Mathematics / PreCalculus Honors
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Precalculus Honors: This course continues the study of the pre-calculus topics from Algebra 2 Trigonometry Honors and begins the study of Advanced Placement Calculus as outlined by the College Board. It includes the analysis of functions, vectors, sequences and series and differential calculus. The emphasis is on proofs and intensive discussions of related topics with student presentations required. The final exam is a departmental exam. This course consists approximately ½ year of Pre-calculus Topics (indicated with "a" next to the unit number) and approximately ½ year of Calculus AB topics (indicated by a "b" next to the unit number) Teachers can pick/choose from the myriad "a" topic from year to year as time permits and as needs arise year to year. Topics indicated with a "b" are non-negotiable. The topics "a" that have not been filled out were not taught this year and will be filled in if/when they are in the future.  |
Please note that the timelines listed below are a guide. Teachers modify their pacing based on student needs in order to ensure concept mastery.
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Unit 1a |
Set Theory and Notation |
September |
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Section |
Concepts |
Resources |
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Dolciani "Introductory Analysis" |
Notation and Symbols in Set Theory |
Handout |
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Chapter 1 |
Expressing sentences using existential and universal quantifiers |
" |
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Properties of number sets and operations on sets |
" |
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Subsets, supersets, and proper sub/supersets, power sets |
" |
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Unit 2a |
Proof by Mathematical Induction |
September |
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Section |
Concepts |
Resources |
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Algebraic Induction Proofs: utilizing concepts of rational numbers, exponents, factoring |
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Divisibility proofs |
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Unit 3a |
Complex Numbers |
October |
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Section |
Concepts |
Resources |
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Dolciani "Introductory Analysis" |
Review of properties of and operations on complex numbers |
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Chapter 5, 13 |
Graphing in the complex plane; vector graphs |
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Recursion and the Mandelbrot set |
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Complex number proofs (modulus and conjugate) |
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Determining square roots of complex numbers |
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Solving quadratic and factorable higher-order equations with complex coefficients |
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Trig (cis) form of a complex number |
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Multiplying/dividing/powers of a complex number in cis form (DeMoivre's Theorems) |
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Finding nth Roots of complex number in cis form (DeMoivre's) |
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Unit 4a |
Roots of Polynomials |
Oct - Nov |
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Section |
Concepts |
Resources |
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Dolciani "Introductory Analysis" |
Vocabulary and definitions relating to polynomials (review) |
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(photocopied) |
Factoring and writing equations of quadratics and higher-order polynomials given roots and additional information (review) |
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Chapter 5 |
Polynomial long division and synthetic division |
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The division algorithm and the remainder theorem |
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Rational Root theorem |
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Bounds for real roots (LUB/GLB) |
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Descartes' rule of signs |
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Determining all roots to a higher-order polynomial |
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End Of Quarter 1 |
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Unit 5a |
Vectors and Matrices |
Nov - Dec |
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Section |
Concepts |
Resources |
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Dolciani "Introductory Analysis" Chapter 11 -13 |
Drawing in 3-space, distance and midpoint |
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" |
Linear combinations of vectors, parallel vectors |
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" |
Norms of vectors, dot-products of vectors |
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" |
Basis vectors |
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" |
Matrix and matrix operations |
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" |
Determinants and Cross-products of vectors |
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" |
Solving Systems of Equations by augmented matrices |
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Unit 6a |
Parametric Equations |
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Section |
Concepts |
Resources |
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Was not taught 2016-2017 |
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Unit 7a |
Polar Coordinates and Graphs |
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Section |
Concepts |
Resources |
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Dolciani "Introductory Analysis" |
Graphing polar coordinates, converting to/from rectangular form |
WileyPlus Calculus Chapter 10 |
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Exploration of polar curve types |
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Unit 8a |
Sequences and Series |
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Section |
Concepts |
Resources |
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Was not taught 2016-2017 |
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Unit 9a |
Conic Sections |
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Section |
Concepts |
Resources |
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Was not taught 2016-2017 |
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Unit 9b |
Foundations of Calculus |
January |
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Section |
Concepts |
Resources |
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Inequalities using interval notation: polynomial, rational, compound |
https://apcalculusstillwater.wordpress.com/ap-calculus-videos/ |
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Absolute Value equations and inequalities, including rational absolute value inequalities and Inequalities of the form |
" |
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Piecewise functions (maybe now can go because of introduction in CC A2) |
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Re-writing Absolute Value as piecewise functions |
" |
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End Of Quarter 2 |
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Unit 10b |
Limits and Continuity |
February |
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Section |
Concepts |
Resources |
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Anton CalculusText Chapter 1 |
Conceptual and graphical idea of a limit |
WileyPlus online videos and self-tests for rest of the year |
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" |
Computing limits algebraically |
" |
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" |
Limits by inspection |
" |
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" |
Limits involving piecewise functions |
" |
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" |
Holes and asymptotes in rational functions |
" |
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" |
End behavior of polynomial functions (limits at infinity) |
" |
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" |
Definition of continuity |
" |
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" |
Removable, essential, jump discontinuities |
" |
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" |
Continuity on open vs. Closed intervals |
" |
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" |
Intermediate Value Theorem (IVT) and its applications |
" |
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Unit 11b |
The Derivative |
March |
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Section |
Concepts |
Resources |
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Anton Calcuclus Text Chapter 2 |
Tangent and secant lines |
" |
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" |
Visualizing the derivative (comparing graphs of the derivative to original function) |
" |
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" |
Using limit definition of the derivative to derive and apply the power rule |
" |
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" |
Average and instantaneous rates of change |
" |
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" |
Equations of tangent and normal lines to a function |
" |
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" |
Product rule |
" |
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" |
Quotient rule |
" |
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End Of Quarter 3 |
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" |
Chain rule |
" |
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" |
Higher order derivatives |
" |
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" |
Derivatives from tabular or graphical data |
" |
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" |
Implicit differentiation |
" |
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Unit 12b |
Applications of Derivatives |
April - June |
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Section |
Concepts |
Resources |
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Anton Calculus Text Chapter 3 |
Curve Sketching |
" |
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" |
Optimization |
" |
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END OF YEAR |
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