2002 Todd Fuller Math Competition Topics

1. Solving Equations and Inequalities
        a. linear
        b. quadratic
        c. polynomial (including use of the factor, remainder, and rational root theorems)
        d. rational
        e. radical
        f. exponential and logarithmic
        g. trigonometric
        h. absolute value
        i. systems of equations in two variables
2. Functions
        a. functional notation
        b. composition and inverses
        c. properties and graphs of the elementary functions:
                i. linear, quadratic, polynomial, rational, absolute value,
                ii. exponential (any positive base), logarithmic (any positive base),
                iii. trigonometric (including phase shift, frequency, amplitude)
        d. informal limits and continuity
3. Other Trigonometry Topics
        a. solution of triangles (Laws of Sines and Cosines)
        b. identities
        c. addition, multiple, and half-angle formulas
        d. inverse trigonometric functions
        e. values of trigonometric functions of special angles (0, pi/6, pi/4, etc.)
4. Miscellaneous Topics
        a. binomial theorem
        b. simplifying rational expressions
        c. simplifying radical expressions
        d. simplifying expressions involving factional exponents
        e. mensuration formulas for elementary geometric figures (rectangles, circle, triangles, rectanglar parallelpipeds, spheres, cones, etc.)
        f. equations of circles, ellipses, parabolas, and hyperbolas in standard position
        g. induction
        h. permutations and combinations
        i. probability
        j. progressions
        k. plane geometry
        l. base notation
        m. compound interest (new this year)
5. applied problems involving use of any of the above mentioned topics

Todd Fuller Math Competition Committee Department of Mathematics Campus Box 8205 North Carolina State University Raleigh, NC 27695-8205 email: undergrad@math.ncsu.edu