STANDARD COMPETENCIES:

 

 1.   Perform set operations, including finding unions and intersections, and identifying subsets.

 2.   Find the analytical and graphical solutions of linear equations and inequalities in both standard form and slope-intercept form.

 3.   Solve quadratic equations by factoring, by the square root method, and by the quadratic formula.

 4.   Analyze functions, including determining their domains and ranges, and graphing up to second degree functions.

 5.   Use exponential functions graphically and in growth applications.

 6.   Use logarithmic functions graphically and in growth applications.

 7.   Solve a system of two equations in two variables by graphing, by the method of substitution, and by the method of addition.

 8.   Solve a system of equations by determining the augmented matrix and using Gauss-Jordan elimination.

 9.   Perform matrix operations, including addition, multiplication, and determining the inverse of a square matrix.

 10. Solve two-variable linear programming problems by graphing the system of inequalities, determining the feasible regions, and graphically finding the optimal solutions.

 11. Solve linear programming problems using the simplex method, including solving maximization problems as well as solving minimization problems using duality.

 12. Solve simple and compound interest problems.

 13. Solve various types of annuity problems, including ordinary annuities, sinking funds, and amortizations.

 14. Solve permutation and combination problems.

 15. Perform basic probability functions, including defining sample spaces and events, converting between probabilities and odds, and finding the probabilities of events as well as probabilities of the unions and intersections of events.

 16. Apply conditional probability analysis, including the identification of dependent and independent events and the use of Bayes' Formula.

 17. Find the probability distributions of discrete random variables.

 18. Create various probability graphs, including bar graphs, broken-line graphs, pie graphs, frequency distributions, histograms, and frequency polygons.

 19. Calculate various statistical measures, including means, medians, modes, ranges, variances, standard deviations, and expected values.

 20. Calculate probabilities for normal and binomial distributions.

 TOPICAL OUTLINE:

 

 I.      Introduction: Sets, Linear Equations and Inequalities, Quadratic Equations, Coordinate System, Functions, Exponential Functions, and Logarithmic Functions.

 II.     Systems of Linear Equations: Two equations in two variables, and Matrices.

 III.    Linear Inequalities: Systems of Inequalities in 2 Variables, Linear Programming, Simplex Method, And Dual Problems.

 IV.   Finance Mathematics: Simple Interest, Compound Interest, Future Value, and Present Value.

 V.    Probability: Permutations and Combinations, Probabilities of Events, Empirical Probability, Probability Distribution.

 VI.   Data Description:  Graphing Data, Measures of Central Tendency, Measures of Dispersion, Binomial Distributions and Normal distributions.

 VII.  Games and Decisions: Strictly determined games, Mixed strategy games.

 VIII.  Linear programming - Geometric approach, and Linear programming - Simplex method.