Course Description

Grade 11 to 12 Math

Course Objective: Calculus is designed to give students an overview of Calculus topics such as limits and continuity, derivatives, anti-derivatives, integrals and differential equations. While this course covers many of the same concepts found in Advanced Placement Calculus, it is not bound by the pace and rigor necessary for success on the AP Calculus exam. Therefore, this course best suits the student who is mathematically ready to learn Calculus but does not want the “stress” of AP Calculus. Students have the option of taking the AP Calculus exam after completing this course

Textbook: Math 11 to 12

  • Contemporary Calculus I and II by Dale Hoffman.

Materials:

  • Student textbook
  • Practice and enrichment worksheets
  • Manipulative materials
  • Calculators

Time Allotment:

  • 45 minutes per day, 2 days per week

Course Content:

1. Functions, Limits, Continuity
2. Derivatives
3. Applications of Derivatives
4. Integration
5. Applications of Definite Integrals
6. Transcendental Functions
7. Integration Techniques

The instructor reserves the right to modify this syllabus for the needs of the class.
Course Outline
Chapter 1 — Functions, Graphs, Limits and Continuity
• 1.0 Slopes & Velocities
• 1.1 Limit of a Function
• 1.2 Limit Properties
• 1.3 Continuous Functions
• 1.4 Formal Definition of Limit

Chapter 2 — The Derivative

• 2.0 Slope of a Tangent Line
• 2.1 Definition of Derivative
• 2.2 Differentiation Formulas
• 2.3 More Differentiation Patterns
• 2.4 Chain Rule (!!!)
• 2.5 Using the Chain Rule
• 2.6 Related Rates
• 2.7 Newton’s Method
• 2.8 Linear Approximation
• 2.9 Implicit Differentiation

Chapter 3 — Derivatives and Graphs

• 3.1 Introduction to Maximums & Minimums
• 3.2 Mean Value Theorem
• 3.3 f’ and the Shape of f
• 3.4 f” and the Shape of f
• 3.5 Applied Maximums & Minimums
• 3.6 Asymptotes
• 3.7 L’Hospital’s Rule

Chapter 4 — The Integral

• 4.0 Introduction to Integrals
• 4.1 Sigma Notation & Riemann Sums
• 4.2 The Definite Integral
• 4.3 Properties of the Definite Integral
• 4.4 Areas, Integrals and Antiderivatives
• 4.5 The Fundamental Theorem of Calculus
• 4.6 Finding Antiderivatives
• 4.7 First Applications of Definite Integrals
• 4.8 Using Tables to Find Antiderivatives
• 4.9 Approximating Definite Integrals

Chapter 5 — Applications of Definite Integrals

• 5.0 Introduction to Applications
• 5.1 Volumes
• 5.2 Arc Lengths & Surface Areas
• 5.3 More Work
• 5.4 Moments & Centers of Mass
• 5.5 Additional Applications

Chapter 6 — Introduction to Differential Equations

• 6.0 Introduction to Differential Equations
• 6.1 Differential Equation y’=f(x)
• 6.2 Separable Differential Equations
• 6.3 Exponential Growth, Decay & Cooling

Chapter 7 — Inverse Trigonometric Functions

• 7.0 Introduction to Transcendental Functions
• 7.1 Inverse Functions
• 7,2 Inverse Trigonometric Functions
• 7.3 Calculus with Inverse Trigonometric Functions

Chapter 8 — Improper Integrals and Integration Techniques

• 8.0 Introduction Improper Integrals & Integration Techniques
• 8.1 Improper Integrals
• 8.2 Integration Review
• 8.3 Integration by Parts
• 8.4 Partial Fraction Decomposition
• 8.5 Trigonometric Substitution
• 8.6 Trigonometric Integrals

 

Areas to be evaluated:

  • Class participation
  • Homework assignments
  • Computation time tests
  • Tests
  • Quizzes

Additional activities:

  • Math vocabulary journals
  • Math games