Courses

Course Description

$ 18 per hour for 10 hours or choose from COURSE PLAN.

Math Tech AP Calculus course is designed for students to take them through the entire college board Calculus syllabus in a problem-solving mode. Topics are discussed in a way to bring out your weak areas so as to improvise your AP Calculus score. AP Calculus exam preparation course is provided in an online classroom model to the students. This course is ideally taken up by students who are in grade 11th / 12th and are planning to write AP college board papers or other entrance examinations for getting admission in universities.

This is a high-paced course where every aspect of Calculus in totality is covered but, the course focus is building problem-solving aptitude in students.

Calculus AB is a full-year courses in the calculus of functions of a single variable which emphasize:

(1) student understanding of concepts and applications of calculus over manipulation and memorization;

(2) developing the student’s ability to express functions, concepts, problems, and conclusions analytically, graphically, numerically, and verbally, and to understand how these are related; and

(3) using a graphing calculator as a tool for mathematical investigations and for problem-solving.

This course is intended for those students who have already studied college-preparatory mathematics: algebra, geometry, trigonometry, analytic geometry, and elementary functions (linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise). The AB topical course outline that follows can be covered in a full high-school academic year even if some time is allotted to studying elementary functions.

Big Idea 1: Limits [ 10 hours]

1. The definition of limit

Ø Two-sided limits. One-sided limits.  Cases limits don’t exist

2. Evaluating limits

Ø From a table From a graph. Using technology Using algebra

3. Properties of limits

Ø The limit laws  Calculating limits using the limit laws

4. Continuity

Ø Defining continuity in terms of limit  Properties of continuous functions

• The Intermediate Value Theorem The Extreme Value Theorem

Ø Discontinuous functions – types of discontinuity

• Removable discontinuity Jump discontinuity

• Infinite discontinuity

5. Limits involving infinity

Ø Horizontal asymptotes End model behavior

Big Idea 2: Derivatives [ 10 hours]

1. Introduction of derivatives

Ø Average rate of change and secant lines

Ø Instantaneous rate of change and tangent lines

Ø Defining the derivative as the limit of the difference quotient

Ø Approximating rates of change from tables and graphs

2. Relating the graph of a function and its derivative

3. Differentiability

Ø Relationship between continuity and differentiability

Ø When a function fails to have a derivative

4. Differentiation formulas

Ø Polynomial and rational functions Trigonometric functions

Ø Exponential and logarithmic functions Inverse trigonometric functions

Ø Second derivatives

5. Methods of differentiation [16 hours/15 blocks/10 weeks]

Ø The chain rule  Implicit differentiation Logarithmic differentiation

6. Applications of derivatives

Ø Velocity, acceleration, and other rates of change The Mean Value Theorem

Ø Increasing and decreasing functions Extreme values of functions

Ø Local (relative) extrema vs. global (absolute) extrema Concavity

Ø Modeling and optimization Linearization

Ø Newton’s method L’Hôpital’s Rule

Big Idea 3: Integrals and the Fundamental Theorem of Calculus [9 hours]

1. Antiderivatives and indefinite integrals

2. Approximating areas

Ø The rectangle approximation method Riemann sums The trapezoidal rule

3. Definite integrals and their properties

4. The Fundamental Theorem of Calculus

Ø The Fundamental Theorem of Calculus Part I

Ø The Fundamental Theorem of Calculus Part II

Ø The Mean Value Theorem for integrals Average value of a function

5. Methods of integration [20 hours/17 blocks/7 weeks]

Ø Algebraic manipulation Integration by substitution

6. Solving differential equations Separation of variables Slope fields

7. Applications

Ø Exponential growth and decay Particle motion

Ø Area between two curves Volumes

a. Volumes of solids with known cross sections

b. Volumes of solids of revolution