
Coach Letter
Toggle More InfoOctober 1, 2022
Dear Math Team Coach/Sponsor:
We are now in the final planning stages for the 17th annual FGCU Invitational Mathematics Competition. The competition will be held on Monday, December 19th, 2022 at Florida Gulf Coast University's main campus.
For Math subjectsThere will be prizes for the top 15 finishers in each of the six individual subject tests  algebra 1, algebra 2, geometry, statistics, precalculus, and calculus. The top 5 teams will receive team trophies and medallions, and there will be sweepstakes trophies for the top 5 schools and door prizes.
Each student will receive a certificate of participation by mail. An answer guide to each exam will be provided to each coach at the conclusion of the testing.
We have set a $12.00 per student registration fee which covers the cost of a tee shirt for each student. Raffle tickets will be provided to each student during checkin. Tee shirts will be distributed after the awards ceremony. Free bus and other vehicle parking on campus will be available.The FGCU Math Club will provide ushers for the test venues and maintain an information desk at the checkin point. Directions to FGCU and a campus map are available here.We hope your school will be able to participate and encourage you to RSVP with registration information by December 5th at the latest. The detailed schedule, contest rules, and registration form are available from the contest home page. Please note that this year we are offering email registration in order to facilitate the grading of exams in the limited time frame we have. We would appreciate your taking advantage of this method.
If you have any questions regarding registration or other details, please email Contest CoDirector, Dr. Jerry Ellis , or call (239) 5907253.

Registration
Toggle More InfoWe would appreciate having all registration info ASAP and fees by no later than December 9th. Please estimate the number of tee shirts of each size for your contingent (S, M, L, XL) and include that information with your payment.
Also, please advise with your payement if any students will require disability accommodation and the nature of that accommodation. We will make every reasonable effort to comply. If your group needs assistance in arranging overnight accommodations, please contact jkellis@fgcu.edu by November 24.
By registering for the contest, schools acknowledge that the contest rules are understood and agreed to. 
Directions to FGCU
Toggle More InfoFROM THE NORTH: Take I75 to Alico Road, exit east to Ben Hill Griffin Parkway, then go south to the main entrance at FGCU Blvd. Don't turn at the north entrance.
FROM THE SOUTH: Take I75 to Corkscrew Road, exit east to Ben Hill Griffin Parkway (light at Publix), then go north to the main entrance at FGCU Blvd.
In either case, check with the attendant at the parking kiosk located 1/8 mile from the main entrance for parking instructions. Checkin for competitors is at Whitaker Hall, first floor, on the south side of the building (across from observatory) in the Telford gallery. Please park in Parking Lot #7 and take the walking bridge across the lake directly to Whitaker Hall. 
Dining Options
Toggle More InfoOn Campus (link to map)
Name Location Open/Close Einstein Bros Bagels Cohen Center 7:00a  4:00p ChickFilA Cohen Center 9:00a  8:00p BYOB at Howard Hall Howard Hall 11:00a  4:00p Starbucks Library 7:00a  9:00p The Marketplace at Howard Hall Howard Hall 8:00a  5:00p Dunkin' Donuts Homes Hall 7:30a  4:00p The Marketplace at The Link Howard Hall 8:00a  4:00p 239 BURGER BAR Cohen Center 11:00a  5:00p Brahma Sushi Cohen Center 10:00a  6:00p Boar's Head Howard Hall 11:00a  4:00p SoVi Dining Hall South Village 7:00a  10:00p Boardwalk / Azul's Brewhouse North Lake Village 4:00p  10:00p Off Campus
 Perkins  Publix Mall / Corner of Corkscrew Road and Ben Hill Griffin Blvd.
 McDonald's  Publix Mall / Corner of Corkscrew Road and Ben Hill Griffin Blvd.
 Beef O'Brady's  Publix Mall / Corner of Corkscrew Road and Ben Hill Griffin Blvd.
 Subway  Publix Mall / Corner of Corkscrew Road and Ben Hill Griffin Blvd.
 China Gourmet  Publix Mall / Corner of Corkscrew Road and Ben Hill Griffin Blvd.
 Amore Brick Oven Pizza  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Aurelio's Pizza  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Burger 21  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Famous Dave's BBQ  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Fosters Grille  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 McDonalds  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Moe's Southwestern Grill  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Pita Pit  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Pollo Tropical  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Red Robin Gourmet Burgers  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Tijuana Flatts  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Chipotle  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 Chili's  Gulf Coast Town Center / West side of Ben Hill Griffin Blvd. just south of Alico Rd.
 All American Grille / West side of Ben Hill Griffin Blvd. just north of Corkscrew Rd.
 Ford's Garage / West side of Ben Hill Griffin Blvd. just north of Corkscrew Rd.
 French Deli / West side of Ben Hill Griffin Blvd. just north of Corkscrew Rd.
 Luna Pizza / West side of Ben Hill Griffin Blvd. just north of Corkscrew Rd.
 Luna Rosa Italian Grille / West side of Ben Hill Griffin Blvd. just north of Corkscrew Rd.
 Duffy's / Southeast corner of Ben Hill Griffin Blvd. @ Corkscrew Rd. (before gate to Stoneybrook)

Contest Rules
Toggle More InfoWe will follow current FAMAT rules for calculator usage 
NO CALCULATORS PERMITTED FOR ANY SUBJECT TESTS, INDIVIDUAL OR TEAM, EXCEPT STATISTICS
GRAPHING CALCULATORS MAY BE USED FOR THE INDIVIDUAL OR TEAM STATISTICS TESTSIt is the responsibility of each team's sponsor to make sure students are using calculators in accordance with these rules. Failure to comply may result in individual or team disqualification.
Scantrons will be provided. Students need to bring their own pencils. If students are involved in statistics or an open exam they are allowed to bring calculators. More information about calculator usage can be found on Schedule page.
Teams will be composed of four students for each exam. Only one team per school per test category, please !
No limit on number of students participating in individual rounds.
Results from Algebra 1 and Statistics will not count toward overall school scores, however individual and team awards will be given for both subject areas. The reason for this is that not every school is able to field a team in these areas, and those schools not doing so would be unfairly penalized in the overall standings.
Contest officials at their sole discretion may resolve any tie scores, adjudicate the interpretation of any test question, invalidate the scoring of any test question, determine the admissibility of any response to a test question, and take any action which in their judgment benefits the conduct of the math competition.
All appeals to the dispute judge must be initiated no later than 15 minutes after the test containing the disputed question(s) ends.
AWARDS
I.Individual Awards
a. Trophies for the top 15 places in each of the content area exams.
b. See Scoring Rubric for awarding of points.
II. Division (content area) Awards
a. A team trophy for the top 5 teams.
b. A medallion for each team member.
c. See Scoring Rubric for awarding of points.
d. Scores of each team member (maximum of 4) plus the team score during the team round will count towards the division award.
III. Overall School Award
a. Trophies for the top 5 schools.
b. Tscores for each of the 4 counted divisions (Geometry, Algebra 2, Precalculus, & Calculus) will be added together for the overall school award.
ELIGIBILITY FOR COMPETITION
Eligibility for Algebra 1, Geometry, Algebra 2, and Statistics is one year each. The chart below outlines the tests students enrolled in each course may take. In general, students are expected to take the test that corresponds to the current course they are enrolled in. Students may “test up” by competition in a division for which they have not taken. Students may never “test down” by taking a test corresponding to a course they have already passed.* Length of eligibility is 1 year for each of Algebra 1, 2, and Geometry, after which time the student will move to the next highest division.
** Students enrolled in Statistics and no other math class who have completed Algebra 2/Geometry, but no higher math class and never competed in Algebra 2/Geometry, may compete in Algebra 2/Geometry while enrolled in Statistics.
*** Any student enrolled in or having completed Algebra 2 and /or Geometry may compete in Algebra 2 or Geometry or both in the same year. However, there is a oneyear eligibility in each division, and all other eligibility rules are still in effect. The same applies to PreAICE 2 and PreAICE 3.

Sponsors
Toggle More InfoCompetition was cancelled due Hurricane Irma.

Scoring Rubrics
Toggle More InfoScoring Room Supervisor: Prof. Rob Nichols
SCORING:
Scoring for the Individual Tests will be as follows:
1 points for each correct response
0 points for leaving the answer blank
0 point for answering incorrectlyScoring for the Team Round will be as follows:
16 points for getting question correct in the first minute
12 points for getting question correct in the second minute
8 points for getting question correct in the third minute
4 points for getting question correct in the fourth minute
0 points for getting question correct after time expiresTIES:
INDIVIDUAL TESTS:
All tie scores will be broken according to the following rules which apply to a given subject test:
(1) Any student who receives a score of N on the general round will be ranked above a student who receives a score of M if N>M, regardless of the outcome of any subsequent tiebreaking rounds.
(2) Any students achieving a perfect score during the general round will be deemed to be tied, and will participate in a tiebreaking round according to the procedure in (5) below.
(3) Any students achieving the same score other than in (2) during the general round and having done so by answering the identical questions correctly, will be deemed to be tied, and will participate in a tiebreaking round according to the procedure in (5) below.
(4) Any students achieving the same score other than in (2) during the general round, and having done so by answering a different set of questions correctly, will be deemed to have different ranking. The lower ranking will go to the student who misses the earlier question posed in the general round.
(5) Any students who are deemed to be tied will participate in a sudden death tiebreaker consisting of a supplemental round of questions comparable to the questions asked in the general round. At the sole discretion of the Scoring Room Supervisor, the tiebreaker round for a given subject test may be administered simultaneously to all students who are tied according to both (2) or (3) above. Students participating in a tie breaker round will simultaneously receive one question at a time, and have a fixed amount of time to respond in writing. Within a group of mutually tied students, any student missing a given question will be ranked below any other student not missing that question. A student whose ranking according to this procedure is definitely and irrefutably established will be excused from further participation in the round. The supplemental round will continue until all ties are broken.TEAM TESTS:
All tie scores will be broken according to the following rules which apply to a given subject test:
(1) Teams with the same overall score at the end of the team round will be ranked according to the individual scores constituting that overall score. More specifically, the individual scores for a team will be arranged from highest to lowest. The highest score will be considered the first score, the next highest score (possibly equal to the highest score) will be considered the second score, and so forth according to the obvious rule. The sequences of scores obtained in this manner from teams that are tied at a given overall score will be compared from first to last. Any team whose sequence of scores agrees with another team from the first to the Nth position, but whose N+1st score is lower than that of the other team, will be ranked below the team with the higher N+1st score.
(2) Teams with the same overall score at the end of the team round, and whose sequences of individual scores as defined in (1) of this section are the same, will participate in a team tiebreaker round. The procedure for the team tiebreaker round will be the same as for the individual tiebreaker round in (5) of the preceding section, with the word “team” substituted consistently for “student”.MISC:
Interpretation and application of the preceding rules, including the discretion to modify them to resolve unforeseen circumstances, is the sole prerogative of the Scoring Room Supervisor or Designee thereof.

Test Preparation Standards
Toggle More InfoTESTING STANDARDS
Algebra 1 (MAT 1033):
 Basic Concepts
 The Real Number System
 Operations with Real Numbers
 Powers, Square Roots, and the Order of Operations
 Integer Exponents and Scientific Notation
 Operations with Variables and Grouping Symbols
 Evaluating Variable Expressions and Formulas
 Linear Equations and Inequalities
 FirstDegree Equations with One Unknown
 Literal Equations and Formulas
 Absolute Value Equations
 Using Equations to Solve Word Problems
 Solving MoreInvolved Word Problems
 Linear Inequalities
 Compound Inequalities
 Absolute Value Inequalities
III. Equations and Inequalities in Two Variables and Functions
 Graphing Linear Equations with Two Unknowns
 Slope of a Line
 Graphs and the Equations of a Line
 Linear Inequalities in Two Variables
 Concept of a Function
 Graphing Functions from Equations and Tables of Data
 Systems of Linear Equations and Inequalities
 Systems of Linear Equations in Two Variables
 Systems of Linear Equations in Three Variables
 Applications of Systems of Linear Equations
 Systems of Linear Inequalities
 Polynomials
 Introduction to Polynomials and Polynomial Functions: Adding, Subtracting, and Multiplying
 Dividing Polynomials
 Synthetic Division
 Removing Common Factors; Factoring by Grouping
 Factoring Trinomials
 Special Case Factoring
 Factoring a Polynomial Completely
 Solving Equations and Applications Using Polynomials
Geometry:
 Points, Lines, Planes, and Angles
 Points, Lines, and Planes
 Segments, Rays, and Distance
 Angles
 Postulates and Theorems Relating Points, Lines, and Planes
 Deductive Reasoning
 IfThen Statements; Converses
 Properties from Algebra
 Proving Theorems
 Special Pairs of Angles
 Perpendicular Lines
 Planning a Proof
III. Parallel Lines and Planes
 Definitions
 Properties of Parallel Lines
 Proving Lines Parallel
 Angles of a Triangle
 Angles of a Polygon
 Inductive Reasoning
 Congruent Triangles
 Congruent Figures
 Some Ways to Prove Triangles Congruent
 Using Congruent Triangles
 The Isosceles Triangle Theorems
 Other Methods of Proving Triangles Congruent
 Using More than One Pair of Congruent Triangles
 Medians, Altitudes, and Perpendicular Bisectors
 Quadrilaterals
 Properties of Parallelograms
 Ways to Prove that Quadrilaterals Are Parallelograms
 Theorems Involving Parallel Lines
 Special Parallelograms
 Trapezoids
 Inequalities in Geometry
 Inequalities
 Inverses and Contrapositives
 Indirect Proof
 Inequalities for One Triangle
 Inequalities for Two Triangles
VII. Similar Polygons
 Ratio and Proportion
 Properties of Proportions
 Similar Polygons
 A Postulate for Similar Triangles
 Theorems for Similar Triangles
 Proportional Lengths
VIII. Right Triangles
 Similarity in Right Triangles
 The Pythagorean Theorem
 The Converse of the Pythagorean Theorem
 Special Right Triangles
 The Tangent Ratio
 The Sine and Cosine Ratios
 Applications of Right Triangle Trigonometry
Algebra 2 (MAC 1105):
 Fundamental Concepts of Algebra
 Real Numbers and Algebraic Expressions
 Exponents and Scientific Notation
 Radicals and Rational Exponents
 Polynomials
 Factoring Polynomials
 Rational Expressions
 Equations, Inequalities, and Mathematical Models
 Graphs and Graphing Utilities
 Linear Equations
 Formulas and Applications
 Complex Numbers
 Quadratic Equations
 Other Types of Equations
 Linear Inequalities
 Quadratic and Rational Inequalities
III. Functions and Graphs
 Lines and Slope
 Distance and Midpoint Formulas; Circles
 Basics of Functions
 Graphs of Functions
 Transformations of Functions
 Combinations of Functions; Composite Functions
 Inverse Functions
 Polynomial and Rational Functions
 Quadratic Functions
 Polynomial Functions and Their Graphs
 Dividing Polynomials: Remainder and Factor Theorems
 Zeros of Polynomial Functions
 More on Zeros of Polynomial Functions
 Rational Functions and Their Graphs
 Modeling Using Variation
 Exponential and Logarithmic Functions
 Exponential Functions
 Logarithmic Functions
 Properties of Logarithms
 Exponential and Logarithmic Equations
 Modeling with Exponential and Logarithmic Functions
 Systems of Equations and Inequalities
 Systems of Linear Equations in Two Variables
 Systems of Linear Equations in Three Variables
 Partial Fractions
 Systems of Nonlinear Equations in Two Variables
 Systems of Inequalities
 Linear Programming
VII. Conic Sections and Analytic Geometry
 The Ellipse
 The Hyperbola
 The Parabola
Precalculus (MAC 1147):
 Functions and Graphs
 Graphs and Graphing Utilities
 Basics of Functions and Their Graphs
 More on Functions and Their Graphs
 Linear Functions and Slope
 More on Slope
 Transformations of Functions
 Combinations of Functions; Composite Functions
 Inverse Functions
 Distance and Midpoint Formulas; Circles
 Modeling with Functions
 Polynomial and Rational Functions
 Complex Numbers
 Quadratic Functions
 Polynomial Functions and Their Graphs
 Dividing Polynomials; Remainder and Factor Theorems
 Zeros of Polynomial Functions
 Rational Functions and Their Graphs
 Polynomial and Rational Inequalities
 Modeling Using Variation
III. Exponential and Logarithmic Functions
 Exponential Functions
 Logarithmic Functions
 Properties of Logarithms
 Exponential and Logarithmic Equations
 Exponential Growth and Decay: Modeling Data
 Trigonometric Functions
 Angles and Radian Measure
 Trigonometric Functions: The Unit Circle
 Right Triangle Trigonometry
 Trigonometric Functions of Any Angle
 Graphs of Sine and Cosine Functions
 Graphs of Other Trigonometric Functions
 Inverse Trigonometric Functions
 Applications of Trigonometric Functions
 Analytic Trigonometry
 Verifying Trigonometric Identities
 Sum and Difference Formulas
 DoubleAngle, PowerReducing, and HalfAngle Formulas
 ProducttoSum and SumtoProduct Formulas
 Trigonometric Equations
 Additional Topics in Trigonometry
 The Law of Sines
 The Law of Cosines
VII. Systems of Equations and Inequalities
 Systems of Linear Equations in Two Variables
 Systems of Linear Equations in Three Variables
 Partial Fractions
 Systems of Nonlinear Equations in Two Variables
 Systems of Inequalities
 Linear Programming
VIII. Matrices and Determinants
 Matrix Solutions to Linear Systems
 Inconsistent and Dependent Systems and Their Applications
 Matrix Operations and Their Applications
 Multiplicative Inverses of Matrices and Matrix Equations
 Determinants and Cramer’s Rule
 Conic Sections and Analytic Geometry
 The Ellipse
 The Hyperbola
 The Parabola
 Rotation of Axes
 Parametric Equations
Calculus (MAC 2311):
 Functions and Models
 Four Ways to Represent a Function
 Mathematical Models: A Catalog of Essential Functions
 New Functions from Old Functions
 Exponential Functions
 Inverse Functions and Logarithms
 Limits and Derivatives
 The Tangent and Velocity Problems
 The Limit of a Function
 Calculating Limits Using the Limit Laws
 The Precise Definition of a Limit
 Continuity
 Limits at Infinity; Horizontal Asymptotes
 Derivatives and Rates of Change
 The Derivative as a Function
III. Differentiation Rules
 Derivatives of Polynomials and Exponential Functions
 The Product and Quotient Rules
 Derivatives of Trigonometric Functions
 The Chain Rule
 Implicit Differentiation
 Derivatives of Logarithmic Functions
 Exponential Growth and Decay
 Related Rates
 Linear Approximations and Differentials
 Hyperbolic Functions
 Applications of Differentiation
 Maximum and Minimum Values
 The Mean Value Theorem
 Indeterminate Forms and l’Hospital’s Rule
 Summary of Curve Sketching
 Optimization Problems
 Newton’s Method
 Antiderivatives
 Integrals
 Areas and Distances
 The Definite Integral
 The Fundamental Theorem of Calculus
 Indefinite Integrals and the Net Change Theorem
 The Substitution Rule
 Applications of Integration
 Areas Between Curves
 Volumes
 Volumes by Cylindrical Shells
 Work
 Average Value of a Function
VII. Techniques of Integration
 Integration by Parts
 Trigonometric Integrals
 Trigonometric Substitution
 Integration of Rational Functions by Partial Fractions
 Strategy for Integration
 Approximate Integration
 Improper Integrals
Statistics (STA 2023)
 Getting Started
 What Is Statistics?
 Random Samples
 Introduction to Experimental Design
 Organizing Data
 Frequency Distributions, Histograms, and Related Topics
 Bar Graphs, Circle Graphs, and TimeSeries Graphs
 StemandLeaf Displays
III. Averages and Variation
 Measures of Central Tendency: Mode, Median, and Mean
 Measures of Variation
 Percentiles and Boxand Whisker Plots
 Correlation and Regression
 Scatter Diagrams and Linear Correlation
 Linear Regression and the Coefficient of Determination
 Elementary Probability Theory
 What is Probability?
 Some Probability Rules – Compound Events
 Tree Diagrams and Counting Techniques
 The Binomial Probability Distribution and Related Topics
 Introduction to Random Variables and Probability Distributions
 Binomial Probabilities
 Additional Properties of Binomial Distributions
VII. Normal Curves and Sampling Distributions
 Graphs of Normal Probability Distributions
 Standard Units and Areas Under the Standard Normal Distribution
 Areas Under Any Normal Curve
 Sampling Distributions
 The Central Limit Theorem
 Normal Approximation to the Binomial Distribution

Proctor Instructions
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