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*

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.