# Syllabi ## ALGEBRA I SYLLABUS

MAT 101 (basic), MAT 111, MAT 121 (honors)
text: Elementary Algebra, Redden, 978-1-4533-2737-1

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
Graph and the relationship of numbers
graphing elementary functions using a table of values
graphing transformaztions

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
graphing

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

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

removing common monomial (GCF)
ax2+bx+c
difference of 2 squares
grouping

Polynomials
definition, four-function operations

operations
solving equations algebraically
modeling

Rational Expressions
operations
solving equations algebraically
modeling

Exponential Expressions and Functions
properties of exponents
exponential functions
modeling

## GEOMETRY SYLLABUS

MAT 201 (basic), MAT 211, MAT 221 (honors)
text: Geometry for Enjoyment and Challenge, Rhoad, 0-86609-965-4

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

Proofs
sequential reasoning and IF-THEN Statements
2 column proofs
formal logic (honors, MAT221)

Parallel and Perpendicular Lines
formal definitions
associated theorems

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

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

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

Polygons
regular polygons
angle measures

Ratios, Proportions and Similarity
similarity theorems for triangles
proofs
dimensions, area, volume
modeling

Circles
formal definitions
relationships between arcs and angles
power theorems (honors, MAT221)
circumference, arc length

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

Three Dimensional Figures
volume and surface area of spheres, prisms, pyramids, cylinders, cones
inscribed figures (honors, MAT221)
modeling

## ALGEBRA II SYLLABUS

MAT 301 (basic), MAT 311, MAT 321 (honors)

301 text: Algebra and Trigonometry, 131657100
311,321 text: Algebra and Trigonometry, 978-0-07-727651-5

Graphing Techniques
domain and range
f(x) = x, f(x) = |x|, f(x)=x^2, f(x)=x^3, f(x)=1/x, f(x) = x^1/2, f(x) = x^1/3, f(x)=1/x^2,
f(x)=2^x
transformations (shifts, stretches, reflections): y = a*f[b(x+c)]+d
finding the equation from a graph

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

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

Circles
graphing
distance formula

Complex Numbers
definition of i
operations on complex numbers

Factoring
removing common factors
ax^2+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 with and without technology: extreme values
finding roots algebraically and with technology
modeling

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

Logarithmic Expressions and Functions
rules of logarithms (honors, MAT321)
graphing with and without technology
domain and range
solving equations algebraically and with technology
modeling

Rational Expressions and Functions
operations on rational expressions
direct and inverse variation
solving equations
graphing
modeling

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

Matrices (honors, MAT 321)
operations
solving systems of equations

## ALGEBRA SURVEY SYLLABUS

MAT 401
text: teacher materials

Equations and Inequalities
Solving basic equations, simplifying expressions to solve equations, problem solving, formulas, solving inequalities

Graphing
Rectangular coordinate system, graphing linear equations, solving systems of equations by: (graphing, substitution, addition)

Equations of Lines, Functions
Slope of a non vertical line, writing equations of lines, review of functions, graphs of Nonlinear functions

Rational Expressions
Simplifying rational expressions, multiply/divide/add/subtract rational expressions, complex fractions, solving equations that contain rational expressions

Quadratic Functions, Inequalities, and Algebra of Functions
Completing the square, quadratic formula, graphs of quadratic functions, quadratic and other nonlinear inequalities, algebra and composition of functions, inverse functions

Exponential and Logarithmic Functions
Exponential functions, base-e exponential functions, logarithmic functions, base-e logarithms, properties of logarithms, exponential and logarithmic equations

## TOPICS IN TRIGONOMETRY

MAT402

A review of the elementary functions, with an emphasis on trigonometry and the circular functions.

## PRECALCULUS SYLLABUS

MAT 411, MAT 421 (honors)
text: Precalculus: Graphical, Numerical and Algebraic, Demana, Waits, et al 978-0-1331320-14

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

Polynomial Functions
higher degree polynomial functions: finding zeros, complex numbers

Rational Functions
graphing: domain and range, intercepts, asymptotes, removable discontinuities, limits at extrema
solving equations and inequalities

Exponential, Logarithmic and Logistic Functions
properties
graphing: domain and range, intercepts, asymptotes
modeling

Trigonometric Functions
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

Probability and Statistics
mean, median, mode
five number summary
probability events

Sequences and Series
arithmetic and geometric, including infinite
sigma notation
modeling

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

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

Conics (if time allows)
circles, parabolas, ellipses and hyperbolas
graphing by hand, translations, modeling

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

Algorithms and Programming

## STATISTICS SYLLABUS

Math 413
text: The Practice of Statistics, 4th ed., Yates, 978-1-4292-4559-3

Sampling and Experimental Design
Methods of Data Collection
Planning and Conduction
Surveys
Planning and Conducting Experiments
Investigation of conclusions that can be drawn from theses methods

Exploring Data
Graphical Displays of Data
Numerical Summaries of Data
Mathematical Models and Distributions
Comparing Distributions.
Exploring Bivariate Data
Exploring Categorical Data

Randomness and Probability
Randomness
Basic Probability and Probability Rules
Simulation
Independence
Random Variables
Sampling Distributions
Central Limit Theorem

Inferential Statistics
Confidence Intervals
Proportions
Means
One Sample Inference Tests
Proportions
Means
Paired t-test
Two Sample Inference Tests
Proportions
Means
Inference for Categorical Data
Chi-Square Goodness of Fit

## AP STATISTICS SYLLABUS

MATH 513
text: The Practice of Statistics, 4th ed., Yates, 978-1-4292-4559-3

This course follows the syllabus designed and published annually by the College Board.

The topics may vary slightly from year to year and comprise a college course in Probability and Statistics.
Successful completion of the Advanced Placement Examination may lead to a student being awarded one semester of college credit.

## CALCULUS SYLLABUS

MAT 431
text: online text at:

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, straight line motion

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

## ADVANCED PLACEMENT AB CALCULUS SYLLABUS

MAT 511
text: Calculus: Graphical, Numerical and Algebraic , 4th ed., *AP edition, Finney, et al, 978-0133180749

This course follows the syllabus designed and published annually by the College Board.

The topics may vary slightly from year to year and comprise a challenging first level college calculus course.
Successful completion of the Advanced Placement Examination may lead to a student being awarded one semester of college credit.

## ADVANCED PLACEMENT BC CALCULUS SYLLABUS

MAT 521
text: Calculus: Graphical, Numerical and Algebraic , 4th ed., *AP edition, Finney, et al, 978-0133180749

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

## MULTIVARIABLE CALCULUS SYLLABUS

MAT 611
The text is online.

This is a very challenging course at the second-year college 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

## LINEAR ALGEBRA SYLLABUS

MAT 612
A study of the basic theory of vector spaces and systems of linear equations.

## NUMBER THEORY SYLLABUS

MAT 613
A study of the basic theory of the properties of the natural numbers.

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