Grade 12 - Mathematics

Mastery of course expectations enables students to demonstrate the conceptual underpinnings of calculus to determine limits, derivatives, integrals, rates of change and averages, using geometrical representations.

12.C.1

Mastery of course expectations enables students to translate among symbolic, diagram and graphical representations of situations that describe both continuous and discrete functions of one real variable.

12.D.1

Mastery of course expectations enables students to determine limits, derivatives, integrals and rates of change.

12.E.1

Mastery of course expectations enables students to use calculus concepts to describe data distributions and random variables at an introductory level.

12.A.1.1

Conceptual Understanding

12.A.1.2

Procedural Knowledge

12.A.1.3

Problem-Solving Contexts

12.B.1.1

Conceptual Understanding

12.B.1.2

Procedural Knowledge

12.B.1.3

Problem-Solving Contexts

12.C.1.1

Conceptual Understanding

12.C.1.2

Procedural Knowledge

12.C.1.3

Problem-Solving Contexts

12.D.1.1

Conceptual Understanding

12.D.1.2

Procedural Knowledge

12.D.1.3

Problem-Solving Contexts

12.E.1.1

Conceptual Understanding

12.E.1.2

Procedural Knowledge

12.E.1.3

Problem-Solving Contexts

12.A.1.1.a

Students will demonstrate understanding of the concepts of Mathematics 31, by: identifying and giving examples of the strengths and limitations of the use of technology in the computation of limits, derivatives and integrals and giving examples of the differences between intuitive and rigorous proofs in the context of limits, derivatives and integrals.

12.A.1.2.a

Students will demonstrate competence in the procedures of Mathematics 31, by: combining and modifying familiar solution procedures to form a new solution procedure to a related problem.

12.A.1.3.a

Students will demonstrate problem-solving skills in Mathematics 31, by: using the connections between a given problem and either a simpler or equivalent problem, or a previously solved problem, to solve the given problem and producing approximate answers to complex calculations by simplifying the models used.

12.B.1.1.a

Students will demonstrate understanding of the concepts of Mathematics 31, by: describing the relationships among functions after performing translations, reflections, stretches and compositions on a variety of functions and linking displacement, velocity and acceleration of an object moving in a straight line with nonuniform velocity.

12.B.1.2.a

Students will demonstrate competence in the procedures of Mathematics 31, by: drawing the graphs of functions by applying transformations to the graphs of known functions and calculating the displacement, velocity and acceleration of an object moving in a straight line with nonuniform velocity.

12.B.1.3.a

Students will demonstrate problem-solving skills in Mathematics 31, by: constructing geometrical proofs at an intuitive level that generalize the concepts of slope, area, average and rate of change.

12.C.1.1.a

Students will demonstrate understanding of the concepts of Mathematics 31, by: giving examples of the limits of functions and sequences, both at finite and infinite values of the independent variable.

12.C.1.2.a

Students will demonstrate competence in the procedures of Mathematics 31, by: expressing final algebraic and trigonometric answers in a variety of equivalent forms, with the form chosen to be the most suitable form for the task at hand and computing limits of functions, using definitions, limit theorems and calculator/computer methods.

12.C.1.3.a

Students will demonstrate problem-solving skills in Mathematics 31, by: constructing mathematical models for situations in a broad range of contexts, using algebraic and trigonometric functions of a single real variable.

12.D.1.1.a

Students will demonstrate understanding of the concepts of Mathematics 31, by: connecting the derivative with a particular limit, and expressing this limit in situations like secant and tangent lines to a curve, relating the derivative of a complicated function to the derivative of simpler functions, relating the zeros of the derivative function to the critical points on the original curve and recognizing that integration can be thought of as an inverse operation to that of finding derivatives.

12.D.1.2.a

Students will demonstrate competence in the procedures of Mathematics 31, by: computing derivatives of functions, using definitions, derivative theorems and calculator/ computer methods and computing definite and indefinite integrals of simple functions, using antiderivatives, integral theorems and calculator/computer methods.

12.D.1.3.a

Students will demonstrate problem-solving skills in Mathematics 31, by: determining the optimum values of a variable in various contexts, using the concepts of maximum and minimum values of a function, using the concept of critical values to sketch the graphs of functions, and comparing these sketches to computer-generated plots of the same functions and connecting a derivative and the appropriate rate of change, and using this connection to relate complicated rates of change to simpler ones.

12.E.1.1.a

Students will demonstrate understanding of the concepts of Mathematics 31, by: describing the connections between the operation of integration and the finding of areas and averages.

12.E.1.2.a

Students will demonstrate competence in the procedures of Mathematics 31, by: calculating the mean value of a function over an interval.

12.E.1.3.a