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.

Students will need a TI-83+ calculator for the duration of the program.

Effective Fall of 2024: All year 1 students will be required to attend 3 study labs per semester.

• Fall Semester: Algebra 1
• 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
• 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

Spring Semester: College Algebra/Trigonometry

• Textbook Advanced Mathematics (Precalculus with Discrete Mathematics and Data Analysis) by Richard Brown

### 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
• 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