# 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