**Semester:** Second

**Grade:11**

**No. of hours: **80 hours/semester

**I. Course Description:**

The course specifically covers the limit of a function, differentiate, and integrate algebraic, exponential, logarithmic, and trigonometric functions in one variable, and to formulate and solve problems involving continuity, extreme and intermediate value theorem

**II. Course Objectives: **At the end of the semester, the students should be able to:

1. formulate and solve accurately real-life problems involving continuity of functions;

2. formulate and solve accurately situational problems involving extreme values;

3. formulate and solve accurately situational problems involving related rates;

4. formulate and solve accurately situational problems involving population models;

5. formulate and solve accurately situational problems involving circular functions;

6. formulate and solve accurately real-life problems involving areas of plane regions.

**III. Course Content**

1**.**** Limit of a Function**

1.1 Limit of a Function

1.2. Limit Theorems

1.3 Limit of Transcendental , Logarithmic and Exponential Functions

2**. Continuity of a Function**

2.1 Continuity

2.2 Types of continuity

2.3 Properties of Continuity ,Intermediate and Extreme Value theorem

3. **Differentiation**

3.1 Derivative of a Function and the Slope of the Tangent Line

3.2 Differentiability and Continuity

3.3 Differentiation Rule for Algebraic Functions

3.4 Application of Derivative

3.5 Derivative of Exponential, Trigonometric and Logarithmic functions

3.6 Implicit differentiation

3.7 Higher Order Derivatives

3. **Integral Calculus**

4.1 Antiderivatives

4.2 Integration by Substitution

4.3 Integration by using Substitution and Table of Integrals

4.4 Separable Differential Equations

4.5 The Definite Integral

**IV. Course Subject Performance Assessments**

Quizzes (BD,SW) 25%

Performance Task 45%

Exam 35%

Total 100%

**Prepared by: Arlo M. Libanan**