of base: 4) Applications of exponentials and logs

VIII. Probability, Permutations, and Combinations1) Fundamental counting principal, Permutations, Combinations2) Probability (including and and or statements)3) Probability of at least one = 1 – P(none)

Assessments



This course has four major areas of concentration: The extension of Euclidean geometry to circles, classic constructions, area and coordinate geometry; Trigonometry, which is introduced from the point of view of circular functions and culminates in applications of the law of sines and the law of cosines; Combinatorics and probability, including the binomial theorem and conditional probability; Exponents and logarithms. In addition to the applications of theorems and formulas, much time is devoted to their derivations. A comprehensive final examination is given in June and is a course requirement. The major units of study include:

Semester 1 Semester 2Key

Concepts and Content

Proportions, Geometry, Transformations Trigonometry, Advanced Geometry, Exponents and Logarithms, Probability

Skills

General skills:See 7th grade General skillsContent specific skillsI. DIRECT AND INVERSE PROPORTIONS

Graph of and is a hyperbolaII. GEOMETRY

Circles: radius, chords, diameter, angles, arcs, secants, tangents, internal and external tangents

Constructions Area: triangle, parallelogram, Heron’s formula,

areas of similar polygons and circles Coordinate Geometry: solve problems that are

not initially in a coordinate geometry setting. Area of a polygon, Pick’s Theorem

III. TRANSFORMATIONS Functions: domain and range; even and add,

inverse functions, function composition. Translations, reflections, dilations, rotations

of functions, composition of transformations.

IV. TRIGONOMETRY Trigonometric functions as circular functions, Radian measure. Graphing and transforming trigonometric functions. Properties of trigonometric functions. Inverse trigonometric

functions. Co-functions. Proving trigonometric identities. Solving trigonometric equations: linear and quadratic. Laws of cos, sin and tan, Product-to-Sum and Sum-to-Product. Trigonometry and Physics. Solving triangles, including the

ambiguous case.V. ADVANCED GEOMETRY (Optional – if time permits)

Stewart’s Theorem, Mass Points, Ceva’s Theorem,, Menelaus’ TheoremVI. EXPONENTS AND LOGARITHMS

Properties of exponents, Log functions as inverses of exponential. Properties of logarithms. Applications: Exponential growth and decay.

VII. PROBABILITY Bernoulli experiments. Binomial Expansion Theorem Conditional probability, Bayes’ Theorem, and Law of Total Probability.

Assessments



Algebra extended to the study of rational functions, conic sections, and to direct and inverse variation. The major emphasis of the course - trigonometric functions and applications. The study of the circle is integrated with the topics of geometric transformations and trigonometric functions. The study of intermediate algebra is also a large component of the course work. The course provides a strong foundation for the study of the functions, problem solving and higher mathematics. Other topics studied are probability, sequences and series, polynomial functions, and limits. A comprehensive final examination is given in June and is a course requirement. The major units of study include:


Content Algebra, Conic Sections, Trigonometry Trigonometry cont., Sequences and Series, Introduction to limits, Polynomial equations and fractions, Probability, Polar Coordinates

Skills

Content specific skillsALGEBRA II

Factoring, Rational expressions & equationsII. CONIC SECTIONS – Equations, Graphing

Circles. Ellipse as locus. Orientation, vertices, minor, major axes, foci and area.

Parabola. Hyperbolas: graphing, equation from graph, center, asymptotes, foci

Translating conics; finding equationsIII. TRIGONOMETRY

Definition of sine, cosine and tangent off the unit circle. Coterminal, Quadrantal angles.

Trig functions of angles whose reference angles are from special triangles

Cosecant, secant, cotangent Pythagorean identities, trig equations, &

identities Graphing of sine, cosine, and tangent, include

vertical and horizontal shifts Inverse trigonometric functions, applications. Area of a triangle, Laws of Sines, Cosines Solving the triangle, Ambiguous

IV. SEQUENCES AND SERIES Definitions, arithmetic vs. geometric vs. neither Recursive rules, Finding common difference/ratio, specific terms Geometric series – sums of finite and infinite series

V. INTRODUCTION TO LIMITS Limit of terms in an infinite sequence, rational expressions Finding limits, including one-sided limits; from graphs; from rational

expressionsVI. POLYNOMIAL EQUATIONS AND FUNCTIONS

Solve for all zeros – GCF, grouping, factor theorem, graphs Equation building (zeros and one point) Long division, synthetic division, Remainder Theorem, Rational Roots

Theorem, Descartes Rule, Location Principle. Inequalities.VII. PROBABILITY

Permutations and combinations, Bernoulli, Exactly, at least, at most Binomial Theorem

VIII. POLAR COORDINATES (Optional – if time permits) Graphing on polar axis Graphs – circle, cardioid, limacon, rose Change polar coordinates into rectangular ones and vice versa (points and

equations)

Assessments



Major areas of concentration: higher-degree polynomial equations, graphs of polynomial and rational functions, polynomial and rational inequalities, arithmetic and geometric sequences and series, polar coordinates, complex numbers, mathematical induction, conic sections, vectors in 2-space and 3-space, functions and relations. These topics provide students with a broad base for study of advanced mathematics and a strong foundation for the advanced placement calculus courses. Throughout the course, methods of proof and problem solving are stressed, and the use of graphing technologies is incorporated. A comprehensive final examination is given in June and is a course requirement. The major units of study include:

Semester 1 Semester 2


Complex numbers, Theory of Algebra, Mathematical Induction, Binomial Theorem, Arithmetic and Geometric Progressions

Exponents and Logarithms, Polar Coordinates, Conic Sections, Parametric Equations and Functions, Vectors

Skills

I. REVIEW OF COMPLEX NUMBERSII. THEORY OF ALGEBRA

Division Algorithm; Remainder and Factor Theorems. Synthetic Division.

Fundamental Theorem of Algebra Complex and Square Root Conjugate. Rational

Roots Theorem, Descartes’ Rule of Signs, Location Principle

Graphing Polynomial & Rational functions Linear Quotient and Absolute Value Equations

III. PROOF BY MATHEMATICAL INDUCTION Introduction to Induction Proofs Applying Induction to Prove Theorems

IV. REVIEW AND EXTENSION OF BINOMIAL THEOREM

V. ARITHMETIC AND GEOMETRIC PROGRESSIONS Arithmetic Progressions and Geometric

Progressions; Series (finite and infinite)

VI. EXTENSION OF EXPONENTS AND LOGS VII. POLAR COORDINATES

Rectangular and Polar coordinates, converting Complex Numbers from Rectangular to Polar Form. De Moivre’s Theorem. Polar Equations to Rectangular Form. Polar Graphs; Symmetry Tests, Polar Distance

VIII. CONIC SECTIONS Develop the Standard Form of the conic sections. Reflective Properties. Area of an Ellipse and the Eccentricity of the Conic Sections Heron’s Formula for finding the area of a triangle Optional Topic: Rotation of Axes

IX. PARAMETRIC EQUATIONS AND FUNCTIONS Graphing Parametric Equations Composition of Functions; Inverse Functions, Special Functions Limits of Functions and Sequences; Rules for Limits

X. VECTORS Adding and Subtracting Vectors, Direction Angle of a Vector in 2-space Using the Dot Product. Basis Vectors. Vectors in 3-space, including cross-product, Direction Angles Parametric Equations of a Line in Space. Coordinate Geometry in 3-space

Assessments


CALCULUSFull Year, Credits – 1.0, Prerequisites: Math 11H or Math 11E, and departmental permission, This course meets five times a week.

This full-year, non-Advanced Placement course, will consist of a thorough review of functions, including polynomial, trigonometric, rational, exponential and logarithmic. Along the way, students will review the algebraic skills they will need for the study of calculus and future mathematics courses. The course will also cover the basic elements of both differential and integral calculus of one variable. Applications may include maxima/minima, related rates, area, and volume. The major units of study include:



Functions and their Graphs, Limits, Differentiation Application of Derivatives, Integrals – Indefinite and Definite, Intro to Differential Equations

Skills

Content specific skills

I. Preparation for Calculus - Functions and Graphs II. Limits

Basic Limit Laws, Limits and Continuity Trigonometric Limits Intermediate Value Theorem Infinite Limits and Asymptotes

III. Differentiation The tangent line, derivative at a point Rates of change, Position, Velocity, and acceleration Differentiability and Continuity, Basic Differentiation

rules Derivative of Trigonometric Functions Higher Order Derivatives, The Chain Rule The linearization of a curve Implicit Differentiation, Derivatives of Inverse

Functions Derivative of when

IV. Applications of the Derivative Rolle’s Theorem and the Mean Value Theorem Increasing and Decreasing functions

IV. Applications of the Derivative – cont. The 1st Derivative Test, Absolute Extrema, Closed Interval Test Concavity, 2nd Derivative Test, Curve Sketching Connecting the graphs of , with the graph of Related Rates, ’Hopital’s Rule

V. The Integral The area problem, Basic integration rules Position, velocity, acceleration problems Indefinite integrals for trig., exponential and logarithmic functions, u-

substitution Reimann Sums, Trapezoidal Rule, Definite integrals, Properties of

definite integrals The First Fundamental Theorem of Calculus, Average value Second Fundamental Theorem of Calculus

VI. Applications of the Definite Integral Area Between Two Curves, Volume of Solids of Revolution Volume of Solids with known cross sections

VII. Optional-Introduction to Differential Equations Slopefields and differential equations Separation of variables, Exponential Growth and Decay

Assessments


ADVANCED PLACEMENT AB CALCULUSFull Year, Credits – 1.0, Prerequisites: Math 11H or Math 11E, and departmental permission, This course meets five times a week.

From 11H to AB: Minimum grade of B for year (no lower than B- per semester)From 11E to AB: Minimum grade of B- for year (no lower than C+ per semester)

This full year course is equivalent to one semester of a university level intensive course in the calculus of functions of a single variable. It requires a strong background in algebra, geometry and trigonometry. The topics included are: elementary functions and analytic geometry; limits; differentiation and applications (curve tracing, maxima and minima problems, related rates); integration and applications (area, volume, rectilinear motion). The graphing calculator is used throughout to clarify and expand on concepts. The course is demanding and requires consistent and diligent attention. A comprehensive Advanced Placement examination is given in May; it is anticipated that all students enrolled will take this exam. The major units of study include:


Concepts Limits, Derivatives Application of derivatives, Integrals, Intro to differential equations.

Skills

Content specific skillsI. Limits

1. Limits and Limit laws2. Evaluating limits, Continuity, Trig limits3. Intermediate value theorem

II. Basic Differentiation1. The tangent line, Average and instantaneous rates of

change2. The derivative as a function, Differentiability and

continuity, Basic differentiation rules3. Graph of a function and graph of its derivative4. Higher order derivatives, implicit differentiation

III. Applications of the Derivative1. Position, velocity, and acceleration, Local linearity,

L’Hopital’s Rule, Related rates2. Rolle’s Theorem and Mean Value Theorem3. Intervals of increase and decrease, Critical points,

relative extrema, Concavity, Second derivative test, absolute extrema

4. Curve sketching, Max/min problems

IV. Differentiation with Non-Polynomials1. Derivatives of Inverse Functions2. Derivatives of ex, ln x, and ax

V. The Integral1. Indefinite integrals, u substitutions, integrals with ex and ln x2. Reimann Sums: left, right, and midpoint RAM, Trapezoidal rule3. First Fundamental Theorem of Calculus4. Average value of a function (M.V.T. for integrals)5. Second Fundamental Theorem of Calculus

VI. Applications of the Definite Integral1. Rectilinear motion, Area between two curves, Volumes of solids of

revolution2. Volumes of solids with known cross sections

VII. Introduction to Differential Equations1. Slope fields, Separable differential equations2. Exponential growth and decay

Assessments

Formative assessment.The goal of formative assessment is to gain an understanding of what students know (and don't know) in order to make responsive changes in teaching and learning.Examples of formative assessment: students discuss their thinking, students write their understanding of vocabulary or concepts before and after instruction, summarize the main ideas, interview students individually or while working in groups – the entire groupEvaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects, AP AB Calc Examination in May

ADVANCED PLACEMENT BC CALCULUSFull Year, Credits – 1.0, Prerequisites: Math 11H or Math 11E, and departmental permission, This course meets five times a week.

From11H to BC: Minimum grade of A for year (No lower than A- per semester)From 11E to BC: Minimum Grade of A- for year (No lower than B+ per semester)

This full year course is equivalent to two semesters of a university level course in single variable calculus. Topics covered include: limits; differentiation and applications (curve tracing, max and min problems, related rates); integration and applications (area, volume, arc length); parametric and polar equations; sequences and series; Euler’s method and slope fields. The graphing calculator is an integral part of the class. A comprehensive Advanced Placement examination is given in May; it is anticipated that all students enrolled will take this exam. The major units of study include:


ConceptsLimits, Derivatives, Integration, Integration techniques, Applications

Inverse functions, Integrals involving inverse functions, Differential equations, Parametric equations, Polar Coordinates, Sequences and Series

Skills

Content specific skillsI. PRE-CALCULUS REVIEW AND LIMITSII. DIFFERENTIATION TECHNIQUES:

Differentiation Formulas. Higher Order Derivatives, The Chain Rule. Trig Functions. Implicit.

III. APPLICATIONS OF THE DERIVATIVE Graphing the Derivative of a Function, Linear

approx. Newton’s Method. Rolle’s and Mean Value Curve Sketching. Max/Min Problems, Related Rates

IV. INTEGRATION TECHNIQUES Antiderivatives, Integration Formulas, Trig Functions U-Substitutions, Improper Integrals. By Parts Powers of Trig Functions, Trig Substitutions The Partial Fractions Method

V. APPLICATIONS OF THE INTEGRAL The 1st Theorem of Calculus. Definite Integrals, the

Mean Value Thr for Integrals. Area btwn 2 curves, Volumes of solids of rev, Arc length, Area of a surface of rev, the 2nd Thr of Calc

V. INVERSE FUNCTIONS AND INVERSE TRIG FUNCTIONS Derivatives and integrals of Inverse Functions

VII. LOGARITHMIC AND EXPONENTIAL FUNCTIONS The Natural Logarithm function, Derivatives and Integrals involving.

log and exp functions, Log Differentiation.VIII. DIFFERENTIAL EQUATIONS

First Order Separable Equations, Exp Growth and Decay, Logistic Slope Fields, Euler’s Method

IX. PARAMETRIC EQUATIONS AND VECTOR VALUED FUNCTIONS Finding derivatives of Param Equations. Arc length and Surface area

of Param Equations, Vector Valued FunctionsX. POLAR COORDINATES

Area in Polar Coordinates, Arc Length of a Polar CurveXI. INFINITE SEQUENCES AND INFINITE SERIES:

Monotonic Sequences. Infinite Series, Telescoping Sums, Harmonic Series, Geometric Series, P-Series, Convergence Tests

Power Series, Interval of Convergence, Maclaurin, Taylor Series Differentiation and Integration of Power Series, Error

Assessments

Formative assessment.Examples of formative assessment: students discuss their thinking, students write their understanding of vocabulary or concepts before and after instruction, summarize the main ideas, interview students individually or while working in groups – the entire groupEvaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projectsAP BC Calculus Examination in May

ADVANCED PLACEMENT STATISTICSFull Year, Credits – 1.0, Prerequisites: Math 11H or Math 11E, and departmental permission, This course meets five times a week.

From Math 10H or 10E: Minimum grade of B for year (no lower than a B per semester)From Math 11H or 11E: Minimum grade of C for year (No lower than C per semester)

This full year course is equivalent to one semester of a university level course in Statistics. Students are exposed to four broad conceptual themes: exploring data, planning a study, anticipating patterns in advance, and statistical inference. The graphing calculator is extensively used as a tool to analyze data sets. The course emphasizes analysis and interpretation. Students prepare and present individual projects. A comprehensive Advanced Placement examination is given in May; it is anticipated that all students enrolled will take the exam. The major units of study include:


Content Organizing data, Producing Data, Probability Probability - cont., Sampling, Inference, Tests

Skills

Content specific skillsOrganizing DataExploring Data

1. Data, Variables, and Distributions.2. Center, spread, skewness, outliers, clusters, gaps

Normal DistributionExamining Relationships

1. Scatterplots, Correlation, Least-Squares Regression

2. Log and power. Cautions about correlation and regression. Relations in categorical data

Producing Data1. Designing samples and the relationship between

populations2. Designing Experiments and Simulating

ExperimentsProbability

1. Concept of randomness.2. Probability Models – Sample space. Probability

rules, Venn diagrams and Bayes’s rule.

Probability – cont.1. Discrete and continuous random variables2. Means and variances of random variables3. Binomial distributions. Geometric distributions

Sampling DistributionsInference

1. Confidence intervals. Tests of Significance. Cautions about significance2. Inference as decision – Type I, Type II errors, signific levels and power.

Inference for Means Confidence intervals and significance tests using the t-distributions. Inference for a single mean, Inference for two means.Inference for proportions - Inference for a single prop. Inference for two props.Chi Square procedures.

1. Chi-square test for goodness of fit.2. Chi square test for 2-way tables. Conditions and procedures. Expected

values and degrees of freedomInference for Regression – inference for the slope of a line

1. Regression models and standard error. 2. Confidence intervals for the slope3. Significance test for the slope

Assessments

Formative assessment.Examples of formative assessment: students discuss their thinking, students write their understanding of vocabulary or concepts before and after instruction, summarize the main ideas, interview students individually or while working in groups – the entire groupEvaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projectsComprehensive AP Statistics examination in May

ADVANCED PLACEMENT COMPUTER SCIENCE AFull Year, Credits – 1.0, Prerequisites: Departmental permission, This course meets five times a week.

This full year course is equivalent to one semester of a university level course in computer science. This course deals with program verification and algorithm analysis. In addition to the study of program methodology and procedural abstraction, there is a major emphasis on the study of data structures and data abstraction. This course focuses on object oriented programming, and uses JAVA as the programming language. A comprehensive Advanced Placement examination is given in May; it is anticipated that all students enrolled will take the exam. The major units of study include:



Computer architecture, Fundamental Data types, Objects, Conditional statements

Debugging, Loops, Arrays, Recursion, Data Structure, Object Oriented Design

Skills

Content specific skills1. Introduction

a. Parts of a Computer and How a Computer Works

b. Binary Numbers, ASCII Codec. Introduction to BlueJ Compiler

2. Fundamental Data Typesa. Primitive Data Typesb. Simple String Operations,

Concatenation, length, substringc. Using Numeric variables

3. Using Objectsa. Objects and Classesb. Methods and Variables

4. Implementing Objects 5. Decisions

a. If statementb. Boolean Expressions/DeMorgan’s

Law

6. Design, Test and Debugging Classes7. Iteration - loops8. Array Lists and Arrays9. Recursion, Factorial, Fibonacci Series 10.Sorting and Searching11.Introduction to Data Structures - Linked Lists, Stacks,

Queues12.Advanced Data Structures Interfaces

a. Sets, Mapsb. Hash Tables, Binary Search Tree, Tree Traversalc. Heaps

13.Inheritancea. Superclass, Subclass, base class, derived classb. Abstract, final, overridingc. Instanceof, this

14.Exception Handling15.Object Oriented Design

Assessments

Formative assessment.The goal of formative assessment is to gain an understanding of what students know (and don't know) in order to make responsive changes in teaching and learning.Examples of formative assessment: students discuss their thinking, students write their understanding of vocabulary or concepts before and after instruction, summarize the main ideas, interview students individually or while working in groups – the entire groupEvaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projectsComprehensive AP examination in May

COMPUTER I: INTRODUCTION TO COMPUTER SCIENCEFull Year, Credits – 1.0, Prerequisites: Departmental permission, This course meets five times a week.

The purpose of this course is to acquaint students with the basic concepts of Computer Science and different aspects of computer hardware, with the emphasis on computer architecture and systems. The course offers hands-on projects. Students use C++ as a programming language. This course also serves as a pre-requisite for Advanced Placement Computer Science. The major units of study include:



Fundamentals of Computer architecture and Programming, Introduction to C++ Introduction to C++ - cont., Common Algorithms, Computer Ethics

Skills

Content specific skills1. Fundamentals of Computers and

Programminga. History of Computersb. How Computers are

Programmedc. Introduction to the Internet

2. Introduction to C++a. Entering, Compiling and

Running a Programb. Variables and Constantsc. Math Operationsd. Strings and Screen I/O

3. Programming Flowa. Decision Makingb. Loopsc. Functions

4. Advanced Data Handlinga. Pointers and enum Keywordsb. Arraysc. Structures and String Functionsd. Data File Basics

5. Common Algorithmsa. Recursion and Searchingb. Sorting

6. Computer Ethics

Assessments


MATHEMATICS SEMINAR/PROBLEM SOLVINGOne semester, Credits – 0.5, Prerequisites: Math 10, and departmental permission, This course will run in the Fall and in the Spring.

Students may sign up for either semester independently, or both.This one semester course is a course for students who wish to expand their mathematical knowledge by covering a variety of advanced mathematical topics. Topics will be chosen based on the interests of the students, and may include abstract algebra (groups, rings and fields), advanced geometry, combinatorics and probability, graph theory, linear algebra, number theory, sequences and series, and advanced problem solving. The emphasis in the course is on problem solving, and on encouraging and nurturing advanced independent thinking in mathematics. This course does not count toward the mathematics requirement for graduation. The major units of study include:

Semester 1 or 2Key


Problem Solving Techniques, Principles, Additional topics

Skills

Content Specific Skills1. Problem Solving Techniques

search for a pattern, draw a figure/diagram formulate an equivalent problem modify a problem, divide into cases, work backwards argue by contradiction exploit symmetry (geometric and algebraic) pursue parity consider extreme cases, generalize, look for invariants

2. Principles Induction and Strong Induction Recursion Extreme Principle Pigeonhole principle Inclusion-Exclusion Principle

3. Additional topics: graph theory generating functions complex numbers geometry inequalities combinatorics number theory coloring problems polynomials sequences and series games

Assessments


mathematics grade 7 - math123.netmath123.net/hchs/mathdept/web/grids.doc · web viewequations...

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