CCML Topics 2016-2017

<<Amendments from 2015 - 2016>>

For all levels, contest topics may be cumulative of earlier contests.
* indicates topics for the division A contest only.

Algebra 1

Presumed Knowledge

  • Distance - rate formula
  • Vocabulary from previous math courses
  • Pythagorean theorem
  • Perimeter and area formulas for rectangle, square, triangle, and circle
  • Volume and surface area of rectangular prism and sphere

Contest 1

  • Simplifying numeric expressions
  • Performing operations with real numbers
  • Number patterns (sequences, decimal expansions)
  • Prime factorization, GCD, LCM
  • Divisibility tests
  • Venn diagrams

Contest 2 - NO CALCULATOR

  • Solving linear equations
  • Solving application problems using linear equations
  • Number bases
  • Simple probability and counting (one or two events, simple casework, etc.)

Contest 3

  • Finding the slope of a line
  • Graphing in the Cartesian coordinate system
  • Writing equations of lines given geometric conditions (parallel, perpendicular, etc.)
  • Basic statistics, including mean, median, mode.

Contest 4 - NO CALCULATOR

  • Solving linear inequalities
  • Solving linear systems of equations
  • Solving absolute value equations and inequalities
  • Functions

Contest 5

  • Performing operations with polynomials
  • Factoring a polynomial
  • Solving word problems involving factoring
  • Using laws of exponents to solve problems
  • Simplifying radicals and operations with radicals
  • Simplifying complex fractions
  • Solving rational equations*
  • Solving word problems involving rational expressions*
  • Solving quadratic equations and applications*

Geometry

Presumed Knowledge

  • Vocabulary from previous math courses
  • Topics from previous contests
  • Measurement in degrees, minutes, and seconds

Contest 1

  • Algebra review
  • Intersections and unions of geometric figures
  • Angles and segments (vertical, midpoints, bisectors, trisectors, complements and supplements)
  • Classification of triangles (by sides and angles)
  • Solving quadratic equations and applications

Contest 2 - NO CALCULATOR

  • Parallel lines (angles, slope)
  • Perpendicular lines
  • Perimeter and area problems involving quadrilaterals
  • Exterior angles of a triangle
  • Coordinate geometry (distance and midpoint formulas, slope)
  • Geometric counting problems (how many paths, how many triangles, etc.)
  • Geometric probability involving basic shapes

Contest 3

  • Properties of all quadrilaterals
  • Properties of polygons (angle measure, number of diagonals, regular, exterior angles)
  • The triangle inequality
  • Pythagorean theorem (including Pythagorean triples, applications, etc.)
  • Similar figures

Contest 4 - NO CALCULATOR

  • Special triangles (45/45/90 and 30/60/90)
  • Coordinate geometry (polygons)
  • Transformations in the coordinate plane (reflections, translations, rotations, dilations)
  • Circles (angles formed by chords, secants and tangents)
  • Circles (chord/secant/tangent length relationships)*

Contest 5

  • Area of plane and surface area of 3D figures
  • Basic trigonometry
  • Volume of solids

Algebra 2

Presumed Knowledge

  • Vocabulary from previous math courses
  • Topics from previous contests

Contest 1

  • Solving linear equations and inequalities
  • Solving rational equations
  • Solving systems of linear equations
  • Coordinate geometry (midpoints, slope, parallel, perpendicular)

Contest 2 - NO CALCULATOR

  • Equations and expressions involving radicals and rational exponents
  • Solving absolute value equations and inequalities
  • Solving quadratic equations and inequalities
  • Counting and probability

Contest 3

  • Domain and range of relations
  • Function arithmetic and composition
  • Inverse relations and functions
  • Iterations and fixed points of functions
  • Statistics (measures of central tendency, two-way frequency tables, regression curves, etc.)

Contest 4 - NO CALCULATOR

  • Solving systems of non-linear equations and inequalities
  • Linear programming
  • Exponential and logarithmic equations
  • Matrix algebra and determinants (up to 2 x 2 for determinants)

Contest 5

  • Right triangle trigonometry
  • Unit circle trigonometry
  • Equations of circles
  • Theory of equations: rational roots theorem, Vièta's formulas, Descartes's rule of signs
  • Solving quadratics with nonreal zeros
  • Transformations of functions*
  • Rational functions*
  • Binomial theorem*

Precalculus

Presumed Knowledge

  • Vocabulary from previous math courses
  • Topics from previous contests

Contest 1

  • Linear and quadratic functions
  • Properties of functions -- domain, range, composition, inverses
  • Analyzing graphs of functions (patterns, periods, special points, etc.)
  • Performing operations with polynomials (including division)

Contest 2 - NO CALCULATOR

  • Polynomials and rational functions (and their graphs)
  • Limits (easy limits, end behavior, etc.)
  • Performing operations involving complex numbers
  • Solving systems of equations and inequalities
  • Probability - independent and dependent events, conditional probability

Contest 3

  • Analytic trigonometry
  • Trigonometric applications
  • Vectors
  • Permutations, combinations, and arrangements
  • Statistics - measures of central tendency, standard deviation

Contest 4 - NO CALCULATOR

  • Trigonometric identities
  • Exponential and logarithmic functions
  • Arithmetic and geometric sequences
  • Summation, finite and infinite series
  • Matrices (operations, inverses, determinants up to 3 x 3)
  • Conic sections (ellipse, parabola, hyperbola)*

Contest 5

  • All topics from contests 1-4
  • Binomial theorem and binomial probability
  • Parametric equations
  • Demoivre's theorem*
  • Polar coordinates*