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CPMP Course 2 Units
©2008
| Unit 1 (sample material) | ||
|---|---|---|
| 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. |
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| Unit 2 | ||
| Matrix
Methods Develops student understanding of matrices and ability to use matrices to represent and solve problems in a variety of real-world and mathematical settings. |
Topics
include: Constructing and interpreting matrices, row and column sums, matrix addition, scalar multiplication, matrix multiplication, powers of matrices, inverse matrices, properties of matrices, and using matrices to solve systems of linear equations. |
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| Unit 3 (sample material) | ||
| 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. |
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| Unit 4 | ||
| Regression
and Correlation Develops student understanding of the characteristics and interpretation of the least squares regression equation and of the use of correlation to measure the strength of the linear association between two variables. |
Topics
include: Interpreting scatterplots; least squares regression, residuals and errors in prediction, sum of squared errors, influential points; Pearson's correlation coefficient and its properties, lurking variables, and cause and effect. |
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| 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. |
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| Unit 6 (sample material) | ||
| Network
Optimization Develops student understanding of vertex-edge graphs and ability to use these graphs to solve network optimization problems. |
Topics
include: Optimization, mathematical modeling, algorithmic problem solving, digraphs, trees, minimum spanning trees, distance matrices, Hamilton circuits and paths, the Traveling Salesperson Problem, critical paths, and the PERT technique. |
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| Unit 7 (sample material) | ||
| 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; Law of Sines and Law of Cosines. |
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| Unit 8 (sample material) | ||
| Probability
Distributions Further develops student ability to understand and visualize situations involving chance by using simulation and mathematical analysis to construct probability distributions. |
Topics
include: Multiplication Rule, independent and dependent events, conditional probability, probability distributions and their graphs, waiting-time (or geometric) distributions, expected value, and rare events. |
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CPMP
Courses 1–4 Unit Descriptions (206 KB)
Courses 1–3
and Course 4: Preparation for Calculus Unit and Lesson Objectives (1.58 MB)
Scope and Sequence (1.14
MB) of topics across Courses 1–4