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 BC 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 BC course assumes that students already have a thorough knowledge of all the topics noted above.

Unit 1 Limits and Continuity

Ø 1.1 Introducing Calculus: Can Change Occur at an Instant?

Ø 1.2 Defining Limits and Using Limit Notation

Ø 1.3 Estimating Limit Values from Graphs and Tables

Ø 1.4 Determining Limits Using Properties of Limits and by Algebraic Manipulation

Ø 1.4 Selecting Procedures for Determining Limits

Ø 1.6 Determining Limits Using the Squeeze Theorem

Ø 1.7 Connecting Multiple Representations of Limits

Ø 1.8 Exploring Types of Discontinuities

Ø 1.9 Defining continuity at a point

Ø 1.10 Confirming Continuity over an Interval

Ø 1.11 Removing Discontinuities

Ø 1.12 connecting infinite limits and vertical Asymptotes and horizontal Asymptotes

Ø 1.13 Working with the Intermediate Value Theorem (IVT)

Unit 2 Differentiation: Definition and Basic Derivative Rules

Ø 2.1 Defining Average and Instantaneous Rates of Change at a Point

Ø 2.2 Defining the Derivative of a Function and Using Derivative Notation

Ø 2.3 Estimating Derivatives of a Function at a Point

Ø 2.4 Connecting differentiability and continuity: derivatives exist or not

Ø 2.5 Applying the Power Rule

Ø 2.6 Derivative rules

Ø 2.7 Derivatives of cos x, sin x, ex, and ln x

Ø 2.8 The Product Rule

Ø 2.9 The Quotient Rule

Ø 2.10 Derivatives of reciprocal trigonometric functions

Unit 3 Differentiation: Composite, Implicit, and Inverse Functions

Ø 3.1 The Chain Rule

Ø 3.2 Implicit Differentiation

Ø 3.3 Differentiating Inverse Functions

Ø 3.4 Differentiating Inverse Trigonometric Functions

Ø 3.5 Selecting Procedures for Calculating Derivatives

Ø 3.6 Calculating Higher-order derivatives

Unit 4 Applications of Differentiation

Ø 4.1 Interpreting the Meaning of the Derivative in Context

Ø 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration

Ø 4.3 Rates of Change in Applied Contexts Other Than Motion

Ø 4.4 Introduction to Related Rates

Ø 4.5 Solving Related Rates Problems

Ø 4.6 Approximating Values of a Function Using Local Linearity and Linearization

Ø 4.7 Using L’Hôpital’s Rule for Determining Limits

Unit 5 Analytical Applications of Differentiation

Ø 5.1 Using the Mean Value Theorem

Ø 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

Ø 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing

Ø 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema

Ø 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema

Ø 5.6 Determining Concavity of Functions over Their Domains

Ø 5.7 Using the Second Derivative Test to Determine Extrema

Ø 5.8 Sketching Graphs of Functions and Their Derivatives

Ø 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative

Ø 5.10 Introduction to Optimization problems

Ø 5.11 Solving Optimization problems

Ø 5.12 Exploring Behaviors of Implicit Relations

Unit 6 Integration and Accumulation of Change

Ø 6.1 Exploring Accumulations of Change

Ø 6.2 Approximating Area with Riemann Sums

Ø 6.3 Riemann Sums Summation Notation, and Definite Integral Notation

Ø 6.4 The Fundamental Theorem of Calculus and Accumulation Functions

Ø 6.5 Interpreting the Behavior of Accumulation Functions Involving Area

Ø 6.6 Applying Properties of Definite Integrals

Ø 6.7 The Fundamental Theorem of Calculus and Definite Integrals

Ø 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

Ø 6.9 Integrating Using Substitution

Ø 6.10 Integrating Functions Using Long Division and Completing the Square

Ø 6.11 Integrating Using Integration by Parts bc only

Ø 6.12 Using Linear Partial Fractions bc only

Ø 6.13 Evaluating Improper Integrals bc only

Ø 6.14 Selecting Techniques for Antidifferentiation

Unit 7 Differential Equations

Ø 7.1 Modeling Situations with Differential Equations

Ø 7.2 Verifying Solutions for Differential Equations

Ø 7.3 Sketching Slope Fields

Ø 7.4 Reasoning Using Slope Fields

Ø 7.5 Approximating Solutions Using Euler’s Method bc only

Ø 7.6 Finding General Solutions Using Separation of Variables

Ø 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables

Ø 7.8 Exponential Models with Differential Equations

Ø 7.9 Logistic Models with Differential Equations bc only

Unit 8 Applications of Integration

Ø 8.1 Finding the Average Value of a Function on an Interval

Ø 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals

Ø 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts

Ø 8.4 Finding the Area Between Curves Expressed as Functions of x

Ø 8.5 Finding the Area Between Curves Expressed as Functions of y

Ø 8.6 Finding the Area Between Curves That Intersect at More Than Two Points

Ø 8.7 Volumes with Cross Sections: Squares and Rectangles

Ø 8.8 Volumes with Cross Sections: Triangles and Semicircles

Ø 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis

Ø 8.10 Volume with Disc Method: Revolving Around the axes

Ø 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis

Ø 8.12 Volume with Washer Method: Revolving Around the axes

Ø 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled bc only

Unit 9 Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Ø 9.1 Defining and Differentiating Parametric Equations

Ø 9.2 Second Derivatives of Parametric Equations

Ø 9.3 Finding Arc Lengths of Curves Given by Parametric Equations

Ø 9.4 Defining and Differentiating Vector-Valued Functions

Ø 9.5 Integrating Vector-Valued Functions

Ø 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions

Ø 9.7 Defining polar coordinates and differentiating in polar form

Ø 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

Ø 9.9 Finding the Area of the Region Bounded by Two Polar Curves

Unit 10 Infinite sequences and Series

Ø 10.1 Defining convergent and Divergent Infinite series

Ø 10.2 Working with Geometric Series

Ø 10.3 The nth term test for divergence

Ø 10.4 Integral test for convergence

Ø 10.5 Harmonic series and p- series

Ø 10.6 comparison test for convergence

Ø 10.7 Alternate Series test for convergence

Ø 10.8 Ratio Test for Convergence

Ø 10.9 Determine absolute or conditional Convergence

Ø 10.10 Alternating series Error bound

Ø 10.11 Finding Taylor Polynomial Approximations of Functions

Ø 10.12 Lagrange Error bound

Ø 10.13 Radius and Interval of Convergence of Power series

Ø 10.14 Finding Taylor or Maclaurin Series for a Function

Ø 10.15 Representing functions as power series.