NOTE: CONTESTS 2-5 WILL BE CUMULATIVE, CONTAINING ANY TOPIC FROM PREVIOUS CONTESTS.
PRESUMED
KNOWLEDGE
1. Distance
- Rate formula 2. Vocabulary
from previous math courses
3. Pythagorean
Theorem 4. Perimeter
and area formulas for rectangle, square, triangle and circle
SPECIFIC
TOPICS FOR CONTESTS
Contest I
1. Simplifying
numeric expressions
2.
Performing operations with real numbers
3. Venn
Diagrams
4. Number
Patterns
5.
Prime Factorization
6.
Divisibility Tests
Contest
II
1.
Solving linear inequalities
2.
Performing algebraic operations with polynomials
3.
Simple probability
4.
Solving linear equations
5.
Solving verbal problems using linear equations
6.
Basic Statistics, including Mean, median, mode
Contest III [No Calculator]
1.
Performing operations with polynomial fractions
2.
Finding the slope of a line
3.
Graphing on the Cartesian coordinate system
4.
Writing equations of lines given geometric conditions
Contest IV
1. Functions
2. Using laws of exponents to solve problems
3.
Simplifying radicals and operations with radicals
4. Triangles-similarity and proportion
5.
Solving linear systems of equations
Contest
V
1. Solving fractional equations.
2.
Solving quadratic equations and applications
3.
Simplifying complex fractions
4.
Factoring a polynomial
5. Solving
verbal problems involving factoring and fractions
PRESUMED
KNOWLEDGE
1. Pythagorean
Theorem 2.
Perimeter, circumference, area of rectangles, triangles and circles
3. Algebra I
Material from previous courses 4.
Measurement in degrees/minutes/seconds
CONTESTS II
THRU V WILL BE CUMULATIVE, CONTAINING ANY TOPIC FROM PREVIOUS
CONTESTS.
SPECIFIC
TOPICS FOR CONTESTS
Contest I Points, Lines, Planes
1.
Intersections and unions of geometric figures
2. Angles
(vertical, bisectors, complements, and supplements)
3. Triangles
4.
Perpendiculars
5. Algebra
review topics: systems of equations; properties of exponents; solving linear
equations; quadratics
Accelerated
Only:
6. Coordinate
geometry (distance and midpoint formulas, slope)
Contest II Parallels and Quadrilaterals
1. Parallels
2. Properties
of quadrilaterals including perimeter and area problems
3. Diagonals
4. Exterior
angles
5. Geometric
problems involving counting
6. Coordinate Geometry ( distance, midpoint, slope)
7. Quadrilateral, trapezoids, parallelograms
Accelerated
Only:
8. Polygons
9. The
Triangle Inequality
Contest
III [No Calculator]
1. Polygons
2. Similar
figures
3. Geometric
probability
Contest IV Similarity,
Special Triangles, Isometries, Circles
1. 30/60/90
triangles and 45/45/90 triangles
2. Rotations,
translations, and reflections in the
coordinate plane
3. Circles
– angles formed by chords, secants, and tangents
4. Quadilateral, rhombus, and kites
Accelerated
Only:
5. Area of
plane and three dimensional figures
6. Basic
trigonometry
7. 36/72/72
triangles
Contest V
Volume, Area, Circles
1. Area of
plane figures
2. Surface
area of solids
3. Volume of
solids
Accelerated
only:
4. lengths of
chords, secants, and tangent lines
PRESUMED
KNOWLEDGE
1. Algebra and
Geometry material
2. Vocabulary
from pervious math courses
SPECIFIC
TOPICS FOR CONTESTS
Contest I
1. Geometry
topics including triangle trigonometry
2. Solving
linear equations and inequalities
3. Solving equations involving fractions
4. Coordinates, midpoints, slope, parallel, perpendicular
Contest II
1. Probability and Statistics
2. Simplifying
radical expressions and expressions involving fractional exponents
3. Solving
absolute value equations and inequalities
Contest
III [No Calculator]
1. Determining
the rational zeros of a function
2. Determining
the domain and range of a function
3. Finding the
inverse of a function
4.
Applications of the properties of functions to combining functions and solving
word problems
5. Solving radical equations
6. Systems
7. Solving quadratic equations and
inequalities
Contest IV
1. Solving
systems of equations and inequalities
2. Right
triangle trigonometry
3.
Trigonometric equations and the unit circle
4. Exponential
and logarithmic functions
Accelerated only
5. Equations of Circles
6. Matrix
Algebra
Contest V
1.
Permutations and combinations
2. Sequences and series (progressions)
Accelerated only
3. Transformations
4.
Rational Functions
5. Theory of Equations
6.
Binomial Theorem
PRESUMED
KNOWLEDGE
1. Algebra 1, Geometry, and Algebra 2 material
2. Vocabulary from previous courses
SPECIFIC TOPICS FOR CONTESTS
Contest I
1. Linear and quadratic functions
2. Properties of functions, including domain, range, composition, and inverses
3. Utilizing the properties of graphs of equations to assist in problem solving
4. Performing operations with polynomials
5. Performing operations involving complex numbers
Contest II
1. Polynomials and rational functions
2. Solving systems of equations and inequalities
3. Probability and Statistics
4. Matrices
Contest III
1. Exponential and logarithmic functions
2. Parametric equations
3. Arithmetic and geometric sequences and series
4. Finding the nth term of a sequence and partial sums
Accelerated only:
5. Determining the equation of a circle, an ellipse, a parabola, and a hyperbola
6. Locating the foci of a circle, an ellipse, a parabola, and a hyperbola
Contest IV
1. Analytical trigonometry
2. Trig applications
3. Determining the number of permutations and combinations of a set
Accelerated only:
4. Vectors
5. Applying the Binomial Theorem in problem solving
Contest V
The In-Progress test will only include topics from the first four contests.
Accelerated only:
1. Calculating the sum of a series
2. Finding the limit of a convergent series
3. Graphical and intuitive investigation of limits of functions
4. DeMoivre’s theorem
5. Polar coordinates
