I.    General Math*                                                                                        10%

 

      A.   Applications Involving Integers, Fractions, Decimals, and Percents*

 

      B.   Basic Counting Techniques*

            1.   Multiplication principle*

            2.   Permutations and combinations*

 

      C.   Probability of Equally Likely Events*

 

 

II. Algebra*                                                                                                    30%

 

      A.   Solving Polynomial Equations*

            1.   Linear and quadratic equations*

            2.   Higher order equations*

                  a)   Quadratic form*

                  b)   Remainder and factor theorem*

                  c)    Rational roots theorem*

 

      B.   Solving Inequalities*

            1.   Linear and quadratic*

            2.   Absolute value*

 

      C.   Functions: Rational, Exponential, and Logarithmic*

            1.   Domain range*

            2.   Composition*    

            3.   Inverses*

            4.   Graphing*

 

      D.   Complex Numbers*

            1.   Operations with complex numbers*

            2.   Complex numbers as roots of equations*

 

      E.   Reading Graphs of Functions*

 

      F.   Sequences and Series*

            1.   Arithmetic*

            2.   Geometric*

            3.   Special sequences and series*

 

 

III. Geometry*                                                                                                30%

 

      A.   Right Triangles*

            1.   Pythagorean theorem*

            2.   Special triangles*

           

      B.   Coordinate Geometry*

            1.   Midpoint*

            2.   Slope*

            3.   Distance formula*

            4.   Parallel and perpendicular lines*

            5.   Properties of quadrilaterals as represented in a coordinate system*

 

      C.   Plane and Solid Figures*

            1.   Area and properties of polygons*

            2.   Area and volume of prisms, pyramids, cylinders, spheres, and cones*

            3.   Properties of similar figures*

            4.   Circles*

                  a)   Area*

                  b)   Angle measures*

                  c)   Tangents, secants, and intersecting chords*

 

      D.   Congruency and Similarity*

 

 

IV. Trigonometry*                                                                                        20%

 

      A.   Right Triangle Relationships*

            1.   Measurements of angles*

            2.   Measurements of sides*

 

      B.   Trigonometric Functions*

 

      C.   Inverse Trigonometric Functions*

 

      D.   Graphs*

 

      E.   Identities*

 

      F.   Trigonometric Equations*

            1.   Law of sines and cosines*

            2.   Algebraic equations involving trigonometric functions*

 

 

V.   Differential Calculus*                                                                        10%

 

      A.   Basic Limits and Continuity*

            1.   Finite*

            2.   Infinite*

            3.   L'Hopital's rule*

 

      B.   First Derivatives, Second Derivatives, and Antiderivatives and their Graphical            Interpretation*

 

      C.   Equation of a Tangent Line*

 

      D.   Rates of Change*

            1.   Single variable*

            2.   Two-variable related rates of change*

 

      E.   Maxima and Minima*

 

      F.   Inflection Points and Concavity*

 

*Asterisks indicate topics that students will need to research independently. All of the topics in the math outline will require independent research, as USAD does not offer a Math Resource Guide. Information on the math topics can be found in most high school mathematics textbooks. USAD does offer a Math Basic Guide, which can be downloaded at no cost here. The Math Basic Guide offers a very general overview of major topics in high school math, including algebra, geometry, trig, calculus, and statistics.