|
1977-1978 Meet 1 Frosh
|
|
number bases
|
|
1977-1978 Meet 2 Frosh
|
|
linear equations
|
|
1977-1978 Meet 3 Frosh
|
|
logic puzzles
|
|
1977-1978 Meet 4 Frosh
|
|
word problems
|
|
1977-1978 Meet 1 Sophomores
|
|
systems of equations
|
|
1977-1978 Meet 2 Sophomores
|
|
ratio, proportion, variation
|
|
1977-1978 Meet 3 Sophomores
|
|
factoring over the rationals
|
|
1977-1978 Meet 4 Sophomores
|
|
right triangle geometry
|
|
1977-1978 Meet 1 Juniors
|
|
circles
|
|
1977-1978 Meet 2 Juniors
|
|
algebraic word problems
|
|
1977-1978 Meet 3 Juniors
|
|
inequalities
|
|
1977-1978 Meet 4 Juniors
|
|
algebraic and geometric progressions
|
|
1977-1978 Meet 1 Seniors
|
|
complex numbers
|
|
1977-1978 Meet 2 Seniors
|
|
trigonometric equations
|
|
1977-1978 Meet 3 Seniors
|
|
matrix algebra
|
|
1977-1978 Meet 4 Seniors
|
|
probability
|
|
1978-1979 Meet 1 Frosh
|
|
probability
|
|
1978-1979 Meet 2 Frosh
|
|
Linear equations and inequalities
|
|
1978-1979 Meet 3 Frosh
|
|
Modular Arithmetic
|
|
1978-1979 Meet 4 Frosh
|
|
word problems
|
|
1978-1979 Meet 5 Frosh
|
|
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 Frosh
|
|
calculation skills
|
|
1979-1980 Meet 2 Frosh
|
|
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 Frosh
|
|
number bases
|
|
1979-1980 Meet 4 Frosh
|
|
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
|
|
Circles
|
|
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 Frosh
|
|
ratio, proportion, percent
|
|
1980-1981 Meet 2 Frosh
|
|
primes and factors
|
|
1980-1981 Meet 3 Frosh
|
|
graphing
|
|
1980-1981 Meet 4 Frosh
|
|
linear systems
|
|
1980-1981 Meet 5 Frosh
|
|
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 Frosh
|
|
rational arithmetic
|
|
1981-1982 Meet 2 Frosh
|
allowed |
pre-algebra
|
|
1981-1982 Meet 3 Frosh
|
|
linear equations in one variable
|
|
1981-1982 Meet 4 Frosh
|
|
word problems (non-quadratic
|
|
1981-1982 Meet 5 Frosh
|
|
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 II
|
|
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 Frosh
|
|
calculation skills
|
|
1982-1983 Meet 2 Frosh
|
|
number bases
|
|
1982-1983 Meet 3 Frosh
|
|
linear equations
|
|
1982-1983 Meet 4 Frosh
|
|
factoring over rationals
|
|
1982-1983 Meet 5 Frosh
|
|
Algebra 1
|
|
1982-1983 Meet 1 Sophomores
|
|
sets and venn diagrams
|
|
1982-1983 Meet 2 Sophomores
|
|
systems of equations
|
|
1982-1983 Meet 3 Sophomores
|
|
perimeter, area
|
|
1982-1983 Meet 4 Sophomores
|
|
right triangles
|
|
1982-1983 Meet 5 Sophomores
|
|
Geometry
|
|
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
|
|
Algebra II
|
|
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
|
|
Pre-Calculus
|
|
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 Frosh
|
|
arithmetic topics
|
|
1983-1984 Meet 2 Frosh
|
|
primes and factors
|
|
1983-1984 Meet 3 Frosh
|
|
Modular Arithmetic
|
|
1983-1984 Meet 4 Frosh
|
|
rational expressions
|
|
1983-1984 Meet 5 Frosh
|
|
Algebra 1
|
|
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
|
|
Geometry
|
|
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
|
|
Algebra II
|
|
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
|
|
Pre-Calculus
|
|
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 Frosh
|
|
arithmetic topics
|
|
1984-1985 Meet 2 Frosh
|
|
number bases
|
|
1984-1985 Meet 3 Frosh
|
|
linear programming and inequalities
|
|
1984-1985 Meet 4 Frosh
|
|
word problems
|
|
1984-1985 Meet 5 Frosh
|
|
Algebra 1
|
|
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
|
|
Geometry
|
|
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
|
|
Algebra II
|
|
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
|
|
Pre-Calculus
|
|
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 Frosh
|
|
arithmetic topics
|
|
1985-1986 Meet 2 Frosh
|
|
linear equations
|
|
1985-1986 Meet 3 Frosh
|
|
primes and factors
|
|
1985-1986 Meet 4 Frosh
|
|
word problems
|
|
1985-1986 Meet 5 Frosh
|
|
Algebra I
|
|
1985-1986 Meet 1 Sophomores
|
|
systems
|
|
1985-1986 Meet 2 Sophomores
|
|
principles 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
|
|
Pre-Calculus
|
|
1986-1987 Meet 1 Frosh
|
|
arithmetic topics
|
|
1986-1987 Meet 2 Frosh
|
|
Linear equations and inequalities
|
|
1986-1987 Meet 3 Frosh
|
|
number bases
|
|
1986-1987 Meet 4 Frosh
|
|
word problems
|
|
1986-1987 Meet 5 Frosh
|
|
Algebra I
|
|
1986-1987 Meet 1 Sophomores
|
|
quadratics
|
|
1986-1987 Meet 2 Sophomores
|
|
word problems
|
|
1986-1987 Meet 3 Sophomores
|
|
right triangles
|
|
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 Frosh
|
|
Pre-Algebra
arithmetic topics
|
|
1987-1988 Meet 2 Frosh
|
|
primes and factors
|
|
1987-1988 Meet 3 Frosh
|
|
Linear equations and inequalities
|
|
1987-1988 Meet 4 Frosh
|
|
word problems
|
|
1987-1988 Meet 5 Frosh
|
|
Algebra 1
|
|
1987-1988 Meet 1 Sophomores
|
|
sets and venn diagrams
|
|
1987-1988 Meet 2 Sophomores
|
|
systems of equations
|
|
1987-1988 Meet 3 Sophomores
|
|
angles and polygons
|
|
1987-1988 Meet 4 Sophomores
|
|
similar triangles
|
|
1987-1988 Meet 5 Sophomores
|
|
Geometry
|
|
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
|
|
Pre-Calculus
|
|
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 Frosh
|
|
ration, proportion, percent
|
|
1988-1989 Meet 2 Frosh
|
|
formula
|
|
1988-1989 Meet 3 Frosh
|
|
simple probability
|
|
1988-1989 Meet 4 Frosh
|
|
data analysis
|
|
1988-1989 Meet 5 Frosh
|
|
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 Frosh
|
|
arithmetic topics
Geometry For Enjoyment And Challenge, Rhoad, Milauskas and Whipple. McDougall Littell.)
|
|
1989-1990 Meet 2 Frosh
|
|
primes and factors
|
|
1989-1990 Meet 3 Frosh
|
|
Linear equations and inequalities
|
|
1989-1990 Meet 4 Frosh
|
|
probability
|
|
1989-1990 Meet 5 Frosh
|
|
|
|
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
|
|
Geometry
|
|
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
|
|
Algebra II
|
|
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
|
|
Pre-Calculus
|
|
1989-1990 Meet 2 Orals
|
|
graph theory
Discrete Mathematics, Roman
|
|
1990-1991 Meet 1 Frosh
|
|
arithmetic topics
|
|
1990-1991 Meet 2 Frosh
|
|
number bases
|
|
1990-1991 Meet 3 Frosh
|
|
data analysis
|
|
1990-1991 Meet 4 Frosh
|
|
ratio, proportion
|
|
1990-1991 Meet 5 Frosh
|
|
|
|
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
|
|
Geometry
|
|
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
|
|
Algebra II
|
|
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
|
|
Pre-Calculus
|
|
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 Frosh
|
|
perimeter, area
|
|
1991-1992 Meet 2 Frosh
|
|
basic counting principals
|
|
1991-1992 Meet 3 Frosh
|
|
Linear equations and inequalities
|
|
1991-1992 Meet 4 Frosh
|
|
quadratics
|
|
1991-1992 Meet 5 Frosh
|
|
|
|
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
|
|
Algebra II
|
|
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
|
|
Pre-Calculus
|
|
1991-1992 Meet 1 Orals
|
|
polar coordinates
|
|
1991-1992 Meet 2 Orals
|
|
mathematical induction
Discrete Mathematics, John Dossey, Scott Foresman. Sections 2.5 and 2.6
|
|
1991-1992 Meet 3 Orals
|
|
growth and decay
Calculus and Analytic Geometry, Leithold, Harper, and Row. Section 6.6 [5th edition] or section 7.7 [6th edition].)
|
|
1991-1992 Meet 4 Orals
|
|
markov chains
Finite Mathematics, Lial and Miller. Scott Foresman 4th edition. Chapter 8
|
|
1991-1992 Meet 3 GraphingCalculatorContest
|
|
|
|
1992-1993 Meet 1 Frosh
|
|
ratio, proportion, percent
|
|
1992-1993 Meet 2 Frosh
|
|
algebra/geometry applications
|
|
1992-1993 Meet 3 Frosh
|
|
sets and venn diagrams
|
|
1992-1993 Meet 4 Frosh
|
|
linear equations
|
|
1992-1993 Meet 5 Frosh
|
|
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 Space 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 Frosh
|
|
non-algebraic word problems
|
|
1993-1994 Meet 2 Frosh
|
|
linear equations
|
|
1993-1994 Meet 3 Frosh
|
|
coordinate geometry
|
|
1993-1994 Meet 4 Frosh
|
|
quadratics
|
|
1993-1994 Meet 5 Frosh
|
|
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 Frosh
|
|
ratio, proportion, percent
|
|
1994-1995 Meet 2 Frosh
|
|
number theory
|
|
1994-1995 Meet 3 Frosh
|
|
word problems
|
|
1994-1995 Meet 4 Frosh
|
|
algebra/geometry applications
|
|
1994-1995 Meet 5 Frosh
|
|
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 Frosh
|
|
perimeter, area
|
|
1995-1996 Meet 2 Frosh
|
|
simple probability
|
|
1995-1996 Meet 3 Frosh
|
|
sets and venn diagrams
|
|
1995-1996 Meet 4 Frosh
|
|
Linear equations and inequalities
|
|
1995-1996 Meet 5 Frosh
|
|
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 (Geometric Loci)
|
|
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 Frosh
|
|
perimeter, area
|
|
1996-1997 Meet 2 Frosh
|
|
number bases
|
|
1996-1997 Meet 3 Frosh
|
|
linear equations
|
|
1996-1997 Meet 4 Frosh
|
|
quadratics
|
|
1996-1997 Meet 5 Frosh
|
|
Algebra I
|
|
1996-1997 Meet 1 Sophomores
|
|
quadratics
|
|
1996-1997 Meet 2 Sophomores
|
|
Coordinate Geometry
|
|
1996-1997 Meet 3 Sophomores
|
|
Perimeter, Area, and Volume
|
|
1996-1997 Meet 4 Sophomores
|
|
similarity
|
|
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
|
|
Right triangle trig
|
|
1996-1997 Meet 4 Juniors
|
|
logs and exponents with applications
|
|
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 Frosh
|
none |
number bases
|
|
1997-1998 Meet 2 Frosh
|
|
basic counting principals
|
|
1997-1998 Meet 3 Frosh
|
|
coordinate geometry
|
|
1997-1998 Meet 4 Frosh
|
|
Linear equations and inequalities
|
|
1997-1998 Meet 5 Frosh
|
|
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
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 Frosh
|
none |
ratio, proportion, percent
|
|
1998-1999 Meet 2 Frosh
|
|
applications of algebra to junior high geometry
|
|
1998-1999 Meet 3 Frosh
|
|
coordinate geometry
|
|
1998-1999 Meet 4 Frosh
|
|
linear systems of equations and inequalities
|
|
1998-1999 Meet 5 Frosh
|
|
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 Frosh
|
|
modular arithmetic
|
|
1999-2000 Meet 2 Frosh
|
|
basic counting principals and simple probability
|
|
1999-2000 Meet 3 Frosh
|
|
linear equations
|
|
1999-2000 Meet 4 Frosh
|
|
word problems
|
|
1999-2000 Meet 5 Frosh
|
|
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 Frosh
|
none |
number bases
includes conversion and computation in different bases (bases from 2 - 16); finding the base given some information.
|
|
2000-2001 Meet 2 Frosh
|
|
volume, surface 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 Frosh
|
|
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 Frosh
|
|
quadratic functions and equations with applications
|
|
2000-2001 Meet 5 Frosh
|
|
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
|
CAS |
parametrics
equations and graphs defined parametrically (no calculus)
|
|
2000-2001 Meet 4 Seniors
|
CAS |
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 Frosh
|
none |
number theory
may include patterns (such as trailing zeros), factors, primes, divisibility rules, prime factors of powers, unique factorization, LCM, GCD, and their relationships.
|
|
2001-2002 Meet 3 Frosh
|
graphing |
Linear equations and inequalities
includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.
|
|
2001-2002 Meet 4 Frosh
|
graphing |
quadration functions and equations with applications
no complex numbers
|
|
2001-2002 Meet 5 Frosh
|
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 |
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.
|
|
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
Geometric Inequalities by Kazarinoff, MAA, Chapter 2
|
|
2002-2003 Meet 1 Frosh
|
graphing |
linear equations
including word problems leading to linear equations in one variable and simple absolute value equations. (No systems)
|
|
2002-2003 Meet 2 Frosh
|
none |
number bases
including conversion and computation in different bases and finding the base given some information.
|
|
2002-2003 Meet 3 Frosh
|
graphing |
basic counting principals and simple probability
including tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. Question writers are aware that this is an unfamiliar topic for freshmen.
|
|
2002-2003 Meet 4 Frosh
|
none |
rational expressions
simplifying rational expressions, solving equations involving rational expressions, word problems, basic algebra 1 factoring.
|
|
2002-2003 Meet 5 Frosh
|
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 Word Problems
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 Frosh
|
graphing |
ratios, proportions, and percent
may include money, interest, discounts, unit conversions, percents of increase, decrease and error, and direct variations. It should not require knowledge of algebra and does not include advanced problem solving skills. While the questions should not be trivial, they should be approachable to most contestants.
|
|
2003-2004 Meet 2 Frosh
|
none |
sets and venn diagrams
Notation, intersection, union, subsets, empty set, complements, universal set, cardinality, solution sets, and number of subsets. Does not include power sets.
|
|
2003-2004 Meet 3 Frosh
|
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 Frosh
|
none |
applying algebra to geometry problems
geometry including area, Pythagorean. Theorem, coordinate plane (no graphing equations), angle sums of triangles and quads, Isosceles Triangle theorems, parallel line relationships, supplements, and complements. The emphasis here should be on the algebraic representation of geometric relationships. Problems should yield linear equations and perhaps a simple quadratic equation.
|
|
2003-2004 Meet 5 Frosh
|
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 Frosh
|
graphing |
area & perimeter
including squares, triangles, rectangles, circles, and shapes made from these. May include the Pythagorean Theorem.
|
|
2004-2005 Meet 2 Frosh
|
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 Frosh
|
graphing |
basic counting principals and simple probability
including tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. Question writers are aware that this is an unfamiliar topic for freshmen.
|
|
2004-2005 Meet 4 Frosh
|
none |
Linear equations and inequalities
includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.
|
|
2004-2005 Meet 5 Frosh
|
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 |
trig 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 Frosh
|
graphing |
ratios, proportions, and percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of Algebra and does not include advanced problem solving skills. While questions should not be trivial, they should be approachable to most contestants.
|
|
2005-2006 Meet 2 Frosh
|
none |
systems of linear equations and inequalities with applications
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.
|
|
2005-2006 Meet 3 Frosh
|
none |
counting basics and simple probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. Question writers are aware that this is a new topic for freshmen.
|
|
2005-2006 Meet 4 Frosh
|
graphing |
word problems
Standard and nonstandard algebra word problems. Will include those solvable by linear equation systems in one or two variables.
|
|
2005-2006 Meet 5 Frosh
|
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, Abstract Mathematics
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 Frosh
|
graphing |
ratios, proportions, and percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of Algebra and does not include advanced problem solving skills. While questions should not be trivial, they should be approachable to most contestants.
|
|
2006-2007 Meet 2 Frosh
|
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 Frosh
|
graphing |
area & perimeter
including squares, triangles, rectangles, circles, and shapes made from these. May include the Pythagorean Theorem. Area and perimeters of above shapes assumed; all others will be given.
|
|
2006-2007 Meet 4 Frosh
|
none |
systems of linear equations and inequalities with applications
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.
|
|
2006-2007 Meet 5 Frosh
|
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 Frosh
|
none |
sets and venn diagrams
Notation, intersection, unions, subsets, empty set, compliments, supplements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections.
|
|
2007-2008 Meet 2 Frosh
|
graphing |
counting basics and simple probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. Question writers are aware that this is a new topic for freshmen.
|
|
2007-2008 Meet 3 Frosh
|
graphing |
systems of linear equations and inequalities with applications
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.
|
|
2007-2008 Meet 4 Frosh
|
none |
quadratic functions
includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications.
|
|
2007-2008 Meet 5 Frosh
|
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 Frosh
|
graphing |
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of Algebra and does not include advanced problem solving skills. While questions should not be trivial, they should be approachable to most contestants.
|
|
2008-2009 Meet 2 Frosh
|
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 Frosh
|
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 Frosh
|
none |
Rational expressions
simplifying rational expressions, solving equations involving rational expressions, word problems, basic algebra 1 factoring.
|
|
2008-2009 Meet 5 Frosh
|
|
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
|
|
Markov Chains
Finite Mathematics, by Lial and Miller (4th ed). Chapter 8.
|
|
2008-2009 Meet 2 Orals
|
|
Linear Programming
For All Practical Purposes, by COMAP (6th ed). Chapter 4.
|
|
2008-2009 Meet 3 Orals
|
|
Conic Sections
Analytic Geometry, by Fuller and Tarwater. Chapter 3.
|
|
2008-2009 Meet 4 Orals
|
|
Networks
For All Practical Purposes, by COMAP (6th ed). Chapter 1.
|
|
2009-2010 Meet 1 Frosh
|
none |
Sets and Venn Diagrams
Notation, intersection, unions, subsets, empty set, compliments, supplements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections.
|
|
2009-2010 Meet 2 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. Question writers are aware that this is a new topic for freshmen.
|
|
2009-2010 Meet 3 Frosh
|
graphing |
Systems of Linear Equations and Inequalities with Applications
Limited to two variables. May include
absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.
|
|
2009-2010 Meet 4 Frosh
|
none |
Coordinate Geometry
Includes distance, midpoint, slope, parallels, perpendiculars
and applications.
|
|
2009-2010 Meet 5 Frosh
|
|
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
|
|
Taxicab Geometry
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
|
|
Parametric Equations
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
|
|
Theory of Congruence
Elementary Number Theory, by Burton, David M.. Chapter 4 (any edition).
|
|
2009-2010 Meet 4 Orals
|
|
Symmetry and Patterns
For All Practical Purposes, by COMAP (6th ed). Chapter 19.
|
|
2010-2011 Meet 1 Frosh
|
none |
Number Theory and Divisibility
may include patterns (such as trailing zeros), factors, primes, divisibility rules, prime factors of powers, unique factorization, LCM, GCD, and their relationships.
|
|
2010-2011 Meet 2 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.
|
|
2010-2011 Meet 3 Frosh
|
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 Frosh
|
graphing |
Systems of Linear Equations and Inequalities with Applications
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.
|
|
2010-2011 Meet 5 Frosh
|
|
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
|
|
Combinatorics
Introduction to Discrete Mathematics, by Roman, Steven. 4.1-4.8, 5.1-5.2.
|
|
2010-2011 Meet 3 Orals
|
|
Topics in Geometry
Geometry Revisited, by Coxeter and Greitzer. 1.1-1.3.
|
|
2010-2011 Meet 4 Orals
|
|
Planning and Scheduling
, by . .
|
|
2011-2012 Meet 1 Frosh
|
graphing |
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants.
|
|
2011-2012 Meet 2 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.
|
|
2011-2012 Meet 3 Frosh
|
none |
Number Theory and Divisibility
may include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships.
|
|
2011-2012 Meet 4 Frosh
|
none |
Systems of Linear Equations and Inequalities with Applications
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.
|
|
2011-2012 Meet 5 Frosh
|
|
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
|
|
Graph 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
|
|
Matrix Games
Excursions into Mathematics, by Beck, Bleicher, Crowe (Millenium Edition). Sections 5.1, 5.6, 5.7.
|
|
2011-2012 Meet 4 Orals
|
|
Taxicab Geometry
, by Krause. Chapters 1-5.
|
|
2012-2013 Meet 1 Frosh
|
graphing |
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants.
|
|
2012-2013 Meet 2 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.
|
|
2012-2013 Meet 3 Frosh
|
none |
Number Bases
|
|
2012-2013 Meet 4 Frosh
|
none |
Quadratics (Quadratic Functions)
|
|
2012-2013 Meet 5 Frosh
|
|
Algebra I
|
|
2012-2013 Meet 1 Sophomores
|
graphing |
Coordinate Geometry
(description lost)
Coordinate geometry with applications
|
|
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 |
Logic, Sets, and Venn Diagrams
(description lost)
|
|
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
FIXME
|
|
2012-2013 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. (2011-12)
|
|
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 |
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 2010-11)
|
|
2012-2013 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. (2009-10)
|
|
2012-2013 Meet 5 Juniors
|
|
Algebra II
|
|
2012-2013 Meet 1 Seniors
|
CAS |
Triangle Trigonometry
|
|
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 |
Diophantine Equations
|
|
2012-2013 Meet 4 Seniors
|
none |
Vector Analytic Geometry/Graphing
|
|
2012-2013 Meet 5 Seniors
|
|
Pre-Calculus
|
|
2012-2013 Meet 1 Orals
|
|
Conic Sections
For All Practical Purposes, by COMAP. Chapters 12 and 13.
|
|
2012-2013 Meet 2 Orals
|
|
Markov Chains
Elementary Number Theory, by David Burton. Chapter 4.
|
|
2012-2013 Meet 3 Orals
|
|
Tritangent Circles
Anayltic Geometry, by Gordon Fuller and Dalton Tarwater. Chapter 8.
|
|
2012-2013 Meet 4 Orals
|
|
Vectors
, by . .
|
|
2013-2014 Meet 1 Frosh
|
graphing |
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants.
|
|
2013-2014 Meet 2 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.
|
|
2013-2014 Meet 3 Frosh
|
none |
Linear Equations and Inequalities
Includes word problems leading to linear equations and inequalities, as well as simple absolute value equations and inequalities.
|
|
2013-2014 Meet 4 Frosh
|
none |
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships.
|
|
2013-2014 Meet 5 Frosh
|
|
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
|
|
Voting Methods
For All Practical Purposes, by COMAP. Chapters 12 (Social Choice) and 13 (Weighted Voting Systems) in edition 6. These are chapters 11 and 12 in the 4th edition..
|
|
2013-2014 Meet 2 Orals
|
|
Theory of Congruence
Elementary Number Theory, by David Burton. Chapter 4.
|
|
2013-2014 Meet 3 Orals
|
|
Parametrics
Anayltic Geometry, by Gordon Fuller and Dalton Tarwater. Chapter 8.
|
|
2013-2014 Meet 4 Orals
|
|
Geometric Probability
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 Frosh
|
none |
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (Last used 2013-14)
|
|
2014-2015 Meet 2 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (Last used 2013-14)
|
|
2014-2015 Meet 3 Frosh
|
none |
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (Last used 2012-13)
|
|
2014-2015 Meet 4 Frosh
|
graphing |
Linear Equations and Inequalities and Quadratic Equations
Includes word problems leading to linear or absolute value equations and inequalities, as well as quadratic equations. No quadratic inequalities. (Last used 2013-14; not quadratics - they are new to this topic)
|
|
2014-2015 Meet 5 Frosh
|
|
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)
Note: Contest is labeled with the incorrect title.
|
|
2014-2015 Meet 5 Seniors
|
|
Pre-Calculus
|
|
2014-2015 Meet 1 Orals
|
|
Geometric Constructions
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
|
|
Graph Theory
Graphs and their Uses, by Oystein Ore / Robin Wilson (1990). Note: Terminology differs between 1960 and 1990 editions. Questions will be written using the terminology from the 1990 edition.. Chapters 1-3.
|
|
2014-2015 Meet 3 Orals
|
|
Continued Fractions
Continued Fractions, by C.D. Olds. Chapters 1-3.
|
|
2014-2015 Meet 4 Orals
|
|
Combinatorics and Probability
Probability Module, by Rhoad and Whipple. 1.1-1.7 & 1.12 (pp 1-40 & 77-84).
|
|
2015-2016 Meet 1 Frosh
|
graphing |
Ratios, Proportions, and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of Algebra and does not include advanced problem solving skills. While questions should not be trivial, they should be approachable to most contestants. (2013-14)
|
|
2015-2016 Meet 2 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2014-15)
|
|
2015-2016 Meet 3 Frosh
|
none |
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2014-15)
|
|
2015-2016 Meet 4 Frosh
|
none |
Applications of Systems of Linear Equations and Inequalities
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent. (2011-12)
|
|
2015-2016 Meet 5 Frosh
|
|
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
|
|
Taxicab Geometry
Taxicab Geometry, by Eugene Krause. Chapters 1 - 5.
|
|
2015-2016 Meet 2 Orals
|
|
Cake Cutting - Fair Cake Divisions
Cake Cutting Algorithms, by Jack Robertson and William Webb (Chapter 1). See COMAP For All Practical Purposes for additional practice material. .
|
|
2015-2016 Meet 3 Orals
|
CAS |
Planning and Scheduling
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 Frosh
|
graphing |
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (2015-16)
|
|
2016-2017 Meet 2 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2015-16)
|
|
2016-2017 Meet 3 Frosh
|
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 Frosh
|
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 5 Frosh
|
|
Algebra I
|
|
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 5 Sophomores
|
|
Geometry
|
|
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 5 Juniors
|
|
Algebra II
|
|
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 5 Seniors
|
|
Pre-Calculus
|
|
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.
|
|
2017-2018 Meet 1 Frosh
|
graphing |
Ratios, Proportion and Percent
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (2016-17)
|
|
2017-2018 Meet 2 Frosh
|
none |
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2015-16)
|
|
2017-2018 Meet 3 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2016-17)
|
|
2017-2018 Meet 4 Frosh
|
none |
Quadratics
Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (2016-17)
|
|
2017-2018 Meet 5 Frosh
|
graphing |
Algebra I
|
|
2017-2018 Meet 1 Sophomores
|
graphing |
Perimeter, Area, and Surface Area
Including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem. (2015-16)
|
|
2017-2018 Meet 2 Sophomores
|
none |
Logic, Sets, and Venn Diagrams
Notation, intersection, unions, subsets, empty set, complements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (2014-15)
|
|
2017-2018 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. (2016-17)
|
|
2017-2018 Meet 4 Sophomores
|
none |
Advanced Geometry Topics
Restricted to Brahmagupta’s formula, point to line distance formula, area of a triangle given vertices, Stewart’s Theorem, Ptolemy’s Theorem, Mass points, inradius and circumradius, Ceva’s Theorem, and Theorem of Menelaus. A good reference would be Geometry for Enjoyment and Challenge by Rhoad, Milauskas, and Whipple, Chapter 16. (2016-17)
|
|
2017-2018 Meet 5 Sophomores
|
graphing |
Geometry
|
|
2017-2018 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. (2016-17)
|
|
2017-2018 Meet 2 Juniors
|
none |
Rational Functions
Including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots. (2014-15)
|
|
2017-2018 Meet 3 Juniors
|
CAS |
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value. (2016-17)
|
|
2017-2018 Meet 4 Juniors
|
none |
Logs and Exponents
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential logarithmic growth and decay, and applications. No complex numbers. (2015-16)
|
|
2017-2018 Meet 5 Juniors
|
CAS |
Algebra II
|
|
2017-2018 Meet 1 Seniors
|
CAS |
Triangle Trigonometry with Applications
Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (2016-17)
|
|
2017-2018 Meet 2 Seniors
|
none |
Parametric Equations
Slopes, equations of lines, simple conics (no rotations), intersection points, position (applications), translating between rectangular and parametric equations. A good reference is Analytic Geometry, by Gordon Fuller and Dalton Tarwater; Addison Wesley. Chapter 7 (5th Ed), or Chapter 8 (6th and 7th Ed). (NEW)
|
|
2017-2018 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. (2016-17)
|
|
2017-2018 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. (2014-15)
|
|
2017-2018 Meet 5 Seniors
|
CAS |
Pre-Calculus
|
|
2017-2018 Meet 1 Orals
|
|
Networks
Source: For All Practical Purposes by COMAP, 6th edition, Chapter 1
|
|
2017-2018 Meet 2 Orals
|
|
Generating Functions
NO CALCULATOR ALLOWED -- Source: Intermediate Counting and Probability (Art of Problem Solving) by David Patrick, Chapter 14
|
|
2017-2018 Meet 3 Orals
|
|
Inversion
Source: Circle Inversions and Applications to Euclidean Geometry by Kenji Kozai and Shlomo Libeskind, Chapters 0 - 2. -- Available here: http://jwilson.coe.uga.edu/EMT600/Libeskind.Kozai.Inversion.pdf --
Supplementary Source (lots of problems and solutions): A Decade of the Berkeley Math Circle, edited by Z. Stankova and T. Rike, Session 1
|
|
2017-2018 Meet 4 Orals
|
|
Markov Chains
Sections 9.1-9.2 (Markov Chains) of Tan, Finite Mathematics for the Managerial, Life and Social Sciences, 11th Edition 2015 (ISBN 9781275464657)
|
|
2018-2019 Meet 1 Frosh
|
graphing |
Ratios, Proportion and Percent
May include money, simple interest (not compound interest), discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (2017-18)
|
|
2018-2019 Meet 2 Frosh
|
none |
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2016-17)
|
|
2018-2019 Meet 3 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2017-18)
|
|
2018-2019 Meet 4 Frosh
|
none |
Linear Equations and Inequalities and Quadratic Equations
Includes word problems leading to linear or absolute value equations and inequalities, as well as quadratic equations. No quadratic inequalities. (2014-15)
|
|
2018-2019 Meet 5 Frosh
|
graphing |
Algebra I
|
|
2018-2019 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. (2016-17)
|
|
2018-2019 Meet 2 Sophomores
|
none |
Logic, Sets, and Venn Diagrams
Notation, intersection, unions, subsets, empty set, complements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (2017-18)
|
|
2018-2019 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. (2017-18)
|
|
2018-2019 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. (2016-17)
|
|
2018-2019 Meet 5 Sophomores
|
graphing |
Geometry
|
|
2018-2019 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. (2015-16)
|
|
2018-2019 Meet 2 Juniors
|
none |
Modular Arithmetic
May include arithmetic operations in different moduli, divisibility, solving simple linear congruences in one or two variables, Fermat’s Little Theorem, Wilson’s Theorem, and Chinese Remainder Theorem. (2016-17)
|
|
2018-2019 Meet 3 Juniors
|
CAS |
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value. (2017-18)
|
|
2018-2019 Meet 4 Juniors
|
none |
Rational Functions
Including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots. (2017-18)
|
|
2018-2019 Meet 5 Juniors
|
CAS |
Algebra II
|
|
2018-2019 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 (Oral #2, 2007-8; senior 2013-14)
|
|
2018-2019 Meet 2 Seniors
|
none |
Diophantine Equations
May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (2016-17)
|
|
2018-2019 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. (2017-18)
|
|
2018-2019 Meet 4 Seniors
|
none |
Conics
Including locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations. (2013-14)
|
|
2018-2019 Meet 5 Seniors
|
CAS |
Pre-Calculus
|
|
2018-2019 Meet 1 Orals
|
|
Theory of Congruences - NO CALCULATOR
Source: Elementary Number Theory by David Burton, Fifth Edition (or newer edition) -- Chapter 4. ISBN: 0072325690
|
|
2018-2019 Meet 2 Orals
|
|
Inequalities
Source: AOPS Intermediate Algebra by Richard Rusczyk -- Chapter 12. ISBN-13: 978-1-934124-04-8
|
|
2018-2019 Meet 3 Orals
|
|
Fibonacci Numbers and Recursion - NO CALCULATOR
Source: AOPS Intermediate Counting and Probability by David Patrick -- Chapters 9 and 10. ISBN: 1934124060
|
|
2018-2019 Meet 4 Orals
|
|
Game Theory
For All Practical Purposes: Mathematical Literacy in Today’s World, Sections 15.1 and 15.2, 10th edition COMAP materials; published by W.H. Freeman; ISBN 9781464124730.
|
|
2019-2020 Meet 1 Frosh
|
none |
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2018-19)
|
|
2019-2020 Meet 2 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2018-19)
|
|
2019-2020 Meet 3 Frosh
|
none |
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2017-2018)
|
|
2019-2020 Meet 4 Frosh
|
graphing |
Coordinate Geometry
Includes distance, midpoint, slope, parallels, perpendiculars and applications. (2009-10)
|
|
2019-2020 Meet 5 Frosh
|
graphing |
Algebra I
|
|
2019-2020 Meet 1 Sophomores
|
none |
Functions
|
|
2019-2020 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.
|
|
2019-2020 Meet 3 Sophomores
|
graphing |
Circles
Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles. (2010-11)
|
|
2019-2020 Meet 4 Sophomores
|
none |
Coordinate Geometry
|
|
2019-2020 Meet 5 Sophomores
|
graphing |
Geometry
|
|
2019-2020 Meet 1 Juniors
|
none |
Polynomials
Including factor, remainder, and rational root theorems; Descartes’ Rule of Signs; coefficient analysis; determining equations given various information.
|
|
2019-2020 Meet 2 Juniors
|
CAS |
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. Does not include binomial distribution nor expected value. (2019-20)
|
|
2019-2020 Meet 3 Juniors
|
CAS |
Logs and Exponents
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential and logarithmic growth and decay, and applications. No complex numbers.
|
|
2019-2020 Meet 4 Juniors
|
none |
Transformations using Matricies on a Plane
In two dimensions. Includes reflections, rotations, translations, dilations, shears, and compositions. Standard treatment using Algebra 2 texts. For shears refer to Mathematics of Matrices, by Phillip Davis. Ginn and Co., 1965, Library of Congress: 64-24818. Pages 125-161 (Oral #2, 2007-8).
|
|
2019-2020 Meet 5 Juniors
|
CAS |
Algebra II
|
|
2019-2020 Meet 1 Seniors
|
none |
Theory of Equations
Including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, DesCartes' Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older Pre-Calculus texts. (2017-18)
|
|
2019-2020 Meet 2 Seniors
|
CAS |
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2019-20)
|
|
2019-2020 Meet 3 Seniors
|
CAS |
Series and Sequences
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus. (2015-16)
|
|
2019-2020 Meet 4 Seniors
|
none |
Vectors
(Previously called Vector Analytic Graphing) Includes two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar, inner and cross products, perpendicularly and parallels. distance between lines, points and planes. No calculus. (2016-17)
|
|
2019-2020 Meet 5 Seniors
|
CAS |
Pre-Calculus
|
|
2019-2020 Meet 1 Orals
|
none |
Planning and Scheduling
Source: For All Practical Purpose by COMAP (Sixth Edition) -- Chapter 3 -- ISBN: 0716747820
|
|
2019-2020 Meet 2 Orals
|
none |
Geometric Constructions
Source: College Geometry by Nathan Altshiller Court -- Chapter 1 -- ISBN: 0486458059 -- Oralists are not expected to construct precise diagrams with compass and straightedge on the chalk/white board during presentation, but rather sketch their constructions and explain them. Emphasis is on understanding and proving constructions, rather than precision with tools.
|
|
2019-2020 Meet 3 Orals
|
none |
Continued Fractions
Source: Continued Fractions by C.D. Olds -- MAA New Mathematical library -- Chapters 1--3--ISBN: 0883856093
|
|
2019-2020 Meet 4 Orals
|
|
Voting Methods
For All Practical Purposes, by COMAP. 10th Edition: Chapter 9 (Social Choice) & Chapter 10 (Manipulability of Voting Systems).
|
|
2020-2021 Meet 1 Frosh
|
none |
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2019-20)
|
|
2020-2021 Meet 2 Frosh
|
graphing |
Basic Statistics
Measures of central tendency (mean, median, and mode), box-and-whisker plots, two-way tables, stem and leaf, range. No variance. No standard deviation. (New Topic. Resource: OpenStax: https://openstax.org/details/books/introductory-statistics)
|
|
2020-2021 Meet 3 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2019-20)
|
|
2020-2021 Meet 4 Frosh
|
none |
Applications of Systems of Linear Equations and Inequalities
Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent. (2015-16)
|
|
2020-2021 Meet 5 Frosh
|
graphing |
Algebra I
|
|
2020-2021 Meet 1 Sophomores
|
none |
Area and Perimeter
Including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem. May include surface area of right pyramids and right prisms. No trigonometry. (Refer to Area, Perimeter, and Surface Area 2017-18)
|
|
2020-2021 Meet 2 Sophomores
|
graphing |
Similarity
The standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem. (2018-19)
|
|
2020-2021 Meet 3 Sophomores
|
graphing |
Circles
Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles. (2010-11)
|
|
2020-2021 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. (2017-18)
|
|
2020-2021 Meet 5 Sophomores
|
graphing |
Geometry
|
|
2020-2021 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. (2018-19)
|
|
2020-2021 Meet 2 Juniors
|
none |
Polynomials
*NO CALCULATOR* Including factor, remainder, and rational root theorems; Descartes’ Rule of Signs; coefficient analysis; determining equations given various information. (2019-20) UPDATE 2020-10-07 NO CALCULATOR FOR THIS TOPIC.
|
|
2020-2021 Meet 3 Juniors
|
CAS |
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. Does not include binomial distribution nor expected value. (2019-20)
|
|
2020-2021 Meet 4 Juniors
|
none |
Logs and Exponentials
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential and logarithmic growth and decay, and applications. No complex numbers. (2018-19)
|
|
2020-2021 Meet 5 Juniors
|
CAS |
Algebra II
|
|
2020-2021 Meet 1 Seniors
|
none |
Sequences and Series
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, alternating, and harmonic sequences and series. No calculus. (2019-20)
|
|
2020-2021 Meet 2 Seniors
|
none |
Algebra of Complex Numbers
*NO CALCULATOR* Simplifying and factoring, solving linear and quadratic equations with complex coefficients, solving linear systems with complex coefficients, vectors, polars, and powers of pure imaginary numbers, including DeMoivre’s Theorem. (2015-16) UPDATE 2020-10-20 NO CALCULATOR FOR THIS TOPIC.
|
|
2020-2021 Meet 3 Seniors
|
CAS |
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2019-20)
|
|
2020-2021 Meet 4 Seniors
|
none |
Conics
Including locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations. (2018-19)
|
|
2020-2021 Meet 5 Seniors
|
CAS |
Pre-Calculus
|
|
2020-2021 Meet 1 Orals
|
|
Taxicab Geometry
Source: Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene Krause – Chapters 1–5 – ISBN: 0486252027. NO CALCULATOR.
|
|
2020-2021 Meet 2 Orals
|
|
Conics
Source: AOPS Intermediate Algebra by Richard Rusczyk & Mathew Crawford – Chapter 5 – ISBN: 9781934124048. NO CALCULATOR.
|
|
2020-2021 Meet 3 Orals
|
|
Advanced Geometry
Source: Geometry Revisited by Coxeter and Greitzer – Chapter 1 – ISBN: 987-0883856192. (Printings from 1967 and 1996 have same content.) NO CALCULATOR.
Geometry Revisited, has been republished so it has more than one ISBN. They have the same text.
|
|
2020-2021 Meet 4 Orals
|
|
Combinatorial Identities
Art of Problem Solving, Intermediate Counting and Probability, Chapter 12. NO CALCULATOR.
|
|
2021-2022 Meet 1 Frosh
|
graphing |
Ratios, Proportion and Percent
May include money, simple interest (not compound interest), discounts, unit conversions, percentages of increase or decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (2018-19)
|
|
2021-2022 Meet 2 Frosh
|
none |
Number Bases
May include conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2020-21)
|
|
2021-2022 Meet 3 Frosh
|
graphing |
Counting Basics and Simple Probability
May include tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2020-21)
|
|
2021-2022 Meet 4 Frosh
|
none |
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2019-20)
|
|
2021-2022 Meet 5 Frosh
|
|
Algebra I
|
|
2021-2022 Meet 1 Sophomores
|
graphing |
Perimeter, Area, and Surface Area
May include squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem. May include prisms, pyramids, and cylinders. No trigonometry. No spheres. No cones. (2017-18)
|
|
2021-2022 Meet 2 Sophomores
|
none |
Logic, Sets, and Venn Diagrams
Notation, intersection, unions, subsets, empty set, complements, universal set, cardinality (number of elements) of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (2018-19)
|
|
2021-2022 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. (2019-20)
|
|
2021-2022 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. (2017-18)
|
|
2021-2022 Meet 5 Sophomores
|
|
Geometry
|
|
2021-2022 Meet 1 Juniors
|
|
Systems of Linear Equations and Inequalities with Applications
May include absolute value, intersections, area and/or perimeter of a region, corner points, slopes, distances, inconsistent/consistent systems, and independent/dependent systems. (2018-19)
|
|
2021-2022 Meet 2 Juniors
|
none |
Polynomials
May include factor, remainder, and rational root theorems; Descartes’ Rule of Signs; upper/lower bounds of roots; coefficient analysis; determining polynomials given various information. (2020-21)
|
|
2021-2022 Meet 3 Juniors
|
CAS |
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. Does not include binomial distribution nor expected value. (2020-21)
|
|
2021-2022 Meet 4 Juniors
|
none |
Logs and Exponentials
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential and logarithmic growth and decay, and applications. No complex numbers. (2020-21)
|
|
2021-2022 Meet 5 Juniors
|
|
Algebra II
|
|
2021-2022 Meet 1 Seniors
|
|
Triangle Trigonometry with Applications
May include right triangle trigonometry, laws of sines and cosines, area, angles of elevation and depression, compass bearing. The emphasis is not on precalculus trigonometric identities. (2017-18)
|
|
2021-2022 Meet 2 Seniors
|
none |
Theory of Equations
Including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, DesCartes’ Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older Pre-Calculus texts. (2019-20)
|
|
2021-2022 Meet 3 Seniors
|
CAS |
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2019-20)
|
|
2021-2022 Meet 4 Seniors
|
none |
Conics
May include locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations. (2020-21)
|
|
2021-2022 Meet 5 Seniors
|
|
Pre-Calculus
|
|
2021-2022 Meet 1 Orals
|
|
Divisibility
Source: Elementary Number Theory – 5th Edition – by David M. Burton – Chapter 2 – ISBN: 978-0072325690. NO CALCULATOR.
|
|
2021-2022 Meet 2 Orals
|
|
Mathematical Induction
Source: A Decade of the Berkeley Math Circle: I by Stankova & Rike – Chapter 6 – ISBN: 978-0821846834. NO CALCULATOR.
|
|
2021-2022 Meet 3 Orals
|
|
Generating Functions
Source: AoPS Intermediate Counting & Probability by David Patrick – Chapter 14, ISBN: 1934124060. NO CALCULATOR.
|
|
2021-2022 Meet 4 Orals
|
|
Combinatorics
"Combinatorics" based on a document by Rhoad and Whipple. See ICTM web site for AA schools for the source. Contact the president of NSML if you do not have access. CALCULATOR ALLOWED IN PREP.
|
|
2022-2023 Meet 1 Frosh
|
graphing |
Basic Statistics
Measures of central tendency (mean, median, and mode), histograms, box-and-whisker plots, stem and leaf plots, range, interquartile range (IQR), potential outliers. No variance. No standard deviation. No comparison of sample and population means. (Resource: Sections 1.3 and 2.1-2.5 in the text OpenStax: https://openstax.org/details/books/introductory-statistics). (2020-21)
|
|
2022-2023 Meet 2 Frosh
|
graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2021-22)
|
|
2022-2023 Meet 3 Frosh
|
none |
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2021-22)
|
|
2022-2023 Meet 4 Frosh
|
none |
Number Theory and Divisibility
May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2021-22)
|
|
2022-2023 Meet 5 Frosh
|
graphing |
Algebra I
|
|
2022-2023 Meet 1 Sophomores
|
graphing |
Quadratic Functions
Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (So 2004-05, Fr 2016-17, Fr 2017-18)
|
|
2022-2023 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. (2021-22)
|
|
2022-2023 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. (2020-21)
|
|
2022-2023 Meet 4 Sophomores
|
none |
Circles
Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles. (2020-21)
|
|
2022-2023 Meet 5 Sophomores
|
graphing |
Geometry
|
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2022-2023 Meet 1 Juniors
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CAS |
Algebraic Coordinate Geometry Including Circles
Includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, applications, and equations of circles. Coordinates are included. No trig. (2017-18)
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2022-2023 Meet 2 Juniors
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CAS |
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. Does not include binomial distribution nor expected value. (2021-22)
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2022-2023 Meet 3 Juniors
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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. (2020-21)
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2022-2023 Meet 4 Juniors
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none |
Conics
Including locus definitions, eccentricity, directrix, and area of an ellipse. No parametrics, no polar, and no rotations. (Jr 1979-80, Sr 2021-22)
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2022-2023 Meet 5 Juniors
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CAS |
Algebra II
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2022-2023 Meet 1 Seniors
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CAS |
Applications of Matrices and Markov Chains
includes solving large systems of equations, using matrix inverses and using transition matrices (aka Markov Chains). Does not include geometric transformations. (Jr 2014-15, Sr 2007-08). Source: "Finite Mathematics for Managerial, Life, and Social Sciences", Tan, Sections 9.1-9.3. ISBN: 978-1285464657. Reportedly this is the ICTM orals source from 2018. Includes: regular Markov chain, steady-state distribution vector, absorbing states.
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2022-2023 Meet 2 Seniors
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CAS |
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2021-22)
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2022-2023 Meet 3 Seniors
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none |
Linear Diophantine Equations
May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (2018-19)
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2022-2023 Meet 4 Seniors
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none |
Sequences and Series
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, alternating, and harmonic sequences and series. No calculus. (2020-21)
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2022-2023 Meet 5 Seniors
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CAS |
Pre-Calculus
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2022-2023 Meet 1 Orals
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Linear Programming
Source: For All Practical Purposes – 9th Edition – by COMAP – Chapter 4 – ISBN: 978-1429254823. (CALCULATOR ALLOWED IN PREP)
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2022-2023 Meet 2 Orals
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Inequalities
Source: AoPS Intermediate Algebra by Rusczyk and Crawford. Chapter 12. ISBN: 978-1-934124-04-8. (NO CALCULATOR ALLOWED IN PREP OR PRESENTATION.)
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2022-2023 Meet 3 Orals
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Fibonacci Numbers and Recursion
Source: AoPS Intermediate Counting & Probability by David Patrick – Chapters 9 & 10, ISBN: 1934124060. (NO CALCULATOR ALLOWED IN PREP OR PRESENTATION.)
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2022-2023 Meet 4 Orals
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Graph Theory
Source: Discrete Mathematics by John Dossey et al., 5th edition. Sections 4.1-4.3. PDF with solutions distributed by ICTM. (CALCULATOR ALLOWED IN PREP.)
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2023-2024 Meet 1 Frosh
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graphing |
Ratios, Proportion and Percent
May include money, simple interest (not compound interest), discounts, unit conversions, percentages of increase or decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (2021-22)
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2023-2024 Meet 2 Frosh
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graphing |
Counting Basics and Simple Probability
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2022-23)
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2023-2024 Meet 3 Frosh
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none |
Number Bases
Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2022-23)
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2023-2024 Meet 4 Frosh
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none |
Quadratics
Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (2017-18)
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2023-2024 Meet 5 Frosh
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none |
Algebra I
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2023-2024 Meet 1 Sophomores
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graphing |
Functions
Linear, quadratic, greatest integer, absolute value, step functions, piecewise, exponential. No logarithms. (2019-20)
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2023-2024 Meet 2 Sophomores
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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. (2022-23)
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2023-2024 Meet 3 Sophomores
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none |
Perimeter, Area, and Surface Area
Including squares, triangles, rectangles, circles, and shapes made from these; includes the Pythagorean Theorem and simple similarity (no angle bisector theorem). (2021-22)
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2023-2024 Meet 4 Sophomores
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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. (2021-22)
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2023-2024 Meet 5 Sophomores
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none |
Geometry
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2023-2024 Meet 1 Juniors
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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. (2021-22)
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2023-2024 Meet 2 Juniors
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CAS |
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, and expected value (new to this level; see old senior contests). Does not include binomial distribution. (2023-24)
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2023-2024 Meet 3 Juniors
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none |
Sequences and Series
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, alternating, and harmonic sequences and series. No calculus. (2016-17)
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2023-2024 Meet 4 Juniors
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none |
Logarithms and Exponentials
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential and logarithmic growth and decay, and applications. No complex numbers. (2021-22)
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2023-2024 Meet 5 Juniors
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none |
Algebra II
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2023-2024 Meet 1 Seniors
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CAS |
Triangle Trigonometry with Applications
Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (2021-22)
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2023-2024 Meet 2 Seniors
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CAS |
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2022-23)
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2023-2024 Meet 3 Seniors
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none |
Theory of Equations
Including factor, remainder, and rational root theorems, upper bounds, coefficient analysis, Descartes’ Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older precalculus texts. (2021-22)
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2023-2024 Meet 4 Seniors
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none |
Polar Coordinates and Equations
Graphs, systems, and de Moivre’s Theorem. Includes conics and intersections of polar curves that are not simultaneous solutions to the system (“ghost points”). Analytic Geometry, by Gordon Fuller and Dalton Tarwater (6th-7th ed) is a good source. (2009-2010)
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2023-2024 Meet 5 Seniors
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none |
Pre-Calculus
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2023-2024 Meet 1 Orals
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Divisibility Rules
(NO CALCULATOR IN PREP OR PRESENTATION.)
Source: Introduction to Number Theory
by Mathew Crawford – the Art of Problem Solving – Chapter 13 -- ISBN: 978-1-934124-12-3
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2023-2024 Meet 2 Orals
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Game Theory
(CALCULATOR ALLOWED IN PREP)
Source: For All Practical Purposes – 9th Edition – by COMAP – Chapter 15 – ISBN: 9781429243162.
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2023-2024 Meet 3 Orals
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Continued Fractions
(NO CALCULATOR IN PREP OR PRESENTATION.)
Source: Continued Fractions by C.D. Olds – MAA New Mathematical Library – Chapters 1 – 3 – https://bookstore.ams.org/nml-9 (Yes, this text is really from 1963 even if you find it republished later.)
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2023-2024 Meet 4 Orals
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Logic and Logic Circuits
Appendix A. and Sections 9.1 and 9.2 of Discrete Mathematics, 4th edition, by Dossey, Otto, Spence, and Vanden Enden. (This is exactly the same content as the ICTM Regionals source, except there it is called Chapter 10.)
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2024-2025 Meet 1 Frosh
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graphing |
Counting Basics and Simple Probability
The emphasis is on organized thinking, not using formulas. May include tree type problems, combinations, and permutations. (2023-24) (ANY CALCULATOR EVEN CAS.)
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2024-2025 Meet 2 Frosh
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none |
Number Bases
May include conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2023-24)
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2024-2025 Meet 3 Frosh
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none |
Basic Statistics
Measures of central tendency (mean, median, and mode), histograms, box-and-whisker plots, stem and leaf plots, range, interquartile range (IQR), potential outliers. No variance. No standard deviation. No comparison of sample and population means. (Resource: OpenStax Introductory Statistics, 1.3 and 2.1-2.5 from https://openstax.org/details/books/introductory-statistics). (2022-23)
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2024-2025 Meet 4 Frosh
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none |
Applications of Systems of Linear Equations and Inequalities and Quadratic Equations
Limited to two variables. May include absolute value, domain, range, composition, max and min values, applications, graphs of quadratic functions, quadratic formula, and vocabulary such as consistent, inconsistent, dependent, independent. (2020-21)
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2024-2025 Meet 5 Frosh
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none |
Algebra I
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2024-2025 Meet 1 Sophomores
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graphing |
Geometric Probability
Standard treatment of probability problems with continuous variables using ratios of lengths, areas, and volumes. (2023-24) (ANY CALCULATOR EVEN CAS.)
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2024-2025 Meet 2 Sophomores
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none |
Logic, Sets, and Venn Diagrams
May include notation, intersection, unions, subsets, empty set, complements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (2021-22)
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2024-2025 Meet 3 Sophomores
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none |
Circles
Standard material. May include arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles. (2022-23)
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2024-2025 Meet 4 Sophomores
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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. (2013-14) (Similar topic for juniors 2008-09.)
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2024-2025 Meet 5 Sophomores
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none |
Geometry
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2024-2025 Meet 1 Juniors
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CAS |
Probability
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, and expected value (new to this level in 2023-2024; see old senior contests). Does not include binomial distribution. (2023-24) (ANY CALCULATOR INCLUDING CAS.)
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2024-2025 Meet 2 Juniors
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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. (2022-23)
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2024-2025 Meet 3 Juniors
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none |
Logarithms and Exponentials
May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential and logarithmic growth and decay, and applications. No complex numbers. (2023-24)
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2024-2025 Meet 4 Juniors
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none |
Polynomials
Including factor, remainder, and rational root theorems; Descartes’ Rule of Signs; coefficient analysis; determining equations given various information. (2021-22)
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2024-2025 Meet 5 Juniors
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none |
Algebra II
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2024-2025 Meet 1 Seniors
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CAS |
Probability
May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2023-24) (ANY CALCULATOR INCLUDING CAS.)
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2024-2025 Meet 2 Seniors
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none |
Linear Diophantine Equations
May include linear Diophantine Equations, systems of linear Diophantine Equations, contextual problems, or simple nonlinear Diophantine Equations. (2022-23)
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2024-2025 Meet 3 Seniors
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none |
Vectors
(Previously called Vector Analytic Graphing) May include two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar, cross products, perpendicularity and parallels, distance between points, lines, and planes. No calculus. (2019-20)
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2024-2025 Meet 4 Seniors
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none |
Conics
May include locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations. (2021-22)
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2024-2025 Meet 5 Seniors
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none |
Pre-Calculus
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2024-2025 Meet 1 Orals
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Taxicab Geometry
NO CALCULATOR: Source: Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene Krause – Chapters 1–5 – ISBN: 0486252027
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2024-2025 Meet 2 Orals
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Voting Methods
NO CALCULATOR: Source: For All Practical Purposes – 9th Edition – by COMAP – Chapters 9, 10, and 11 (Social Choice, The Manipulability of Voting Systems, and Weighted Voting Systems) – ISBN: 9781429243162
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2024-2025 Meet 3 Orals
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Functional Equations
NO CALCULATOR: Source: AOPS Intermediate Algebra by Richard Rusczyk & Mathew Crawford – Chapter 19 – ISBN: 9781934124048
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2024-2025 Meet 4 Orals
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Norms, Metrics and Limits
NO CALCULATOR: The topic for the ICTM Regional competition. (Please contact the president if you do not have access to the source through your ICTM account.)
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2025-2026 Meet 1 Frosh
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none |
Counting Basics and Simple Probability
The emphasis is on organized thinking, not using formulas. Topics: tree type problems, combinations, and permutations. (2024-25)
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2025-2026 Meet 2 Frosh
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none |
Number Theory and Divisibility
Patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2022-23)
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2025-2026 Meet 1 Sophomores
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none |
Geometric Probability
Standard treatment of probability problems with continuous variables using ratios of lengths, areas, and volumes. [Note to question writers: 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. (2024-25)
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2025-2026 Meet 2 Sophomores
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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. (2022-23)
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2025-2026 Meet 1 Juniors
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none |
Probability
The standard treatment of probability: combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, and expected value. Does not include binomial distribution. (2024-25; also see old senior contests)
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2025-2026 Meet 2 Juniors
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none |
Triangle Trigonometry with Applications
Right triangle trigonometry, laws of sines and cosines, and of course, word problems. (Senior 2023-24)
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2025-2026 Meet 1 Seniors
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none |
Probability
Combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2024-25)
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2025-2026 Meet 2 Seniors
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none |
Trigonometric Equations and Identities
Solving trig equations. Simplifying trig expressions using standard formulas (e.g., double-angle, half-angle, sum-to-product, and product-to-sum). (2009-10)
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2025-2026 Meet 1 Orals
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Planning and Scheduling
(NO CALCULATOR) Source: For All Practical Purposes – 9th Edition – by COMAP – Chapter 3 – ISBN: 9781429243162
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2025-2026 Meet 2 Orals
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Conics
(NO CALCULATOR) Source: AoPS Intermediate Algebra by Richard Rusczyk & Mathew Crawford – Chapter 5 – ISBN: 9781934124048
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