Past Topics

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calculators allowed
graphing (non-CAS) calculators allowed
CAS calculators allowed

Contest Topic
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1977-1978 Meet 1 Freshmen number bases
1977-1978 Meet 2 Freshmen linear equations
1977-1978 Meet 3 Freshmen logic puzzles
1977-1978 Meet 4 Freshmen word problems
1977-1978 Meet 1 Sophomores systems
1977-1978 Meet 2 Sophomores ratio, proportion, variation
1977-1978 Meet 3 Sophomores factoring over rationals
1977-1978 Meet 4 Sophomores right triangles
1977-1978 Meet 1 Juniors circles
1977-1978 Meet 2 Juniors word problems
1977-1978 Meet 3 Juniors inequalities
1977-1978 Meet 4 Juniors progressions
1977-1978 Meet 1 Seniors complex numbers
1977-1978 Meet 2 Seniors trig equations
1977-1978 Meet 3 Seniors matrix algebra
1977-1978 Meet 4 Seniors probability
1978-1979 Meet 1 Freshmen probability
1978-1979 Meet 2 Freshmen Linear equations and inequalities
1978-1979 Meet 3 Freshmen Modular Arithmetic
1978-1979 Meet 4 Freshmen word problems
1978-1979 Meet 5 Freshmen sequences and series
1978-1979 Meet 1 Sophomores algebraic equations
1978-1979 Meet 2 Sophomores sets and venn diagrams
1978-1979 Meet 3 Sophomores Perimeter, Area, Volume
1978-1979 Meet 4 Sophomores similar polygons
1978-1979 Meet 5 Sophomores right triangles
1978-1979 Meet 1 Juniors coordinates
1978-1979 Meet 2 Juniors factoring over reals
1978-1979 Meet 3 Juniors word problems
1978-1979 Meet 4 Juniors progressions
1978-1979 Meet 5 Juniors inequalities
1978-1979 Meet 1 Seniors logs and exponents
1978-1979 Meet 2 Seniors probability
1978-1979 Meet 3 Seniors trig
1978-1979 Meet 4 Seniors theory of equations
1978-1979 Meet 5 Seniors conics
1979-1980 Meet 1 Freshmen calculation skills
1979-1980 Meet 2 Freshmen linear equations Modern Introductory Analysis, Dolciani, et al. section 3-1; Principals of Advanced Mathematics, Meserve et al. Singer Random House 1970. Section 10-9
1979-1980 Meet 3 Freshmen number bases
1979-1980 Meet 4 Freshmen factoring over rationals
1979-1980 Meet 1 Sophomores equations and inequalities
1979-1980 Meet 2 Sophomores recreational logic
1979-1980 Meet 3 Sophomores perimeter, area
1979-1980 Meet 4 Sophomores coordinate geometry
1979-1980 Meet 1 Juniors circles
1979-1980 Meet 2 Juniors systems
1979-1980 Meet 3 Juniors probability
1979-1980 Meet 4 Juniors logs and exponents
1979-1980 Meet 1 Seniors matrices
1979-1980 Meet 2 Seniors trig
1979-1980 Meet 3 Seniors complex numbers
1979-1980 Meet 4 Seniors differential calculus
1979-1980 Meet 1 Orals binomial theorem Modern Introductory Analysis, Dolciani, et al. section 3-5
1979-1980 Meet 2 Orals mathematical induction
1979-1980 Meet 3 Orals DeMoivre's Theorem Modern Introductory Analysis, Dolciani, et al. Section 12-10, pages 498-503
1979-1980 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 11-12, pages 646-652.)
1980-1981 Meet 1 Freshmen ratio, proportion, percent
1980-1981 Meet 2 Freshmen primes and factors
1980-1981 Meet 3 Freshmen graphing
1980-1981 Meet 4 Freshmen linear systems
1980-1981 Meet 5 Freshmen Algebra
1980-1981 Meet 1 Sophomores quadratics
1980-1981 Meet 2 Sophomores triangles
1980-1981 Meet 3 Sophomores quadrilaterals
1980-1981 Meet 4 Sophomores angles and polygons
1980-1981 Meet 5 Sophomores Geometry
1980-1981 Meet 1 Juniors lines
1980-1981 Meet 2 Juniors factoring over reals
1980-1981 Meet 3 Juniors rational exponents
1980-1981 Meet 4 Juniors complex numbers
1980-1981 Meet 5 Juniors Algebra
1980-1981 Meet 1 Seniors coordinates
1980-1981 Meet 2 Seniors polars
1980-1981 Meet 3 Seniors limits
1980-1981 Meet 4 Seniors derivatives
1980-1981 Meet 5 Seniors Pre-Calculus
1980-1981 Meet 1 Orals matrices and determinants Principles of Advanced Mathematics, Meserve, et al. Singer 1970. Chapter 12, Sections 1-5
1980-1981 Meet 2 Orals sequences and series Limits, a Transition to Calculus, Buchanan. Houghton Mifflin 1966. Chapter 2, pages 17-48
1980-1981 Meet 3 Orals areas under a curve Principles of Advanced Mathematics, Meserve, et al. Singer 1970. Chapter 10, Section 10, pages 573-580
1980-1981 Meet 4 Orals Max & Min problems Calculus and Analytic Geometry, Riddle, Wadsworth. 2nd edition. Chapter 20, Sections 3-4, pages 624-634
1981-1982 Meet 1 Freshmen rational arithmetic
1981-1982 Meet 2 Freshmen allowed pre-algebra
1981-1982 Meet 3 Freshmen linear equations in one variable
1981-1982 Meet 4 Freshmen word problems (non-quadratic
1981-1982 Meet 5 Freshmen Algebra
1981-1982 Meet 1 Sophomores quadratics
1981-1982 Meet 2 Sophomores word problems
1981-1982 Meet 3 Sophomores coordinate geometry
1981-1982 Meet 4 Sophomores similar triangles
1981-1982 Meet 5 Sophomores Geometry
1981-1982 Meet 1 Juniors similar triangles
1981-1982 Meet 2 Juniors circles
1981-1982 Meet 3 Juniors word problems
1981-1982 Meet 4 Juniors allowed probability
1981-1982 Meet 5 Juniors Algebra
1981-1982 Meet 1 Seniors word problems
1981-1982 Meet 2 Seniors allowed probability
1981-1982 Meet 3 Seniors trig
1981-1982 Meet 4 Seniors theory of equations
1981-1982 Meet 5 Seniors Pre-Calculus
1981-1982 Meet 1 Orals polynomial function theory Modern Introductory Analysis, Dolciani, et al. Chapter 6, sections 5-9, pages 230-248
1981-1982 Meet 2 Orals vector and lines Modern Introductory Analysis, Dolciani, et al. Chapter 5, sections 1-5, pages 167-185
1981-1982 Meet 3 Orals probability Probability and Statistics, Willoughby. Silver Burdett 1968. Chapter 3
1981-1982 Meet 4 Orals growth and decay Calculus and Analytic Geometry, Leithold. Harper & Row 1976. Pages 420-27
1982-1983 Meet 1 Freshmen calculation skills
1982-1983 Meet 2 Freshmen number bases
1982-1983 Meet 3 Freshmen linear equations
1982-1983 Meet 4 Freshmen factoring over rationals
1982-1983 Meet 5 Freshmen
1982-1983 Meet 1 Sophomores sets and venn diagrams
1982-1983 Meet 2 Sophomores systems
1982-1983 Meet 3 Sophomores perimeter, area
1982-1983 Meet 4 Sophomores right triangles
1982-1983 Meet 5 Sophomores
1982-1983 Meet 1 Juniors circles
1982-1983 Meet 2 Juniors surface area, volume
1982-1983 Meet 3 Juniors inequalities
1982-1983 Meet 4 Juniors complex numbers
1982-1983 Meet 5 Juniors
1982-1983 Meet 1 Seniors logs and exponents
1982-1983 Meet 2 Seniors matrices
1982-1983 Meet 3 Seniors trig
1982-1983 Meet 4 Seniors functions
1982-1983 Meet 5 Seniors
1982-1983 Meet 1 Orals conics Modern Introductory Analysis, Dolciani, et al. Houghton Mifflin. Pages 507-531
1982-1983 Meet 2 Orals sequences and series Modern Introductory Analysis, Dolciani, et al. Houghton Mifflin. Pages 75-87
1982-1983 Meet 3 Orals induction Modern Introductory Analysis, Dolciani, et al. Houghton Mifflin Pages 69-74
1982-1983 Meet 4 Orals related rates Elements of Calculus, Thomas. Addison Wesley 1972. Pages 105-108
1983-1984 Meet 1 Freshmen arithmetic topics
1983-1984 Meet 2 Freshmen primes and factors
1983-1984 Meet 3 Freshmen Modular Arithmetic
1983-1984 Meet 4 Freshmen rational expressions
1983-1984 Meet 5 Freshmen
1983-1984 Meet 1 Sophomores absolute value
1983-1984 Meet 2 Sophomores quadratics
1983-1984 Meet 3 Sophomores quadrilaterals
1983-1984 Meet 4 Sophomores circles
1983-1984 Meet 5 Sophomores
1983-1984 Meet 1 Juniors similar polygons
1983-1984 Meet 2 Juniors coordinate geometry
1983-1984 Meet 3 Juniors equations
1983-1984 Meet 4 Juniors word problems
1983-1984 Meet 5 Juniors
1983-1984 Meet 1 Seniors probability
1983-1984 Meet 2 Seniors theory of equations
1983-1984 Meet 3 Seniors trig equations and inequalities
1983-1984 Meet 4 Seniors vectors
1983-1984 Meet 5 Seniors
1983-1984 Meet 1 Orals geometry constructions Geometry for Enjoyment and Challenge, Rhoad, Milauskas, & Whipple. McDougall, Littell 1981 or 1983. Pages 649-671
1983-1984 Meet 2 Orals Gaussian integers Enrichment Mathematics for High School, 28th NCTM Yearbook. Pages 46-55
1983-1984 Meet 3 Orals rational function graphing Calculus and Analytic Geometry, Riddle, Douglas F. Wadsworth 3rd edition. Pages 99-121
1983-1984 Meet 4 Orals advanced geometry theorems Geometry Revisited, Coxeter and Greitzer.Addison Wesley 1967. Pages 1-26
1984-1985 Meet 1 Freshmen arithmetic topics
1984-1985 Meet 2 Freshmen number bases
1984-1985 Meet 3 Freshmen linear programming
1984-1985 Meet 4 Freshmen word problems
1984-1985 Meet 5 Freshmen
1984-1985 Meet 1 Sophomores equations and inequalities
1984-1985 Meet 2 Sophomores factoring over rationals
1984-1985 Meet 3 Sophomores perimeter, area
1984-1985 Meet 4 Sophomores right triangles
1984-1985 Meet 5 Sophomores
1984-1985 Meet 1 Juniors surface area, volume
1984-1985 Meet 2 Juniors systems of equations & inequalities
1984-1985 Meet 3 Juniors word problems
1984-1985 Meet 4 Juniors complex numbers
1984-1985 Meet 5 Juniors
1984-1985 Meet 1 Seniors logs and exponents
1984-1985 Meet 2 Seniors progressions
1984-1985 Meet 3 Seniors limits
1984-1985 Meet 4 Seniors differential calculus
1984-1985 Meet 5 Seniors
1984-1985 Meet 1 Orals locus Geometry for Enjoyment and Challenge. Pages 631-648
1984-1985 Meet 2 Orals binomial theorem Modern Introductory Analysis. Pages 88-94
1984-1985 Meet 3 Orals linear programming Finite Mathematics. Chapter 7 and/or 8
1984-1985 Meet 4 Orals convexity Modern Geometries. First 3 sections of chapter 3)
1985-1986 Meet 1 Freshmen arithmetic topics
1985-1986 Meet 2 Freshmen linear equations
1985-1986 Meet 3 Freshmen primes and factors
1985-1986 Meet 4 Freshmen word problems
1985-1986 Meet 5 Freshmen Algebra I
1985-1986 Meet 1 Sophomores systems
1985-1986 Meet 2 Sophomores principals of counting
1985-1986 Meet 3 Sophomores angles and polygons
1985-1986 Meet 4 Sophomores similar triangles
1985-1986 Meet 5 Sophomores Geometry
1985-1986 Meet 1 Juniors circles
1985-1986 Meet 2 Juniors probability
1985-1986 Meet 3 Juniors coordinate geometry
1985-1986 Meet 4 Juniors inequalities
1985-1986 Meet 5 Juniors Algebra II
1985-1986 Meet 1 Seniors similarity
1985-1986 Meet 2 Seniors number theory
1985-1986 Meet 3 Seniors trig equations
1985-1986 Meet 4 Seniors functions
1985-1986 Meet 5 Seniors
1986-1987 Meet 1 Freshmen arithmetic topics
1986-1987 Meet 2 Freshmen Linear equations and inequalities
1986-1987 Meet 3 Freshmen number bases
1986-1987 Meet 4 Freshmen word problems
1986-1987 Meet 5 Freshmen Algebra I
1986-1987 Meet 1 Sophomores quadratics
1986-1987 Meet 2 Sophomores word problems
1986-1987 Meet 3 Sophomores right angles
1986-1987 Meet 4 Sophomores circles
1986-1987 Meet 5 Sophomores Geometry
1986-1987 Meet 1 Juniors systems of equations & inequalities
1986-1987 Meet 2 Juniors coordinate geometry
1986-1987 Meet 3 Juniors logs and exponents
1986-1987 Meet 4 Juniors sequences and series
1986-1987 Meet 5 Juniors Algebra II
1986-1987 Meet 1 Seniors similarity
1986-1987 Meet 2 Seniors conics
1986-1987 Meet 3 Seniors trig
1986-1987 Meet 4 Seniors matrices
1986-1987 Meet 5 Seniors Pre-Calculus
1986-1987 Meet 1 Orals probability Modern Introductory Analysis, Dolciani, et al. 1964. Chapter 15, Sections 1-8, Pages 599-626
1986-1987 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 1-3, pages 295-334
1987-1988 Meet 1 Freshmen arithmetic topics
1987-1988 Meet 2 Freshmen primes and factors
1987-1988 Meet 3 Freshmen Linear equations and inequalities
1987-1988 Meet 4 Freshmen word problems
1987-1988 Meet 5 Freshmen
1987-1988 Meet 1 Sophomores sets and venn diagrams
1987-1988 Meet 2 Sophomores systems
1987-1988 Meet 3 Sophomores angles and polygons
1987-1988 Meet 4 Sophomores similar triangles
1987-1988 Meet 5 Sophomores
1987-1988 Meet 1 Juniors surface area, volume
1987-1988 Meet 2 Juniors absolute value
1987-1988 Meet 3 Juniors statistics
1987-1988 Meet 4 Juniors quadratics
1987-1988 Meet 5 Juniors Algebra II
1987-1988 Meet 1 Seniors probability
1987-1988 Meet 2 Seniors functions
1987-1988 Meet 3 Seniors trig
1987-1988 Meet 4 Seniors limits
1987-1988 Meet 5 Seniors
1987-1988 Meet 1 Orals sets, one-to-one 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 1-3, pages 1-35
1987-1988 Meet 2 Orals mathematics of matrices Mathematics of Matrices, by Davis. 1965. Pages 125-158
1987-1988 Meet 3 Orals geometric transformations Modern Geometries, James Smart. Brooks Cole Pub. Co. [Monteray, CA 93940] 2nd edition. Sections 2.1-2.4, pages 33-57
1987-1988 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 1-4, pages 61-97
1988-1989 Meet 1 Freshmen ration, proportion, percent
1988-1989 Meet 2 Freshmen formula
1988-1989 Meet 3 Freshmen simple probability
1988-1989 Meet 4 Freshmen data analysis
1988-1989 Meet 5 Freshmen Algebra I
1988-1989 Meet 1 Sophomores functions
1988-1989 Meet 2 Sophomores ratio, proportion
1988-1989 Meet 3 Sophomores right triangles
1988-1989 Meet 4 Sophomores circles
1988-1989 Meet 5 Sophomores Geometry
1988-1989 Meet 1 Juniors coordinate geometry
1988-1989 Meet 2 Juniors parabolas
1988-1989 Meet 3 Juniors logs and exponents
1988-1989 Meet 4 Juniors binomial theorem
1988-1989 Meet 5 Juniors Algebra II
1988-1989 Meet 1 Seniors polynomial equations
1988-1989 Meet 2 Seniors trig
1988-1989 Meet 3 Seniors vectors
1988-1989 Meet 4 Seniors Max & Min problems
1988-1989 Meet 5 Seniors Pre-Calculus
1988-1989 Meet 1 Orals geometric probability UMAP Module 660: Applications of High School Mathematics in Geometric Probability, Richard Dalke and Robert Falkner.)
1988-1989 Meet 2 Orals euclidean geometry of the polygon and circle Modern Geometries, James Smart. Brooks Cole Pub. Co. [Monteray, CA 93940] 2nd edition. Sections 4.1-4.3; p. 127-147
1988-1989 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 1-8, pages 167-221
1988-1989 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 5-8, pages 205-231)
1988-1989 Meet 1 Essay
1988-1989 Meet 2 Essay
1988-1989 Meet 3 Essay
1988-1989 Meet 4 Essay
1989-1990 Meet 1 Freshmen arithmetic topics Geometry For Enjoyment And Challenge, Rhoad, Milauskas and Whipple. McDougall Littell.)
1989-1990 Meet 2 Freshmen primes and factors
1989-1990 Meet 3 Freshmen Linear equations and inequalities
1989-1990 Meet 4 Freshmen probability
1989-1990 Meet 5 Freshmen
1989-1990 Meet 1 Sophomores sets and venn diagrams
1989-1990 Meet 2 Sophomores applications of algebra to geometry
1989-1990 Meet 3 Sophomores 2-D similarity
1989-1990 Meet 4 Sophomores perimeter, area
1989-1990 Meet 5 Sophomores
1989-1990 Meet 1 Juniors geometric probability
1989-1990 Meet 2 Juniors absolute value
1989-1990 Meet 3 Juniors logs and exponents
1989-1990 Meet 4 Juniors sequences and series
1989-1990 Meet 5 Juniors
1989-1990 Meet 1 Seniors functions
1989-1990 Meet 2 Seniors trig with applications
1989-1990 Meet 3 Seniors combinatorics
1989-1990 Meet 4 Seniors analysis of graphs (with calculus)
1989-1990 Meet 5 Seniors
1989-1990 Meet 2 Orals graph theory Discrete Mathematics, Roman
1990-1991 Meet 1 Freshmen arithmetic topics
1990-1991 Meet 2 Freshmen number bases
1990-1991 Meet 3 Freshmen data analysis
1990-1991 Meet 4 Freshmen ratio, proportion
1990-1991 Meet 5 Freshmen
1990-1991 Meet 1 Sophomores functions
1990-1991 Meet 2 Sophomores ratio, proportion, variation
1990-1991 Meet 3 Sophomores right triangles
1990-1991 Meet 4 Sophomores surface area
1990-1991 Meet 5 Sophomores
1990-1991 Meet 1 Juniors circles
1990-1991 Meet 2 Juniors one-variable inequalities with absolute value
1990-1991 Meet 3 Juniors applications of quadratics and graph analysis
1990-1991 Meet 4 Juniors logs and exponents
1990-1991 Meet 5 Juniors
1990-1991 Meet 1 Seniors polynomial equations
1990-1991 Meet 2 Seniors trig
1990-1991 Meet 3 Seniors advanced probability including combinatorics
1990-1991 Meet 4 Seniors Max & Min problems
1990-1991 Meet 5 Seniors
1990-1991 Meet 1 Orals linear programming Finite Mathematics, Lial, Miller
1990-1991 Meet 2 Orals sets, one-to-one correspondence, countable and uncountable sets Discrete Mathematics, Roman
1990-1991 Meet 3 Orals probability Finite Mathematics, Weiss, Yoseloff
1990-1991 Meet 4 Orals mathematics of matrices Mathematics of Matrices, Davis
1990-1991 Meet 4 GraphingCalculatorContest
1991-1992 Meet 1 Freshmen perimeter, area
1991-1992 Meet 2 Freshmen basic counting principals
1991-1992 Meet 3 Freshmen Linear equations and inequalities
1991-1992 Meet 4 Freshmen quadratics
1991-1992 Meet 5 Freshmen
1991-1992 Meet 1 Sophomores quadratics
1991-1992 Meet 2 Sophomores algeba/geometry connections Analytic Geometry, Gordon Fuller. Addison Wesley. Chapter 7 [6th edition] or Chapter 6 [5th edition])
1991-1992 Meet 3 Sophomores geomtric probability
1991-1992 Meet 4 Sophomores regular polygons
1991-1992 Meet 5 Sophomores
1991-1992 Meet 1 Juniors similarity
1991-1992 Meet 2 Juniors rational functions
1991-1992 Meet 3 Juniors logs and exponents
1991-1992 Meet 4 Juniors linear diophantine equations
1991-1992 Meet 5 Juniors
1991-1992 Meet 1 Seniors coordinate geometry
1991-1992 Meet 2 Seniors trig
1991-1992 Meet 3 Seniors allowed graphs of functions
1991-1992 Meet 4 Seniors vectors
1991-1992 Meet 5 Seniors
1991-1992 Meet 3 GraphingCalculatorContest
1992-1993 Meet 1 Freshmen ratio, proportion, percent
1992-1993 Meet 2 Freshmen algebra/geometry applications
1992-1993 Meet 3 Freshmen sets and venn diagrams
1992-1993 Meet 4 Freshmen linear equations
1992-1993 Meet 5 Freshmen Algebra I
1992-1993 Meet 1 Sophomores linear systems
1992-1993 Meet 2 Sophomores geometric probability
1992-1993 Meet 3 Sophomores similarity
1992-1993 Meet 4 Sophomores circles
1992-1993 Meet 5 Sophomores Geometry
1992-1993 Meet 1 Juniors right triangle trig
1992-1993 Meet 2 Juniors combinations and permutations
1992-1993 Meet 3 Juniors Max & Min problems
1992-1993 Meet 4 Juniors logs and exponents
1992-1993 Meet 5 Juniors Algebra II
1992-1993 Meet 1 Seniors 3-D Geometry: area and volume
1992-1993 Meet 2 Seniors allowed trig applications
1992-1993 Meet 3 Seniors sequences and series
1992-1993 Meet 4 Seniors advanced probability
1992-1993 Meet 5 Seniors Pre-Calculus
1992-1993 Meet 1 Orals combinatorial analysis Finite Mathematics, Weiss and Youseloff. Worth Pub. 1975. Chapter 3
1992-1993 Meet 2 Orals set theory Finite Mathematics; Weiss & Youseloff, Worth Pub. 1975. Chapter 2
1992-1993 Meet 3 Orals iteration Chaos, Fractals, and Dynamics, Robert Devaney. Addison Wesley. Chapters 1 and 2
1992-1993 Meet 4 Orals groups and graphs Groups & Their Graphs, Grossman and Mangus. MAA New Mathematical Library, Book 14. Pages 3-55
1993-1994 Meet 1 Freshmen non-algebraic word problems
1993-1994 Meet 2 Freshmen linear equations
1993-1994 Meet 3 Freshmen coordinate geometry
1993-1994 Meet 4 Freshmen quadratics
1993-1994 Meet 5 Freshmen Algebra I
1993-1994 Meet 1 Sophomores functions
1993-1994 Meet 2 Sophomores coordinate geometry
1993-1994 Meet 3 Sophomores similarity
1993-1994 Meet 4 Sophomores right triangles
1993-1994 Meet 5 Sophomores Geometry
1993-1994 Meet 1 Juniors locus
1993-1994 Meet 2 Juniors surface area, volume
1993-1994 Meet 3 Juniors logs and exponents
1993-1994 Meet 4 Juniors rational functions
1993-1994 Meet 5 Juniors Algebra II
1993-1994 Meet 1 Seniors operations on functions
1993-1994 Meet 2 Seniors probability
1993-1994 Meet 3 Seniors rational equations and inequalities
1993-1994 Meet 4 Seniors polars
1993-1994 Meet 5 Seniors Pre-Calculus
1993-1994 Meet 1 Orals parametric equations Analytic Geometry, Gordon Fuller. Addison Wesley. Chapter 8 [6th edition] or Chapter 7 [5th edition])
1993-1994 Meet 2 Orals induction Discrete Algorithmic Mathematics, Stephen Maurer and Anthony Ralston. Addison Wesley 1991. Sections 2.1-2.5, pages 137-178
1993-1994 Meet 3 Orals statistics and probability distributions Finite Mathematics, Lial and Miller. Scott Foresman. Sections 7.1-7.4
1993-1994 Meet 4 Orals fractals Fractals for the Classroom, volume 2. NCTM Publication
1994-1995 Meet 1 Freshmen ratio, proportion, percent
1994-1995 Meet 2 Freshmen number theory
1994-1995 Meet 3 Freshmen word problems
1994-1995 Meet 4 Freshmen algebra/geometry applications
1994-1995 Meet 5 Freshmen Algebra I
1994-1995 Meet 1 Sophomores sets and venn diagrams
1994-1995 Meet 2 Sophomores systems of equations and inequalities
1994-1995 Meet 3 Sophomores similarity
1994-1995 Meet 4 Sophomores Perimeter, Area, Volume
1994-1995 Meet 5 Sophomores Geometry
1994-1995 Meet 1 Juniors similarity
1994-1995 Meet 2 Juniors probability
1994-1995 Meet 3 Juniors logs and exponents
1994-1995 Meet 4 Juniors analysis of functions
1994-1995 Meet 5 Juniors Algebra II
1994-1995 Meet 1 Seniors sequences and series
1994-1995 Meet 2 Seniors trig
1994-1995 Meet 3 Seniors vector analytic graphing
1994-1995 Meet 4 Seniors Max & Min problems
1994-1995 Meet 5 Seniors Pre-Calculus
1994-1995 Meet 1 Orals digraphs and networks Finite Mathematics, by Lial and Miller. Scott Foresman. Chapter 11
1994-1995 Meet 2 Orals difference equations Discrete Algorithmic Mathematics, Stephen Maurer and Anthony Ralston. Addison Wesley 1991. Sections 5.1 ? 5.5.)
1994-1995 Meet 3 Orals theory of congruences Elementary Number Theory, David M. Burton. William C. Brown Pub. 3rd edition. Chapter 4.)
1994-1995 Meet 4 Orals error correcting codes Elementary Number Theory, David M. Burton. William C. Brown Pub. 3rd edition. Chapter 4.)
1995-1996 Meet 1 Freshmen perimeter, area
1995-1996 Meet 2 Freshmen simple probability
1995-1996 Meet 3 Freshmen sets and venn diagrams
1995-1996 Meet 4 Freshmen Linear equations and inequalities
1995-1996 Meet 5 Freshmen Algebra I
1995-1996 Meet 1 Sophomores linear systems
1995-1996 Meet 2 Sophomores geometric probability
1995-1996 Meet 3 Sophomores coordinate geometry
1995-1996 Meet 4 Sophomores similarity
1995-1996 Meet 5 Sophomores Geometry
1995-1996 Meet 1 Juniors circles
1995-1996 Meet 2 Juniors 2-D and 3-D locus
1995-1996 Meet 3 Juniors functions
1995-1996 Meet 4 Juniors sequences and series
1995-1996 Meet 5 Juniors Algebra II
1995-1996 Meet 1 Seniors triangle trig
1995-1996 Meet 2 Seniors pre-calculus word problems
1995-1996 Meet 3 Seniors none limits
1995-1996 Meet 4 Seniors polars
1995-1996 Meet 5 Seniors Pre-Calculus
1995-1996 Meet 1 Orals graph theory An Introduction to Discrete Mathematics, Steven Roman. Saunders College Pub. 1986. Sections 6.1-6.3
1995-1996 Meet 2 Orals linear programming: The simplex method Finite Mathematics, Lial and Miller. Scott Foresman 4th edition. Sections 4.1-4.4 [Chapter 3 may need to be read as well for background]
1995-1996 Meet 3 Orals logic Discrete Algorithmic Mathematics, Stephen Maurer and Anthony Ralston. Addison Wesley 1991. Sections 7.1-7.5
1995-1996 Meet 4 Orals taxicab geometry Taxicab Geometry, an Adventure in Non-Euclidean Geometry, Eugene Krause. Dover Publications. Chapters 1-5.)
1996-1997 Meet 1 Freshmen perimeter, area
1996-1997 Meet 2 Freshmen number bases
1996-1997 Meet 3 Freshmen linear equations
1996-1997 Meet 4 Freshmen quadratics
1996-1997 Meet 5 Freshmen Algebra I
1996-1997 Meet 1 Sophomores quadratics
1996-1997 Meet 2 Sophomores Perimeter, Area, Volume
1996-1997 Meet 3 Sophomores similarity
1996-1997 Meet 4 Sophomores coordinate geometry
1996-1997 Meet 5 Sophomores Geometry
1996-1997 Meet 1 Juniors matrices with applications
1996-1997 Meet 2 Juniors surface area, volume
1996-1997 Meet 3 Juniors triangle trig
1996-1997 Meet 4 Juniors logs and exponents
1996-1997 Meet 5 Juniors Algebra II
1996-1997 Meet 1 Seniors probability
1996-1997 Meet 2 Seniors trig equations and functions
1996-1997 Meet 3 Seniors parametrics
1996-1997 Meet 4 Seniors vector analytic graphing
1996-1997 Meet 5 Seniors Pre-Calculus
1996-1997 Meet 1 Orals induction (Discrete Math, John Dossey, et al. Scott Foresman, Sections 2.5 and 2.6
1996-1997 Meet 2 Orals matrix games Finite Mathematics, Weiss and Youseloff. Worth Pub. 1975. Pages 479-521
1996-1997 Meet 3 Orals groups Contemporary Abstract Algebra, Joseph A. Gallian. D.C. Heath 3rd edition, 1994. Pages 23-67. [ISBN #0-669-33907-5] [There is a solution manual available as well.])
1996-1997 Meet 4 Orals mathematics in medicine Contemporary Applied Mathematics, Sacco, Copes, Sloyer, and Stark. Jansen Publications [ISBN #: 0-939-765-06-3] [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
1997-1998 Meet 1 Freshmen none number bases
1997-1998 Meet 2 Freshmen basic counting principals
1997-1998 Meet 3 Freshmen coordinate geometry
1997-1998 Meet 4 Freshmen Linear equations and inequalities
1997-1998 Meet 5 Freshmen Algebra I
1997-1998 Meet 1 Sophomores none coordinate geometry
1997-1998 Meet 2 Sophomores geometric probability
1997-1998 Meet 3 Sophomores Perimeter, Area, Volume
1997-1998 Meet 4 Sophomores triangle trig
1997-1998 Meet 5 Sophomores Geometry
1997-1998 Meet 1 Juniors none manipulation of algebraic expressions and equations
1997-1998 Meet 2 Juniors similarity
1997-1998 Meet 3 Juniors sequences and series
1997-1998 Meet 4 Juniors probability
1997-1998 Meet 5 Juniors Algebra II
1997-1998 Meet 1 Seniors none functions
1997-1998 Meet 2 Seniors none Max & Min problems
1997-1998 Meet 3 Seniors trig
1997-1998 Meet 4 Seniors parametrics
1997-1998 Meet 5 Seniors Pre-Calculus
1997-1998 Meet 1 Orals iteration Chaos, Fractals, and Dynamics, Robert Devaney. Addison Wesley 1990 [ISBN #0-201-23288-X]. Chapters 1 and 2
1997-1998 Meet 2 Orals transformations Mathematics of Matrices, Phillip Davis. Ginn and Co. 1965. [Library of Congress #64-24818] Sections 4.1 - 4.5
1997-1998 Meet 3 Orals differential equations Calculus, Deborah Hughes-Hallet et al. John Wiley and Sons 1994. Sections 9.1-9.8, pages 477-552
1997-1998 Meet 4 Orals mathematics in politics Mathematics in Politics - Strategies, Voting, Power, and Proof, Allen D. Taylor. [ISBN #0-387-94391-9] Chapters 1 and 2.
1998-1999 Meet 1 Freshmen none ratio, proportion, percent
1998-1999 Meet 2 Freshmen applications of algebra to junior high geometry
1998-1999 Meet 3 Freshmen coordinate geometry
1998-1999 Meet 4 Freshmen linear systems of equations and inequalities
1998-1999 Meet 5 Freshmen Algebra I
1998-1999 Meet 1 Sophomores none equations and inequalities
1998-1999 Meet 2 Sophomores exponents with applications
1998-1999 Meet 3 Sophomores similarity
1998-1999 Meet 4 Sophomores circles
1998-1999 Meet 5 Sophomores Geometry
1998-1999 Meet 1 Juniors none similarity
1998-1999 Meet 2 Juniors linear, quadratic, and rational functions
1998-1999 Meet 3 Juniors probability
1998-1999 Meet 4 Juniors triangle trig
1998-1999 Meet 5 Juniors Algebra II
1998-1999 Meet 1 Seniors none logs and exponents
1998-1999 Meet 2 Seniors optimization
1998-1999 Meet 3 Seniors trig
1998-1999 Meet 4 Seniors vectors
1998-1999 Meet 5 Seniors Pre-Calculus
1998-1999 Meet 1 Orals markov chains Finite Mathematics, Lial and Miller. Scott Foresman 4th edition. Chapter 8
1998-1999 Meet 2 Orals groups Contemporary Abstract Algebra, Joseph A. Gallian. D.C. Heath 3rd edition, 1994. Pages 23-67. [ISBN #0-669-33907-5] [There is a solution manual available as well
1998-1999 Meet 3 Orals induction Discrete Math, John Dossey, et al. Scott Foresman. Sections 2.5 and 2.6.)  
1998-1999 Meet 4 Orals topics in geometry Discrete Math, John Dossey, et al. Scott Foresman. Sections 2.5 and 2.6.)  
1999-2000 Meet 1 Freshmen modular arithmetic
1999-2000 Meet 2 Freshmen basic counting principals and simple probability
1999-2000 Meet 3 Freshmen linear equations
1999-2000 Meet 4 Freshmen word problems
1999-2000 Meet 5 Freshmen Algebra I
1999-2000 Meet 1 Sophomores absolute value equations and inequalities
1999-2000 Meet 2 Sophomores geometric probability
1999-2000 Meet 3 Sophomores right triangle trig with applications
1999-2000 Meet 4 Sophomores similarity
1999-2000 Meet 5 Sophomores Geometry
1999-2000 Meet 1 Juniors coordinate geometry
1999-2000 Meet 2 Juniors algebraic word problems
1999-2000 Meet 3 Juniors analysis of polynomials
1999-2000 Meet 4 Juniors logs and exponents
1999-2000 Meet 5 Juniors Algebra II
1999-2000 Meet 1 Seniors trig equations
1999-2000 Meet 2 Seniors sequences and series
1999-2000 Meet 3 Seniors complex numbers
1999-2000 Meet 4 Seniors probability
1999-2000 Meet 5 Seniors Pre-Calculus
1999-2000 Meet 1 Orals parametric equations Analytic Geometry, Gordon Fuller. 7th edition. Chapter 8
1999-2000 Meet 2 Orals linear diophantine equations Linear Systems - Beyond the Unique Solution, Wally Dodge and Paul Sally
1999-2000 Meet 3 Orals linear transformations of the plane Mathematics of Matrices, Phillip David. Ginn and Co. Sections 4.1-4.5
1999-2000 Meet 4 Orals geometric inversions Excursions in Geometry, C. Stanley Ogilvy. Chapters 3 and 4
2000-2001 Meet 1 Freshmen none number bases includes conversion and computation in different bases (bases from 2 - 16); finding the base given some information.
2000-2001 Meet 2 Freshmen volume, surgace area, and 3-D 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
2000-2001 Meet 3 Freshmen systems of equations linear and non-linear - 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.
2000-2001 Meet 4 Freshmen quadratic functions and equations with applications
2000-2001 Meet 5 Freshmen Algebra I
2000-2001 Meet 1 Sophomores none sets and venn diagrams
2000-2001 Meet 2 Sophomores coordinate geometry including equations of circles. (Radius perpendicular to tangent) Students should be able to complete the square.
2000-2001 Meet 3 Sophomores similarity linear and non-linear - 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.
2000-2001 Meet 4 Sophomores triangle trig includes Law of Sines and Law of Cosines, as well as area of triangles. (May include ambiguous case)
2000-2001 Meet 5 Sophomores Geometry
2000-2001 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.
2000-2001 Meet 2 Juniors algebra of functions includes piecewise; no trig, no exponents, no logs
2000-2001 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.
2000-2001 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.
2000-2001 Meet 5 Juniors Algebra II
2000-2001 Meet 1 Seniors none theory of equations including factor, remainder, and rational root theorems; upper bounds, coefficient analysis; determining equations given various info.
2000-2001 Meet 2 Seniors 3-D Geometry: area and volume
2000-2001 Meet 3 Seniors parametrics equations and graphs defined parametrically (no calculus)
2000-2001 Meet 4 Seniors conics including polars and eccentricity, no parametrics or rotations
2000-2001 Meet 5 Seniors Pre-Calculus
2000-2001 Meet 1 Orals graph theory Histomap Module 21: "Drawing Pictures with One Line," Darrah Chavey. COMAP, 1992 (ISSN: 0889-2652) (Suite 210, 57 Bedford St., Lexington, Ma. 02173-4496
2000-2001 Meet 2 Orals rings and integral domains Contemporary Abstract Algebra, Joseph A. Gallian, D.C. Heath, 3rd edition, 1994, Chapters 12,13,14 (ISBN#: 0-669-33907-5) (There is a solution manual available as well
2000-2001 Meet 3 Orals logic Discrete Algorithmic Mathematics, Stephen Maurer and Anthony Ralston: Addison Wesley; 1991; Sections 7.1-7.3,7.5
2000-2001 Meet 4 Orals linear transformation of the plane Mathematics of Matrices, Phillip Davis, Ginn and Co., 1965, Library of Congress: 64-24818, Pages 125-161 (Out of Print)
2001-2002 Meet 1 Freshmen 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.
2001-2002 Meet 3 Freshmen graphing Linear equations and inequalities includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.
2001-2002 Meet 4 Freshmen graphing quadration functions and equations with applications no complex numbers
2001-2002 Meet 5 Freshmen graphing Algebra I
2001-2002 Meet 1 Sophomores none coordinate geometry includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications. No circles.
2001-2002 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.
2001-2002 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.
2001-2002 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
2001-2002 Meet 5 Sophomores graphing Geometry
2001-2002 Meet 1 Juniors none 3-D 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 3-space.
2001-2002 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.
2001-2002 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.
2001-2002 Meet 4 Juniors graphing analysis of polynomials including factor, remainder, and rational root theorems; coefficient analysis; determining equations given various information.
2001-2002 Meet 5 Juniors graphing Algebra II
2001-2002 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.
2001-2002 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.
2001-2002 Meet 3 Seniors CAS trig applications including laws of sines and cosines, sinusoidal functions and, of course, word problems.
2001-2002 Meet 4 Seniors CAS conics including polars and eccentricity. There should be no parametrics nor rotations.
2001-2002 Meet 5 Seniors CAS Pre-Calculus
2001-2002 Meet 1 Orals markov chains Finite Mathematics by Lial and Miller, Scott Foresman, 4th edition, Chapter 8.
2001-2002 Meet 2 Orals induction Discrete Math by John Dossey et al, Scott Foresman, Sections 2.5-2.6
2001-2002 Meet 3 Orals perfect numbers Excursions into Mathematics by Beck, Bleicher, and Crowe, A.K. Peters, LTd. (ISBM: 1568811152), Chapter 2, Sections 1-5
2001-2002 Meet 4 Orals geometry Geometric Inequalities by Kazarinoff, MAA, Chapter 2
2002-2003 Meet 1 Freshmen graphing linear equations including word problems leading to linear equations in one variable and simple absolute value equations. (No systems)
2002-2003 Meet 2 Freshmen none number bases including conversion and computation in different bases and finding the base given some information.
2002-2003 Meet 3 Freshmen 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.
2002-2003 Meet 4 Freshmen none rational expressions simplifying rational expressions, solving equations involving rational expressions, word problems, basic algebra 1 factoring.
2002-2003 Meet 5 Freshmen graphing Algebra I
2002-2003 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.
2002-2003 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.
2002-2003 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.
2002-2003 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.
2002-2003 Meet 5 Sophomores graphing Geometry
2002-2003 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.
2002-2003 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.
2002-2003 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.
2002-2003 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.
2002-2003 Meet 5 Juniors graphing Algebra II
2002-2003 Meet 1 Seniors CAS Pre-Calculus including interest, regression, growth and decay, linear quadratic and exponential relations. Excludes trig applications.
2002-2003 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.
2002-2003 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.
2002-2003 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.
2002-2003 Meet 5 Seniors CAS Pre-Calculus
2002-2003 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
2002-2003 Meet 2 Orals taxicab geometry Taxicab Geometry, an Adventure in Non-Euclidean Geometry, Eugene Krause. Dover Publications. Chapters 2-5 (pp.12-49)
2002-2003 Meet 3 Orals matrix games excursions into Mathematics by Beck, Bleicher, and Crowe, chapter 5, sections 6 & 7
2002-2003 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.
2003-2004 Meet 1 Freshmen 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.
2003-2004 Meet 2 Freshmen 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. 
2003-2004 Meet 3 Freshmen graphing applications of systems of linear equations and inequalities including linear programming limited to considering the vertices of an enclosed area.
2003-2004 Meet 4 Freshmen 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. 
2003-2004 Meet 5 Freshmen graphing Algebra I
2003-2004 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).
2003-2004 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.
2003-2004 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.
2003-2004 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.
2003-2004 Meet 5 Sophomores graphing Geometry
2003-2004 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 (Addison-Wesley). 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.
2003-2004 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. 
2003-2004 Meet 3 Juniors graphing triangle trig includes right triangle trig, laws of sines and cosines, area of a triangle, and Hero's Formula 
2003-2004 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)
2003-2004 Meet 5 Juniors graphing Algebra II
2003-2004 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.
2003-2004 Meet 2 Seniors none theory of equations including factor, remainder, and rational root theorems; upper bounds, coefficient analysis; determining equations given various info.
2003-2004 Meet 3 Seniors CAS conics including locus definitions, eccentricity, directrix, no parametrics, no polar, and no rotations.
2003-2004 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.
2003-2004 Meet 5 Seniors CAS Pre-Calculus
2003-2004 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.)
2003-2004 Meet 2 Orals vectors Analytic Geometry, 7th edition, by Gordon Fuller and Dalton Tarwalter, Ch 10. (In earlier editions, this is still Ch. 10)
2003-2004 Meet 3 Orals combinatorics An Introduction to Discrete Mathematics, Steven Roman. Ch. 4, sections 1-8, and Ch. 5 sections 1 & 2
2003-2004 Meet 4 Orals markov chains Finite Mathematics7th edition, by Lial, Greenwell, and Ritchey (Pearson Addison Wesley, 2002). Ch. 10, Sections 1-2 (p. 490 - 510).
2004-2005 Meet 1 Freshmen graphing area & perimeter including squares, triangles, rectangles, circles, and shapes made from these. May include the Pythagorean Theorem.
2004-2005 Meet 2 Freshmen none number bases including conversion and computation in different bases (bases from 2 to 16); finding the base given some information.
2004-2005 Meet 3 Freshmen 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.
2004-2005 Meet 4 Freshmen none Linear equations and inequalities includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.
2004-2005 Meet 5 Freshmen graphing Algebra I
2004-2005 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.
2004-2005 Meet 2 Sophomores none coordinate geometry includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications. No circles.
2004-2005 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.
2004-2005 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.
2004-2005 Meet 5 Sophomores graphing Geometry
2004-2005 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.
2004-2005 Meet 2 Juniors none linear, quadratic, and rational functions including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots.
2004-2005 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.
2004-2005 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)
2004-2005 Meet 5 Juniors graphing Algebra II
2004-2005 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.
2004-2005 Meet 2 Seniors none complex numbers including solutions to polynomial equations, complex algebra (including complex coefficients), and CIS format (rectangular and polar form).
2004-2005 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.
2004-2005 Meet 4 Seniors none tirg equations and identities including solving trig equations and simplifying trig expressions using standard formulas (double-angle, half-angle, sum-to-product, and product-to-sum).
2004-2005 Meet 5 Seniors CAS Pre-Calculus
2004-2005 Meet 1 Orals divisibility theory Number Theory, by Burton. Third edition. (the entire chapter). ISBN: 0-697-13330-3
2004-2005 Meet 2 Orals groups Contemporary Abstract Algebra, by Gallian. Third edition. (pp 23-67.)
2004-2005 Meet 3 Orals mathematical induction Discrete Math, by Dossey, et al. Chapter 2.5-2.6 (or 2.6-2.7 in other editions.)
2004-2005 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.
2005-2006 Meet 1 Freshmen 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.
2005-2006 Meet 2 Freshmen 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.
2005-2006 Meet 3 Freshmen 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.
2005-2006 Meet 4 Freshmen graphing word problems Standard and nonstandard algebra word problems. Will include those solvable by linear equation systems in one or two variables.
2005-2006 Meet 5 Freshmen graphing Algebra I
2005-2006 Meet 1 Sophomores graphing coordinate geometry includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications. No circles.
2005-2006 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.
2005-2006 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.
2005-2006 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 3-space.
2005-2006 Meet 5 Sophomores graphing Geometry
2005-2006 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
2005-2006 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.
2005-2006 Meet 3 Juniors none functions and relations non-recursive, standard functions, limited to linear, quadratic, rational, and including domain and range. May include inverse concepts.
2005-2006 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
2005-2006 Meet 5 Juniors CAS Algebra II
2005-2006 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.
2005-2006 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.
2005-2006 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.
2005-2006 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.
2005-2006 Meet 5 Seniors CAS Pre-Calculus
2005-2006 Meet 1 Orals taxicab geometry Taxicab Geometry: An Adventure in Non-Euclidean Geometry, by Eugene F Krause; Dover 1987. Chapters 2-5 (pages 12-49).
2005-2006 Meet 2 Orals difference equations Discrete Algorithmic Mathematics, by Stephen Maurer and Anthony Ralston; Addison Wesley. Sections 5.1-5.5.
2005-2006 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.).
2005-2006 Meet 4 Orals relations and functions Fundamental Notions of Abstract Mathematics, by Carol Schumacher; Addison-Wesley, 2001. ISBN: 0-201-43724-4. Regional: 4.1-4.3. State: 5.1-5.4. (Source contingent on copyright permissions.)
2006-2007 Meet 1 Freshmen 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.
2006-2007 Meet 2 Freshmen none number bases including conversion and computation in different bases (bases from 2 to 16); finding the base given some information.
2006-2007 Meet 3 Freshmen 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.
2006-2007 Meet 4 Freshmen 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.
2006-2007 Meet 5 Freshmen graphing Algebra I
2006-2007 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.
2006-2007 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.
2006-2007 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.
2006-2007 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.
2006-2007 Meet 5 Sophomores graphing Geometry
2006-2007 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.
2006-2007 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.
2006-2007 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.
2006-2007 Meet 4 Juniors none rational functions including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots.
2006-2007 Meet 5 Juniors CAS Algebra II
2006-2007 Meet 1 Seniors CAS trigonometry applications, equations, and theory including laws of sines and cosines, and of course, word problems.
2006-2007 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.
2006-2007 Meet 3 Seniors CAS conics including locus definitions, eccentricity, directrix, no parametrics, no polar, and no rotations.
2006-2007 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
2006-2007 Meet 5 Seniors CAS Pre-Calculus
2006-2007 Meet 1 Orals polar coordinates and equations Analytic Geometry, by Gordon Fuller and Dalton Tarwater. (6th-7th ed: Ch. 7 except 7.6; 5th ed: Ch. 6 except 6.7). Previously used as a topic in 2002-2003.
2006-2007 Meet 2 Orals graph theory Graphs and Their Uses, by Ore, Oystein (MAA, 1963). (Ch. 1-3, excluding 1.7, 3.4-5 in newer ed.) Previously used as a topic in 1994-1995 and 1995-1996 with different sources.
2006-2007 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 1999-2000. A PDF copy of this source is available.
2006-2007 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.)
2007-2008 Meet 1 Freshmen 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.
2007-2008 Meet 2 Freshmen 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.
2007-2008 Meet 3 Freshmen 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.
2007-2008 Meet 4 Freshmen none quadratic functions includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications.
2007-2008 Meet 5 Freshmen graphing Algebra I
2007-2008 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.
2007-2008 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.
2007-2008 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 3-space.
2007-2008 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.
2007-2008 Meet 5 Sophomores graphing Geometry
2007-2008 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.
2007-2008 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.
2007-2008 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.
2007-2008 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)
2007-2008 Meet 5 Juniors CAS Algebra II
2007-2008 Meet 1 Seniors none complex numbers including solutions to polynomial equations, complex algebra (including complex coefficients), and CIS format (rectangular and polar form).
2007-2008 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
2007-2008 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)
2007-2008 Meet 4 Seniors none trig equations and identities includes solving trig equations and simplifying trig expressions using standard formulas (double-angle, half-angle, sum-to-product, and product-to-sum).
2007-2008 Meet 5 Seniors CAS Pre-Calculus
2007-2008 Meet 1 Orals game theory For All Practical Purposes (COMAP), 6th ed. Chapter 16.
2007-2008 Meet 2 Orals linear transformations of the plane Mathematics of Matrices, by Phillip Davis. Ginn and Co., 1965, Library of Congress: 64-24818. Pages 125-161.
2007-2008 Meet 3 Orals perfect numbers and factorization Excursions into Mathematics, by Beck, Bleicher, Crowe. Sections 2.1-2.5.
2007-2008 Meet 4 Orals voting methods For All Practical Purposes (COMAP), 6th ed. Chapters 12-13.
2008-2009 Meet 1 Freshmen 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.
2008-2009 Meet 2 Freshmen none Number bases including conversion and computation in different bases (bases from 2 to 16); finding the base given some information.
2008-2009 Meet 3 Freshmen graphing Linear equations and inequalities includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.
2008-2009 Meet 4 Freshmen none Rational expressions simplifying rational expressions, solving equations involving rational expressions, word problems, basic algebra 1 factoring.
2008-2009 Meet 5 Freshmen Algebra I
2008-2009 Meet 1 Sophomores graphing Perimeter, Area, and Surface Area including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem.
2008-2009 Meet 2 Sophomores none Coordinate geometry without circles includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications.
2008-2009 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.
2008-2009 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.
2008-2009 Meet 5 Sophomores Geometry
2008-2009 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.
2008-2009 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.
2008-2009 Meet 3 Juniors CAS Linear, Quadratic, and Rational Functions including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots.
2008-2009 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).
2008-2009 Meet 5 Juniors Algebra II
2008-2009 Meet 1 Seniors CAS Combinatorics Fundamantal counting principle, combinations and permutations, permutations with and without repetition, arrangements of distinguishable and non-distinguishable items with and without replacement, and probability involving these topics. No circular permutations. Possible sources: Advanced Mathematics by Richard G. Brown, sections 15-2 to 15-4, or Probability, a monograph by Rhoad and Whipple, used as oral reference for ICTM in '04-'05.
2008-2009 Meet 2 Seniors none Conics including locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations.
2008-2009 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.
2008-2009 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 Pre-Calculus texts.
2008-2009 Meet 5 Seniors Pre-Calculus
2008-2009 Meet 1 Orals Combinatorics Finite Mathematics, by Lial and Miller (4th ed). Chapter 8.
2008-2009 Meet 2 Orals Conics For All Practical Purposes, by COMAP (6th ed). Chapter 4.
2008-2009 Meet 3 Orals Trigonometry Analytic Geometry, by Fuller and Tarwater. Chapter 3.
2008-2009 Meet 4 Orals Theory of Equations For All Practical Purposes, by COMAP (6th ed). Chapter 1.
2009-2010 Meet 1 Freshmen 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.
2009-2010 Meet 2 Freshmen 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.
2009-2010 Meet 3 Freshmen 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.
2009-2010 Meet 4 Freshmen none Coordinate Geometry Includes distance, midpoint, slope, parallels, perpendiculars and applications.
2009-2010 Meet 5 Freshmen Algebra I
2009-2010 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.
2009-2010 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.
2009-2010 Meet 3 Sophomores graphing Geometric Transformations on a Plane Includes reflections, rotations, translations, dilations, shears, and compositions in two dimensions.
2009-2010 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.
2009-2010 Meet 5 Sophomores Geometry
2009-2010 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.
2009-2010 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.
2009-2010 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.
2009-2010 Meet 4 Juniors none Functions and Relations Non-recursive, standard functions, limited to linear, quadratic, rational, and piecewise including domain, range, and composition. May include inverse concepts. No logs, exponential, nor trig.
2009-2010 Meet 5 Juniors Algebra II
2009-2010 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.
2009-2010 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.
2009-2010 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 (6th-7th ed) is a good source.
2009-2010 Meet 4 Seniors none Trig. Equations and Identities includes solving trig equations and simplifying trig expressions using standard formulas (double-angle, half-angle, sum-to-product, and product-to-sum).
2009-2010 Meet 5 Seniors Pre-Calculus
2009-2010 Meet 1 Orals Algebra of Complex numbers Taxicab Geometry: An Adventure in Non-Euclidean Geometry, by Eugene F. Krause. ISBN 0-486-25202-7. Chapters 2?5 (pp. 12?49).
2009-2010 Meet 2 Orals Probability Analytic Geometry, by Gordon Fuller and Dalton Tarwater. ISBN 0-201-13484-5 (7th ed). (6th-7th ed: Ch. 8; 5th ed: Ch. 7).
2009-2010 Meet 3 Orals Polar Coordinates and Equations Elementary Number Theory, by Burton, David M.. Chapter 4 (any edition).
2009-2010 Meet 4 Orals Trig. Equations and Identities For All Practical Purposes, by COMAP (6th ed). Chapter 19.
2010-2011 Meet 1 Freshmen 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.
2010-2011 Meet 2 Freshmen graphing Counting Basics and Simple Probability Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.
2010-2011 Meet 3 Freshmen none Number bases including conversion and computation in different bases (bases from 2 to 16); finding the base given some information.
2010-2011 Meet 4 Freshmen 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.
2010-2011 Meet 5 Freshmen Algebra I
2010-2011 Meet 1 Sophomores none Quadrilaterals properties, classification, angle measures and sums, area, diagonals, convex and non-convex, cyclic quadrilaterals, Brahmagupta?s formula, etc.
2010-2011 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.
2010-2011 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.
2010-2011 Meet 4 Sophomores graphing Geometric Transformations on a Plane Includes reflections, rotations, translations, dilations, shears, and compositions in two dimensions.
2010-2011 Meet 5 Sophomores Geometry
2010-2011 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.
2010-2011 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.
2010-2011 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.
2010-2011 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).
2010-2011 Meet 5 Juniors Algebra II
2010-2011 Meet 1 Seniors none Diophantine Equations may include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems.
2010-2011 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.
2010-2011 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.
2010-2011 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.
2010-2011 Meet 5 Seniors Pre-Calculus
2010-2011 Meet 1 Orals Polar Coordinates and Equations Analytic Geometry, by Fuller and Tarwater. (6th-7th ed: Ch. 7; 5th ed: Ch. 6).
2010-2011 Meet 2 Orals Probability Introduction to Discrete Mathematics, by Roman, Steven. 4.1-4.8, 5.1-5.2.
2010-2011 Meet 3 Orals Sequences and Series Geometry Revisited, by Coxeter and Greitzer. 1.1-1.3.
2010-2011 Meet 4 Orals Vector Analytic Graphing , by . .
2011-2012 Meet 1 Freshmen 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.
2011-2012 Meet 2 Freshmen graphing Counting Basics and Simple Probability Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.
2011-2012 Meet 3 Freshmen none Number Theory and Divisibility may include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships.
2011-2012 Meet 4 Freshmen 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.
2011-2012 Meet 5 Freshmen Algebra I
2011-2012 Meet 1 Sophomores graphing Perimeter, Area, and Surface Area including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem.
2011-2012 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.
2011-2012 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.
2011-2012 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.
2011-2012 Meet 5 Sophomores Geometry
2011-2012 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.
2011-2012 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.
2011-2012 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: 64-24818. Pages 125-161 (Oral #2, 2007-8).
2011-2012 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.
2011-2012 Meet 5 Juniors Algebra II
2011-2012 Meet 1 Seniors CAS Trigonometry Applications, Equations and Theory including laws of sines and cosines, and of course, word problems.
2011-2012 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.
2011-2012 Meet 3 Seniors none Conics including locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations.
2011-2012 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 Pre-Calculus texts.
2011-2012 Meet 5 Seniors Pre-Calculus
2011-2012 Meet 1 Orals Trigonometry Applications, Equations and Theory Graphs and Their Uses, by Oystein Ore (MAA). Chapters 1 through 3.
2011-2012 Meet 2 Orals Divisibility Elementary Number Theory, by David Burton. Chapter 2.
2011-2012 Meet 3 Orals Conics Excursions into Mathematics, by Beck, Bleicher, Crowe (Millenium Edition). Sections 5.1, 5.6, 5.7.
2011-2012 Meet 4 Orals Theory of Equations , by Krause. Chapters 1-5.
2012-2013 Meet 1 Freshmen 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.
2012-2013 Meet 2 Freshmen graphing Counting Basics and Simple Probability Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.
2012-2013 Meet 3 Freshmen none Linear Equations and Inequalities Includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.
2012-2013 Meet 4 Freshmen none Number Theory and Divisibility May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships.
2012-2013 Meet 5 Freshmen Algebra I
2012-2013 Meet 1 Sophomores graphing Perimeter, Area, and Surface Area including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem.
2012-2013 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.
2012-2013 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.
2012-2013 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.
2012-2013 Meet 5 Sophomores Geometry
2012-2013 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.
2012-2013 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.
2012-2013 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.
2012-2013 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.
2012-2013 Meet 5 Juniors Algebra II
2012-2013 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: 64-24818. Pages 125-161
2012-2013 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.
2012-2013 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.
2012-2013 Meet 4 Seniors none Conics including locus definitions, eccentricity, and focus/directrix properties. No parametrics, no polar, and no rotations.
2012-2013 Meet 5 Seniors Pre-Calculus
2012-2013 Meet 1 Orals Geometric Transformations Using Matrices on a Plane For All Practical Purposes, by COMAP. Chapters 12 and 13.
2012-2013 Meet 2 Orals Probability Elementary Number Theory, by David Burton. Chapter 4.
2012-2013 Meet 3 Orals Algebra of Complex Numbers Anayltic Geometry, by Gordon Fuller and Dalton Tarwater. Chapter 8.
2012-2013 Meet 4 Orals Conics , by . .
2013-2014 Meet 1 Freshmen 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.
2013-2014 Meet 2 Freshmen graphing Counting Basics and Simple Probability Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.
2013-2014 Meet 3 Freshmen none Linear Equations and Inequalities Includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.
2013-2014 Meet 4 Freshmen none Number Theory and Divisibility May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships.
2013-2014 Meet 5 Freshmen Algebra I
2013-2014 Meet 1 Sophomores graphing Perimeter, Area, and Surface Area including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem.
2013-2014 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.
2013-2014 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.
2013-2014 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.
2013-2014 Meet 5 Sophomores Geometry
2013-2014 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.
2013-2014 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.
2013-2014 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.
2013-2014 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.
2013-2014 Meet 5 Juniors Algebra II
2013-2014 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: 64-24818. Pages 125-161
2013-2014 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.
2013-2014 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.
2013-2014 Meet 4 Seniors none Conics including locus definitions, eccentricity, and focus/directrix properties. No parametrics, no polar, and no rotations.
2013-2014 Meet 5 Seniors Pre-Calculus
2013-2014 Meet 1 Orals Geometric Transformations Using Matrices on a Plane 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..
2013-2014 Meet 2 Orals Probability Elementary Number Theory, by David Burton. Chapter 4.
2013-2014 Meet 3 Orals Algebra of Complex Numbers Anayltic Geometry, by Gordon Fuller and Dalton Tarwater. Chapter 8.
2013-2014 Meet 4 Orals Conics Geometric Probability, by Art Johnson (COMAP Module Sections 1 - 3; pages 1- 36). AND NCTM Publication . Sections 1-4, 9.1 (#1, #2), 10, 10.1, exercises (section 11) 1-6, 10.
2014-2015 Meet 1 Freshmen 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 2013-14)
2014-2015 Meet 2 Freshmen graphing Counting Basics and Simple Probability Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (Last used 2013-14)
2014-2015 Meet 3 Freshmen none Number Bases Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (Last used 2012-13)
2014-2015 Meet 4 Freshmen 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 2013-14; not quadratics - they are new to this topic)
2014-2015 Meet 5 Freshmen Algebra I
2014-2015 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 2012-13)
2014-2015 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 2013-14)
2014-2015 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 2011-12)
2014-2015 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 2013-14; note that a calculator is allowed this year)
2014-2015 Meet 5 Sophomores Geometry
2014-2015 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 2012-13)
2014-2015 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 2013-14)
2014-2015 Meet 3 Juniors none Rational Functions Including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots. (Last used 2006-07)
2014-2015 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 2010-11)
2014-2015 Meet 5 Juniors Algebra II
2014-2015 Meet 1 Seniors none Diophantine Equations May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (2012-13)
2014-2015 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 2013-14)
2014-2015 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 Pre-Calculus texts. (Last used 2011-12)
2014-2015 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 2012-13)
2014-2015 Meet 5 Seniors Pre-Calculus
2014-2015 Meet 1 Orals Geometric Constructios College Geometry, by Nathan Altshiller-Court. 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.
2014-2015 Meet 2 Orals Probability 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 1-3.
2014-2015 Meet 3 Orals Theory of Equations Continued Fractions, by C.D. Olds. Chapters 1-3.
2014-2015 Meet 4 Orals Vector Analytic Graphing Probability Module, by Rhoad and Whipple. 1.1-1.7 & 1.12 (pp 1-40 & 77-84).
2015-2016 Meet 1 Freshmen 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. (2013-14)
2015-2016 Meet 2 Freshmen graphing Counting Basics and Simple Probability Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2014-15)
2015-2016 Meet 3 Freshmen none Number Theory and Divisibility May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2014-15)
2015-2016 Meet 4 Freshmen 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. (2011-12)
2015-2016 Meet 5 Freshmen Algebra I
2015-2016 Meet 1 Sophomores graphing Perimeter, Area, and Surface Area Including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem. (2013-14)
2015-2016 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. (2013-14)
2015-2016 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. (2010-11, supplemented)
2015-2016 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. (2014-15)
2015-2016 Meet 5 Sophomores Geometry
2015-2016 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. (2013-14)
2015-2016 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. (2013-14)
2015-2016 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. (2013-14)
2015-2016 Meet 4 Juniors none Functions and Relations Non-recursive, standard functions, limited to linear, quadratic, rational, and piecewise including domain, range, and composition. May include inverse concepts. No logs, exponential, nor trig. (2012-13)
2015-2016 Meet 5 Juniors Algebra II
2015-2016 Meet 1 Seniors CAS Triangle Trigonometry with Applications Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (2012-13)
2015-2016 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. (2013-14)
2015-2016 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. (2013-14)
2015-2016 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. (2010-11)
2015-2016 Meet 5 Seniors CAS Pre-Calculus
2015-2016 Meet 1 Orals Triangle Trigonometry with Applications Taxicab Geometry, by Eugene Krause. Chapters 1 - 5.
2015-2016 Meet 2 Orals Probability Cake Cutting Algorithms, by Jack Robertson and William Webb (Chapter 1). See COMAP For All Practical Purposes for additional practice material. .
2015-2016 Meet 3 Orals Algebra of Complex Numbers For All Practical Purposes, by COMAP. Chapter 3.
2015-2016 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. .
2016-2017 Meet 1 Freshmen 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. (2015-16)
2016-2017 Meet 2 Freshmen graphing Counting Basics and Simple Probability Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2015-16)
2016-2017 Meet 3 Freshmen none Quadratics Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (2012-13)
2016-2017 Meet 4 Freshmen none Number Bases Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2014-15)
2016-2017 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). (2012-13)
2016-2017 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. (2015-16)
2016-2017 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. (2014-15)
2016-2017 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. (2015-16)
2016-2017 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. (2012-13)
2016-2017 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. (2015-16)
2016-2017 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. (2014-15)
2016-2017 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. (2015-16)
2016-2017 Meet 1 Seniors CAS Triangle Trigonometry with Applications Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (2015-16)
2016-2017 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. (2015-16)
2016-2017 Meet 3 Seniors none Diophantine Equations May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (2014-15)
2016-2017 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) (2014-15)
2016-2017 Meet 1 Orals Divisibility Source: Elementary Number Theory by David Burton -- Chapter 2
2016-2017 Meet 2 Orals Markov Chains Finite Mathematics by Lial and Miller -- Chapter 9 (6th edition) -- Other editions are similar.
2016-2017 Meet 3 Orals Linear Programming For All Practical Purposes by COMAP -- Chapter 4
2016-2017 Meet 4 Orals The Algebra of Logic Chapter 1, pp. 1-29, of Elliot Mendelson, Boolean Algebra and Switching Circuits, 1970 Ed., in the Schaum Outline Series.