I. GENERAL MATHEMATICS*

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*

10%

II. ALGEBRA*

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*

30%

III. GEOMETRY*

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*

30%

IV. TRIGONOMETRY*

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*

20%

V. DIFFERENTIAL CALCULUS*

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*

10%

*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 Mathematics Resource Guide. Information on the mathematics topics can be found in most high school mathematics textbooks. USAD does offer a Mathematics Basic Guide, which can be downloaded at no cost. The Mathematics Basic Guide offers a very general overview of major topics in high school mathematics, including algebra, geometry, trig, calculus, and statistics. The Mathematics Basic Guide will not be a direct source of any USAD mathematics test items.