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At the conclusion of this course, the student should be able to do the listed objectives from four of the following seven subject areas:
I. Functions
A. Define function, domain, and range, and use function notation appropriately.
B. Use a graphing calculator to analyze the graph of a function.
C. Solve application and modeling problems that involve functions.
II. Financial Math
A. Use simple interest, compound interest, future value, present value, and effective yield formulas to calculate unknown values.
B. Use a graphing calculator to solve for unknown values.
C. Create and explore amortization tables.
III. Geometry: Instructor choice of at least three of the following objectives.
A. Identify two- and three-dimensional shapes and use basic distance, area, surface area and volume formulae.
B. Recognize, and apply appropriately, constructions, relationships and formulae involving quadrilaterals; sides and angles of triangles; parallel lines and planes; and chords, secants and tangents of circles.
C. Describe and apply symmetry and rigid and non-rigid transformations.
D. Use deductive reasoning to reach conclusions based on underlying axioms or previously proved theorems.
E. Discuss and apply relationships in non-Euclidean geometry.
F. Recognize types of graphs and use relationships between vertices and edges to discuss and solve problems from graph theory.
IV. Linear Programming
A. Graph systems of linear inequalities.
B. Define the feasible region for a linear programming problem and calculate the vertices the region.
C. Calculate the optimum value or values of a function of two variables based on the graph of the feasible region.
D. Solve application and modeling problems that involve linear programming.
V. Probability and Statistics
A. Create and use graphical displays of data and frequency distributions.
B. Define mean, median, mode, percentiles, variability and standard deviation and compute each for sets of data.
C. Use laws of probability.
D. Discuss linear regression and correlation, and use technology to compute regression equations for applied problems.
VI. Reasoning
A. Apply inductive reasoning to patterns and sequences.
B. Apply deductive reasoning to analyze statements and arguments using logic, Venn diagrams and set theory.
VII. Trigonometry
A. Calculate the lengths of the sides of a triangle using the Pythagorean theorem.
B. Define the basic trigonometric functions in terms of right triangle ratios with angles given in degrees.
C. Use a calculator to find the values of basic trigonometric functions and angles.
D. Solve application and modeling problems that involve trigonometry.
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Instructor will choose four of the following seven topics:
I. Functions
A. Variation
B. Rates of change
C. Population growth
D. Other applications and models
II. Financial Math
A. Simple and compound interest
B. Future value
C. Present value
D. Annuities
E. Loans
F. Effective yield
G. Applicatons
III. Geometry
Topics chosen from at least seven of the following topics:
A. Basic figures in geometry
B. Deductive reasoning
C. Parallel lines and planes
D. Similarity and congruence
E. Inequalities in geometry
F. Right triangles
G. Circles
H. Constructions
I. Areas and volumes
J. Non-Euclidean Geometry
K. Polyhedra
L. Transformations and symmetries
M. Graph theory
N. Applications
IV. Linear Programming
A. Linear modeling
B. Optimization
C. Applications
V. Probability and Statistics
A. Counting techniques
B. Probability rules
C. Sampling and collecting data
D. Organizing data
E. Measures of center and spread
F. Graphical display of data
G. Linear regression
H. Applications
VI. Reasoning
A. Inductive reasoning including patterns and sequences
B. Deductive reasoning including logic and sets
C. Applications
VII. Trigonometry
A. Angles
B. Basic definitions
C. Right triangles
D. Pythagorean Theorem
E. Applications
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Thinking Mathematically 8th ed. Blitzer, R. Pearson 2022.
Mathematics: A Human Endeavor. 3rd ed. Jacobs, Harold. W.H. Freeman. 1994 (classic).nstructor prepared materials