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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