Curriculum

All CHAMP curricula is aligned with the Michigan High School Curriculum Expectations and Core Curriculum Core State Standards.

CHAMP Year 1

These courses emphasize basic algebraic concepts and skills, as well as higher level reasoning involving problem solving and proof.

  • Fall Semester: Algebra 1
    • Textbook Algebra I: Expressions, Equations, and Applications by Paul A. Foerster
  • Spring Semester: Algebra 2
    • Textbook Algebra and Trigonometry: Functions and Applications by Paul A. Foerster

Algebra 1

  • Polynomials: terminology, evaluation, algebraic combinations, degree, long division
  • Factoring: prime and common factors, difference of squares, quadratic trinomials, factoring by grouping
  • Rational expressions: dividing by monomials, simplifying by factoring, algebraic combinations, least common multiples, combinations of rational expressions
  • Linear equations: roots, literal equations, solutions of equations with rational expressions, story problems
  • Linear inequalities
  • Graphs and the Cartesian coordinate system
  • Positive integral exponents and roots
  • Graphs of linear functions
  • Functions: notation, evaluation, inverse of functions
  • Lines: slope, various forms for equations of lines, parallel and perpendicular lines
  • Variation: direct, inverse, joint
  • Quadratic equations: solutions by factoring, completing the square, the quadratic formula
  • Story problems involving linear and quadratic equations

Algebra 2

  • Factoring of sums and differences of cubes
  • Exponents: zero, negative exponents, laws of exponents, rational exponents, exponential growth and decay
  • Radicals: rules, notation, combinations, rationalizing the denominator
  • Complex numbers
  • Logarithms: definition, properties, antilogs, computations
  • Quadratic equations: solutions by factoring, quadratic formula, character of solutions, equations involving “disguised quadratics”
  • Inequalities: solutions, graphing linear and quadratic inequalities
  • Simultaneous equations: solutions by graphing, elimination, and substitution; linear programming in two variables
  • Simultaneous inequalities: solutions by graphing
  • Direct and inverse variation
  • Conic sections in simple positions: basic features of graphs of circles, parabolas, ellipses and hyperbolas, algebraic solutions of quadratic systems, translation of axes
  • Polynomial and rational functions: remainder theorem, factor theorem, synthetic division, fundamental theorem of algebra, factors and zeros, Descartes rule of signs, rational solutions of polynomial equations
  • Graphs of rational functions: intercepts, asymptotes, symmetry, asymptotic behavior
  • Binomial theorem
  • Sequences and series: arithmetic and geometric sequences, infinite geometric series, summation notation, sums of arithmetic and geometric series
  • Matrices: determinants and inverses of 2 x 2 and 3 x 3 matrices; Cramer’s rule
  • Problem solving in an algebraic setting
  • A brief introduction to trigonometry: sines, cosines, and tangents; solutions to right triangles

CHAMP Year 2

These courses cover geometry with emphasis on logical structure using proof and problem solving and college algebra and trigonometry intended to prepare students for a university level calculus course.

  • Fall Semester: Geometry
    • Textbook Geometry by Moise and Downs
  • Spring Semester: College Algebra/Trigonometry
    • Textbook Advanced Mathematics: A Pre-calculus Course by Brown and Robbins

Geometry

  • Introduction to mathematical logic: undefined terms, definitions, postulates, theorems
  • Methods of proof: direct proof, indirect proof
  • Points, lines, planes, length, angle measurement, perpendicularity
  • Parallel lines, parallel postulate Angle measures in triangles and polygons
  • Triangle congruence postulates and theorems: SAS, ASA, SSS, SAA
  • Right triangles: the Pythagorean theorem, the hypotenuse-leg theorem
  • Similarity of triangles and polygons
  • Area and perimeter of triangles, polygons, and circles
  • Circles: chords, angle measurement for central and inscribed angles
  • Medians of a triangle, incenter, circumcenter, concurrence theorems for the medians, angle bisectors, and perpendicular bisectors of sides
  • Inequalities in geometry
  • Coordinate geometry in the plane and space
  • Transformations in the plane: reflections, translations, rotations, rigid motions, similarity transformations
  • Informal geometry in space: skew lines, parallel planes, perpendiculars to planes, dihedral angles, volume and surface areas, prisms, pyramids, spheres, cones, cylinders

Pre-Calculus 

  • Functions: zeros, graphs, inverses
  • Exponents and logarithms, growth and decay
  • Basic analytic geometry: loci, intercepts, symmetry, lines, distance formula, midpoint formula slope, parallel and perpendicular lines
  • Parametric equations, distance from a point to a line, angle between lines, linear inequalities
  • Graphs of algebraic relations: loci, nonlinear equations and inequalities
  • Analytic geometry in space: coordinates, distance formula, direction cosines, planes, lines
  • Angles and radian measure
  • General definition of trigonometric functions: values at convenient angles
  • Graphs of trigonometric functions: periodicity, ranges
  • Trigonometric equations and inequalities
  • Trigonometric identities: addition of angles formulas
  • Inverse trigonometric functions
  • Laws of sines and cosines: solution of triangles
  • Circular and harmonic motion
  • Graphs of composite trigonometric functions
  • Vectors
  • Polar coordinates: graphs using polar coordinates
  • Conic sections, vertices, asymptotes, graphs
  • Sequences and series
  • Systems of linear equations, matrices
  • Probability and counting problems