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Math 1 (681) Course Outline


1. Linear Equations
Display data on a graphing utility, scatterplots and line graphs, ratio and slope, slope as a rate of change, parallel lines, linear equations in slope-intercept form and two-point form, domain and range, graphic solution of systems of linear equations and rewriting formulas.

2. Areas, Tessellations, and Nets of Solids
Determine nets for three-dimensional solids, surface area of solids, tessellate polygons, find the area of regular polygons, and calculate waste created by a template.

3. Volumes and Linear Models
Volumes of triangular, rectangular, and trapezoidal prisms, estimate the volumes of three dimensional solids, converting rates to different units, construct and interpret graphs, use linear models, determine rates of change, examine residuals and use them to evaluate models.

4. Exponential Growth
Develop and use a mathematical model for population growth, determine the growth rate of a population, graph and interpret an exponential function in the form y = abx.

5. Areas, volumes, Direct and Inverse Proportions
Areas of irregularly shaped figures, volume of cylinders and prisms, develop and graph direct and inverse proportions, develop mathematical models of real world events, use the models to make predictions about data sets.

6. Probability
Determine experimental probability using a variety of methods for simulation, calculate theoretical probability, identify and extend data patterns, calculate expected value.

7. Similarity
Model growth using similarity, use relationships among scale factor, length, area, and volume of similar objects, relationship between changes in length and changes in area and volume, use relationships among mass, density, weight, and pressure to describe proportional size changes, examine how the values of a and b affect graphs of power equations of the form y = axb.

8. Exponential equations, Venn Diagrams and Probability
Collect and analyze data, model the spread of disease using exponential equations, use Venn diagrams to organize data and determine probabilities, fundamental counting principle, use tree diagrams to determine probabilities.

9. Fundamental Counting Principle
Use the fundamental counting principle, factorial notation, solve problems involving Hamiltonian circuits, develop algorithms for solving problems.

10. Inequalities and Step Functions
Represent compound inequalities on a number line and algebraically, use interval notation to represent inequalities, graph and interpret step functions, use the greatest function to write equations of step functions.

11. Sequences and Series
Analyze number patterns, develop arithmetic and geometric sequences, compare explicit formulas for arithmetic and geometric sequences with linear and exponential equations, evaluation of series.

12. Inequalities and Linear Programming
Graph linear inequalities, solve systems of linear equations, use linear inequalities to define regions graphically, determine optimum values for linear objective equations.

13. Matrix Operations
Organize and interpret data using matrices, use matrices in business applications, operations with matrices, interpret the meaning of the elements within a product matrix.

14. Pythagorean Theorem and Right Triangles
Use similarity to determine unknown measures in triangles, use the Pythagorean theorem and its converse to solve right triangle problems, use technology to develop a table of trigonometric values, develop and apply the sine, cosine, and tangent ratios and their inverses.


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