PCM12SCO Specific Curriculum Outcomes: PCM 12

Chapter One: Sequences and Series

1.1 Recursive Relations

A1 demonstrate an understanding of recursive formulas

C1 model problem situations using discrete structures such as sequences and recursive formulas

A3 represent arithmetic and geometric sequences as ordered pairs and discrete graphs

A4 represent a series in expanded form and using sigma notation

B2 develop, analyse, and apply algorithms to generate terms in a sequence

B3 develop, analyse, and apply algorithms to determine the sum of a series

C18 demonstrate understanding for recursive formulas, and how recursive formulas relate to a variety of sequences

1.2 More Recursive Sequences

A1 demonstrate an understanding of recursive formulas

C1 model problem situations using discrete structures such as sequences and recursive formulas

A3 represent arithmetic and geometric sequences as ordered pairs and discrete graphs

A4 represent a series in expanded form and using sigma notation

B2 develop, analyse, and apply algorithms to generate terms in a sequence

B3 develop, analyse, and apply algorithms to determine the sum of a series

C18 demonstrate understanding for recursive formulas, and how recursive formulas relate to a variety of sequences

1.3 Proof by Induction

E2 develop and evaluate mathematical arguments and proofs

A4 represent a series in expanded form and using sigma notation

E3 prove, using the principle of mathematical induction

1.4 Limits

C25 demonstrate an intuitive understanding of the concept of limit

C26 investigate and apply the concept of infinity by examining sequences and series

A4 represent a series in expanded form and using sigma notation

B3 develop, analyse, and apply algorithms to determine the sum of a series

C24 demonstrate an understanding of convergence and divergence

B4 apply convergent and divergent geometric series

D2 demonstrate an understanding of how to approximate the area under a curve using limits

Chapter Two: Functions—A New Perspective 2.1 Combining

Functions

C2 model problem situations with combinations and compositions of functions

C14 analyse relations, functions, and their graphs

C5 use tables and graphs as tools to interpret expressions

C19 Investigate and interpret combinations and compositions of functions

C27 represent complex numbers in a variety of ways

2.2 Polynomial Equations and Inequalities

C14 analyse relations, functions, and their graphs

C5 use tables and graphs as tools to interpret expressions

C10 analyse and solve polynomial, rational, irrational, absolute value, and trigonometric equations

C11 analyse and solve polynomial, rational, and absolute value inequalities

E1 model real-world phenomena with a variety of functions/relations

C15 determine the equations of polynomial and rational functions

C20 factor polynomial equations

2.3 Composition of Functions

C2 model problem situations with combinations and compositions of functions

C19 investigate and interpret combinations and compositions of functions

C14 analyse relations, functions, and their graphs

C5 use tables and graphs as tools to interpret expressions

2.4 The Limit of a Rate of Change

E1 model real-world phenomena with a variety of functions/relations

C3 model real-world phenomena using polynomial functions and rational functions

C25 demonstrate an intuitive understanding of the concept of limit

C12 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

B5 evaluate and apply limits

2.5 The Slope of the Tangent and the Derivative

C7 demonstrate an understanding for slope functions and their connection to differentiation

B8 determine and supply the derivative of a function

C12 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

B7 derive and apply the power rule

B5 evaluate and apply limits

C14 analyse relations, functions, and their graphs

C5 use tables and graphs as tools to interpret expressions

2.6 Graphs of Polynomial Functions

C14 analyse relations, functions, and their graphs

C16 analyse the effect of parameter changes on the graphs of functions and express the changes using transformations

Chapter Three: Functions, Part II

3.1 Simple Rational Functions

C3 model real-world phenomena using polynomial functions and rational functions

C2 model problem situations with combinations and compositions of functions

C14 analyse relations, functions, and their graphs

C5 use tables and graphs as tools to interpret expressions

C19 investigate and interpret combinations and compositions of functions

C6 demonstrate an understanding for asymptotic behaviour

C10 analyse and solve polynomial, rational, irrational, absolute value, and trigonometric equations

3.2 Rational Functions and Asymptotes

B1 describe the relationships between arithmetic operations and operations on rational algebraic expressions and equations

C14 analyse relations, functions, and their graphs

C5 use tables and graphs as tools to interpret expressions

C6 demonstrate an understanding for asymptotic behaviour

C10 analyse and solve polynomial, rational, irrational, absolute value, and trigonometric equations

C23 explore and describe the connections between continuity, limits, and functions

C25 demonstrate an intuitive understanding of the concept of limit

3.3 Solving Rational Equations

B1 describe the relationships between arithmetic operations and operations on rational algebraic expressions and equations

C15 determine the equations of polynomial and rational functions

C7 demonstrate an understanding for slope functions and their connection to differentiation

C14 analyse relations, functions, and their graphs

C5 use tables and graphs as tools to interpret expressions

C6 demonstrate an understanding for asymptotic behaviour

C3 model real-world phenomena using polynomial functions and rational functions

C11 analyse and solve polynomial, rational, and absolute value inequalities

3.4 Irrational Functions

C14 analyse relations, functions, and their graphs

C5 use tables and graphs as tools to interpret expressions

C19 investigate and interpret combinations and compositions of functions

C10 analyse and solve polynomial, rational, irrational, absolute value, and trigonometric equations

C8 explore and describe the connections between quadratic equations and their inverses

C20 factor polynomial equations

C11 analyse and solve polynomial, rational, and absolute value inequalities

3.5 Absolute—Value Functions

C2 model problem situations with combinations and compositions of functions

C14 analyse relations, functions, and their graphs

C5 use tables and graphs as tools to interpret expressions

C19 investigate and interpret combinations and compositions of functions

C10 analyse and solve polynomial, rational, irrational, absolute value, and trigonometric equations

C11 analyse and solve polynomial, rational, and absolute value inequalities

3.6 Piecewise Functions

C23 explore and describe the connections between continuity, limits, and functions

C25 demonstrate an intuitive understanding of the concept of limit

C12 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

C2 model problem situations with combinations and compositions of functions

C5 use tables and graphs as tools to interpret expressions

B5 evaluate and apply limits

3.7 Modeling with Exponential and Logarithmic Functions

A2 determine, describe, and apply the value for “e”

B6 determine and apply the derivative of a function

C13 extend the understanding of exponential growth and decay through multiple contexts

C14 analyse relations, functions, and their graphs

C5 use tables and graphs as tools to interpret expressions

C12 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

B5 evaluate and apply limits

Chapter Four: Trigonometry

4.1 Circular and Periodic Motion

D1 describe and apply the connection between arc length and radian measure

A5 demonstrate an understanding for the use of, and need for, radian measure in the domain of trigonometric functions

C4 model situations with periodic curves

C10 analyse and solve polynomial, rational, absolute value, and trigonometric equations

C14 analyse relations, functions and their graphs

C16 analyse the effect of parameter changes on the graphs of functions and express the changes using transformations

C6 demonstrate an understanding for asymptotic behaviour

4.2 Graphing Trigonometric Functions

C4 model situations with periodic curves

C14 analyse relations, functions and their graphs

C16 analyse the effect of parameter changes on the graphs of functions and express the changes using transformations

C17 explore and analyse the graphs of the reciprocal trigonometric functions

C19 investigate and interpret combinations and compositions of functions

4.3 The General Rotational Matrix

C21 perform various transformations using multiplication of matrices

B8 derive and apply the general rotational matrix (cos 0 -sin 0 sin0 cos

0)

4.4 Trigonometric Identities and Inverse Trigonometric

Functions

C9 examine, interpret, and apply the relationship between trigonometric functions and their inverses

C22 explore and verify trigonometric identities

C10 analyse and solve polynomial, rational, irrational, absolute value, and trigonometric equations

4.5 Combinations of Functions

C2 model problem situations with combinations and compositions of functions

C19 investigate and interpret combinations and compositions of functions

Chapter Five: Numbers Most Complex!

5.1 Number Systems and Complex Numbers

A6 explain the connections between real and complex numbers

C27 represent complex numbers in a variety of ways

B9 apply operations on complex numbers both in rectangular and polar form

C28 construct and examine graphs in the complex and polar planes

E2 develop and evaluate mathematical arguments and proofs

C10 analyse and solve polynomial, rational, irrational, absolute value, and trigonometric equations

5.2 Polar Coordinates

C27 represent complex numbers in a variety of ways

B9 apply operations on complex numbers both in rectangular and polar form

C28 construct and examine graphs in the complex and polar planes

A7 translate between polar and rectangular representation

5.3 Operations Using Polar Coordinates

B9 apply operations on complex numbers both in rectangular and polar form

A7 translate between polar and rectangular representation

B10 develop and apply De Moivre’s Theorem for powers