Download MATHEMATICS GRADE 7

MATHEMATICS GRADE 7
Key
Concepts and
Content
Skills
This 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
Elementary set theory, properties of divisibility of whole Investigating Rational and Irrational numbers, the Pythagorean Theorem, scientific
numbers, numerical and algebraic expressions, solving
notation, elementary algebraic operations with polynomials – addition, subtraction,
algebraic equations and inequalities, solving verbal
multiplication and division.
problems algebraically
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 skills
Create, read and apply Venn diagrams to finite and
Understand and applying the properties of the Rational and Irrational numbers, e.g.
infinite sets, subsets, universal, complement, etc sets
 determining which of two rational numbers is larger
Be able to find prime factors, greatest common factor,
 decimal equivalents of rational numbers; terminating vs. non-terminating
recognize relative prime factors, apply properties of
decimals
divisibility
 adding, subtracting, and multiplying with repeating decimals
Set and solve algebraic equations and inequalities with
 converting a repeating decimal to fractional form
variables on one side, both sides, etc.
 multiplying, dividing, adding and subtracting numbers in scientific notation
 solving verbal problems involving proportions
 approximating a square root to the nearest tenth



Assessments
proof that 2 is irrational
simplifying radicals with index >2
adding, subtracting, multiplying, and dividing monomial radicals
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 group
Evaluative assessment
Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
MATHEMATICS GRADE 8H
Key
Concepts and
Content
Skills
Assessments
This 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
Symbolic logic, probability and combinatorics,
operations on polynomial expressions, solving linear and Functions, factoring, quadratic equations, radicals (operations and simple
quadratic equations, solving linear inequalities, literal
equations), fractional equations, area problems
equations
General skills:
See 7th grade General skills
Content specific skills
 Understand the terminology of and apply laws of
 Understand and apply functions and be able to:
Symbolic logic and be able to work with:
 Graph Linear Functions; Vertical and Horizontal Lines
 Truth Tables
 Determine Rate of Change of a Linear Function
 Conjunction, Disjuntion, and Negations
 Apply the Formula for Slope
 Conditionals and Biconditionals
 Be able to represent an equation of line in
 Tautologies and Contradictions
 Slope-Intercept Form
 Apply basic laws of combinatorics and theory of
 Point-Slope Form
probability
 Be able to find an Equation of a Line
 Multiplying Binomials
 Solve fractional equations and area problems
 Solve Equations and Inequalities Involving Absolute
Value
 Solve Verbal Problems: motion problems
 Work with Negative Exponents
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
MATHEMATICS GRADE 8E
This 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
Skills
Assessments
Symbolic logic, algebra (functions/linear equations) with
verbal problem applications throughout
Algebra (factoring, quadratic equations, radicals, and rational expressions),
probability and combinations
General skills:
See 7th grade General skills
Content specific skills
 Understand the terminology of and apply laws of
 Polynomials – be able to
Symbolic logic and be able to work with:
 Multiply polynomials
 Conjunction, Disjuntion, and Negations
 Find monomial common factors
 Conditionals and Biconditionals
 Square of a binomial and difference of two squares
 Tautologies and Contradictions
 Factor trinomials of the form (including those with )
 Disjunctive addition
 Divide of polynomials (long division)
 Simplification
 Solve quadratic equations by factoring, completing the square, quadratic
 Chain rule/syllogism
formula
 Be able to do
 Solve Verbal problems
 Deductive proofs in statement-reason format
 Determine the nature of roots/based on discriminant and graphs
 Indirect proofs/using RAA
 Radicals – simplifying, performing operations involving radicals – additions,
 Conditional proof rule/in conjunction with proofs
subtraction, multiplication
 Solve Equations and Inequalities Involving Absolute
 Rational expressions - simplifying, and determining when undefined,
Value
multiplying and dividing
 Solve Verbal Problems: motion problems
 Simplify complex fractions
 Work with Negative Exponents
 Solve fractional equations
 Define and discuss – relation, function, 1-1 function
 Apply basic laws of combinatorics and theory of probability
 Apply vertical and horizontal line tests
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
MATHEMATICS GRADE 9H
Full 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 2
Concepts and
Content
Skills
Assessments
Logic and Euclidean Geometry. Solid Geometry
Coordinate Geometry, Algebra of Polynomials and Quadratic Equations,
Intro to Statistics
General skills:
See 7th grade General skills
Content specific skills
I. LOGIC
IV. COORDINATE GEOMETRY
 Review truth tables
 Formulas - distance, midpoint, slope. Slopes - parallel and perpendicular
lines
 Proofs applying the Laws of Double Negation,
 Coordinate geometry proofs – both numerical and variable
Disjunctive Inference, Detachment, Modus
Tollens, Syllogism, De Morgan’s Laws, Material
 Finding the equation of a line: slope-intercept; point-slope; general
Implication, Non-Contradiction
 Solving a system of equations. Lin inequalities. Systems of lin inequalities
 Optional topic – Conditional Proof Rule
V. ALGEBRA
II. EUCLIDEAN GEOMETRY
 Factoring Trinomials, Long division of polynomials.
 Axioms about line, planes, and segments, angles
 Rational expressions. Simplifying complex fractions. Equations with
 Mini-proofs using all of the above
rational expressions; application to word problems.
 Parallel and Perpendicular Lines, Theorems
 Quadratic Equations
 Congruent Triangles
VI. STATISTICS
 Inequalities in triangles – angles, sides
 Central tendency, Spread, Quartiles and percentiles
 Pythagorean test for acute, right, obtuse triangle
 Distributions of data – histograms; stem-and-leaf plots; box plots
 Quadrilaterals – definitions, theorems, areas
 Empirical normal distribution (68-95-99.7 rule)
III. SOLID GEOMETRY
 Optional topic – Identify skewness of data; estimate mean and median on
 Volume and Surface Area of: right rectangular
graphical data
prism, pyramid, right cylinder, right cone.
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
MATHEMATICS GRADE 9E
Concepts and
Content
Skills
Assessments
Full 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:
Semester 1
Semester 2
Exponents, Complex Numbers, Coordinate Geometry,
Euclidean Geometry – cont., Right Angle Trigonometry, Statistics
Axioms in Theorems in Euclidean Geometry
General skills:
See 7th grade General skills
Content specific skills
1. EXPONENTS
4. EUCLIDEAN GEOMETRY – cont.
 Rational exponents, Radical & Exponential equations
 Congruency of triangles and discuss the ambiguity of SSA
2. COMPLEX NUMBERS
 Properties of isosceles and equilateral triangles
 Introduction of "i," consecutive powers of i,
 Geometric inequalities involving one triangle
 Simplifying expressions involving complex numbers,
 Parallel Lines Postulates and Theorems
 Solving equations with complex roots
 Sum of all interior angles in a triangle and in any polygon, sum of the
3. COORDINATE GEOMETRY
exterior angles of a polygon
 Relation, function, domain and range
 Quadrilaterals. Areas of a parallelogram, a triangle, a trapezoid
 Composition of functions and inverse functions;
 Similarity. Mean Proportional & Pythagorean Theorem. Areas/volumes.
 Midpoint and a distance formulae;
5. RIGHT TRIANGLE TRIGONOMETRY
 Derivation of equations from their locus definitions 6. STATISTICS
for circle, parabola, ellipse, and hyperbola
 Central tendency, Spread, Quartiles and percentiles
4. EUCLIDEAN GEOMETRY
 Distributions of data graphically & Normal distribution.
 Introduction to an axiomatic system, postulates
 Skewness of data; estimate mean and median an graphical data
versus theorems.
 Relationships between angles
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
MATHEMATICS GRADE 10H
Concepts and
Content
Skills
Full Year, Credits – 1.0, Prerequisites: Math 9H, This course meets five times a week.
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:
Semester 1
Semester 2
Analytic Geometry, Transformations, Exponents and logs, Theory of
Euclidean geometry: similarity, constructions, circles
Complex numbers
Probability
General skills:
See 7th grade General skills
Content specific skills
I. Euclidean Geometry
V. Analytic Geometry
1) Ratio and Proportion, Similar figures and
1) Proofs with points in the plane regarding figures. Area of a polygon.
theorems, incl. area, volumes
2) Locus, equation of a circle and parabola
2) Right triangle trig - elevation/depression
VI. Transformational Geometry
II. Constructions
1) Functions, relations - domain, range, composition, inverse
III. Circles
2) Transformations, composition of transformations
1) Circle, radius, chord, diameter, secant, tangent
VII. Exponential and Logarithmic Functions
2) Circumference, Area of a circle, sectors and
1) Rational exponents, Exponential functions and equations
segments
2) Definition of logarithm, graphing exp and log functions
3) Chords, arcs, tangents, secants and their theorems
3) Properties of logarithms, incl. change of base:
4) Angles in a circle and their relationship to arcs
4) Applications of exponentials and logs
IV. Complex Numbers
2
VIII.
Probability, Permutations, and Combinations
1) Definition of i = -1 and complex numbers, a + bi
1) Fundamental counting principal, Permutations, Combinations
2) Powers of i, computations with complex numbers
2) Probability (including and and or statements)
3) Roots and factors
3) Probability of at least one = 1 – P(none)
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
MATHEMATICS GRADE 10E
Full Year, Credits – 1.0, Prerequisites: Math 9E, This course meets five times a week.
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 2
Key
Concepts and
Content
Skills
Proportions, Geometry, Transformations
General skills:
See 7th grade General skills
Content specific skills
I. DIRECT AND INVERSE PROPORTIONS
 Graph of y  kx and xy  k is a hyperbola
II. 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.
Assessments
TRANSFORMATIONS
 Functions: domain and range; even and add,
inverse functions, function composition.
 Translations, reflections, dilations, rotations
of functions, composition of transformations.
Trigonometry, Advanced Geometry, Exponents and Logarithms, Probability
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’ Theorem
VI. 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.
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
MATHEMATICS GRADE 11H
Full Year, Credits – 1.0, Prerequisites: Math 10H, This course meets five times a week.
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:
Semester 1
Semester 2
Concepts and
Content
Skills
Assessments
Algebra, Conic Sections, Trigonometry
Trigonometry cont., Sequences and Series, Introduction to limits,
Polynomial equations and fractions, Probability, Polar Coordinates
Content specific skills
IV. SEQUENCES AND SERIES
ALGEBRA II
 Factoring, Rational expressions & equations
 Definitions, arithmetic vs. geometric vs. neither
II.
CONIC SECTIONS – Equations, Graphing
 Recursive rules, Finding common difference/ratio, specific terms
 Circles. Ellipse as locus. Orientation, vertices,
 Geometric series – sums of finite and infinite series
minor, major axes, foci and area.
V. INTRODUCTION TO LIMITS
 Parabola. Hyperbolas: graphing, equation from
 Limit of terms in an infinite sequence, rational expressions
graph, center, asymptotes, foci
 Finding limits, including one-sided limits; from graphs; from rational
 Translating conics; finding equations
expressions
III. TRIGONOMETRY
VI. POLYNOMIAL EQUATIONS AND FUNCTIONS
 Definition of sine, cosine and tangent off the unit
 Solve for all zeros – GCF, grouping, factor theorem, graphs
circle. Coterminal, Quadrantal angles.
 Equation building (zeros and one point)
 Trig functions of angles whose reference angles
 Long division, synthetic division, Remainder Theorem, Rational Roots
are from special triangles
Theorem, Descartes Rule, Location Principle. Inequalities.
 Cosecant, secant, cotangent
VII. PROBABILITY
 Pythagorean identities, trig equations, &
 Permutations and combinations, Bernoulli, Exactly, at least, at most
identities
 Binomial Theorem
 Graphing of sine, cosine, and tangent, include
VIII. POLAR COORDINATES (Optional – if time permits)
vertical and horizontal shifts
 Graphing on polar axis
 Inverse trigonometric functions, applications.
 Graphs – circle, cardioid, limacon, rose
 Area of a triangle, Laws of Sines, Cosines
 Change polar coordinates into rectangular ones and vice versa (points and
 Solving the triangle, Ambiguous
equations)
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
MATHEMATICS GRADE 11E
Concepts and
Content
Full Year, Credits – 1.0, Prerequisites: Math 10E, This course meets five times a week.
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
Exponents and Logarithms, Polar Coordinates, Conic Sections, Parametric
Induction, Binomial Theorem, Arithmetic and Geometric
Equations and Functions, Vectors
Progressions
I.
II.
Skills
Assessments
REVIEW OF COMPLEX NUMBERS
VI. EXTENSION OF EXPONENTS AND LOGS
THEORY OF ALGEBRA
VII. POLAR COORDINATES
 Division Algorithm; Remainder and Factor
 Rectangular and Polar coordinates, converting Complex Numbers from
Theorems. Synthetic Division.
Rectangular to Polar Form. De Moivre’s Theorem. Polar Equations to
Rectangular Form. Polar Graphs; Symmetry Tests, Polar Distance
 Fundamental Theorem of Algebra
VIII.
CONIC
SECTIONS
 Complex and Square Root Conjugate. Rational

Develop
the Standard Form of the conic sections. Reflective Properties.
Roots Theorem, Descartes’ Rule of Signs,
Location Principle
 Area of an Ellipse and the Eccentricity of the Conic Sections
 Graphing Polynomial & Rational functions
 Heron’s Formula for finding the area of a triangle
 Linear Quotient and Absolute Value Equations
 Optional Topic: Rotation of Axes
III. PROOF BY MATHEMATICAL INDUCTION
IX. PARAMETRIC EQUATIONS AND FUNCTIONS
 Introduction to Induction Proofs
 Graphing Parametric Equations
 Applying Induction to Prove Theorems
 Composition of Functions; Inverse Functions, Special Functions
IV. REVIEW AND EXTENSION OF BINOMIAL
 Limits of Functions and Sequences; Rules for Limits
THEOREM
X. VECTORS
V. ARITHMETIC AND GEOMETRIC
 Adding and Subtracting Vectors, Direction Angle of a Vector in 2-space
PROGRESSIONS
 Using the Dot Product. Basis Vectors.
 Arithmetic Progressions and Geometric
 Vectors in 3-space, including cross-product, Direction Angles
Progressions; Series (finite and infinite)
 Parametric Equations of a Line in Space. Coordinate Geometry in 3-space
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
CALCULUS
Full 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:
Semester 1
Semester 2
Key
Concepts and
Content
Functions and their Graphs, Limits, Differentiation
Application of Derivatives, Integrals – Indefinite and Definite, Intro to
Differential Equations
Content specific skills
Skills
Assessments
I. Preparation for Calculus - Functions and Graphs
IV. Applications of the Derivative – cont.
II. Limits
 The 1st Derivative Test, Absolute Extrema, Closed Interval Test
 Basic Limit Laws, Limits and Continuity
 Concavity, 2nd Derivative Test, Curve Sketching
 Trigonometric Limits
 Connecting the graphs of f  , f  with the graph of f
 Intermediate Value Theorem
 Related Rates, ’Hopital’s Rule
 Infinite Limits and Asymptotes
V. The Integral
III. Differentiation
 The area problem, Basic integration rules
 The tangent line, derivative at a point
 Position, velocity, acceleration problems
 Rates of change, Position, Velocity, and acceleration
 Indefinite integrals for trig., exponential and logarithmic functions, u Differentiability and Continuity, Basic Differentiation
substitution
rules
 Reimann Sums, Trapezoidal Rule, Definite integrals, Properties of
 Derivative of Trigonometric Functions
definite integrals
 Higher Order Derivatives, The Chain Rule
 The First Fundamental Theorem of Calculus, Average value
 The linearization of a curve
 Second Fundamental Theorem of Calculus
 Implicit Differentiation, Derivatives of Inverse
VI. Applications of the Definite Integral
Functions
 Area Between Two Curves, Volume of Solids of Revolution
 Derivative of e x , ln x, a x when a  1
 Volume of Solids with known cross sections
VII.
Optional-Introduction to Differential Equations
IV. Applications of the Derivative
 Slopefields and differential equations
 Rolle’s Theorem and the Mean Value Theorem
 Separation of variables, Exponential Growth and Decay
 Increasing and Decreasing functions
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
ADVANCED PLACEMENT AB CALCULUS
Full 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:
Semester 1
Semester 2
Key
Concepts
Skills
Assessments
Limits, Derivatives
Application of derivatives, Integrals, Intro to differential equations.
Content specific skills
I. Limits
IV. Differentiation with Non-Polynomials
1. Limits and Limit laws
1. Derivatives of Inverse Functions
2. Evaluating limits, Continuity, Trig limits
2. Derivatives of ex, ln x, and ax
3. Intermediate value theorem
V. The Integral
II. Basic Differentiation
1. Indefinite integrals, u substitutions, integrals with ex and ln x
1. The tangent line, Average and instantaneous rates of
2. Reimann Sums: left, right, and midpoint RAM, Trapezoidal rule
change
3. First Fundamental Theorem of Calculus
2. The derivative as a function, Differentiability and
4. Average value of a function (M.V.T. for integrals)
continuity, Basic differentiation rules
5. Second Fundamental Theorem of Calculus
3. Graph of a function and graph of its derivative
VI. Applications of the Definite Integral
4. Higher order derivatives, implicit differentiation
1. Rectilinear motion, Area between two curves, Volumes of solids of
III. Applications of the Derivative
revolution
1. Position, velocity, and acceleration, Local linearity,
2. Volumes of solids with known cross sections
L’Hopital’s Rule, Related rates
VII. Introduction to Differential Equations
2. Rolle’s Theorem and Mean Value Theorem
1. Slope fields, Separable differential equations
3. Intervals of increase and decrease, Critical points,
2. Exponential growth and decay
relative extrema, Concavity, Second derivative test,
absolute extrema
4. Curve sketching, Max/min problems
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects, AP AB Calc Examination in May
ADVANCED PLACEMENT BC CALCULUS
Full 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:
Key
Concepts
Semester 1
Limits, Derivatives, Integration, Integration techniques,
Applications
Content specific skills
Semester 2
Inverse functions, Integrals involving inverse functions, Differential equations,
Parametric equations, Polar Coordinates, Sequences and Series
I.
II.
V.
III.



Skills
IV.




V.

Assessments
PRE-CALCULUS REVIEW AND LIMITS
DIFFERENTIATION TECHNIQUES:
Differentiation Formulas. Higher Order Derivatives,
The Chain Rule. Trig Functions. Implicit.
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
INTEGRATION TECHNIQUES
Antiderivatives, Integration Formulas, Trig Functions
U-Substitutions, Improper Integrals. By Parts
Powers of Trig Functions, Trig Substitutions
The Partial Fractions Method
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
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 Functions
X. POLAR COORDINATES
 Area in Polar Coordinates, Arc Length of a Polar Curve
XI. 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
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
AP BC Calculus Examination in May
ADVANCED PLACEMENT STATISTICS
Full 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:
Semester 1
Concepts and
Content
Skills
Assessments
Organizing data, Producing Data, Probability
Content specific skills
Organizing Data
Exploring Data
1. Data, Variables, and Distributions.
2. Center, spread, skewness, outliers, clusters, gaps
Normal Distribution
Examining Relationships
1. Scatterplots, Correlation, Least-Squares
Regression
2. Log and power. Cautions about correlation and
regression. Relations in categorical data
Producing Data
1. Designing samples and the relationship between
populations
2. Designing Experiments and Simulating
Experiments
Probability
1. Concept of randomness.
2. Probability Models – Sample space. Probability
rules, Venn diagrams and Bayes’s rule.
Semester 2
Probability - cont., Sampling, Inference, Tests
Probability – cont.
1. Discrete and continuous random variables
2. Means and variances of random variables
3. Binomial distributions. Geometric distributions
Sampling Distributions
Inference
1. Confidence intervals. Tests of Significance. Cautions about significance
2. 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 freedom
Inference for Regression – inference for the slope of a line
1. Regression models and standard error.
2. Confidence intervals for the slope
3. Significance test for the slope
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
Comprehensive AP Statistics examination in May
ADVANCED PLACEMENT COMPUTER SCIENCE A
Full 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:
Key
Concepts and
Content
Semester 1
Semester 2
Computer architecture, Fundamental Data types, Objects,
Conditional statements
Debugging, Loops, Arrays, Recursion, Data Structure, Object Oriented
Design
Content specific skills
1. Introduction
a. Parts of a Computer and How a Computer
Works
b. Binary Numbers, ASCII Code
c. Introduction to BlueJ Compiler
Skills
Assessments
6.
7.
8.
9.
10.
11.
12.
Design, Test and Debugging Classes
Iteration - loops
Array Lists and Arrays
Recursion, Factorial, Fibonacci Series
Sorting and Searching
Introduction to Data Structures - Linked Lists, Stacks, Queues
Advanced Data Structures Interfaces
a. Sets, Maps
b. Hash Tables, Binary Search Tree, Tree Traversal
c. Heaps
13. Inheritance
a. Superclass, Subclass, base class, derived class
b. Abstract, final, overriding
c. Instanceof, this
14. Exception Handling
15. Object Oriented Design
2. Fundamental Data Types
a. Primitive Data Types
b. Simple String Operations, Concatenation,
length, substring
c. Using Numeric variables
3. Using Objects
a. Objects and Classes
b. Methods and Variables
4. Implementing Objects
5. Decisions
a. If statement
b. Boolean Expressions/DeMorgan’s Law
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
Comprehensive AP examination in May
COMPUTER I: INTRODUCTION TO COMPUTER SCIENCE
Full 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:
Semester 1
Key
Concepts and
Content
Fundamentals of Computer architecture and
Programming, Introduction to C++
Semester 2
Introduction to C++ - cont., Common Algorithms, Computer Ethics
Content specific skills
1. Fundamentals of Computers and
Programming
a. History of Computers
b. How Computers are Programmed
c. Introduction to the Internet
Skills
Assessments
2. Introduction to C++
a. Entering, Compiling and Running a
Program
b. Variables and Constants
c. Math Operations
d. Strings and Screen I/O
3. Programming Flow
a. Decision Making
b. Loops
c. Functions
4. Advanced Data Handling
a. Pointers and enum Keywords
b. Arrays
c. Structures and String Functions
d. Data File Basics
5. Common Algorithms
a. Recursion and Searching
b. Sorting
6. Computer Ethics
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects
MATHEMATICS SEMINAR/PROBLEM SOLVING
One 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 2
Key
Concepts and
Content
Skills
Problem Solving Techniques, Principles, Additional topics
Content Specific Skills
1. 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
Assessments
3. Additional topics:
 graph theory
 generating functions
 complex numbers
 geometry
 inequalities
 combinatorics
 number theory
 coloring problems
 polynomials
 sequences and series
 games
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 group
Evaluative assessment: Unit tests, quizzes, midyear and final examinations, possibly – assigning projects