19771978 Meet 1 Frosh


number bases

19771978 Meet 2 Frosh


linear equations

19771978 Meet 3 Frosh


logic puzzles

19771978 Meet 4 Frosh


word problems

19771978 Meet 1 Sophomores


systems of equations

19771978 Meet 2 Sophomores


ratio, proportion, variation

19771978 Meet 3 Sophomores


factoring over the rationals

19771978 Meet 4 Sophomores


right triangle geometry

19771978 Meet 1 Juniors


circles

19771978 Meet 2 Juniors


algebraic word problems

19771978 Meet 3 Juniors


inequalities

19771978 Meet 4 Juniors


algebraic and geometric progressions

19771978 Meet 1 Seniors


complex numbers

19771978 Meet 2 Seniors


trigonometric equations

19771978 Meet 3 Seniors


matrix algebra

19771978 Meet 4 Seniors


probability

19781979 Meet 1 Frosh


probability

19781979 Meet 2 Frosh


Linear equations and inequalities

19781979 Meet 3 Frosh


Modular Arithmetic

19781979 Meet 4 Frosh


word problems

19781979 Meet 5 Frosh


sequences and series

19781979 Meet 1 Sophomores


algebraic equations

19781979 Meet 2 Sophomores


sets and venn diagrams

19781979 Meet 3 Sophomores


Perimeter, Area, Volume

19781979 Meet 4 Sophomores


similar polygons

19781979 Meet 5 Sophomores


right triangles

19781979 Meet 1 Juniors


coordinates

19781979 Meet 2 Juniors


factoring over reals

19781979 Meet 3 Juniors


word problems

19781979 Meet 4 Juniors


progressions

19781979 Meet 5 Juniors


inequalities

19781979 Meet 1 Seniors


logs and exponents

19781979 Meet 2 Seniors


probability

19781979 Meet 3 Seniors


trig

19781979 Meet 4 Seniors


theory of equations

19781979 Meet 5 Seniors


conics

19791980 Meet 1 Frosh


calculation skills

19791980 Meet 2 Frosh


linear equations
Modern Introductory Analysis, Dolciani, et al. section 31; Principals of Advanced Mathematics, Meserve et al. Singer Random House 1970. Section 109

19791980 Meet 3 Frosh


number bases

19791980 Meet 4 Frosh


factoring over rationals

19791980 Meet 1 Sophomores


equations and inequalities

19791980 Meet 2 Sophomores


recreational logic

19791980 Meet 3 Sophomores


perimeter, area

19791980 Meet 4 Sophomores


coordinate geometry

19791980 Meet 1 Juniors


circles

19791980 Meet 2 Juniors


systems

19791980 Meet 3 Juniors


probability

19791980 Meet 4 Juniors


logs and exponents

19791980 Meet 1 Seniors


matrices

19791980 Meet 2 Seniors


trig

19791980 Meet 3 Seniors


complex numbers

19791980 Meet 4 Seniors


differential calculus

19791980 Meet 1 Orals


binomial theorem
Modern Introductory Analysis, Dolciani, et al. section 35

19791980 Meet 2 Orals


mathematical induction

19791980 Meet 3 Orals


DeMoivre's Theorem
Modern Introductory Analysis, Dolciani, et al. Section 1210, pages 498503

19791980 Meet 4 Orals


Applications of Vectors
(Volume of parallelepiped, equation of a sphere plane tangent to sphere, angle between 2 planes, distance from point to plane) (Principles of Advanced Mathematics, Meserve, et al. Singer Random House 1970. Section 1112, pages 646652.)

19801981 Meet 1 Frosh


ratio, proportion, percent

19801981 Meet 2 Frosh


primes and factors

19801981 Meet 3 Frosh


graphing

19801981 Meet 4 Frosh


linear systems

19801981 Meet 5 Frosh


Algebra

19801981 Meet 1 Sophomores


quadratics

19801981 Meet 2 Sophomores


triangles

19801981 Meet 3 Sophomores


quadrilaterals

19801981 Meet 4 Sophomores


angles and polygons

19801981 Meet 5 Sophomores


Geometry

19801981 Meet 1 Juniors


lines

19801981 Meet 2 Juniors


factoring over reals

19801981 Meet 3 Juniors


rational exponents

19801981 Meet 4 Juniors


complex numbers

19801981 Meet 5 Juniors


Algebra

19801981 Meet 1 Seniors


coordinates

19801981 Meet 2 Seniors


polars

19801981 Meet 3 Seniors


limits

19801981 Meet 4 Seniors


derivatives

19801981 Meet 5 Seniors


PreCalculus

19801981 Meet 1 Orals


matrices and determinants
Principles of Advanced Mathematics, Meserve, et al. Singer 1970. Chapter 12, Sections 15

19801981 Meet 2 Orals


sequences and series
Limits, a Transition to Calculus, Buchanan. Houghton Mifflin 1966. Chapter 2, pages 1748

19801981 Meet 3 Orals


areas under a curve
Principles of Advanced Mathematics, Meserve, et al. Singer 1970. Chapter 10, Section 10, pages 573580

19801981 Meet 4 Orals


Max & Min problems
Calculus and Analytic Geometry, Riddle, Wadsworth. 2nd edition. Chapter 20, Sections 34, pages 624634

19811982 Meet 1 Frosh


rational arithmetic

19811982 Meet 2 Frosh

allowed 
prealgebra

19811982 Meet 3 Frosh


linear equations in one variable

19811982 Meet 4 Frosh


word problems (nonquadratic

19811982 Meet 5 Frosh


Algebra

19811982 Meet 1 Sophomores


quadratics

19811982 Meet 2 Sophomores


word problems

19811982 Meet 3 Sophomores


coordinate geometry

19811982 Meet 4 Sophomores


similar triangles

19811982 Meet 5 Sophomores


Geometry

19811982 Meet 1 Juniors


similar triangles

19811982 Meet 2 Juniors


circles

19811982 Meet 3 Juniors


word problems

19811982 Meet 4 Juniors

allowed 
probability

19811982 Meet 5 Juniors


Algebra

19811982 Meet 1 Seniors


word problems

19811982 Meet 2 Seniors

allowed 
probability

19811982 Meet 3 Seniors


trig

19811982 Meet 4 Seniors


theory of equations

19811982 Meet 5 Seniors


PreCalculus

19811982 Meet 1 Orals


polynomial function theory
Modern Introductory Analysis, Dolciani, et al. Chapter 6, sections 59, pages 230248

19811982 Meet 2 Orals


vector and lines
Modern Introductory Analysis, Dolciani, et al. Chapter 5, sections 15, pages 167185

19811982 Meet 3 Orals


probability
Probability and Statistics, Willoughby. Silver Burdett 1968. Chapter 3

19811982 Meet 4 Orals


growth and decay
Calculus and Analytic Geometry, Leithold. Harper & Row 1976. Pages 42027

19821983 Meet 1 Frosh


calculation skills

19821983 Meet 2 Frosh


number bases

19821983 Meet 3 Frosh


linear equations

19821983 Meet 4 Frosh


factoring over rationals

19821983 Meet 5 Frosh



19821983 Meet 1 Sophomores


sets and venn diagrams

19821983 Meet 2 Sophomores


systems

19821983 Meet 3 Sophomores


perimeter, area

19821983 Meet 4 Sophomores


right triangles

19821983 Meet 5 Sophomores



19821983 Meet 1 Juniors


circles

19821983 Meet 2 Juniors


surface area, volume

19821983 Meet 3 Juniors


inequalities

19821983 Meet 4 Juniors


complex numbers

19821983 Meet 5 Juniors



19821983 Meet 1 Seniors


logs and exponents

19821983 Meet 2 Seniors


matrices

19821983 Meet 3 Seniors


trig

19821983 Meet 4 Seniors


functions

19821983 Meet 5 Seniors



19821983 Meet 1 Orals


conics
Modern Introductory Analysis, Dolciani, et al. Houghton Mifflin. Pages 507531

19821983 Meet 2 Orals


sequences and series
Modern Introductory Analysis, Dolciani, et al. Houghton Mifflin. Pages 7587

19821983 Meet 3 Orals


induction
Modern Introductory Analysis, Dolciani, et al. Houghton Mifflin Pages 6974

19821983 Meet 4 Orals


related rates
Elements of Calculus, Thomas. Addison Wesley 1972. Pages 105108

19831984 Meet 1 Frosh


arithmetic topics

19831984 Meet 2 Frosh


primes and factors

19831984 Meet 3 Frosh


Modular Arithmetic

19831984 Meet 4 Frosh


rational expressions

19831984 Meet 5 Frosh



19831984 Meet 1 Sophomores


absolute value

19831984 Meet 2 Sophomores


quadratics

19831984 Meet 3 Sophomores


quadrilaterals

19831984 Meet 4 Sophomores


circles

19831984 Meet 5 Sophomores



19831984 Meet 1 Juniors


similar polygons

19831984 Meet 2 Juniors


coordinate geometry

19831984 Meet 3 Juniors


equations

19831984 Meet 4 Juniors


word problems

19831984 Meet 5 Juniors



19831984 Meet 1 Seniors


probability

19831984 Meet 2 Seniors


theory of equations

19831984 Meet 3 Seniors


trig equations and inequalities

19831984 Meet 4 Seniors


vectors

19831984 Meet 5 Seniors



19831984 Meet 1 Orals


geometry constructions
Geometry for Enjoyment and Challenge, Rhoad, Milauskas, & Whipple. McDougall, Littell 1981 or 1983. Pages 649671

19831984 Meet 2 Orals


Gaussian integers
Enrichment Mathematics for High School, 28th NCTM Yearbook. Pages 4655

19831984 Meet 3 Orals


rational function graphing
Calculus and Analytic Geometry, Riddle, Douglas F. Wadsworth 3rd edition. Pages 99121

19831984 Meet 4 Orals


advanced geometry theorems
Geometry Revisited, Coxeter and Greitzer.Addison Wesley 1967. Pages 126

19841985 Meet 1 Frosh


arithmetic topics

19841985 Meet 2 Frosh


number bases

19841985 Meet 3 Frosh


linear programming

19841985 Meet 4 Frosh


word problems

19841985 Meet 5 Frosh



19841985 Meet 1 Sophomores


equations and inequalities

19841985 Meet 2 Sophomores


factoring over rationals

19841985 Meet 3 Sophomores


perimeter, area

19841985 Meet 4 Sophomores


right triangles

19841985 Meet 5 Sophomores



19841985 Meet 1 Juniors


surface area, volume

19841985 Meet 2 Juniors


systems of equations & inequalities

19841985 Meet 3 Juniors


word problems

19841985 Meet 4 Juniors


complex numbers

19841985 Meet 5 Juniors



19841985 Meet 1 Seniors


logs and exponents

19841985 Meet 2 Seniors


progressions

19841985 Meet 3 Seniors


limits

19841985 Meet 4 Seniors


differential calculus

19841985 Meet 5 Seniors



19841985 Meet 1 Orals


locus
Geometry for Enjoyment and Challenge. Pages 631648

19841985 Meet 2 Orals


binomial theorem
Modern Introductory Analysis. Pages 8894

19841985 Meet 3 Orals


linear programming
Finite Mathematics. Chapter 7 and/or 8

19841985 Meet 4 Orals


convexity
Modern Geometries. First 3 sections of chapter 3)

19851986 Meet 1 Frosh


arithmetic topics

19851986 Meet 2 Frosh


linear equations

19851986 Meet 3 Frosh


primes and factors

19851986 Meet 4 Frosh


word problems

19851986 Meet 5 Frosh


Algebra I

19851986 Meet 1 Sophomores


systems

19851986 Meet 2 Sophomores


principals of counting

19851986 Meet 3 Sophomores


angles and polygons

19851986 Meet 4 Sophomores


similar triangles

19851986 Meet 5 Sophomores


Geometry

19851986 Meet 1 Juniors


circles

19851986 Meet 2 Juniors


probability

19851986 Meet 3 Juniors


coordinate geometry

19851986 Meet 4 Juniors


inequalities

19851986 Meet 5 Juniors


Algebra II

19851986 Meet 1 Seniors


similarity

19851986 Meet 2 Seniors


number theory

19851986 Meet 3 Seniors


trig equations

19851986 Meet 4 Seniors


functions

19851986 Meet 5 Seniors



19861987 Meet 1 Frosh


arithmetic topics

19861987 Meet 2 Frosh


Linear equations and inequalities

19861987 Meet 3 Frosh


number bases

19861987 Meet 4 Frosh


word problems

19861987 Meet 5 Frosh


Algebra I

19861987 Meet 1 Sophomores


quadratics

19861987 Meet 2 Sophomores


word problems

19861987 Meet 3 Sophomores


right angles

19861987 Meet 4 Sophomores


circles

19861987 Meet 5 Sophomores


Geometry

19861987 Meet 1 Juniors


systems of equations & inequalities

19861987 Meet 2 Juniors


coordinate geometry

19861987 Meet 3 Juniors


logs and exponents

19861987 Meet 4 Juniors


sequences and series

19861987 Meet 5 Juniors


Algebra II

19861987 Meet 1 Seniors


similarity

19861987 Meet 2 Seniors


conics

19861987 Meet 3 Seniors


trig

19861987 Meet 4 Seniors


matrices

19861987 Meet 5 Seniors


PreCalculus

19861987 Meet 1 Orals


probability
Modern Introductory Analysis, Dolciani, et al. 1964. Chapter 15, Sections 18, Pages 599626

19861987 Meet 3 Orals


graph theory
An Introduction to Discrete Mathematics, Steven Roman; Saunders College Publishing [383 Madison Avenue, New York, NY 10017] 1986. Chapter 6, sections 13, pages 295334

19871988 Meet 1 Frosh


arithmetic topics

19871988 Meet 2 Frosh


primes and factors

19871988 Meet 3 Frosh


Linear equations and inequalities

19871988 Meet 4 Frosh


word problems

19871988 Meet 5 Frosh



19871988 Meet 1 Sophomores


sets and venn diagrams

19871988 Meet 2 Sophomores


systems

19871988 Meet 3 Sophomores


angles and polygons

19871988 Meet 4 Sophomores


similar triangles

19871988 Meet 5 Sophomores



19871988 Meet 1 Juniors


surface area, volume

19871988 Meet 2 Juniors


absolute value

19871988 Meet 3 Juniors


statistics

19871988 Meet 4 Juniors


quadratics

19871988 Meet 5 Juniors


Algebra II

19871988 Meet 1 Seniors


probability

19871988 Meet 2 Seniors


functions

19871988 Meet 3 Seniors


trig

19871988 Meet 4 Seniors


limits

19871988 Meet 5 Seniors



19871988 Meet 1 Orals


sets, onetoone correspondence, countable and uncountable sets
An Introduction to Discrete Mathematics, Steven Roman. Saunders College Publishing [383 Madison Avenue, New York, NY 10017] 1986, Chapter 1, sections 13, pages 135

19871988 Meet 2 Orals


mathematics of matrices
Mathematics of Matrices, by Davis. 1965. Pages 125158

19871988 Meet 3 Orals


geometric transformations
Modern Geometries, James Smart. Brooks Cole Pub. Co. [Monteray, CA 93940] 2nd edition. Sections 2.12.4, pages 3357

19871988 Meet 4 Orals


logic and logic circuits
An Introduction to Discrete Mathematics, Steven Roman. Saunders College Publishing [383 Madison Avenue, New York, NY 10017] 1986. Chapter 2, sections 14, pages 6197

19881989 Meet 1 Frosh


ration, proportion, percent

19881989 Meet 2 Frosh


formula

19881989 Meet 3 Frosh


simple probability

19881989 Meet 4 Frosh


data analysis

19881989 Meet 5 Frosh


Algebra I

19881989 Meet 1 Sophomores


functions

19881989 Meet 2 Sophomores


ratio, proportion

19881989 Meet 3 Sophomores


right triangles

19881989 Meet 4 Sophomores


circles

19881989 Meet 5 Sophomores


Geometry

19881989 Meet 1 Juniors


coordinate geometry

19881989 Meet 2 Juniors


parabolas

19881989 Meet 3 Juniors


logs and exponents

19881989 Meet 4 Juniors


binomial theorem

19881989 Meet 5 Juniors


Algebra II

19881989 Meet 1 Seniors


polynomial equations

19881989 Meet 2 Seniors


trig

19881989 Meet 3 Seniors


vectors

19881989 Meet 4 Seniors


Max & Min problems

19881989 Meet 5 Seniors


PreCalculus

19881989 Meet 1 Orals


geometric probability
UMAP Module 660: Applications of High School Mathematics in Geometric Probability, Richard Dalke and Robert Falkner.)

19881989 Meet 2 Orals


euclidean geometry of the polygon and circle
Modern Geometries, James Smart. Brooks Cole Pub. Co. [Monteray, CA 93940] 2nd edition. Sections 4.14.3; p. 127147

19881989 Meet 3 Orals


combinatorics
An Introduction to Discrete Mathematics, Steven Roman. Saunders College Publishing [383 Madison Avenue, New York, NY 10017] 1986. Chapter 4, sections 18, pages 167221

19881989 Meet 4 Orals


applications of the derivative
Max/Min, Related Rates, Rolle?s Theorem, Mean Value Theorem.) (Calculus and Analytic Geometry, Thomas & Finney. Addison Wesley 6th edition. Chapter 3, sections 58, pages 205231)

19881989 Meet 1 Essay



19881989 Meet 2 Essay



19881989 Meet 3 Essay



19881989 Meet 4 Essay



19891990 Meet 1 Frosh


arithmetic topics
Geometry For Enjoyment And Challenge, Rhoad, Milauskas and Whipple. McDougall Littell.)

19891990 Meet 2 Frosh


primes and factors

19891990 Meet 3 Frosh


Linear equations and inequalities

19891990 Meet 4 Frosh


probability

19891990 Meet 5 Frosh



19891990 Meet 1 Sophomores


sets and venn diagrams

19891990 Meet 2 Sophomores


applications of algebra to geometry

19891990 Meet 3 Sophomores


2D similarity

19891990 Meet 4 Sophomores


perimeter, area

19891990 Meet 5 Sophomores



19891990 Meet 1 Juniors


geometric probability

19891990 Meet 2 Juniors


absolute value

19891990 Meet 3 Juniors


logs and exponents

19891990 Meet 4 Juniors


sequences and series

19891990 Meet 5 Juniors



19891990 Meet 1 Seniors


functions

19891990 Meet 2 Seniors


trig with applications

19891990 Meet 3 Seniors


combinatorics

19891990 Meet 4 Seniors


analysis of graphs (with calculus)

19891990 Meet 5 Seniors



19891990 Meet 2 Orals


graph theory
Discrete Mathematics, Roman

19901991 Meet 1 Frosh


arithmetic topics

19901991 Meet 2 Frosh


number bases

19901991 Meet 3 Frosh


data analysis

19901991 Meet 4 Frosh


ratio, proportion

19901991 Meet 5 Frosh



19901991 Meet 1 Sophomores


functions

19901991 Meet 2 Sophomores


ratio, proportion, variation

19901991 Meet 3 Sophomores


right triangles

19901991 Meet 4 Sophomores


surface area

19901991 Meet 5 Sophomores



19901991 Meet 1 Juniors


circles

19901991 Meet 2 Juniors


onevariable inequalities with absolute value

19901991 Meet 3 Juniors


applications of quadratics and graph analysis

19901991 Meet 4 Juniors


logs and exponents

19901991 Meet 5 Juniors



19901991 Meet 1 Seniors


polynomial equations

19901991 Meet 2 Seniors


trig

19901991 Meet 3 Seniors


advanced probability including combinatorics

19901991 Meet 4 Seniors


Max & Min problems

19901991 Meet 5 Seniors



19901991 Meet 1 Orals


linear programming
Finite Mathematics, Lial, Miller

19901991 Meet 2 Orals


sets, onetoone correspondence, countable and uncountable sets
Discrete Mathematics, Roman

19901991 Meet 3 Orals


probability
Finite Mathematics, Weiss, Yoseloff

19901991 Meet 4 Orals


mathematics of matrices
Mathematics of Matrices, Davis

19901991 Meet 4 GraphingCalculatorContest



19911992 Meet 1 Frosh


perimeter, area

19911992 Meet 2 Frosh


basic counting principals

19911992 Meet 3 Frosh


Linear equations and inequalities

19911992 Meet 4 Frosh


quadratics

19911992 Meet 5 Frosh



19911992 Meet 1 Sophomores


quadratics

19911992 Meet 2 Sophomores


algeba/geometry connections
Analytic Geometry, Gordon Fuller. Addison Wesley. Chapter 7 [6th edition] or Chapter 6 [5th edition])

19911992 Meet 3 Sophomores


geomtric probability

19911992 Meet 4 Sophomores


regular polygons

19911992 Meet 5 Sophomores



19911992 Meet 1 Juniors


similarity

19911992 Meet 2 Juniors


rational functions

19911992 Meet 3 Juniors


logs and exponents

19911992 Meet 4 Juniors


linear diophantine equations

19911992 Meet 5 Juniors



19911992 Meet 1 Seniors


coordinate geometry

19911992 Meet 2 Seniors


trig

19911992 Meet 3 Seniors

allowed 
graphs of functions

19911992 Meet 4 Seniors


vectors

19911992 Meet 5 Seniors



19911992 Meet 1 Orals


polar coordinates

19911992 Meet 2 Orals


mathematical induction
Discrete Mathematics, John Dossey, Scott Foresman. Sections 2.5 and 2.6

19911992 Meet 3 Orals


growth and decay
Calculus and Analytic Geometry, Leithold, Harper, and Row. Section 6.6 [5th edition] or section 7.7 [6th edition].)

19911992 Meet 4 Orals


markov chains
Finite Mathematics, Lial and Miller. Scott Foresman 4th edition. Chapter 8

19911992 Meet 3 GraphingCalculatorContest



19921993 Meet 1 Frosh


ratio, proportion, percent

19921993 Meet 2 Frosh


algebra/geometry applications

19921993 Meet 3 Frosh


sets and venn diagrams

19921993 Meet 4 Frosh


linear equations

19921993 Meet 5 Frosh


Algebra I

19921993 Meet 1 Sophomores


linear systems

19921993 Meet 2 Sophomores


geometric probability

19921993 Meet 3 Sophomores


similarity

19921993 Meet 4 Sophomores


circles

19921993 Meet 5 Sophomores


Geometry

19921993 Meet 1 Juniors


right triangle trig

19921993 Meet 2 Juniors


combinations and permutations

19921993 Meet 3 Juniors


Max & Min problems

19921993 Meet 4 Juniors


logs and exponents

19921993 Meet 5 Juniors


Algebra II

19921993 Meet 1 Seniors


3D Geometry: area and volume

19921993 Meet 2 Seniors

allowed 
trig applications

19921993 Meet 3 Seniors


sequences and series

19921993 Meet 4 Seniors


advanced probability

19921993 Meet 5 Seniors


PreCalculus

19921993 Meet 1 Orals


combinatorial analysis
Finite Mathematics, Weiss and Youseloff. Worth Pub. 1975. Chapter 3

19921993 Meet 2 Orals


set theory
Finite Mathematics; Weiss & Youseloff, Worth Pub. 1975. Chapter 2

19921993 Meet 3 Orals


iteration
Chaos, Fractals, and Dynamics, Robert Devaney. Addison Wesley. Chapters 1 and 2

19921993 Meet 4 Orals


groups and graphs
Groups & Their Graphs, Grossman and Mangus. MAA New Mathematical Library, Book 14. Pages 355

19931994 Meet 1 Frosh


nonalgebraic word problems

19931994 Meet 2 Frosh


linear equations

19931994 Meet 3 Frosh


coordinate geometry

19931994 Meet 4 Frosh


quadratics

19931994 Meet 5 Frosh


Algebra I

19931994 Meet 1 Sophomores


functions

19931994 Meet 2 Sophomores


coordinate geometry

19931994 Meet 3 Sophomores


similarity

19931994 Meet 4 Sophomores


right triangles

19931994 Meet 5 Sophomores


Geometry

19931994 Meet 1 Juniors


locus

19931994 Meet 2 Juniors


surface area, volume

19931994 Meet 3 Juniors


logs and exponents

19931994 Meet 4 Juniors


rational functions

19931994 Meet 5 Juniors


Algebra II

19931994 Meet 1 Seniors


operations on functions

19931994 Meet 2 Seniors


probability

19931994 Meet 3 Seniors


rational equations and inequalities

19931994 Meet 4 Seniors


polars

19931994 Meet 5 Seniors


PreCalculus

19931994 Meet 1 Orals


parametric equations
Analytic Geometry, Gordon Fuller. Addison Wesley. Chapter 8 [6th edition] or Chapter 7 [5th edition])

19931994 Meet 2 Orals


induction
Discrete Algorithmic Mathematics, Stephen Maurer and Anthony Ralston. Addison Wesley 1991. Sections 2.12.5, pages 137178

19931994 Meet 3 Orals


statistics and probability distributions
Finite Mathematics, Lial and Miller. Scott Foresman. Sections 7.17.4

19931994 Meet 4 Orals


fractals
Fractals for the Classroom, volume 2. NCTM Publication

19941995 Meet 1 Frosh


ratio, proportion, percent

19941995 Meet 2 Frosh


number theory

19941995 Meet 3 Frosh


word problems

19941995 Meet 4 Frosh


algebra/geometry applications

19941995 Meet 5 Frosh


Algebra I

19941995 Meet 1 Sophomores


sets and venn diagrams

19941995 Meet 2 Sophomores


systems of equations and inequalities

19941995 Meet 3 Sophomores


similarity

19941995 Meet 4 Sophomores


Perimeter, Area, Volume

19941995 Meet 5 Sophomores


Geometry

19941995 Meet 1 Juniors


similarity

19941995 Meet 2 Juniors


probability

19941995 Meet 3 Juniors


logs and exponents

19941995 Meet 4 Juniors


analysis of functions

19941995 Meet 5 Juniors


Algebra II

19941995 Meet 1 Seniors


sequences and series

19941995 Meet 2 Seniors


trig

19941995 Meet 3 Seniors


vector analytic graphing

19941995 Meet 4 Seniors


Max & Min problems

19941995 Meet 5 Seniors


PreCalculus

19941995 Meet 1 Orals


digraphs and networks
Finite Mathematics, by Lial and Miller. Scott Foresman. Chapter 11

19941995 Meet 2 Orals


difference equations
Discrete Algorithmic Mathematics, Stephen Maurer and Anthony Ralston. Addison Wesley 1991. Sections 5.1 ? 5.5.)

19941995 Meet 3 Orals


theory of congruences
Elementary Number Theory, David M. Burton. William C. Brown Pub. 3rd edition. Chapter 4.)

19941995 Meet 4 Orals


error correcting codes
Elementary Number Theory, David M. Burton. William C. Brown Pub. 3rd edition. Chapter 4.)

19951996 Meet 1 Frosh


perimeter, area

19951996 Meet 2 Frosh


simple probability

19951996 Meet 3 Frosh


sets and venn diagrams

19951996 Meet 4 Frosh


Linear equations and inequalities

19951996 Meet 5 Frosh


Algebra I

19951996 Meet 1 Sophomores


linear systems

19951996 Meet 2 Sophomores


geometric probability

19951996 Meet 3 Sophomores


coordinate geometry

19951996 Meet 4 Sophomores


similarity

19951996 Meet 5 Sophomores


Geometry

19951996 Meet 1 Juniors


circles

19951996 Meet 2 Juniors


2D and 3D locus

19951996 Meet 3 Juniors


functions

19951996 Meet 4 Juniors


sequences and series

19951996 Meet 5 Juniors


Algebra II

19951996 Meet 1 Seniors


triangle trig

19951996 Meet 2 Seniors


precalculus word problems

19951996 Meet 3 Seniors

none 
limits

19951996 Meet 4 Seniors


polars

19951996 Meet 5 Seniors


PreCalculus

19951996 Meet 1 Orals


graph theory
An Introduction to Discrete Mathematics, Steven Roman. Saunders College Pub. 1986. Sections 6.16.3

19951996 Meet 2 Orals


linear programming: The simplex method
Finite Mathematics, Lial and Miller. Scott Foresman 4th edition. Sections 4.14.4 [Chapter 3 may need to be read as well for background]

19951996 Meet 3 Orals


logic
Discrete Algorithmic Mathematics, Stephen Maurer and Anthony Ralston. Addison Wesley 1991. Sections 7.17.5

19951996 Meet 4 Orals


taxicab geometry
Taxicab Geometry, an Adventure in NonEuclidean Geometry, Eugene Krause. Dover Publications. Chapters 15.)

19961997 Meet 1 Frosh


perimeter, area

19961997 Meet 2 Frosh


number bases

19961997 Meet 3 Frosh


linear equations

19961997 Meet 4 Frosh


quadratics

19961997 Meet 5 Frosh


Algebra I

19961997 Meet 1 Sophomores


quadratics

19961997 Meet 2 Sophomores


Perimeter, Area, Volume

19961997 Meet 3 Sophomores


similarity

19961997 Meet 4 Sophomores


coordinate geometry

19961997 Meet 5 Sophomores


Geometry

19961997 Meet 1 Juniors


matrices with applications

19961997 Meet 2 Juniors


surface area, volume

19961997 Meet 3 Juniors


triangle trig

19961997 Meet 4 Juniors


logs and exponents

19961997 Meet 5 Juniors


Algebra II

19961997 Meet 1 Seniors


probability

19961997 Meet 2 Seniors


trig equations and functions

19961997 Meet 3 Seniors


parametrics

19961997 Meet 4 Seniors


vector analytic graphing

19961997 Meet 5 Seniors


PreCalculus

19961997 Meet 1 Orals


induction
(Discrete Math, John Dossey, et al. Scott Foresman, Sections 2.5 and 2.6

19961997 Meet 2 Orals


matrix games
Finite Mathematics, Weiss and Youseloff. Worth Pub. 1975. Pages 479521

19961997 Meet 3 Orals


groups
Contemporary Abstract Algebra, Joseph A. Gallian. D.C. Heath 3rd edition, 1994. Pages 2367. [ISBN #0669339075] [There is a solution manual available as well.])

19961997 Meet 4 Orals


mathematics in medicine
Contemporary Applied Mathematics, Sacco, Copes, Sloyer, and Stark. Jansen Publications [ISBN #: 0939765063] [There is also a teacher's guide available.]) (UMAP Module 456 Genetic Counseling) (UMAP Modules 105 and 109 Food Service Management Applications of Matrix Methods: Food Service and Dietary Requirements

19971998 Meet 1 Frosh

none 
number bases

19971998 Meet 2 Frosh


basic counting principals

19971998 Meet 3 Frosh


coordinate geometry

19971998 Meet 4 Frosh


Linear equations and inequalities

19971998 Meet 5 Frosh


Algebra I

19971998 Meet 1 Sophomores

none 
coordinate geometry

19971998 Meet 2 Sophomores


geometric probability

19971998 Meet 3 Sophomores


Perimeter, Area, Volume

19971998 Meet 4 Sophomores


triangle trig

19971998 Meet 5 Sophomores


Geometry

19971998 Meet 1 Juniors

none 
manipulation of algebraic expressions and equations

19971998 Meet 2 Juniors


similarity

19971998 Meet 3 Juniors


sequences and series

19971998 Meet 4 Juniors


probability

19971998 Meet 5 Juniors


Algebra II

19971998 Meet 1 Seniors

none 
functions

19971998 Meet 2 Seniors

none 
Max & Min problems

19971998 Meet 3 Seniors


trig

19971998 Meet 4 Seniors


parametrics

19971998 Meet 5 Seniors


PreCalculus

19971998 Meet 1 Orals


iteration, Chaos, Fractals and Dynamics
Chaos, Fractals, and Dynamics, Robert Devaney. Addison Wesley 1990 [ISBN #020123288X]. Chapters 1 and 2

19971998 Meet 2 Orals


transformations
Mathematics of Matrices, Phillip Davis. Ginn and Co. 1965. [Library of Congress #6424818] Sections 4.1  4.5

19971998 Meet 3 Orals


differential equations
Calculus, Deborah HughesHallet et al. John Wiley and Sons 1994. Sections 9.19.8, pages 477552

19971998 Meet 4 Orals


mathematics in politics
Mathematics in Politics  Strategies, Voting, Power, and Proof, Allen D. Taylor. [ISBN #0387943919] Chapters 1 and 2.

19981999 Meet 1 Frosh

none 
ratio, proportion, percent

19981999 Meet 2 Frosh


applications of algebra to junior high geometry

19981999 Meet 3 Frosh


coordinate geometry

19981999 Meet 4 Frosh


linear systems of equations and inequalities

19981999 Meet 5 Frosh


Algebra I

19981999 Meet 1 Sophomores

none 
equations and inequalities

19981999 Meet 2 Sophomores


exponents with applications

19981999 Meet 3 Sophomores


similarity

19981999 Meet 4 Sophomores


circles

19981999 Meet 5 Sophomores


Geometry

19981999 Meet 1 Juniors

none 
similarity

19981999 Meet 2 Juniors


linear, quadratic, and rational functions

19981999 Meet 3 Juniors


probability

19981999 Meet 4 Juniors


triangle trig

19981999 Meet 5 Juniors


Algebra II

19981999 Meet 1 Seniors

none 
logs and exponents

19981999 Meet 2 Seniors


optimization

19981999 Meet 3 Seniors


trig

19981999 Meet 4 Seniors


vectors

19981999 Meet 5 Seniors


PreCalculus

19981999 Meet 1 Orals


markov chains
Finite Mathematics, Lial and Miller. Scott Foresman 4th edition. Chapter 8

19981999 Meet 2 Orals


groups
Contemporary Abstract Algebra, Joseph A. Gallian. D.C. Heath 3rd edition, 1994. Pages 2367. [ISBN #0669339075] [There is a solution manual available as well

19981999 Meet 3 Orals


induction
Discrete Math, John Dossey, et al. Scott Foresman. Sections 2.5 and 2.6.

19981999 Meet 4 Orals


topics in geometry
Discrete Math, John Dossey, et al. Scott Foresman. Sections 2.5 and 2.6.

19992000 Meet 1 Frosh


modular arithmetic

19992000 Meet 2 Frosh


basic counting principals and simple probability

19992000 Meet 3 Frosh


linear equations

19992000 Meet 4 Frosh


word problems

19992000 Meet 5 Frosh


Algebra I

19992000 Meet 1 Sophomores


absolute value equations and inequalities

19992000 Meet 2 Sophomores


geometric probability

19992000 Meet 3 Sophomores


right triangle trig with applications

19992000 Meet 4 Sophomores


similarity

19992000 Meet 5 Sophomores


Geometry

19992000 Meet 1 Juniors


coordinate geometry

19992000 Meet 2 Juniors


algebraic word problems

19992000 Meet 3 Juniors


analysis of polynomials

19992000 Meet 4 Juniors


logs and exponents

19992000 Meet 5 Juniors


Algebra II

19992000 Meet 1 Seniors


trig equations

19992000 Meet 2 Seniors


sequences and series

19992000 Meet 3 Seniors


complex numbers

19992000 Meet 4 Seniors


probability

19992000 Meet 5 Seniors


PreCalculus

19992000 Meet 1 Orals


parametric equations
Analytic Geometry, Gordon Fuller. 7th edition. Chapter 8

19992000 Meet 2 Orals


linear diophantine equations
Linear Systems  Beyond the Unique Solution, Wally Dodge and Paul Sally

19992000 Meet 3 Orals


linear transformations of the plane
Mathematics of Matrices, Phillip David. Ginn and Co. Sections 4.14.5

19992000 Meet 4 Orals


geometric inversions
Excursions in Geometry, C. Stanley Ogilvy. Chapters 3 and 4

20002001 Meet 1 Frosh

none 
number bases
includes conversion and computation in different bases (bases from 2  16); finding the base given some information.

20002001 Meet 2 Frosh


volume, surgace area, and 3D visualization
Nets (A good print source is the Merrill Geometry book by Burrill, Cummins, Kanold, and Yunker; a good internet source is www.peda.com/poty), cones, prisms, cylinders, regular right pyramids, spheres, area as ?apothem*perimeter

20002001 Meet 3 Frosh


systems of equations
linear and nonlinear  with applications  limited to two variables. May include absolute value. Students should know how to solve a non?linear system graphically and should know vocabulary such as consistent, inconsistent, dependent, independent.

20002001 Meet 4 Frosh


quadratic functions and equations with applications

20002001 Meet 5 Frosh


Algebra I

20002001 Meet 1 Sophomores

none 
sets and venn diagrams

20002001 Meet 2 Sophomores


coordinate geometry
including equations of circles. (Radius perpendicular to tangent) Students should be able to complete the square.

20002001 Meet 3 Sophomores


similarity
linear and nonlinear  with applications  limited to two variables. May include absolute value. Students should know how to solve a non?linear system graphically and should know vocabulary such as consistent, inconsistent, dependent, independent.

20002001 Meet 4 Sophomores


triangle trig
includes Law of Sines and Law of Cosines, as well as area of triangles. (May include ambiguous case)

20002001 Meet 5 Sophomores


Geometry

20002001 Meet 1 Juniors

none 
circles
Standard material including arcs, angles, area, power theorems, inscribed and circumscribed polygons, sectors, and segments. Does not include trig or equations of circles.

20002001 Meet 2 Juniors


algebra of functions
includes piecewise; no trig, no exponents, no logs

20002001 Meet 3 Juniors


sequences and series
may include sequences and series defined by recursion, iteration, or pattern; may include arithmetic and geometric sequences and series.

20002001 Meet 4 Juniors


matrices
Basic operations and applications involving transformations of the plane including rotations about the origin, reflections over lines and through the origin, sheers, dilations.

20002001 Meet 5 Juniors


Algebra II

20002001 Meet 1 Seniors

none 
theory of equations
including factor, remainder, and rational root theorems; upper bounds, coefficient analysis; determining equations given various info.

20002001 Meet 2 Seniors


3D Geometry: area and volume

20002001 Meet 3 Seniors


parametrics
equations and graphs defined parametrically (no calculus)

20002001 Meet 4 Seniors


conics
including polars and eccentricity, no parametrics or rotations

20002001 Meet 5 Seniors


PreCalculus

20002001 Meet 1 Orals


graph theory
Histomap Module 21: "Drawing Pictures with One Line," Darrah Chavey. COMAP, 1992 (ISSN: 08892652) (Suite 210, 57 Bedford St., Lexington, Ma. 021734496

20002001 Meet 2 Orals


rings and integral domains
Contemporary Abstract Algebra, Joseph A. Gallian, D.C. Heath, 3rd edition, 1994, Chapters 12,13,14 (ISBN#: 0669339075) (There is a solution manual available as well

20002001 Meet 3 Orals


logic
Discrete Algorithmic Mathematics, Stephen Maurer and Anthony Ralston: Addison Wesley; 1991; Sections 7.17.3,7.5

20002001 Meet 4 Orals


linear transformation of the plane
Mathematics of Matrices, Phillip Davis, Ginn and Co., 1965, Library of Congress: 6424818, Pages 125161 (Out of Print)

20012002 Meet 1 Frosh

none 
number theory
may include patterns (such as trailing zeros), factors, primes, divisibility rules, prime factors of powers, unique factorization, LCM, GCD, and their relationships.

20012002 Meet 3 Frosh

graphing 
Linear equations and inequalities
includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.

20012002 Meet 4 Frosh

graphing 
quadration functions and equations with applications
no complex numbers

20012002 Meet 5 Frosh

graphing 
Algebra I

20012002 Meet 1 Sophomores

none 
coordinate geometry
includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications. No circles.

20012002 Meet 2 Sophomores

graphing 
coordinate probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11.

20012002 Meet 3 Sophomores

graphing 
similarity
the standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem.

20012002 Meet 4 Sophomores

graphing 
advanced geometry topics
restricted to: Brahmagupta?s formula, point to line distance formula, area of a triangle given vertices, Stewart?s Theorem, Ptolemy?s Theorem, Mass points, inradius and circumradius, Ceva?s Theorem, and Theorem of Menelaus. A good reference would be Geometry by Rhoad, Milauskas, and Whipple, Chapter 16

20012002 Meet 5 Sophomores

graphing 
Geometry

20012002 Meet 1 Juniors

none 
3D space geometry, surface area, volume and distance formula
This is a geometry topic, not a vector topic. It does not include writing equations of planes and lines in space. It does include representation of points on a 3D coordinate system, as well as finding volumes and surface areas of all sorts of different shapes. It assumes a knowledge of special right triangles and the ability to use them in 3space.

20012002 Meet 2 Juniors

graphing 
probability
This is the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution, expected value, nor geometric probability.

20012002 Meet 3 Juniors

graphing 
logs and exponents including applications
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, exponential and logarithmic growth and decay. No complex numbers.

20012002 Meet 4 Juniors

graphing 
analysis of polynomials
including factor, remainder, and rational root theorems; coefficient analysis; determining equations given various information.

20012002 Meet 5 Juniors

graphing 
Algebra II

20012002 Meet 1 Seniors

none 
sequences and series
including but not restricted to sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series.

20012002 Meet 2 Seniors

CAS 
probability
may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability.

20012002 Meet 3 Seniors

CAS 
trig applications
including laws of sines and cosines, sinusoidal functions and, of course, word problems.

20012002 Meet 4 Seniors

CAS 
conics
including polars and eccentricity. There should be no parametrics nor rotations.

20012002 Meet 5 Seniors

CAS 
PreCalculus

20012002 Meet 1 Orals


markov chains
Finite Mathematics by Lial and Miller, Scott Foresman, 4th edition, Chapter 8.

20012002 Meet 2 Orals


induction
Discrete Math by John Dossey et al, Scott Foresman, Sections 2.52.6

20012002 Meet 3 Orals


perfect numbers
Excursions into Mathematics by Beck, Bleicher, and Crowe, A.K. Peters, LTd. (ISBM: 1568811152), Chapter 2, Sections 15

20012002 Meet 4 Orals


Geometry, Geometric Inequalities
Geometric Inequalities by Kazarinoff, MAA, Chapter 2

20022003 Meet 1 Frosh

graphing 
linear equations
including word problems leading to linear equations in one variable and simple absolute value equations. (No systems)

20022003 Meet 2 Frosh

none 
number bases
including conversion and computation in different bases and finding the base given some information.

20022003 Meet 3 Frosh

graphing 
basic counting principals and simple probability
including tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. Question writers are aware that this is an unfamiliar topic for freshmen.

20022003 Meet 4 Frosh

none 
rational expressions
simplifying rational expressions, solving equations involving rational expressions, word problems, basic algebra 1 factoring.

20022003 Meet 5 Frosh

graphing 
Algebra I

20022003 Meet 1 Sophomores

graphing 
applications of algebra to basic plane geometry
May include area, perimeter, similarity, Pythagorean theorem, the coordinate plane (but not graphing equations), parallel line relationships, angle sums of triangles and quadrilaterals, isosceles triangle theorems, supplements, and complements. Does not require an extensive knowledge of geometry.

20022003 Meet 2 Sophomores

none 
logic, sets, and venn diagrams
Notation, intersection, union, subsets, empty set, complements, universal set, cardinality, solution sets, and number of subsets (no power sets). Should include classic type Venn diagram problems involving how many things are in various intersections (i.e. If 23 students take chemistry and 37 take math and altogether there are 45 students in either, how many take both math and chemistry?). Emphasis for logic is on using logic, not formal vocabulary. No truth tables.

20022003 Meet 3 Sophomores

graphing 
geometric probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11.

20022003 Meet 4 Sophomores

none 
similarity
The standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem.

20022003 Meet 5 Sophomores

graphing 
Geometry

20022003 Meet 1 Juniors

graphing 
circles
standard material including power theorems, arcs, angles, area, inscribed and circumscribed polygons, sectors and segments, and equations of circles. No trig.

20022003 Meet 2 Juniors

none 
probability
This is the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution or expected value.

20022003 Meet 3 Juniors

graphing 
logs and exponents including applications
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, exponential and logarithmic growth and decay. No complex numbers.

20022003 Meet 4 Juniors

none 
algebra of complex numbers
Simplifying and factoring, solving linear and quadratic equations with complex coefficients, solving linear systems with complex coefficients, square roots of complex numbers, powers of pure imaginary numbers, absolute value of complex numbers and simple Argand diagrams. Does not include vectors, polars, or DeMoivre?s Theorem.

20022003 Meet 5 Juniors

graphing 
Algebra II

20022003 Meet 1 Seniors

CAS 
PreCalculus
including interest, regression, growth and decay, linear quadratic and exponential relations. Excludes trig applications.

20022003 Meet 2 Seniors

none 
sequences and series
including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series.

20022003 Meet 3 Seniors

CAS 
probability
may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability.

20022003 Meet 4 Seniors

none 
limits of functions
includes all standard functions, i.e. rational, logarithmic, exponential and trig. May include slant as well as horizontal and vertical asymptotes. Will not include sequences and series.

20022003 Meet 5 Seniors

CAS 
PreCalculus

20022003 Meet 1 Orals


polar coordinates and equations
Analytic Geometry, 7th edition, by Gordon Fuller and Dalton Tarwalter, Ch 7. This does not include the polar conics. (This is chapter 6 in the 5th edition, but content is consistent. edition. Chapter 8

20022003 Meet 2 Orals


taxicab geometry
Taxicab Geometry, an Adventure in NonEuclidean Geometry, Eugene Krause. Dover Publications. Chapters 25 (pp.1249)

20022003 Meet 3 Orals


matrix games
excursions into Mathematics by Beck, Bleicher, and Crowe, chapter 5, sections 6 & 7

20022003 Meet 4 Orals


conic sections
there was no set source for this topic; contestants could use whatever source they liked. The ICTM specified the information they needed to know, though.

20032004 Meet 1 Frosh

graphing 
ratios, proportions, and percent
may include money, interest, discounts, unit conversions, percents of increase, decrease and error, and direct variations. It should not require knowledge of algebra and does not include advanced problem solving skills. While the questions should not be trivial, they should be approachable to most contestants.

20032004 Meet 2 Frosh

none 
sets and venn diagrams
Notation, intersection, union, subsets, empty set, complements, universal set, cardinality, solution sets, and number of subsets. Does not include power sets.

20032004 Meet 3 Frosh

graphing 
applications of systems of linear equations and inequalities
including linear programming limited to considering the vertices of an enclosed area.

20032004 Meet 4 Frosh

none 
applying algebra to geometry problems
geometry including area, Pythagorean. Theorem, coordinate plane (no graphing equations), angle sums of triangles and quads, Isosceles Triangle theorems, parallel line relationships, supplements, and complements. The emphasis here should be on the algebraic representation of geometric relationships. Problems should yield linear equations and perhaps a simple quadratic equation.

20032004 Meet 5 Frosh

graphing 
Algebra I

20032004 Meet 1 Sophomores

graphing 
coordinate geometry with applications
includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications (no circles).

20032004 Meet 2 Sophomores

none 
area, perimeter, and volume
standard geometric formulas including ratio relationships between linear measurements, area, and volume. Students should be familiar with vocabulary of solids such as slant height and apothem. Could include any geometric shape that can be approached by standard formulas or special right triangles. Will not require trig or similarity.

20032004 Meet 3 Sophomores

graphing 
geometric probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11.

20032004 Meet 4 Sophomores

none 
geometry of the right triangle including trigonometry
Trig restricted to sine, cosine, and tangent in degrees only; includes values of special angles.

20032004 Meet 5 Sophomores

graphing 
Geometry

20032004 Meet 1 Juniors

graphing 
algebra of matrices and determinants
including linear transformations which can include solving large systems of equations, operations of matrices including row reduction, using matrix inverses, and transition matrices. Possible sources: Chapters on Systems and Linear Programming in Mathematics with Applications (6th, 7th, or 8th Editions) by Lial & Hungerford (AddisonWesley). See also Sections 8.6 & 8.7 in Advanced Algebra Through Data Exploration by Murdock, Kamischke, and Kamischke (Key Curriculum). Clarification: There will be no questions on the Simplex method, linear programming, Leontief model problems. (Essentially, none of the material in chapter 8 of the Applications book will be tested.) There will be at least one question about transition matrices. There will be at least one question that can not be done without a calculator.

20032004 Meet 2 Juniors

none 
probability
this is the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution or expected value.

20032004 Meet 3 Juniors

graphing 
triangle trig
includes right triangle trig, laws of sines and cosines, area of a triangle, and Hero's Formula

20032004 Meet 4 Juniors

none 
logs and exponents
with Applications may include domain and range, graphing, logarithms with positive bases including natural and base ten logs, exponential logarithmic growth and decay. (No complex numbers)

20032004 Meet 5 Juniors

graphing 
Algebra II

20032004 Meet 1 Seniors

CAS 
probability
may include combinations, permutations, mutually exclusive events, conditional probability, Bayes' Theorem, binomial distribution, expected value, and some simple geometric probability.

20032004 Meet 2 Seniors

none 
theory of equations
including factor, remainder, and rational root theorems; upper bounds, coefficient analysis; determining equations given various info.

20032004 Meet 3 Seniors

CAS 
conics
including locus definitions, eccentricity, directrix, no parametrics, no polar, and no rotations.

20032004 Meet 4 Seniors

none 
sequences and series
including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series.

20032004 Meet 5 Seniors

CAS 
PreCalculus

20032004 Meet 1 Orals


theory of congruences
Elementary Number Theory, David M. Burton. William C. Brown Pub. 3rd edition. Chapter 4.) (A new edition of this was released in 2001 and is available at Amazon. Check the used books section for some good deals.)

20032004 Meet 2 Orals


vectors
Analytic Geometry, 7th edition, by Gordon Fuller and Dalton Tarwalter, Ch 10. (In earlier editions, this is still Ch. 10)

20032004 Meet 3 Orals


combinatorics
An Introduction to Discrete Mathematics, Steven Roman. Ch. 4, sections 18, and Ch. 5 sections 1 & 2

20032004 Meet 4 Orals


markov chains
Finite Mathematics7th edition, by Lial, Greenwell, and Ritchey (Pearson Addison Wesley, 2002). Ch. 10, Sections 12 (p. 490  510).

20042005 Meet 1 Frosh

graphing 
area & perimeter
including squares, triangles, rectangles, circles, and shapes made from these. May include the Pythagorean Theorem.

20042005 Meet 2 Frosh

none 
number bases
including conversion and computation in different bases (bases from 2 to 16); finding the base given some information.

20042005 Meet 3 Frosh

graphing 
basic counting principals and simple probability
including tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. Question writers are aware that this is an unfamiliar topic for freshmen.

20042005 Meet 4 Frosh

none 
Linear equations and inequalities
includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.

20042005 Meet 5 Frosh

graphing 
Algebra I

20042005 Meet 1 Sophomores

graphing 
quadratic functions
including domain, range, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. Graphing calculator required.

20042005 Meet 2 Sophomores

none 
coordinate geometry
includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications. No circles.

20042005 Meet 3 Sophomores

graphing 
geometric probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11.

20042005 Meet 4 Sophomores

none 
similarity
the standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem.

20042005 Meet 5 Sophomores

graphing 
Geometry

20042005 Meet 1 Juniors

graphing 
circles
standard material including power theorems, arcs, angles, area, inscribed and circumscribed polygons, sectors and segments, and equations of circles. No trig.

20042005 Meet 2 Juniors

none 
linear, quadratic, and rational functions
including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots.

20042005 Meet 3 Juniors

graphing 
probability
the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution or expected value.

20042005 Meet 4 Juniors

none 
logs and exponents with applications
may include domain and range, graphing, logarithms with positive bases including natural and base ten logs, exponential and logarithmic growth and decay. (No complex numbers)

20042005 Meet 5 Juniors

graphing 
Algebra II

20042005 Meet 1 Seniors

CAS 
sequences and series
including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus.

20042005 Meet 2 Seniors

none 
complex numbers
including solutions to polynomial equations, complex algebra (including complex coefficients), and CIS format (rectangular and polar form).

20042005 Meet 3 Seniors

CAS 
probability
may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes' Theorem, binomial distribution, expected value, and some simple geometric probability.

20042005 Meet 4 Seniors

none 
tirg equations and identities
including solving trig equations and simplifying trig expressions using standard formulas (doubleangle, halfangle, sumtoproduct, and producttosum).

20042005 Meet 5 Seniors

CAS 
PreCalculus

20042005 Meet 1 Orals


Divisibility Theory
Number Theory, by Burton. Third edition. (the entire chapter). ISBN: 0697133303

20042005 Meet 2 Orals


groups
Contemporary Abstract Algebra, by Gallian. Third edition. (pp 2367.)

20042005 Meet 3 Orals


mathematical induction
Discrete Math, by Dossey, et al. Chapter 2.52.6 (or 2.62.7 in other editions.)

20042005 Meet 4 Orals


probability
The source is a monograph written by Rhoad and Whipple, and will be available from ICTM for $8 at the time of ICTM registration. The topic will come from sections 1.1 to 1.7, and will be the same for the ICTM Regional competition.

20052006 Meet 1 Frosh

graphing 
ratios, proportions, and percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of Algebra and does not include advanced problem solving skills. While questions should not be trivial, they should be approachable to most contestants.

20052006 Meet 2 Frosh

none 
systems of linear equations and inequalities with applications
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.

20052006 Meet 3 Frosh

none 
counting basics and simple probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. Question writers are aware that this is a new topic for freshmen.

20052006 Meet 4 Frosh

graphing 
word problems
Standard and nonstandard algebra word problems. Will include those solvable by linear equation systems in one or two variables.

20052006 Meet 5 Frosh

graphing 
Algebra I

20052006 Meet 1 Sophomores

graphing 
coordinate geometry
includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications. No circles.

20052006 Meet 2 Sophomores

none 
logic, sets, and venn diagrams
Notation, intersection, unions, subsets, empty set, compliments, supplements, universal set, cardinality of a set, solution sets, and a number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables or power sets.

20052006 Meet 3 Sophomores

none 
circles
Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig or equations on circles.

20052006 Meet 4 Sophomores

graphing 
surface area & volume
This is a geometry topic, not a vector topic. It does not include writing equations of planes and lines in space. It does include finding volumes and surface areas of all sorts of different shapes. It assumes knowledge of special right triangles and the ability to use them in 3space.

20052006 Meet 5 Sophomores

graphing 
Geometry

20052006 Meet 1 Juniors

CAS 
probability
the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution and expected value

20052006 Meet 2 Juniors

none 
sytems of equations with applications
Up to 3 X 3 linear, linear X quadratic, quadratic X quadratic. Could include absolute value, exponential and literal equations. It will not require knowledge of logarithms.

20052006 Meet 3 Juniors

none 
functions and relations
nonrecursive, standard functions, limited to linear, quadratic, rational, and including domain and range. May include inverse concepts.

20052006 Meet 4 Juniors

CAS 
sequences and series
Including, but not restricted to sequences and series defined by recursion, iteration or pattern. Could include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus

20052006 Meet 5 Juniors

CAS 
Algebra II

20052006 Meet 1 Seniors

CAS 
trigonometry
may include solving, identities, inverses, applications, graphing (although no basic trig graphs, translations, etc.) and anything else that may come up in the study of trigonometry in degrees and radians. DeMoivre's Theorem and polar coordinates WILL NOT be covered.

20052006 Meet 2 Seniors

none 
systems of equations with applications
Systems to be no larger that three equations and three unknowns. Equations may include absolute value, exponential, logarithmic, quadratic, basic conics, and literal equations.

20052006 Meet 3 Seniors

none 
theory of equations
including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, DesCartes' Rule of Signs, synthetic division, complex roots, and determining equations given various info.

20052006 Meet 4 Seniors

CAS 
probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes' Theorem, binomial distribution, expected value, and some simple geometric probability.

20052006 Meet 5 Seniors

CAS 
PreCalculus

20052006 Meet 1 Orals


taxicab geometry
Taxicab Geometry: An Adventure in NonEuclidean Geometry, by Eugene F Krause; Dover 1987. Chapters 25 (pages 1249).

20052006 Meet 2 Orals


difference equations
Discrete Algorithmic Mathematics, by Stephen Maurer and Anthony Ralston; Addison Wesley. Sections 5.15.5.

20052006 Meet 3 Orals


parametric equations
Analytic Geometry, by Gordon Fuller and Dalton Tarwater; Addison Wesley. Chapter 7 (5th Ed.), or Chapter 8 (6th and 7th Ed.).

20052006 Meet 4 Orals


Relations and Functions, Abstract Mathematics
Fundamental Notions of Abstract Mathematics, by Carol Schumacher; AddisonWesley, 2001. ISBN: 0201437244. Regional: 4.14.3. State: 5.15.4. (Source contingent on copyright permissions.)

20062007 Meet 1 Frosh

graphing 
ratios, proportions, and percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of Algebra and does not include advanced problem solving skills. While questions should not be trivial, they should be approachable to most contestants.

20062007 Meet 2 Frosh

none 
number bases
including conversion and computation in different bases (bases from 2 to 16); finding the base given some information.

20062007 Meet 3 Frosh

graphing 
area & perimeter
including squares, triangles, rectangles, circles, and shapes made from these. May include the Pythagorean Theorem. Area and perimeters of above shapes assumed; all others will be given.

20062007 Meet 4 Frosh

none 
systems of linear equations and inequalities with applications
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.

20062007 Meet 5 Frosh

graphing 
Algebra I

20062007 Meet 1 Sophomores

graphing 
applications of algebra to basic plane geometry
May include area, perimeter, similarity, Pythagorean theorem, the coordinate plane (but not graphing equations), parallel line relationships, angle sums of triangles and quadrilaterals, isosceles triangle theorems, supplements, and complements. Does not require an extensive knowledge of geometry.

20062007 Meet 2 Sophomores

none 
logic, sets, and venn diagrams
Notation, intersection, unions, subsets, empty set, compliments, supplements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables or power sets.

20062007 Meet 3 Sophomores

graphing 
geometric probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11. These can be downloaded for around $15.00 each.

20062007 Meet 4 Sophomores

none 
similarity
the standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem.

20062007 Meet 5 Sophomores

graphing 
Geometry

20062007 Meet 1 Juniors

CAS 
circles
standard material including power theorems, arcs, angles, area, inscribed and circumscribed polygons, sectors and segments, and equations of circles. Coordinates are included. No trig.

20062007 Meet 2 Juniors

none 
sequences and series
including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus.

20062007 Meet 3 Juniors

CAS 
probability
the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution and expected value.

20062007 Meet 4 Juniors

none 
rational functions
including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots.

20062007 Meet 5 Juniors

CAS 
Algebra II

20062007 Meet 1 Seniors

CAS 
trigonometry applications, equations, and theory
including laws of sines and cosines, and of course, word problems.

20062007 Meet 2 Seniors

none 
algebra of complex numbers
Simplifying and factoring, solving linear and quadratic equations with complex coefficients, solving linear systems with complex coefficients, vectors, polars, DeMoivre?s Theorem, and powers of pure imaginary numbers.

20062007 Meet 3 Seniors

CAS 
conics
including locus definitions, eccentricity, directrix, no parametrics, no polar, and no rotations.

20062007 Meet 4 Seniors

none 
theory of equations
including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, DesCartes' Rule of Signs, synthetic division, complex roots, and determining equations given various info

20062007 Meet 5 Seniors

CAS 
PreCalculus

20062007 Meet 1 Orals


polar coordinates and equations
Analytic Geometry, by Gordon Fuller and Dalton Tarwater. (6th7th ed: Ch. 7 except 7.6; 5th ed: Ch. 6 except 6.7). Previously used as a topic in 20022003.

20062007 Meet 2 Orals


graph theory
Graphs and Their Uses, by Ore, Oystein (MAA, 1963). (Ch. 13, excluding 1.7, 3.45 in newer ed.) Previously used as a topic in 19941995 and 19951996 with different sources.

20062007 Meet 3 Orals


linear diophantine equations
Linear Systems: Beyond the Unique Solution (monograph), by Wally Dodge and Paul Sally. Previously used as a topic in 19992000. A PDF copy of this source is available.

20062007 Meet 4 Orals


fair division
For All Practical Purposes (COMAP). Entire "Fair Division" chapter. (It is very likely that this book will be used next year, so purchasing it is encouraged.)

20072008 Meet 1 Frosh

none 
sets and venn diagrams
Notation, intersection, unions, subsets, empty set, compliments, supplements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections.

20072008 Meet 2 Frosh

graphing 
counting basics and simple probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. Question writers are aware that this is a new topic for freshmen.

20072008 Meet 3 Frosh

graphing 
systems of linear equations and inequalities with applications
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.

20072008 Meet 4 Frosh

none 
quadratic functions
includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications.

20072008 Meet 5 Frosh

graphing 
Algebra I

20072008 Meet 1 Sophomores

none 
applications of algebra to basic plane geometry
May include area, perimeter, similarity, Pythagorean Theorem, the coordinate plane (but not graphing equations), parallel line relationships, angle sums of triangles and quadrilaterals, isosceles triangle theorems, supplements, and complements. Does not require an extensive knowledge of geometry.

20072008 Meet 2 Sophomores

graphing 
geometric probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11. These can be downloaded for around $15.00 each.

20072008 Meet 3 Sophomores

graphing 
applications of systems involving area, perimeter, and volume
This is a geometry topic, not a vector topic. It does not include writing equations of planes and lines in space. It does include finding areas, volumes and surface areas of all sorts of different shapes and using them in combinations in applied settings. It assumes knowledge of special right triangles and the ability to use them in 3space.

20072008 Meet 4 Sophomores

none 
similarity
the standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem.

20072008 Meet 5 Sophomores

graphing 
Geometry

20072008 Meet 1 Juniors

none 
algebraic coordinate geometry including circles
standard material including power theorems, arcs, angles, area, inscribed and circumscribed polygons, sectors and segments, and equations of circles. Coordinates are included. No trig.

20072008 Meet 2 Juniors

CAS 
probability
the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution and expected value.

20072008 Meet 3 Juniors

CAS 
application of systems of linear, quadratic, and rational equations
with: Up to 3 X 3 linear, linear X quadratic, quadratic X quadratic. Could include absolute value and rational equations. It will not require knowledge of logarithms.

20072008 Meet 4 Juniors

none 
logarithms and exponents
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential logarithmic growth and decay, and applications (No complex numbers)

20072008 Meet 5 Juniors

CAS 
Algebra II

20072008 Meet 1 Seniors

none 
complex numbers
including solutions to polynomial equations, complex algebra (including complex coefficients), and CIS format (rectangular and polar form).

20072008 Meet 2 Seniors

CAS 
probability
may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes' Theorem, binomial distribution, expected value, and some simple geometric probability

20072008 Meet 3 Seniors

CAS 
applications of matrices and markov chains
includes solving large systems of equations, using matrix inverses and using transition matrices (aka Markov Chains)

20072008 Meet 4 Seniors

none 
trig equations and identities
includes solving trig equations and simplifying trig expressions using standard formulas (doubleangle, halfangle, sumtoproduct, and producttosum).

20072008 Meet 5 Seniors

CAS 
PreCalculus

20072008 Meet 1 Orals


game theory
For All Practical Purposes (COMAP), 6th ed. Chapter 16.

20072008 Meet 2 Orals


linear transformations of the plane
Mathematics of Matrices, by Phillip Davis. Ginn and Co., 1965, Library of Congress: 6424818. Pages 125161.

20072008 Meet 3 Orals


perfect numbers and factorization
Excursions into Mathematics, by Beck, Bleicher, Crowe. Sections 2.12.5.

20072008 Meet 4 Orals


voting methods
For All Practical Purposes (COMAP), 6th ed. Chapters 1213.

20082009 Meet 1 Frosh

graphing 
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of Algebra and does not include advanced problem solving skills. While questions should not be trivial, they should be approachable to most contestants.

20082009 Meet 2 Frosh

none 
Number bases
including conversion and computation in different bases (bases from 2 to 16); finding the base given some information.

20082009 Meet 3 Frosh

graphing 
Linear equations and inequalities
includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.

20082009 Meet 4 Frosh

none 
Rational expressions
simplifying rational expressions, solving equations involving rational expressions, word problems, basic algebra 1 factoring.

20082009 Meet 5 Frosh


Algebra I

20082009 Meet 1 Sophomores

graphing 
Perimeter, Area, and Surface Area
including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem.

20082009 Meet 2 Sophomores

none 
Coordinate geometry without circles
includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications.

20082009 Meet 3 Sophomores

graphing 
Geometric Probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11.

20082009 Meet 4 Sophomores

none 
Advanced geometry topics
restricted to: Brahmagupta's formula, point to line distance formula, area of a triangle given vertices, Stewart's Theorem, Ptolemy's Theorem, Mass points, inradius and circumradius, Ceva's Theorem, and Theorem of Menelaus. A good reference would be Geometry by Rhoad, Milauskas, and Whipple, Chapter 16.

20082009 Meet 5 Sophomores


Geometry

20082009 Meet 1 Juniors

CAS 
Geometry of the Right Triangle including Trigonometry
Geometry of right triangles including any special right triangles and trigonometric ratios restricted to sine, cosine, and tangent in degrees only.

20082009 Meet 2 Juniors

none 
Sequences and Series
including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus.

20082009 Meet 3 Juniors

CAS 
Linear, Quadratic, and Rational Functions
including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots.

20082009 Meet 4 Juniors

none 
Logarithms and Exponents
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential logarithmic growth and decay, and applications (No complex numbers).

20082009 Meet 5 Juniors


Algebra II

20082009 Meet 1 Seniors

CAS 
Combinatorics
Fundamantal counting principle, combinations and permutations, permutations with and without repetition, arrangements of distinguishable and nondistinguishable items with and without replacement, and probability involving these topics. No circular permutations. Possible sources: Advanced Mathematics by Richard G. Brown, sections 152 to 154, or Probability, a monograph by Rhoad and Whipple, used as oral reference for ICTM in '04'05.

20082009 Meet 2 Seniors

none 
Conics
including locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations.

20082009 Meet 3 Seniors

CAS 
Trigonometry
may include solving, identities, inverses, applications, graphing (although no basic trig graphs, translations, etc.) and anything else that may come up in the study of trigonometry in degrees and radians. DeMoivre's Theorem and polar coordinates WILL NOT be covered.

20082009 Meet 4 Seniors

none 
Theory of Equations
including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, DesCartes' Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older PreCalculus texts.

20082009 Meet 5 Seniors


PreCalculus

20082009 Meet 1 Orals


Markov Chains
Finite Mathematics, by Lial and Miller (4th ed). Chapter 8.

20082009 Meet 2 Orals


Linear Programming
For All Practical Purposes, by COMAP (6th ed). Chapter 4.

20082009 Meet 3 Orals


Conic Sections
Analytic Geometry, by Fuller and Tarwater. Chapter 3.

20082009 Meet 4 Orals


Networks
For All Practical Purposes, by COMAP (6th ed). Chapter 1.

20092010 Meet 1 Frosh

none 
Sets and Venn Diagrams
Notation, intersection, unions, subsets, empty set, compliments, supplements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections.

20092010 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. Question writers are aware that this is a new topic for freshmen.

20092010 Meet 3 Frosh

graphing 
Systems of Linear Equations and Inequalities with Applications
Limited to two variables. May include
absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.

20092010 Meet 4 Frosh

none 
Coordinate Geometry
Includes distance, midpoint, slope, parallels, perpendiculars
and applications.

20092010 Meet 5 Frosh


Algebra I

20092010 Meet 1 Sophomores

none 
Logic, Sets and Venn Diagrams
Notation, intersection, unions, subsets, empty set, complements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables.

20092010 Meet 2 Sophomores

graphing 
Geometric Probability
emphasis on the concept of geometric probability rather than on difficult
geometry problems. Students are not required to have a comprehensive knowledge of geometry.
UMAP module 660 is a good source, as is HIMAP module 11.

20092010 Meet 3 Sophomores

graphing 
Geometric Transformations on a Plane
Includes reflections, rotations, translations, dilations, shears,
and compositions in two dimensions.

20092010 Meet 4 Sophomores

none 
Similarity
the standard geometric treatment including perimeter, area, and volume
relationships, conditions determining similarity, similarity in right triangles and polygons. It may
include a few proportion theorems that are not specifically similarity, such as the angle bisector
theorem.

20092010 Meet 5 Sophomores


Geometry

20092010 Meet 1 Juniors

none 
Algebraic Coordinate Geometry including Circles
standard material including power theorems, arcs, angles, area, inscribed and circumscribed polygons, sectors and segments, and equations of circles. Coordinates are included. No trig.

20092010 Meet 2 Juniors

CAS 
Probability
the standard treatment of probability. It may include combinations, permutations,
mutually exclusive events, dependent and independent events, and conditional probability. It should
not include binomial distribution and expected value.

20092010 Meet 3 Juniors

CAS 
Applications Systems of Linear, Quadratic, and Rational Equations
Up to 3 X 3 linear, linear X
quadratic, quadratic X quadratic. Could include absolute value and rational equations. It will not
require knowledge of logarithms.

20092010 Meet 4 Juniors

none 
Functions and Relations
Nonrecursive, standard functions, limited to linear,
quadratic, rational, and piecewise including domain, range, and composition. May include inverse
concepts. No logs, exponential, nor trig.

20092010 Meet 5 Juniors


Algebra II

20092010 Meet 1 Seniors

none 
Algebra of Complex numbers
Simplifying and factoring, solving linear and
quadratic equations with complex coefficients, solving linear systems with complex coefficients, vectors, polars, and powers of pure imaginary numbers. No DeMoivre?s Theorem.

20092010 Meet 2 Seniors

CAS 
Probability
may include combinations, permutations, mutually exclusive events, dependent and
independent events, conditional probability, Bayes' Theorem, binomial distribution, expected value,
and some simple geometric probability.

20092010 Meet 3 Seniors

CAS 
Polar Coordinates and Equations
Graphs, systems, and DeMoivre?s Theorem. Includes conics and
intersections of polar curves that are not simultaneous solutions to the system (?ghost points?).
Analytic Geometry, by Gordon Fuller and Dalton Tarwater (6th7th ed) is a good source.

20092010 Meet 4 Seniors

none 
Trig. Equations and Identities
includes solving trig equations and simplifying trig
expressions using standard formulas (doubleangle, halfangle, sumtoproduct, and producttosum).

20092010 Meet 5 Seniors


PreCalculus

20092010 Meet 1 Orals


Taxicab Geometry
Taxicab Geometry: An Adventure in NonEuclidean Geometry, by Eugene F. Krause. ISBN 0486252027. Chapters 2?5 (pp. 12?49).

20092010 Meet 2 Orals


Parametric Equations
Analytic Geometry, by Gordon Fuller and Dalton Tarwater. ISBN 0201134845 (7th ed). (6th7th ed: Ch. 8; 5th ed: Ch. 7).

20092010 Meet 3 Orals


Theory of Congruence
Elementary Number Theory, by Burton, David M.. Chapter 4 (any edition).

20092010 Meet 4 Orals


Symmetry and Patterns
For All Practical Purposes, by COMAP (6th ed). Chapter 19.

20102011 Meet 1 Frosh

none 
Number Theory and Divisibility
may include patterns (such as trailing zeros), factors, primes, divisibility rules, prime factors of powers, unique factorization, LCM, GCD, and their relationships.

20102011 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.

20102011 Meet 3 Frosh

none 
Number bases
including conversion and computation in different bases (bases from 2 to 16); finding the base given some information.

20102011 Meet 4 Frosh

graphing 
Systems of Linear Equations and Inequalities with Applications
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.

20102011 Meet 5 Frosh


Algebra I

20102011 Meet 1 Sophomores

none 
Quadrilaterals
properties, classification, angle measures and sums, area, diagonals, convex and nonconvex, cyclic quadrilaterals, Brahmagupta?s formula, etc.

20102011 Meet 2 Sophomores

graphing 
Geometric Probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry.

20102011 Meet 3 Sophomores

none 
Circles
Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles.

20102011 Meet 4 Sophomores

graphing 
Geometric Transformations on a Plane
Includes reflections, rotations, translations, dilations, shears, and compositions in two dimensions.

20102011 Meet 5 Sophomores


Geometry

20102011 Meet 1 Juniors

none 
Modular Arithmetic
may include arithmetic operations in different moduli, divisibility, solving simple linear congruences in one or two variables, Fermat?s Little Theorem, Wilson?s Theorem, and Chinese Remainder Theorem.

20102011 Meet 2 Juniors

CAS 
Probability
the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value.

20102011 Meet 3 Juniors

none 
Logarithms and Exponents
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential logarithmic growth and decay, and applications. No complex numbers.

20102011 Meet 4 Juniors

CAS 
Applications of Matrices and Markov Chains
includes solving large systems of equations, using matrix inverses and using transition matrices (aka Markov Chains).

20102011 Meet 5 Juniors


Algebra II

20102011 Meet 1 Seniors

none 
Diophantine Equations
may include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems.

20102011 Meet 2 Seniors

CAS 
Probability
may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability.

20102011 Meet 3 Seniors

none 
Sequences and Series
including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus.

20102011 Meet 4 Seniors

CAS 
Vector Analytic Graphing
includes two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar, inner and cross products, perpendicularly and parallels. distance between lines, points and planes. No calculus.

20102011 Meet 5 Seniors


PreCalculus

20102011 Meet 1 Orals


Polar Coordinates and Equations
Analytic Geometry, by Fuller and Tarwater. (6th7th ed: Ch. 7; 5th ed: Ch. 6).

20102011 Meet 2 Orals


Combinatorics
Introduction to Discrete Mathematics, by Roman, Steven. 4.14.8, 5.15.2.

20102011 Meet 3 Orals


Topics in Geometry
Geometry Revisited, by Coxeter and Greitzer. 1.11.3.

20102011 Meet 4 Orals


Planning and Scheduling
, by . .

20112012 Meet 1 Frosh

graphing 
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants.

20112012 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.

20112012 Meet 3 Frosh

none 
Number Theory and Divisibility
may include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships.

20112012 Meet 4 Frosh

none 
Systems of Linear Equations and Inequalities with Applications
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.

20112012 Meet 5 Frosh


Algebra I

20112012 Meet 1 Sophomores

graphing 
Perimeter, Area, and Surface Area
including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem.

20112012 Meet 2 Sophomores

graphing 
Geometric Probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry.

20112012 Meet 3 Sophomores

none 
Similarity
the standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem.

20112012 Meet 4 Sophomores

none 
Advanced Geometry Topics Restricted to
Brahmagupta?s formula, point to line distance formula, area of a triangle given vertices, Stewart?s Theorem, Ptolemy?s Theorem, Mass points, inradius and circumradius, Ceva?s Theorem, and Theorem of Menelaus. A good reference would be Geometry by Rhoad, Milauskas, and Whipple, Chapter 16.

20112012 Meet 5 Sophomores


Geometry

20112012 Meet 1 Juniors

CAS 
Algebraic Coordinate Geometry including Circles
standard material including power theorems, arcs, angles, area, inscribed and circumscribed polygons, sectors and segments, and equations of circles. Coordinates are included. No trig.

20112012 Meet 2 Juniors

CAS 
Probability
the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value.

20112012 Meet 3 Juniors

none 
Geometric Transformations Using Matrices on a Plane
In two dimensions. Includes reflections, rotations, translations, dilations, shears, and compositions. Standard treatment using Algebra 2 texts. For shears refer to Mathematics of Matrices, by Phillip Davis. Ginn and Co., 1965, Library of Congress: 6424818. Pages 125161 (Oral #2, 20078).

20112012 Meet 4 Juniors

none 
Sequences and Series
including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus.

20112012 Meet 5 Juniors


Algebra II

20112012 Meet 1 Seniors

CAS 
Trigonometry Applications, Equations and Theory
including laws of sines and cosines, and of course, word problems.

20112012 Meet 2 Seniors

CAS 
Probability
may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability.

20112012 Meet 3 Seniors

none 
Conics
including locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations.

20112012 Meet 4 Seniors

none 
Theory of Equations
including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, DesCartes' Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older PreCalculus texts.

20112012 Meet 5 Seniors


PreCalculus

20112012 Meet 1 Orals


Graph Theory
Graphs and Their Uses, by Oystein Ore (MAA). Chapters 1 through 3.

20112012 Meet 2 Orals


Divisibility
Elementary Number Theory, by David Burton. Chapter 2.

20112012 Meet 3 Orals


Matrix Games
Excursions into Mathematics, by Beck, Bleicher, Crowe (Millenium Edition). Sections 5.1, 5.6, 5.7.

20112012 Meet 4 Orals


Taxicab Geometry
, by Krause. Chapters 15.

20122013 Meet 1 Frosh

graphing 
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants.

20122013 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.

20122013 Meet 3 Frosh

none 
Number Bases

20122013 Meet 4 Frosh

none 
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships.

20122013 Meet 5 Frosh


Algebra I

20122013 Meet 1 Sophomores

graphing 
Perimeter, Area, and Surface Area
including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem.

20122013 Meet 2 Sophomores

graphing 
Geometric Probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry.

20122013 Meet 3 Sophomores

none 
Right Triangles
All things fun about right triangles. May include Pythagorean Theorem (and triples), altitude to hypotenuse, related circles and centers, special right triangles, right triangle trigonometry.

20122013 Meet 4 Sophomores

none 
Advanced Geometry Topics Restricted to
Brahmagupta?s formula, point to line distance formula, area of a triangle given vertices, Stewart?s Theorem, Ptolemy?s Theorem, Mass points, inradius and circumradius, Ceva?s Theorem, and Theorem of Menelaus. A good reference would be Geometry by Rhoad, Milauskas, and Whipple, Chapter 16.

20122013 Meet 5 Sophomores


Geometry

20122013 Meet 1 Juniors

CAS 
Systems of Linear Equations and Inequalities with Applications
May include absolute value, intersections, area and/or perimeter of a region, corner points, slopes, distances, types of systems.

20122013 Meet 2 Juniors

CAS 
Probability
the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value.

20122013 Meet 3 Juniors

none 
Logarithms and Exponents
May include domain and range, graphing, logarithms with positive bases including natural and common logs, emphasis on properties, exponential logarithmic growth and decay, and applications. No complex numbers.

20122013 Meet 4 Juniors

none 
Sequences and Series
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus.

20122013 Meet 5 Juniors


Algebra II

20122013 Meet 1 Seniors

CAS 
Triangle Trigonometry

20122013 Meet 2 Seniors

CAS 
Probability
may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability.

20122013 Meet 3 Seniors

none 
Diophantine Equations

20122013 Meet 4 Seniors

none 
Vector Analytic Geometry

20122013 Meet 5 Seniors


PreCalculus

20122013 Meet 1 Orals


Conic Sections
For All Practical Purposes, by COMAP. Chapters 12 and 13.

20122013 Meet 2 Orals


Markov Chains
Elementary Number Theory, by David Burton. Chapter 4.

20122013 Meet 3 Orals


Tritangent Circles
Anayltic Geometry, by Gordon Fuller and Dalton Tarwater. Chapter 8.

20122013 Meet 4 Orals


Vectors
, by . .

20132014 Meet 1 Frosh

graphing 
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants.

20132014 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.

20132014 Meet 3 Frosh

none 
Linear Equations and Inequalities
Includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.

20132014 Meet 4 Frosh

none 
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships.

20132014 Meet 5 Frosh


Algebra I

20132014 Meet 1 Sophomores

graphing 
Perimeter, Area, and Surface Area
including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem.

20132014 Meet 2 Sophomores

graphing 
Geometric Probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry.

20132014 Meet 3 Sophomores

none 
Right Triangles
All things fun about right triangles. May include Pythagorean Theorem (and triples), altitude to hypotenuse, related circles and centers, special right triangles, right triangle trigonometry.

20132014 Meet 4 Sophomores

none 
Advanced Geometry Topics Restricted to
Brahmagupta?s formula, point to line distance formula, area of a triangle given vertices, Stewart?s Theorem, Ptolemy?s Theorem, Mass points, inradius and circumradius, Ceva?s Theorem, and Theorem of Menelaus. A good reference would be Geometry by Rhoad, Milauskas, and Whipple, Chapter 16.

20132014 Meet 5 Sophomores


Geometry

20132014 Meet 1 Juniors

CAS 
Systems of Linear Equations and Inequalities with Applications
May include absolute value, intersections, area and/or perimeter of a region, corner points, slopes, distances, types of systems.

20132014 Meet 2 Juniors

CAS 
Probability
the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value.

20132014 Meet 3 Juniors

none 
Logarithms and Exponents
May include domain and range, graphing, logarithms with positive bases including natural and common logs, emphasis on properties, exponential logarithmic growth and decay, and applications. No complex numbers.

20132014 Meet 4 Juniors

none 
Sequences and Series
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus.

20132014 Meet 5 Juniors


Algebra II

20132014 Meet 1 Seniors

CAS 
Geometric Transformations Using Matrices on a Plane
In two dimensions. Includes reflections, rotations, translations, dilations, shears, and compositions. Standard treatment using Algebra 2 texts. For shears refer to Mathematics of Matrices, by Phillip Davis. Ginn and Co., 1965, Library of Congress: 6424818. Pages 125161

20132014 Meet 2 Seniors

CAS 
Probability
may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability.

20132014 Meet 3 Seniors

none 
Algebra of Complex Numbers
Simplifying and factoring, solving linear and quadratic equations with complex coefficients, solving linear systems with complex coefficients, vectors, polars, and powers of pure imaginary numbers, including DeMoivre's Theorem.

20132014 Meet 4 Seniors

none 
Conics
including locus definitions, eccentricity, and focus/directrix properties. No parametrics, no polar, and no rotations.

20132014 Meet 5 Seniors


PreCalculus

20132014 Meet 1 Orals


Voting Methods
For All Practical Purposes, by COMAP. Chapters 12 (Social Choice) and 13 (Weighted Voting Systems) in edition 6. These are chapters 11 and 12 in the 4th edition..

20132014 Meet 2 Orals


Theory of Congruence
Elementary Number Theory, by David Burton. Chapter 4.

20132014 Meet 3 Orals


Parametrics
Anayltic Geometry, by Gordon Fuller and Dalton Tarwater. Chapter 8.

20132014 Meet 4 Orals


Geometric Probability
Geometric Probability, by Art Johnson (COMAP Module Sections 1  3; pages 1 36). AND NCTM Publication . Sections 14, 9.1 (#1, #2), 10, 10.1, exercises (section 11) 16, 10.

20142015 Meet 1 Frosh

none 
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (Last used 201314)

20142015 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (Last used 201314)

20142015 Meet 3 Frosh

none 
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (Last used 201213)

20142015 Meet 4 Frosh

graphing 
Linear Equations and Inequalities and Quadratic Equations
Includes word problems leading to linear or absolute value equations and inequalities, as well as quadratic equations. No quadratic inequalities. (Last used 201314; not quadratics  they are new to this topic)

20142015 Meet 5 Frosh


Algebra I

20142015 Meet 1 Sophomores

none 
Logic, Sets, and Venn Diagrams
Notation, intersection, unions, subsets, empty set, complements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (Last used 201213)

20142015 Meet 2 Sophomores

graphing 
Geometric Probability
Emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. (Last used 201314)

20142015 Meet 3 Sophomores

none 
Similarity
The standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem. (Last used 201112)

20142015 Meet 4 Sophomores

graphing 
Advanced Geometry Topics
Restricted to Brahmagupta?s formula, point to line distance formula, area of a triangle given vertices, Stewart?s Theorem, Ptolemy?s Theorem, Mass points, inradius and circumradius, Ceva?s Theorem, and Theorem of Menelaus. (Last used 201314; note that a calculator is allowed this year)

20142015 Meet 5 Sophomores


Geometry

20142015 Meet 1 Juniors

none 
Modular Arithmetic
May include arithmetic operations in different moduli, divisibility, solving simple linear congruences in one or two variables, Fermat?s Little Theorem, Wilson?s Theorem, and Chinese Remainder Theorem. (Last used 201213)

20142015 Meet 2 Juniors

CAS 
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value. (Last used 201314)

20142015 Meet 3 Juniors

none 
Rational Functions
Including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots. (Last used 200607)

20142015 Meet 4 Juniors

CAS 
Applications of Matrices and Markov Chains
Includes solving large systems of equations, using matrix inverses and using transition matrices (aka Markov Chains). (Last used 201011)

20142015 Meet 5 Juniors


Algebra II

20142015 Meet 1 Seniors

none 
Diophantine Equations
May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (201213)

20142015 Meet 2 Seniors

CAS 
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability. (Last used 201314)

20142015 Meet 3 Seniors

none 
Theory of Equations
Including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, DesCartes' Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older PreCalculus texts. (Last used 201112)

20142015 Meet 4 Seniors

CAS 
Vector Analytic Graphing
Includes two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar, inner and cross products, perpendicularly and parallels. distance between lines, points and planes. No calculus. (Last used 201213)

20142015 Meet 5 Seniors


PreCalculus

20142015 Meet 1 Orals


Geometric Constructions
College Geometry, by Nathan AltshillerCourt. Oralists are not expected to construct precise diagrams with compass and straightedge on the chalk/white board during presentation, but rather sketch their constructions and explain them. Emphasis is on understanding and proving constructions, rather than precision with tools.. Chapter 1.

20142015 Meet 2 Orals


Graph Theory
Graphs and their Uses, by Oystein Ore / Robin Wilson (1990). Note: Terminology differs between 1960 and 1990 editions. Questions will be written using the terminology from the 1990 edition.. Chapters 13.

20142015 Meet 3 Orals


Continued Fractions
Continued Fractions, by C.D. Olds. Chapters 13.

20142015 Meet 4 Orals


Combinatorics and Probability
Probability Module, by Rhoad and Whipple. 1.11.7 & 1.12 (pp 140 & 7784).

20152016 Meet 1 Frosh

graphing 
Ratios, Proportions, and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of Algebra and does not include advanced problem solving skills. While questions should not be trivial, they should be approachable to most contestants. (201314)

20152016 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (201415)

20152016 Meet 3 Frosh

none 
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (201415)

20152016 Meet 4 Frosh

none 
Applications of Systems of Linear Equations and Inequalities
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent. (201112)

20152016 Meet 5 Frosh


Algebra I

20152016 Meet 1 Sophomores

graphing 
Perimeter, Area, and Surface Area
Including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem. (201314)

20152016 Meet 2 Sophomores

graphing 
Geometric Probability
Emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. (201314)

20152016 Meet 3 Sophomores

none 
Circles
Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments, equations of circles. Does not include trig. (201011, supplemented)

20152016 Meet 4 Sophomores

none 
Advanced Geometry Topics
Restricted to Brahmagupta?s formula, point to line distance formula, area of a triangle given vertices, Stewart?s Theorem, Ptolemy?s Theorem, Mass points, inradius and circumradius, Ceva?s Theorem, and Theorem of Menelaus. (201415)

20152016 Meet 5 Sophomores


Geometry

20152016 Meet 1 Juniors

CAS 
Systems of Linear Equations and Inequalities with Applications
May include absolute value, intersections, area and/or perimeter of a region, corner points, slopes, distances, types of systems. (201314)

20152016 Meet 2 Juniors

CAS 
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value. (201314)

20152016 Meet 3 Juniors

none 
Logs and Exponents
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential logarithmic growth and decay, and applications. No complex numbers. (201314)

20152016 Meet 4 Juniors

none 
Functions and Relations
Nonrecursive, standard functions, limited to linear, quadratic, rational, and piecewise including domain, range, and composition. May include inverse concepts. No logs, exponential, nor trig. (201213)

20152016 Meet 5 Juniors


Algebra II

20152016 Meet 1 Seniors

CAS 
Triangle Trigonometry with Applications
Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (201213)

20152016 Meet 2 Seniors

CAS 
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability. (201314)

20152016 Meet 3 Seniors

none 
Algebra of Complex Numbers
Simplifying and factoring, solving linear and quadratic equations with complex coefficients, solving linear systems with complex coefficients, vectors, polars, and powers of pure imaginary numbers, including DeMoivre?s Theorem. (201314)

20152016 Meet 4 Seniors

none 
Sequences and Series
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus. (201011)

20152016 Meet 5 Seniors

CAS 
PreCalculus

20152016 Meet 1 Orals


Taxicab Geometry
Taxicab Geometry, by Eugene Krause. Chapters 1  5.

20152016 Meet 2 Orals


Cake Cutting  Fair Cake Divisions
Cake Cutting Algorithms, by Jack Robertson and William Webb (Chapter 1). See COMAP For All Practical Purposes for additional practice material. .

20152016 Meet 3 Orals

CAS 
Planning and Scheduling
For All Practical Purposes, by COMAP. Chapter 3.

20152016 Meet 4 Orals


Isometries of the Plane
Isometries of the Plane, by Shilgalis. pdf file available from ICTM Regional contest website (for AA schools) or from NSML President. .

20162017 Meet 1 Frosh

graphing 
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (201516)

20162017 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (201516)

20162017 Meet 3 Frosh

none 
Quadratics
Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (201213)

20162017 Meet 4 Frosh

none 
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (201415)

20162017 Meet 5 Frosh


Algebra I

20162017 Meet 1 Sophomores

graphing 
Coordinate Geometry with Applications
Includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications (no circles). (201213)

20162017 Meet 2 Sophomores

graphing 
Geometric Probability
Emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11. (201516)

20162017 Meet 3 Sophomores

none 
Similarity
The standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem. (201415)

20162017 Meet 4 Sophomores

none 
Advanced Geometry Topics
Restricted to: Brahmagupta’s formula, point to line distance formula, area of a triangle given vertices, Stewart’s Theorem, Ptolemy’s Theorem, Mass points, inradius and circumradius, Ceva’s Theorem, and Theorem of Menelaus. A good reference would be Geometry by Rhoad, Milauskas, and Whipple, Chapter 16. (201516)

20162017 Meet 5 Sophomores


Geometry

20162017 Meet 1 Juniors

CAS 
Algebraic Coordinate Geometry (Including Circles)
Includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, applications, and standard circle material including power theorems, arcs, angles, area, inscribed and circumscribed polygons, sectors and segments, and equations of circles. Coordinates are included. No trig. (201213)

20162017 Meet 2 Juniors

CAS 
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value. (201516)

20162017 Meet 3 Juniors

none 
Modular Arithmetic
May include arithmetic operations in different moduli, divisibility, solving simple linear congruences in one or two variables, Fermat’s Little Theorem, Wilson’s Theorem, and Chinese Remainder Theorem. (201415)

20162017 Meet 4 Juniors

none 
Sequences and Series
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus. (201516)

20162017 Meet 5 Juniors


Algebra II

20162017 Meet 1 Seniors

CAS 
Triangle Trigonometry with Applications
Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (201516)

20162017 Meet 2 Seniors

CAS 
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability. (201516)

20162017 Meet 3 Seniors

none 
Diophantine Equations
May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (201415)

20162017 Meet 4 Seniors

none 
Vector Analytic Graphing
Includes two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar, inner and cross products, perpendicularly and parallels. distance between lines, points and planes. (No calculus) (201415)

20162017 Meet 5 Seniors


PreCalculus

20162017 Meet 1 Orals


Divisibility
Source: Elementary Number Theory by David Burton  Chapter 2

20162017 Meet 2 Orals


Markov Chains
Finite Mathematics by Lial and Miller  Chapter 9 (6th edition)  Other editions are similar.

20162017 Meet 3 Orals


Linear Programming
For All Practical Purposes by COMAP  Chapter 4

20162017 Meet 4 Orals


The Algebra of Logic
Chapter 1, pp. 129, of Elliot Mendelson, Boolean Algebra and Switching Circuits, 1970 Ed., in the Schaum Outline Series.

20172018 Meet 1 Frosh

graphing 
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (201617)

20172018 Meet 2 Frosh

none 
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (201516)

20172018 Meet 3 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (201617)

20172018 Meet 4 Frosh

none 
Quadratics
Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (201617)

20172018 Meet 5 Frosh

graphing 
Algebra I

20172018 Meet 1 Sophomores

graphing 
Perimeter, Area, and Surface Area
Including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem. (201516)

20172018 Meet 2 Sophomores

none 
Logic, Sets, and Venn Diagrams
Notation, intersection, unions, subsets, empty set, complements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (201415)

20172018 Meet 3 Sophomores

graphing 
Geometric Probability
Emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11. (201617)

20172018 Meet 4 Sophomores

none 
Advanced Geometry Topics
Restricted to Brahmagupta’s formula, point to line distance formula, area of a triangle given vertices, Stewart’s Theorem, Ptolemy’s Theorem, Mass points, inradius and circumradius, Ceva’s Theorem, and Theorem of Menelaus. A good reference would be Geometry for Enjoyment and Challenge by Rhoad, Milauskas, and Whipple, Chapter 16. (201617)

20172018 Meet 5 Sophomores

graphing 
Geometry

20172018 Meet 1 Juniors

CAS 
Algebraic Coordinate Geometry including Circles
Standard material including power theorems, arcs, angles, area, inscribed and circumscribed polygons, sectors and segments, and equations of circles. Coordinates are included. No trig. (201617)

20172018 Meet 2 Juniors

none 
Rational Functions
Including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots. (201415)

20172018 Meet 3 Juniors

CAS 
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value. (201617)

20172018 Meet 4 Juniors

none 
Logs and Exponents
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential logarithmic growth and decay, and applications. No complex numbers. (201516)

20172018 Meet 5 Juniors

CAS 
Algebra II

20172018 Meet 1 Seniors

CAS 
Triangle Trigonometry with Applications
Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (201617)

20172018 Meet 2 Seniors

none 
Parametric Equations
Slopes, equations of lines, simple conics (no rotations), intersection points, position (applications), translating between rectangular and parametric equations. A good reference is Analytic Geometry, by Gordon Fuller and Dalton Tarwater; Addison Wesley. Chapter 7 (5th Ed), or Chapter 8 (6th and 7th Ed). (NEW)

20172018 Meet 3 Seniors

CAS 
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability. (201617)

20172018 Meet 4 Seniors

none 
Theory of Equations
Including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, DesCartes' Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older PreCalculus texts. (201415)

20172018 Meet 5 Seniors

CAS 
PreCalculus

20172018 Meet 1 Orals


Networks
Source: For All Practical Purposes by COMAP, 6th edition, Chapter 1

20172018 Meet 2 Orals


Generating Functions
NO CALCULATOR ALLOWED  Source: Intermediate Counting and Probability (Art of Problem Solving) by David Patrick, Chapter 14

20172018 Meet 3 Orals


Inversion
Source: Circle Inversions and Applications to Euclidean Geometry by Kenji Kozai and Shlomo Libeskind, Chapters 0  2.  Available here: http://jwilson.coe.uga.edu/EMT600/Libeskind.Kozai.Inversion.pdf 
Supplementary Source (lots of problems and solutions): A Decade of the Berkeley Math Circle, edited by Z. Stankova and T. Rike, Session 1

20172018 Meet 4 Orals


Markov Chains
Sections 9.19.2 (Markov Chains) of Tan, Finite Mathematics for the Managerial, Life and Social Sciences, 11th Edition 2015 (ISBN 9781275464657)

20182019 Meet 1 Frosh

graphing 
Ratios, Proportion and Percent
May include money, simple interest (not compound interest), discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (201718)

20182019 Meet 2 Frosh

none 
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (201617)

20182019 Meet 3 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (201718)

20182019 Meet 4 Frosh

none 
Linear Equations and Inequalities and Quadratic Equations
Includes word problems leading to linear or absolute value equations and inequalities, as well as quadratic equations. No quadratic inequalities. (201415)

20182019 Meet 5 Frosh

graphing 
Algebra I

20182019 Meet 1 Sophomores

graphing 
Coordinate Geometry with Applications
Includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications. No circles. (201617)

20182019 Meet 2 Sophomores

none 
Logic, Sets, and Venn Diagrams
Notation, intersection, unions, subsets, empty set, complements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (201718)

20182019 Meet 3 Sophomores

graphing 
Geometric Probability
Emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11. (201718)

20182019 Meet 4 Sophomores

none 
Similarity
The standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem. (201617)

20182019 Meet 5 Sophomores

graphing 
Geometry

20182019 Meet 1 Juniors

CAS 
Systems of Linear Equations and Inequalities with Applications
May include absolute value, intersections, area and/or perimeter of a region, corner points, slopes, distances, types of systems. (201516)

20182019 Meet 2 Juniors

none 
Modular Arithmetic
May include arithmetic operations in different moduli, divisibility, solving simple linear congruences in one or two variables, Fermat’s Little Theorem, Wilson’s Theorem, and Chinese Remainder Theorem. (201617)

20182019 Meet 3 Juniors

CAS 
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value. (201718)

20182019 Meet 4 Juniors

none 
Rational Functions
Including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots. (201718)

20182019 Meet 5 Juniors

CAS 
Algebra II

20182019 Meet 1 Seniors

CAS 
Geometric Transformations Using Matrices on a Plane
In two dimensions. Includes reflections, rotations, translations, dilations, shears, and compositions. Standard treatment using Algebra 2 texts. For shears refer to Mathematics of Matrices, by Phillip Davis. Ginn and Co., 1965, Library of Congress: 6424818. Pages 125161 (Oral #2, 20078; senior 201314)

20182019 Meet 2 Seniors

none 
Diophantine Equations
May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (201617)

20182019 Meet 3 Seniors

CAS 
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes' Theorem, binomial distribution, expected value, and some simple geometric probability. (201718)

20182019 Meet 4 Seniors

none 
Conics
Including locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations. (201314)

20182019 Meet 5 Seniors

CAS 
PreCalculus

20182019 Meet 1 Orals


Theory of Congruences  NO CALCULATOR
Source: Elementary Number Theory by David Burton, Fifth Edition (or newer edition)  Chapter 4. ISBN: 0072325690

20182019 Meet 2 Orals


Inequalities
Source: AOPS Intermediate Algebra by Richard Rusczyk  Chapter 12. ISBN13: 9781934124048

20182019 Meet 3 Orals


Fibonacci Numbers and Recursion  NO CALCULATOR
Source: AOPS Intermediate Counting and Probability by David Patrick  Chapters 9 and 10. ISBN: 1934124060

20182019 Meet 4 Orals


Game Theory
For All Practical Purposes: Mathematical Literacy in Today’s World, Sections 15.1 and 15.2, 10th edition COMAP materials; published by W.H. Freeman; ISBN 9781464124730.

20192020 Meet 1 Frosh

none 
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (201819)

20192020 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (201819)

20192020 Meet 3 Frosh

none 
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (20172018)

20192020 Meet 4 Frosh

graphing 
Coordinate Geometry
Includes distance, midpoint, slope, parallels, perpendiculars and applications. (200910)

20192020 Meet 5 Frosh

graphing 
Algebra I

20192020 Meet 1 Sophomores

none 
Functions

20192020 Meet 2 Sophomores

graphing 
Geometric Probability
emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11.

20192020 Meet 3 Sophomores

graphing 
Circles
Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles. (201011)

20192020 Meet 4 Sophomores

none 
Coordinate Geometry

20192020 Meet 5 Sophomores

graphing 
Geometry

20192020 Meet 1 Juniors

none 
Polynomials
Including factor, remainder, and rational root theorems; Descartes’ Rule of Signs; coefficient analysis; determining equations given various information.

20192020 Meet 2 Juniors

CAS 
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. Does not include binomial distribution nor expected value. (201920)

20192020 Meet 3 Juniors

CAS 
Logs and Exponents
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential and logarithmic growth and decay, and applications. No complex numbers.

20192020 Meet 4 Juniors

none 
Transformations using Matricies on a Plane
In two dimensions. Includes reflections, rotations, translations, dilations, shears, and compositions. Standard treatment using Algebra 2 texts. For shears refer to Mathematics of Matrices, by Phillip Davis. Ginn and Co., 1965, Library of Congress: 6424818. Pages 125161 (Oral #2, 20078).

20192020 Meet 5 Juniors

CAS 
Algebra II

20192020 Meet 1 Seniors

none 
Theory of Equations
Including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, DesCartes' Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older PreCalculus texts. (201718)

20192020 Meet 2 Seniors

CAS 
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (201920)

20192020 Meet 3 Seniors

CAS 
Series and Sequences
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus. (201516)

20192020 Meet 4 Seniors

none 
Vectors
(Previously called Vector Analytic Graphing) Includes two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar, inner and cross products, perpendicularly and parallels. distance between lines, points and planes. No calculus. (201617)

20192020 Meet 5 Seniors

CAS 
PreCalculus

20192020 Meet 1 Orals

none 
Planning and Scheduling
Source: For All Practical Purpose by COMAP (Sixth Edition)  Chapter 3  ISBN: 0716747820

20192020 Meet 2 Orals

none 
Geometric Constructions
Source: College Geometry by Nathan Altshiller Court  Chapter 1  ISBN: 0486458059  Oralists are not expected to construct precise diagrams with compass and straightedge on the chalk/white board during presentation, but rather sketch their constructions and explain them. Emphasis is on understanding and proving constructions, rather than precision with tools.

20192020 Meet 3 Orals

none 
Continued Fractions
Source: Continued Fractions by C.D. Olds  MAA New Mathematical library  Chapters 13ISBN: 0883856093

20192020 Meet 4 Orals


Voting Methods
For All Practical Purposes, by COMAP. Chapters 12 (Social Choice) and 13 (Weighted Voting Systems) in edition 6. These are chapters 11 and 12 in the 4th edition..

20202021 Meet 1 Frosh

none 
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (201920)

20202021 Meet 2 Frosh

graphing 
Basic Statistics
Measures of central tendency (mean, median, and mode), boxandwhisker plots, twoway tables, stem and leaf, range. No variance. No standard deviation. (New Topic. Resource: OpenStax: https://openstax.org/details/books/introductorystatistics)

20202021 Meet 3 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (201920)

20202021 Meet 4 Frosh

none 
Applications of Systems of Linear Equations and Inequalities
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent. (201516)

20202021 Meet 5 Frosh

graphing 
Algebra I

20202021 Meet 1 Sophomores

none 
Area and Perimeter
Including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem. May include surface area of right pyramids and right prisms. No trigonometry. (Refer to Area, Perimeter, and Surface Area 201718)

20202021 Meet 2 Sophomores

graphing 
Similarity
The standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem. (201819)

20202021 Meet 3 Sophomores

graphing 
Circles
Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles. (201011)

20202021 Meet 4 Sophomores

none 
Advanced Geometry Topics
Restricted to Brahmagupta’s formula, point to line distance formula, area of a triangle given vertices, Stewart’s Theorem, Ptolemy’s Theorem, Mass points, inradius and circumradius, Ceva’s Theorem, and Theorem of Menelaus. (201718)

20202021 Meet 5 Sophomores

graphing 
Geometry

20202021 Meet 1 Juniors

none 
Modular Arithmetic
May include arithmetic operations in different moduli, divisibility, solving simple linear congruences in one or two variables, Fermat’s Little Theorem, Wilson’s Theorem, and Chinese Remainder Theorem. (201819)

20202021 Meet 2 Juniors

none 
Polynomials
*NO CALCULATOR* Including factor, remainder, and rational root theorems; Descartes’ Rule of Signs; coefficient analysis; determining equations given various information. (201920) UPDATE 20201007 NO CALCULATOR FOR THIS TOPIC.

20202021 Meet 3 Juniors

CAS 
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. Does not include binomial distribution nor expected value. (201920)

20202021 Meet 4 Juniors

none 
Logs and Exponentials
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential and logarithmic growth and decay, and applications. No complex numbers. (201819)

20202021 Meet 5 Juniors

CAS 
Algebra II

20202021 Meet 1 Seniors

none 
Sequences and Series
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, alternating, and harmonic sequences and series. No calculus. (201920)

20202021 Meet 2 Seniors

none 
Algebra of Complex Numbers
*NO CALCULATOR* Simplifying and factoring, solving linear and quadratic equations with complex coefficients, solving linear systems with complex coefficients, vectors, polars, and powers of pure imaginary numbers, including DeMoivre’s Theorem. (201516) UPDATE 20201020 NO CALCULATOR FOR THIS TOPIC.

20202021 Meet 3 Seniors

CAS 
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (201920)

20202021 Meet 4 Seniors

none 
Conics
Including locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations. (201819)

20202021 Meet 5 Seniors

CAS 
PreCalculus

20202021 Meet 1 Orals


Taxicab Geometry
Source: Taxicab Geometry: An Adventure in NonEuclidean Geometry by Eugene Krause – Chapters 1–5 – ISBN: 0486252027. NO CALCULATOR.

20202021 Meet 2 Orals


Conics
Source: AOPS Intermediate Algebra by Richard Rusczyk & Mathew Crawford – Chapter 5 – ISBN: 9781934124048. NO CALCULATOR.

20202021 Meet 3 Orals


Advanced Geometry
Source: Geometry Revisited by Coxeter and Greitzer – Chapter 1 – ISBN: 9870883856192. (Printings from 1967 and 1996 have same content.) NO CALCULATOR.
Geometry Revisited, has been republished so it has more than one ISBN. They have the same text.

20202021 Meet 4 Orals


Combinatorial Identities
Art of Problem Solving, Intermediate Counting and Probability, Chapter 12. NO CALCULATOR.

20212022 Meet 1 Frosh

graphing 
Ratios, Proportion and Percent
May include money, simple interest (not compound interest), discounts, unit conversions, percentages of increase or decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (201819)

20212022 Meet 2 Frosh

none 
Number Bases
May include conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (202021)

20212022 Meet 3 Frosh

graphing 
Counting Basics and Simple Probability
May include tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (202021)

20212022 Meet 4 Frosh

none 
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (201920)

20212022 Meet 5 Frosh


Algebra I

20212022 Meet 1 Sophomores

graphing 
Perimeter, Area, and Surface Area
May include squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem. May include prisms, pyramids, and cylinders. No trigonometry. No spheres. No cones. (201718)

20212022 Meet 2 Sophomores

none 
Logic, Sets, and Venn Diagrams
Notation, intersection, unions, subsets, empty set, complements, universal set, cardinality (number of elements) of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (201819)

20212022 Meet 3 Sophomores

graphing 
Geometric Probability
Emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11. (201920)

20212022 Meet 4 Sophomores

none 
Advanced Geometry Topics
Restricted to Brahmagupta’s formula, point to line distance formula, area of a triangle given vertices, Stewart’s Theorem, Ptolemy’s Theorem, Mass points, inradius and circumradius, Ceva’s Theorem, and Theorem of Menelaus. (201718)

20212022 Meet 5 Sophomores


Geometry

20212022 Meet 1 Juniors


Systems of Linear Equations and Inequalities with Applications
May include absolute value, intersections, area and/or perimeter of a region, corner points, slopes, distances, inconsistent/consistent systems, and independent/dependent systems. (201819)

20212022 Meet 2 Juniors

none 
Polynomials
May include factor, remainder, and rational root theorems; Descartes’ Rule of Signs; upper/lower bounds of roots; coefficient analysis; determining polynomials given various information. (202021)

20212022 Meet 3 Juniors

CAS 
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. Does not include binomial distribution nor expected value. (202021)

20212022 Meet 4 Juniors

none 
Logs and Exponentials
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential and logarithmic growth and decay, and applications. No complex numbers. (202021)

20212022 Meet 5 Juniors


Algebra II

20212022 Meet 1 Seniors


Triangle Trigonometry with Applications
May include right triangle trigonometry, laws of sines and cosines, area, angles of elevation and depression, compass bearing. The emphasis is not on precalculus trigonometric identities. (201718)

20212022 Meet 2 Seniors

none 
Theory of Equations
Including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, DesCartes’ Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older PreCalculus texts. (201920)

20212022 Meet 3 Seniors

CAS 
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (201920)

20212022 Meet 4 Seniors

none 
Conics
May include locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations. (202021)

20212022 Meet 5 Seniors


PreCalculus

20212022 Meet 1 Orals


Divisibility
Source: Elementary Number Theory – 5th Edition – by David M. Burton – Chapter 2 – ISBN: 9780072325690. NO CALCULATOR.

20212022 Meet 2 Orals


Mathematical Induction
Source: A Decade of the Berkeley Math Circle: I by Stankova & Rike – Chapter 6 – ISBN: 9780821846834. NO CALCULATOR.

20212022 Meet 3 Orals


Generating Functions
Source: AoPS Intermediate Counting & Probability by David Patrick – Chapter 14, ISBN: 1934124060. NO CALCULATOR.

20212022 Meet 4 Orals


Combinatorics
"Combinatorics" based on a document by Rhoad and Whipple. See ICTM web site for AA schools for the source. Contact the president of NSML if you do not have access. CALCULATOR ALLOWED IN PREP.

20222023 Meet 1 Frosh

graphing 
Basic Statistics
Measures of central tendency (mean, median, and mode), histograms, boxandwhisker plots, stem and leaf plots, range, interquartile range (IQR), potential outliers. No variance. No standard deviation. No comparison of sample and population means. (Resource: Sections 1.3 and 2.12.5 in the text OpenStax: https://openstax.org/details/books/introductorystatistics). (202021)

20222023 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (202122)

20222023 Meet 3 Frosh

none 
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (202122)

20222023 Meet 4 Frosh

none 
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (202122)

20222023 Meet 5 Frosh

graphing 
Algebra I

20222023 Meet 1 Sophomores

graphing 
Quadratic Functions
Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (So 200405, Fr 201617, Fr 201718)

20222023 Meet 2 Sophomores

graphing 
Geometric Probability
Emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11. (202122)

20222023 Meet 3 Sophomores

none 
Similarity
The standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem. (202021)

20222023 Meet 4 Sophomores

none 
Circles
Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles. (202021)

20222023 Meet 5 Sophomores

graphing 
Geometry

20222023 Meet 1 Juniors

CAS 
Algebraic Coordinate Geometry Including Circles
Includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, applications, and equations of circles. Coordinates are included. No trig. (201718)

20222023 Meet 2 Juniors

CAS 
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. Does not include binomial distribution nor expected value. (202122)

20222023 Meet 3 Juniors

none 
Modular Arithmetic
May include arithmetic operations in different moduli, divisibility, solving simple linear congruences in one or two variables, Fermat’s Little Theorem, Wilson’s Theorem, and Chinese Remainder Theorem. (202021)

20222023 Meet 4 Juniors

none 
Conics
Including locus definitions, eccentricity, directrix, and area of an ellipse. No parametrics, no polar, and no rotations. (Jr 197980, Sr 202122)

20222023 Meet 5 Juniors

CAS 
Algebra II

20222023 Meet 1 Seniors

CAS 
Applications of Matrices and Markov Chains
includes solving large systems of equations, using matrix inverses and using transition matrices (aka Markov Chains). Does not include geometric transformations. (Jr 201415, Sr 200708). Source: "Finite Mathematics for Managerial, Life, and Social Sciences", Tan, Sections 9.19.3. ISBN: 9781285464657. Reportedly this is the ICTM orals source from 2018. Includes: regular Markov chain, steadystate distribution vector, absorbing states.

20222023 Meet 2 Seniors

CAS 
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (202122)

20222023 Meet 3 Seniors

none 
Linear Diophantine Equations
May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (201819)

20222023 Meet 4 Seniors

none 
Sequences and Series
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, alternating, and harmonic sequences and series. No calculus. (202021)

20222023 Meet 5 Seniors

CAS 
PreCalculus

20222023 Meet 1 Orals


Linear Programming
Source: For All Practical Purposes – 9th Edition – by COMAP – Chapter 4 – ISBN: 9781429254823. (CALCULATOR ALLOWED IN PREP)

20222023 Meet 2 Orals


Inequalities
Source: AoPS Intermediate Algebra by Rusczyk and Crawford. Chapter 12. ISBN: 9781934124048. (NO CALCULATOR ALLOWED IN PREP OR PRESENTATION.)

20222023 Meet 3 Orals


Fibonacci Numbers and Recursion
Source: AoPS Intermediate Counting & Probability by David Patrick – Chapters 9 & 10, ISBN: 1934124060. (NO CALCULATOR ALLOWED IN PREP OR PRESENTATION.)

20222023 Meet 4 Orals


Graph Theory
Source: Discrete Mathematics by John Dossey et al., 5th edition. Sections 4.14.3. PDF with solutions distributed by ICTM. (CALCULATOR ALLOWED IN PREP.)

20232024 Meet 1 Frosh

graphing 
Ratios, Proportion and Percent
May include money, simple interest (not compound interest), discounts, unit conversions, percentages of increase or decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (202122)

20232024 Meet 2 Frosh

graphing 
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (202223)

20232024 Meet 3 Frosh

none 
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (202223)

20232024 Meet 4 Frosh

none 
Quadratics
Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (201718)

20232024 Meet 5 Frosh

none 
Algebra I

20232024 Meet 1 Sophomores

graphing 
Functions
Linear, quadratic, greatest integer, absolute value, step functions, piecewise, exponential. No logarithms. (201920)

20232024 Meet 2 Sophomores

graphing 
Geometric Probability
Emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11. (202223)

20232024 Meet 3 Sophomores

none 
Perimeter, Area, and Surface Area
Including squares, triangles, rectangles, circles, and shapes made from these; includes the Pythagorean Theorem and simple similarity (no angle bisector theorem). (202122)

20232024 Meet 4 Sophomores

none 
Advanced Geometry Topics
Restricted to Brahmagupta’s formula, point to line distance formula, area of a triangle given vertices, Stewart’s Theorem, Ptolemy’s Theorem, Mass points, inradius and circumradius, Ceva’s Theorem, and Theorem of Menelaus. (202122)

20232024 Meet 5 Sophomores

none 
Geometry

20232024 Meet 1 Juniors

CAS 
Systems of Linear Equations and Inequalities with Applications
May include absolute value, intersections, area and/or perimeter of a region, corner points, slopes, distances, types of systems. (202122)

20232024 Meet 2 Juniors

CAS 
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, and expected value (new to this level; see old senior contests). Does not include binomial distribution. (202324)

20232024 Meet 3 Juniors

none 
Sequences and Series
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, alternating, and harmonic sequences and series. No calculus. (201617)

20232024 Meet 4 Juniors

none 
Logarithms and Exponentials
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential and logarithmic growth and decay, and applications. No complex numbers. (202122)

20232024 Meet 5 Juniors

none 
Algebra II

20232024 Meet 1 Seniors

CAS 
Triangle Trigonometry with Applications
Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (202122)

20232024 Meet 2 Seniors

CAS 
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (202223)

20232024 Meet 3 Seniors

none 
Theory of Equations
Including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, Descartes’ Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older precalculus texts. (202122)

20232024 Meet 4 Seniors

none 
Polar Coordinates and Equations
Graphs, systems, and de Moivre’s Theorem. Includes conics and intersections of polar curves that are not simultaneous solutions to the system (“ghost points”). Analytic Geometry, by Gordon Fuller and Dalton Tarwater (6th7th ed) is a good source. (20092010)

20232024 Meet 5 Seniors

none 
PreCalculus

20232024 Meet 1 Orals


Divisibility Rules
(NO CALCULATOR IN PREP OR PRESENTATION.)
Source: Introduction to Number Theory
by Mathew Crawford – the Art of Problem Solving – Chapter 13  ISBN: 9781934124123

20232024 Meet 2 Orals


Game Theory
(CALCULATOR ALLOWED IN PREP)
Source: For All Practical Purposes – 9th Edition – by COMAP – Chapter 15 – ISBN: 9781429243162.

20232024 Meet 3 Orals


Continued Fractions
(NO CALCULATOR IN PREP OR PRESENTATION.)
Source: Continued Fractions by C.D. Olds – MAA New Mathematical Library – Chapters 1 – 3 – https://bookstore.ams.org/nml9 (Yes, this text is really from 1963 even if you find it republished later.)

20232024 Meet 4 Orals


Logic and Logic Circuits
Appendix A. and Sections 9.1 and 9.2 of Discrete Mathematics, 4th edition, by Dossey, Otto, Spence, and Vanden Enden. (This is exactly the same content as the ICTM Regionals source, except there it is called Chapter 10.)
