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# Syllabi

- ALGEBRA I SYLLABUS
- GEOMETRY SYLLABUS
- ALGEBRA II SYLLABUS
- ALGEBRA SURVEY SYLLABUS
- TOPICS IN TRIGONOMETRY
- PRECALCULUS SYLLABUS
- STATISTICS SYLLABUS
- AP STATISTICS SYLLABUS
- CALCULUS SYLLABUS
- ADVANCED PLACEMENT AB CALCULUS SYLLABUS
- ADVANCED PLACEMENT BC CALCULUS SYLLABUS
- MULTIVARIABLE CALCULUS SYLLABUS
- LINEAR ALGEBRA SYLLABUS
- NUMBER THEORY SYLLABUS

## 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**Quadratic Functions**

roots by factoring and quadratic formula

graphing using roots (factoring)

modeling**Factoring Quadratic Expressions**

removing common monomial (GCF)

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

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

**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

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

**Quadratic Functions**

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

**Radical Expressions and Functions**

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

**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

## TOPICS IN TRIGONOMETRY

## 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**

degree and radian measure

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:

http://tutorial.math.lamar.edu/download.aspx **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