Syllabi

 

Algebra 1 | Geometry | Algebra 2 | Algebra Survey | Precalculus | 
AP Statistics | Calculus | AB Calculus | BC Calculus | Multivariable Calculus

Linear Algebra | Number Theory

Math Flowchart | What Gets Taught and in Which Course
 

ALGEBRA I SYLLABUS
MAT 101 (basic), MAT 111, MAT 121 (honors)
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, four-function 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

 

 

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

The Geometer's Sketchpad software program is used for demonstration and/or 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, kites

Polygons 
regular polygons
angle measures
 

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

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

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
coordinate geometry (honors, MAT 221) 
modeling

 

 

ALGEBRA II SYLLABUS
MAT 301 (basic), MAT 311, MAT 321 (honors)
text: Intermediate Algebra , Lial, Hornsby, McGinnis, 978-0-321-57497-8
 

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) = x^1/3,  f(x)=1/x²,  
f(x)=2^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

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
modeling

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

Circles
graphing
distance formula (honors, MAT 321)

Complex Numbers
definition of i
operations on complex numbers

Factoring
removing common factors
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 (honors, MAT 321)
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
regression
modeling
 

Rational Expressions and Functions
operations on rational expressions
direct and inverse variation
solving equations
graphing (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
arithmetic and geometric sequences and series
sigma notation, infinite series (honors, MAT 321) 
modeling

Logarithmic Expressions and Functions  (honors, MAT 321) 
properties
graphing with and without technology
domain and range
solving equations algebraically and with technology

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

 

 

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

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

Radicals and Rational Exponents
Radical expressions, applications of radicals, rational exponents, simplifying/combining radical expressions, multiply/divide radical expressions, radical equations, complex numbers

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

 

PRECALCULUS SYLLABUS
MAT 411, MAT 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, limits at extrema
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, limits at extrema
direct and inverse variation
solving equations and inequalities
 

Exponential, Logarithmic and Logistic (MAT 421)  Functions
properties
graphing: domain and range, intercepts, asymptotes 
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 (MAT 421)
arithmetic and finite geometric, sigma notation

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

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

 

 

AP STATISTICS SYLLABUS
MATH 513
text: The Practice of Statistics, 4th ed., Yates, 978-1-4292-4559-3 (new 11-12)
 

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: 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, 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, 978-0-13-317857-9 (new 11-12) 

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.
 

MAT 521
text: Calculus: Graphical, Numerical and Algebraic , 4th ed., *AP edition, Finney, et al, 978-0-13-317857-9 (new 11-12)

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
text: Multivariable Calculus, McCallum, et al, 0-471-48480-6
 

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

 NUMBER THEORY SYLLABUS
MAT 613
text: A Friendly Introduction to Number Theory, Silverman, 0-13-186137-9

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