Pre-Calculus Mathematics 12: Mathematical Modeling, Book 4
Sequences and Series
Functions—A New Perspective
Functions, Part II
A1
demonstrate an understanding of recursive formulas
A2
B1
A3
represent arithmetic and geometric sequences as
ordered pairs and discrete graphs
represent a series in expanded form and using sigma
notation
develop, analyse, and apply algorithms to generate terms
in a sequence
develop, analyse, and apply algorithms to determine the
sum of a series
apply convergent and divergent geometric series
model problem situations using discrete structures such
as sequences and recursive formulas
demonstrate understanding for recursive formulas, and
how recursive formulas relate to a variety of sequences
demonstrate an understanding of convergence and
divergence
demonstrate an intuitive understanding of the concept of
limit
investigate and apply the concept of infinity by
examining sequences and series
demonstrate an understanding of how to approximate the
area under a curve using limits
develop and evaluate mathematical arguments and
proofs
prove, using the principle of mathematical induction
B5
B7
B8
C2
A4
B2
B3
B4
C1
C18
C24
C25
C26
D2
E2
E3
C3
C5
C7
C10
C11
C12
C14
C15
C16
C19
C20
C25
C27
E1
evaluate and apply limits
derive and apply the power rule
determine and supply the derivative of a function
model problem situations with combinations and
compositions of functions
model real-world phenomena using polynomial
functions and rational functions
use tables and graphs as tools to interpret expressions
demonstrate an understanding for slope functions and
their connection to differentiation
analyse and solve polynomial, rational, irrational,
absolute value, and trigonometric equations
analyse and solve polynomial, rational, and absolute
value inequalities
demonstrate an understanding for the conceptual
foundations of limit, the area under a curve, the rate of
change, and the slope of the tangent line, and their
applications
analyse relations, functions, and their graphs
determine the equations of polynomial and rational
functions
analyse the effect of parameter changes on the graphs of
functions and express the changes using transformations
investigate and interpret combinations and compositions
of functions
factor polynomial equations
demonstrate an intuitive understanding of the concept of
limit
represent complex numbers in a variety of ways
model real-world phenomena with a variety of
functions/relations
B5
B6
C2
C3
C5
C6
C7
C8
C10
C11
C12
C13
C14
C15
C19
C20
C23
C25
determine, describe, and apply the value for “e”
describe the relationships between arithmetic operations
and operations on rational algebraic expressions and
equations
evaluate and apply limits
determine and apply the derivative of a function
model problem situations with combinations and
compositions of functions
model real-world phenomena using polynomial
functions and rational functions
use tables and graphs as tools to interpret expressions
demonstrate an understanding for asymptotic behaviour
demonstrate an understanding for slope functions and
their connection to differentiation
explore and describe the connections between quadratic
equations and their inverses
analyse and solve polynomial, rational, irrational,
absolute value, and trigonometric equations
analyse and solve polynomial, rational, and absolute
value inequalities
demonstrate an understanding for the conceptual
foundations of limit, the area under a curve, the
rate of change, and the slope of the tangent line, and
their applications
extend the understanding of exponential growth and
decay through multiple contexts
analyse relations, functions, and their graphs
determine the equations of polynomial and rational
functions
investigate and interpret combinations and compositions
of functions
factor polynomial equations
explore and describe the connections between
continuity, limits, and functions
demonstrate an intuitive understanding of the concept of
limit
Trigonometry
Numbers Most Complex!
A5
A6
B8
C2
C4
C6
C9
C10
C14
C16
C17
C19
C21
C22
D1
demonstrate an understanding for the use of, and need
for, radian measure in the domain of trigonometric
functions
derive and apply the general rotational matrix (cos 0 sin 0 sin0 cos 0)
model problem situations with combinations and
compositions of functions
model situations with periodic curves
demonstrate an understanding for asymptotic behaviour
C10
analyse and solve polynomial, rational,
absolute value, and trigonometric equations
examine, interpret, and apply the relationship between
trigonometric functions and their inverses
analyse and solve polynomial, rational, irrational,
absolute value, and trigonometric equations
analyse relations, functions and their graphs
analyse the effect of parameter changes on the graphs of
functions and express the changes using transformations
explore and analyse the graphs of the reciprocal
trigonometric functions
investigate and interpret combinations and compositions
of functions
perform various transformations using multiplication of
matrices
explore and verify trigonometric identities
describe and apply the connection between arc length
and radian measure
A7
B9
B10
C10
C27
C28
E2
explain the connections between real and complex
numbers
translate between polar and rectangular representation
apply operations on complex numbers both in
rectangular and polar form
develop and apply De Moivre’s Theorem for powers
analyse and solve polynomial, rational, irrational,
absolute value, and trigonometric equations
represent complex numbers in a variety of ways
construct and examine graphs in the complex and polar
planes
develop and evaluate mathematical arguments and
proofs