## CSETMathGuru: THE Site for Single Subject Math

**Typical Free-Response Questions are derived from the following categories of topics and subject areas:**

**I Proofs / Demonstrations / Derivations:**

a) Deriving the Quadratic Formula.

b) Deriving the coordinates of the vertex of a parabola in standard form.

c) Proving that the sum of roots of a quadratic function f(x) = ax2 + bx + c is –b/a and the product of roots is c/a.

d) Deriving conditions for parallel / perpendicular lines with respect to slopes, using Matrices / Determinants (Cramer’s Rule / Analytical Geometry)

e) Deriving from their definitions, the equations of parabolas, ellipses and hyperbolas in standard form

f) Proving propositions using Mathematical Induction

g) Finding roots of polynomial functions OR finding polynomial functions, given their roots

h) Solving systems of linear equations using Matrices / Determinants

**II Graphing**

a) Polynomial functions, especially quadratic functions ie. parabolas

b) Rational Functions

c) Sketching Lines, circles, parabolas, ellipses and hyperbolas and determining the intersection of conic sections

d) Linear Programming situations

e) Function and its inverse!

**III Applications**

a) Modeling quadratic function situations to determine maximum / minimum values

b) Modeling linear programming situations

c) Modeling conic sections problems