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Academics : Math

Mathematics Course Syllabi

2008-2009 Academic Year

Algebra 1 | Geometry | Algebra 2 | Algebra Survey | Precalculus |
AP Statistics | Calculus | AB Calculus | BC Calculus | Multivariable Calculus
Math Flowchart | What Gets Taught and in Which Course

ALGEBRA I SYLLABUS
Algebra/Physics 1a and 1b
text: Algebra 1, Paul Foerster, 0-201-32458-X

Algebraic Manipulations
associative, commutative and distributive properties
order of operations and parenthesis
distinction between expression and equation

Graphing Skills
Cartesian coordinate system
dependent and independent variables

Functions
definition of function and associated vocabulary
function notation, domain and range

Linear Functions
graphing concepts: slope, x- and y-intercept
graphing forms: standard, slope-intercept, point-slope, two-intercept
solving equations
modeling

Absolute Value
solving equations and inequalities

Systems of Linear Equations
solutions of linear equations by substitution, linear combination, graphing 
graphing solutions of linear inequalities

Quadratic Functions
roots by factoring and quadratic formula
graphing using roots (factoring)
modeling

Factoring Quadratic Expressions
removing common monomial
ax²+bx+c
difference of 2 squares
grouping

Polynomials
definition, operations

Radical Expressions and Functions
operations
solving equations algebraically
modeling

Rational Expressions
operations
solving equations algebraically
modeling

Exponential Expressions and Functions
properties of exponents
exponential functions
modeling

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GEOMETRY SYLLABUS
MAT 211, MAT 221 (honors)
text: Geometry for Enjoyment and Challenge, Rhoad, 0-86609-965-4

The Geometer's Sketchpad software program is used throughout the course as a discovery and learning tool.

A review of basic skills in algebra is woven throughout the course.

Proofs
sequential reasoning and IF-THEN Statements
2 column and paragraph proofs
converse and bi-conditional

Parallel and Perpendicular Lines
formal definitions
associated theorems

Triangles
congruence theorems
median, altitude
isosceles and equilateral triangles
triangle inequalities

Right Triangles
Pythagorean Theorem
distance formula
special right triangles
geometric mean formulas

Quadrilaterals
parallelograms: properties and proofs
special parallelograms: rectangle, rhombus, square and their characteristics
trapezoids

Polygons
regular polygons
angle measures

Ratios, Proportions and Similarity
similarity theorems for triangles
modeling

Circles
formal definitions
relationships between arcs and angles
power theorems
circumference, arc length
modeling

Areas
triangles, quadrilaterals, polygons and circles, including sectors and segments

Three Dimensional Figures
volume and surface area of spheres, prisms, pyramids, cylinders, cones
inscribed figures
modeling

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ALGEBRA II SYLLABUS
MAT 301 (basic), MAT 311, MAT 321 (honors)
text: Algebra & Trigonometry, Paul Foerster, 0-201-32460-1

Graphing Techniques
domain and range
f(x) = x, f(x) = |x|, f(x)=x², f(x)=x³, f(x)=1/x, f(x) = x^1/2, f(x)=1/x²,  
f(x)=e^x, f(x) = ln(x)
transformations (shifts, stretches, reflections):  y = a*f[b(x+c)]+d
finding the equation from a graph

Absolute Value
equations and inequalities: graphical and algebraic solutions
decomposition into a piecewise-defined function

Relations and Functions
formal definition and notation
domain, range, increasing, decreasing, extrema
composition of two or more functions
inverses, modeling

Linear Expressions and Functions
graphing forms: slope-intercept, point-slope, standard
graphing with technology
algebraic solutions
solutions of systems of linear functions by substitution, linear combination and graphing
solutions of systems of linear inequalities
regression
modeling

Quadratic Functions
completing the square
graphing in vertex form and with technology
solving by quadratic formula, factoring, technology
quadratic regression with technology
modeling

Circles
graphing, distance formula

Complex Numbers
definition of i
operations on complex numbers

Factoring
removing common monomial factor
ax²+bx+c
difference of two squares, sum and difference of two cubes
grouping, quadratic form, use of technology

Polynomial Expressions and Functions of Degree > 2
definition and operations, including factoring
graphing only with technology: extreme values
finding roots algebraically and with technology
cubic and quartic regression
modeling
extreme value problems (honors, MAT 321)

Exponential & Logarithmic Expressions and Functions
properties of exponents and logarithms
rational exponents
graphing with and without technology
domain and range
solving equations algebraically and with technology
regression
modeling

Rational Expressions and Functions
operations on rational expressions
graphing with and without technology: domain and range, intercepts, vertical and horizontal asymptotes
direct and inverse variation
solving equations
end behavior
removable discontinuities (honors, MAT 321)

Radical Expressions and Functions
graphing with and without technology
operations
solving equations graphically and algebraically
direct and inverse variation
domain and range

Probability and Statistics
mean, median, mode
probability events

Sequences and Series (honors, MAT 321)
arithmetic, geometric sequences and series
sigma notation, infinite series
modeling

Parametric Equations, Conic Sections, Unit circle trigonometry (honors, MAT 321)

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ALGEBRA SURVEY  SYLLABUS
MAT 410
text: Beginning & Intermediate Algebra, Gustafson & Frisk, 0495117935

Exploration of the Elementary Functions
This course is based upon the syllabus of Math 311, with further emphasis on the study of the elementary functions: polynomial, rational, exponential and logarithmic functions; probability and statistics, including applications

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PRECALCULUS SYLLABUS
MATH 411, MATH 421 (honors)
text: Precalculus, Larson and Hostetler, 978-0-618-64345-5

Graphing Techniques
Transformations (shifts, stretches, reflections)
f(x) = x, f(x) = |x|, f(x)=x², f(x)=x³, f(x)=1/x, f(x)=x^1/2, f(x)=e^x,f(x) = ln(x),
 f(x)=sin(x), f(x)=cos(x)
transformations (shifts, stretches, reflections),  y = a * f[b(x+c)]+d
finding the equation from a graph
domain and range

Functions
properties: domain and range, continuity, increasing and decreasing, extrema, symmetry, asymptotes, end behavior
building functions: operations, composition, inverse
modeling: scatter plots, regression with technology

Polynomial Functions
linear and quadratic; power functions and variation
higher degree polynomial functions: finding zeros, complex numbers

Rational Functions
operations on rational expressions
graphing: domain and range, intercepts, asymptotes, removable discontinuities, end behavior
direct and inverse variation
solving equations and inequalities

Exponential, Logarithmic and Logistic Functions
properties and graphs
modeling

Trigonometric Functions
angles in degrees and radians
graphs: amplitude, period, phase shift, vertical shift
inverses:domain restrictions, graphs, use of technology
modeling

Analytic Trigonometry   
identities, Law of Sines and Cosines
solving trig equations

Sequences and Series (honors, MAT 421)
arithmetic and finite geometric, sigma notation

Parametric Equations and Projectile Motion (honors, MAT 421)
projectile and circular motion

Vectors, Polar Equations (honors, MAT 421)
vectors in the plane
polar coordinates and graphing by hand and with technology
modeling

Conics
circles, parabolas
graphing by hand, translations
ellipses and hyperbolas, polar and parametric equations of conics, modeling (honors, MAT 421)

Discrete Mathematics (honors, MAT 421)
factorial expressions, combinations and permutations, binomial theorem, prrof by induction
modeling

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AP STATISTICS SYLLABUS
MATH 513
text: The Practice of Statistics, Yates, 978-0-7167-7309-2

This course culminates with a project which requires collection of data, statistical analysis and a written and oral presentation.

introduction to statistics
experimental design and sampling techniques
descriptive statistics
probability
probability distributions
normal probability distributions
Central limit theorem
Students-t distributions
Poisson distributions
binomial distributions
estimation using samples
hypothesis testing
inferences from two samples
correlation and regression
inferences from correlation and regression statistics

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CALCULUS SYLLABUS
MATH 431
text: NMH materials

Functions, Graphs, and Limits
review of the elementary functions and their graphs
analysis of graphs, with the aid of technology
limits of functions, including one-sided limits
definition of continuity 

Derivatives
definition of the derivative
average rate of change; difference quotients
derivative as a function
techniques of differentiation
second derivative
implicit differentiation
applications of derivatives
extreme value problems
related rates

Integrals
interpretations and properties of definite integrals
Riemann sum
techniques of integration
applications of integrals
areas, solids of revolution

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ADVANCED PLACEMENT AB CALCULUS SYLLABUS
MATH 511
text: Calculus: Graphical, Numerical and Algebraic *AP edition, Finney, et al, 0-13-201408-4

This course follows the syllabus designed and published annually by the College Board.
The topics may vary slightly from year to year, but comprise a challenging first level college calculus course.
Successful completion of the Advanced Placement Examination given in May may lead to a student being awarded one semester of college credit.

ADVANCED PLACEMENT BC CALCULUS SYLLABUS
MATH 521
text: Calculus: Graphical, Numerical and Algebraic *AP edition, Finney, et al, 0-13-201408-4

This course follows the syllabus designed and published annually by the College Board.
The topics may vary slightly from year to year, but comprise a very challenging year-long university calculus course.
Successful completion of the Advanced Placement Examination given in May may lead to a student being awarded two semesters of college credit.

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MULTIVARIABLE CALCULUS SYLLABUS
MATH 611
text: Multivariable Calculus, McCallum, et al, 0-471-48480-6

This is a very challenging course at the second year university level.
The differential and integral calculus of several real variables and its application to scalar and vector fields are the principal topics of this course.

Vectors and Analytic Geometry in Space
dot and cross products, lines and planes in space

The Derivatives and Optimization of Functions of Two or More Variables
graphs, contour diagrams - level curves, level surfaces, extremas of space functions, directional derivatives, partial derivatives, gradients, and constrained optimization - Lagrange multipliers.

Multiple Integrals
double and triple integrals in rectangular, polar, cylindrical and spherical coordinates

Vector Fields and Applications
Parameterized curves and surfaces, vector fields, curl and divergence of vector fields, line integrals, conservative fields and potential functions, flux integral, Fundamental Theorem of calculus for line integrals, Green's Theorem, Stoke’s Theorem, and Divergence Theorem