CPMP Course 2 Units

Unit 1
Functions, Equations, and Systems
Reviews and extends student ability to recognize, describe, and use functional relationships among quantitative variables, with special emphasis on relationships that involve two or more independent variables.
Topics include:
Direct and inverse variation and joint variation; power functions; linear equations in standard form; and systems of two linear equations with two variables, including solution by graphing, substitution, and elimination.
Unit 2
Matrix Methods
Develops student understanding of matrices and ability to use matrices to model and solve problems in a variety of real-world and mathematical settings.
Topics include:
Constructing and interpreting matrices, matrix addition, scalar multiplication, matrix multiplication, powers of matrices, inverse matrices, comparing algebraic properties of matrices to those of real numbers, and using matrices to solve systems of equations.
Unit 3
Coordinate Methods
Develops student understanding of coordinate methods for representing and analyzing properties of geometric shapes, for describing geometric change, and for producing animations.
Topics include:
Representing two-dimensional figures and modeling situations with coordinates, including computer-generated graphics; distance in the coordinate plane, midpoint of a segment, and slope; coordinate and matrix models of rigid transformations (translations, rotations, and line reflections), of size transformations, and of similarity transformations; animation effects.
Unit 4
Regression and Correlation
Develops student ability to describe how two quantitative variables on a scatterplot are related, including fitting a function to the data and the use of correlation to measure the strength of a linear association between the two variables.
Topics include:
Construct and interpret scatterplots; compute and interpret a linear model including slope and intercept, residuals, and the correlation coefficient; sum of squared errors; influential points; and distinguish between correlation and causation.
Unit 5
Nonlinear Functions and Equations
Introduces function notation, reviews and extends student ability to construct and reason with functions that model parabolic shapes and other quadratic relationships in science and economics, with special emphasis on formal symbolic reasoning methods, and introduces common logarithms and algebraic methods for solving exponential equations.
Topics include:
Formalization of function concept, notation, domain and range; factoring and expanding quadratic expressions, solving quadratic equations by factoring and the quadratic formula, applications to supply and demand, break-even analysis; common logarithms and solving exponential equations using base 10 logarithms.
Unit 6
Modeling and Optimization
Develops student ability in mathematical modeling, optimization, and problem solving, through study of vertexedge graphs, as students model and solve problems about networks, paths, and circuits.
Topics include:
Mathematical modeling, optimization, algorithmic problem solving, and using minimum spanning trees, Hamilton paths, the Traveling Salesperson Problem, critical paths, and the PERT technique to solve network optimization problems.
Unit 7
Trigonometric Methods
Develops student understanding of trigonometric functions and the ability to use trigonometric methods to solve triangulation and indirect measurement problems.
Topics include:
Sine, cosine, and tangent functions of measures of angles in standard position in a coordinate plane and in a right triangle; indirect measurement; analysis of variable-sided triangle mechanisms; derivation and application of the Law of Sines and Law of Cosines.
Unit 8
Probability Distributions
Develops student understanding of independent events, conditional probability, and expected value and how to use them to interpret data and evaluate outcomes of decisions.
Topics include:
Two-way frequency tables, Multiplication Rule, independent and dependent events, conditional probability, probability distributions and their graphs, waiting-time (or geometric) distributions, and expected value for games of chance and for applications such as insurance.

CPMP Courses 1–4 Unit Descriptions (284 KB)
Courses 1–3 and Course 4: Preparation for Calculus Unit and Lesson Objectives (395 KB)

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