(1) A graduating student at the advanced level in mathematics demonstrates superior performance. He/she gives responses that exhibit advanced understanding of the problem or situation presented. The student consistently demonstrates advanced conceptualization and makes connections within and between the mathematical and real world. The student is able to apply more than one process, use multiple representations, and determine solutions accurately. Reasoning and structure of responses are clearly communicated and justified.

(a) The student demonstrates these abilities under content standard 1 in the areas of:

(i) quantification;

(ii) estimation and accuracy;

(iii) equivalence with multiple notation;

(iv) properties of numbers and number systems; and

(v) modeling relationships and change.

(b) The student demonstrates these abilities under content standard 2 in the areas of:

(i) representing and analyzing data;

(ii) evaluating validity;

(iii) rules of probability and expected value;

(iv) counting methods; and

(v) curve fitting.

(c) The student demonstrates these abilities under content standard 3 in the areas of:

(i) conjectures and inductive reasoning;

(ii) applications of geometric models;

(iii) multiple geometric approaches;

(iv) indirect measurement; and

(v) methods of proof.

(d) The student demonstrates these abilities under content standard 4 in the areas of:

(i) representing functions;

(ii) variables and parameters;

(iii) solving systems of equations and inequalities;

(iv) families of functions and transformations; and

(v) analyzing and conjecturing with models.