College Mathematics Course Structure

ALGEBRA and FUNCTIONS: 20%

• Solving equations, linear inequalities, and systems of linear equations by analytic and graphical methods
• Interpretation, representation, and evaluation of functions: numerical, graphical, symbolic, and descriptive methods
• Graphs of functions: translations, horizontal and vertical reflections, and symmetry about the x-axis, the y-axis, and the origin
• Linear and exponential growth
• Applications

COUNTING and PROBABILITY: 10%

• Counting problems: the multiplication rule, combinations, and permutations
• Probability: union, intersections, independent events, mutually exclusive events, complimentary events, conditional probabilities, and expected value
• Applications

DATA ANALYSIS and STATISTICS: 15%

• Data interpretation and representation: tables, bar graphs, line graphs, circle graphs, pie charts, scatterplots, and histograms
• Numerical summaries of data: mean(average), median, mode, and range
• Standard deviation, normal distribution (conceptual questions only)
• Applications

FINANCIAL MATHEMATICS: 20%

• Percents, percent change, markups, discounts, taxes, profit, and loss
• Interest: simple, compound, continuous interest, effective interest rate, effective annual yield or annual percentage rate (APR)
• Present value and future value
• Applications

GEOMETRY: 10%

• Properties of triangles and quadrilaterals; perimeter, area, similarity, and the Pythagorean theorem
• Parallel and perpendicular lines
• Properties of circles: circumference, area, central angles, inscribed angles, and sectors
• Applications

LOGIC and SETS: 15%

• Logical operations and statements: conditional statements, conjunctions, disjunctions, negations, hypotheses, logical conclusions, converses, inverses, counterexamples, contrapositives, logical equivalence
• Set relationships, subsets, disjoint sets, equality of sets, and Venn diagrams
• Operations on sets: union, intersections, and complement
• Applications

NUMBERS: 10%

• Properties of numbers and their operations: integers and rational, irrational, and real numbers (including recognizing rational and irrational numbers)
• Elementary number theory: factors and divisibility, primes and composites, odd and even integers, and the fundamental theorem of arithmetic
• Measurement: unit conversion, scientific notation, and numerical precision
• Absolute value
• Applications