This course is designed for prospective mathematics majors and students interested in engineering, computer science, physics, business, or the life sciences. Following a condensed, intensive review of the algebra, trigonometry, and analytic geometry topics necessary for success in calculus, the lessons cover topics in the syllabus for AP Calculus. The topics in AP Calculus (AB) are found in the first two-thirds of the course, while the topics for AP Calculus (BC) are found in the final third of the course. Other important topics not found in the AP Calculus course description, but essential for success in a college-level Calculus course, are interspersed throughout. 

The course consists of an extremely rapid review of the AP Calculus AB syllabus (within the first semester), followed by the AP Calculus BC syllabus of: sequences and series, types of series, tests for convergence, approximating functions with series, term-by-term differentiation and integration of power series, Newton’s method, Euler’s method, the trapezoidal rule, slope fields, parametric equations, polar functions, vector functions, logistic growth, arc length, piecewise integration, projectile motion, and volumes of solids defined by cross sections. In addition, students are introduced to several features of the TI-83 or 84 calculator, and are shown how to confirm answers by graphical and numerical means. 

The problem sets are carefully constructed and are the core of the textbook. Students should not skip any problem in the problem sets. During the initial presentation of a new concept, the aim is not mastery. Students are afforded the opportunity to achieve mastery over time. This helps student confidence and leads to a deeper understanding of the concepts and skills being learned. 

This course is designed to finish by the time Seniors begin AP and IB exams in early May. 

• Grades 10 ~ 12

• 4 or 5 on AP Calculus AB Exam (Students will be co-registered to AP Statistics or another math course such as IB until the score releases in early July)

• Teacher Recommendation

• 5% Participation

• 35% Homework

• 60% Tests

Participation

• Students are expected to be on time for every class, and be ready for the day's activities when class begins. Students are expected to come to class prepared with all required supplies each day. 

• Each day, students can earn a participation grade on a scale from 0-5 according to: being on time (1), coming prepared (1), engaging in class and staying on task (2), and demonstrating a positive respectful attitude (1).

Homework

• Every homework given on a daily basis will be graded for completion on a scale from 0-5. All homework must be submitted in the submission box before the class starts. Completion is graded on effort, not accuracy, and is not necessarily a reflection of the type of grade a student should expect on assessments. 

• Generally, all homework will follow the "Even Problems for Even Lessons and Odd Problems for Odd Lessons" rule. The homework will be assigned in the two latter lessons. For example, if we learned L48, L49, L50, and L51 in one class, the homework will be L50 evens and L51 odds. If we learned L88 and L89 in one class, the homework would be L88 evens and L89 odds. After L104, when we move on to BC lessons, we will do one or two lessons in one class. In such case when we do one lesson, the homework would be all problems.

• In order to receive full credit on completion, students must show all work and attempt all problems. Even though a student is not able to solve all problems, one must try the best, and keep all the work process for future review and feedback. This is one of the most important attitudes in mathematics. 

Tests

• Tests will be given after Lesson 8, and every 4 lessons afterwards, graded on a scale from 0-120. 

• Tests are announced in advance. 

• Each test is 45 min for L1 - L104 (AB), then a full class (1 hr 25 min) for L105 to L148 (BC). 

• Some tests may be replaced with individual or group problem solving tasks.

• The emphasis on evaluation will be on the methods and procedures taught in that unit, and NOT on the correct answer. A student with an incorrect answer may earn more credit than a student with a correct answer depending on the work shown and justification given. IB and AP standards from math state: "Correct answers with no work shown will receive no credit."

• At the end of the first semester, there will be a semester exam (final exam). The second semester's final exam will be replaced with the AP Calculus BC exam and a group video project that will be done before the dismissal of the seniors at the end of April. 

*** All gradings follow AP/IB. If I cannot read or follow your work, I am NOT grading it ***

First Quarter

• L1: The Real Numbers / Fundamental Concept Review

• L2: More Concept Review / The Graphing Calculator

• L3: The Contrapositive / The Converse and Inverse / IFF Statements

• L4: Radian Measure of Angles / Trigonometric Ratios / Four Quadrant Signs / Simplifying Trigonometric Expressions

• L5: Word Problem Review

• L6: Functions: Their Equations and Graphs / Functional Notation / Domain and Range

• L7: The Unit Circle / Centerline, Amplitude, and Phase Angles of Sinusoids / Period of a Function / Important Numbers / Exponential Functions

• L8: Pythagorean Identities / Functions of -θ / Trigonometric Identities / Cofunctions / Similar Triangles

• L9: Absolute Value as a Distance / Graphing "Special" Functions / Logarithms / Base 10 and Base e / Simple Logarithm Problems

• L10: Quadratic Polynomials / Remainder Theorem / Synthetic Division / Rational Roots Theorem

• L11: Continuity / Left-Hand and Right-Hand Limits

• L12: Sum and Difference Identities / Double Angle Identities / Half-Angle Identities / Graphs of Logarithmic Functions

• L13: Inverse Trigonometric Functions / Trigonometric Equations

• L14: Limit of a Function

• L15: Interval Notation / Products of Linear Factors / Tangents / Increasing and Decreasing Functions

• L16: Logarithms of Products and Quotients / Logarithms of Powers / Exponential Equations

• L17: Infinity as a Limit / Undefined Limits

• L18: Sums, Differences, Products and Quotients of Functions / Composition of Functions

• L19: The Derivative / Slopes of Curves on a Graphing Calculator

• L20: Change of Base / Graphing Origin-Centered Conics on a Graphing Calculator

• L21: Translations of Functions / Graphs of Rational Functions (Part 1)

• L22: Binomial Expansion / Recognizing the Equations of Conic Sections

• L23: Trigonometric FUnctions of nθ / Graphing Conics on a Graphing Calculator

• L24: New Notation for the Definition of the Derivatives / The Derivative of x^n

• L25: The Constant Multiple Rule for Derivatives / The Derivatives of Sums and Differences / Proof of the Derivative of a Sum

• L26: Derivative of e^x and ln(x) / Derivatives of sin(x) and cos(x) / Exponential Growth and Decay

• L27: Equation of the Tangent Line / Higher Order Derivatives

• L28: Graphs of Rational Functions (Part 2) / A Special Limit

• L29: Newton and Leibniz / Differentials

• L30: Graph of tan(x) / Graphs of Reciprocal Functions

• L31: Product Rule / Proof of the Product Rule

• L32: An Antiderivative / The Indefinite Integral

• L33: Factors of Polynomial Functions / Graphs of Polynomial Functions

• L34: Implicit Differentiation

• L35: Integral of a Constant / Integral of kf(x) / Integral of x^n

• L36: Critical Numbers / A Note about Critical Numbers

• L37: Differentiation by u-Substitution

• L38: Integral of a Sum / Integral of 1/x

• L39: Area Under a Curve (Upper and Lower Sums) / Left, Right, and Midpoint Sums

• L40: Units for Derivatives / Normal Lines / Maximums and Minimums on a Graphing Calculator

• L41: Graphs of Rational Functions (Part 3) / Repeated Factors

• L42: The Derivative of a Quotient / Proof of the Quotient Rule

• L43: Area Under a Curve as an Infinite Summation

• L44: The Chain Rule / Alternate Definition of the Derivative / The Symmetric Derivative

• L45: Using f' to Characterize f / Using f' to Find Maximums and Minimums

• L46: Related-Rates Problems

• L47: Fundamental Theorem of Calculus (Part 1) / Riemann Sums / The Definite Integral

• L48: Derivatives of Trigonometric Functions/ Summary of Rules of Derivatives and Differentials

• L49: Concavity and Inflection Points / Geometric Meaning of the Second Derivative / First and Second Derivative Tests

• L50: Derivatives of Composite Functions / Derivatives of Products and Quotients of Composite Functions

• L51: Integration by Guessing

• L52: Maximization and Minimization Problems

• L53: Numerical Integration of Positive-Valued Functions on a Graphing Calculator

• L54: Velocity and Acceleration / Motion Due to Gravity

• L55: Maclaruin Polynomials

• L56: More Integration by Guessing and a Word of a Caution

• L57: Properties of the Definite Integral

• L58: Explicit and Implicit Equations / Inverse Functions

• L59: Computing Areas / More Numerical Integration on a Graphing Calculator

• L60: Area Between Two Curves / Area Between Curves Using a Graphing Calculator

• L61: Relationship Between the Graphs of f, f', and f''

• L62: Work, Distance, and Rates

• L63: Critical Number (Closed Interval) Theorem

• L64: Derivatives of Inverse Trigonometric Functions / What to Memorize

• L65: Falling-Body Problems

• L66: u-Substitution / Change of Variable / Proof of the Substitution Theorem

• L67: Areas Involving Functions of y

• L68: Even and Odd Functions

Second Quarter

• L69: Integration by Parts (Part 1)

• L70: Properties of Limits / Some Special Limits

• L71: Solids of Revolution (Part 1): Disk

• L72: Derivatives of a^x / Derivatives of log_a(x) / Derivatives of abs(f(x))

• L73: Integrals of a^x / Integrals of log_a(x)

• L74: Fluid Force

• L75: Continuity of Functions

• L76: Integration of Odd Powers of sin(x) and cos(x)

• L77: Pumping Fluids

• L78: Particle Motion (Part 1)

• L79: L'Hopital's Rule (L'HR)

• L80: Asymptotes of Rational Functions

• L81: Solids of Revolution (Part 2): Washers

• L82: Limits and Continuity / Differentiability

• L83: Integration of Even Powers of sin(x) and cos(x)

• L84: Logarithmic Differentiation

• L85: The Mean Value Theorem / Application of the Mean Value Theorem in Mathematics / Proof of Rolle's Theorem / Practical Application of the Mean Value Theorem

• L86: Rules for Even and Odd Functions

• L87: Solids of Revolution (Part 3): Shells

• L88: Separable Differential Equations

• L89: Average Value of a Function / Mean Value Theorem for Integrals / Proof of the Mean Value Theorem for Integrals

• L90: Particle Motion (Part 2)

• L91: Product and Difference Indeterminate Forms

• L92: Derivatives of Inverse Functions

• L93: Newton's Method

• L94: Solids of Revolutions (Part 4): Displaced Axes of Revolution

• L95: Trapezoidal Rule / Error Bound for the Trapezoidal Rule

• L96: Derivatives and Integrals of Functions Involving Absolute Value

• L97: Solids Defined by Cross Sections

• L98: Fundamental Theorem of Calculus (Part 2) / The Natural Logarithm Function

• L99: Linear Approximations using Differentials

• L100: Integrals of Powers of tan(x) and cot(x) / Integrals of sec(x) and csc(x)

• L101: Limit of sin(x)/x for Small x / Proof of the Derivative of sin(x)

• L102: Derivatives of ln(x) and e^x / Definition of e

• L103: Proof of the Fundamental Theorem of Calculus / Epsilon-Delta Proofs

• L104: Graphs of Solutions of Differential Equations / Slope Fields / Recognizing Graphs of Slope Fields

• L105: Sequences / Limits of a Sequence / Graphs of Sequences / Characteristics of Sequences

• L106: Introduction to Parametric Equations / Slopes of Parametric Equations

Third Quarter

• L107: Polar Coordinates / Polar Equations

• L108: Introduction to Vectors / Arithmetic of Vectors / Unit Vectors and Normal Vectors

• L109: Arc Length (Part 1): Rectangular Equations

• L110: Rose Curves

• L111: The Exponential Indeterminate Forms 0^0, 1^∞, and 0^∞

• L112: Foundations of Trigonometric Substitution

• L113: Trigonometric Substitution

• L114: Arc Length (Part 2): Parametric Equations

• L115: Partial Fractions (Part 1) / Logistic Differential Equations

• L116: Series

• L117: Geometric Series / Telescoping Series

• L118: Limaçons and Lemniscates

• L119: Parametric Equations - Second Derivatives and Tangent Lines

• L120: Partial Fractions (Part 2)

• L121: Convergence and Divergence / Series Indexing / Arithmetic of Series

• L122: Integration by Parts (Part 2)

• L123: Vector Functions

• L124: Implicit Differentiation (Part 2)

• L125: Infinite Limits of Integration

• L126: Partial Fractions (Part 3)

• L127: p-Series

• L128: Basic Comparison Test / Integral Test / Proof of p-Series

• L129: Area Bounded by Polar Curves

• L130: Ratio Test / Root Test

• L131: Infinite Integrands

• L132: Limit Comparison Test

• L133: Euler's Method

• L134: Slopes of Polar Curves

• L135: Absolute Convergence

• L136: Using the Chain Rule with the Fundamental Theorem of Calculus

• L137: Piecewise Integration

• L138: Conditional Convergence and Leibniz's Theorem

• L140: Projectile Motion

• L141: Taylor Series

• L142: Velocity and Acceleration as Vector Functions

• L143: Binomial Series

• L144: Remainder Theorem

Fourth Quarter

• L145: Convergence of Power Series

• L146: Term-by-Term Differentiation and Integration of Power Series

• L147: Substitution into Power Series

• L148: Integral Approximation Using Power Series

• Mock and Practice Exams until AP Exam in May

• Late submission will NOT be accepted.

• If a student is absent with an excuse, he or she has as many days to make up the work due to absences as the number of excused days of absence that occurred. Excused absence requires an email from the school office or the student's parents/guardian, or the Transit Form entry.

• AP Calculus BC runs at a very rapid pace. For the most of the time, there is no or almost no time in class to discuss the homework or test questions. Therefore, it is extremely important that the students communicate with Ms. Lee, whenever there are questions. It is the student's responsibility to reach out when they need help.

• We will have a class Whatsapp group. Oftentimes, when you have a question on a problem, your classmates might have the same question as well. Or, sometimes your classmate can have a solution to your questions. So, we want to use the group chat effectively, for discussing questions amongst peers. Ms. Lee will be there to guide if you need a hint. 

• "I can proudly assure, that I am probably the fastest responder of any teacher at SJS! I will answer your questions any time, any day, even if it's 3 AM on Sunday, as long as I am awake. So please, PLEASE use me as much as possible! I am the best, free resource that you have!"