# SECTION 3: CALCULUS I

## Learn the basics of Differentiation and Integration.

DIFFERENTIATION

At the end of this section, students should be able to:

- use the concept of the derivative at a point as the gradient of the tangent to the graph at ;
- use the and notation for the first derivative of ;
- use where is any real number;
- use and
- use simple rules of derivatives to find derivatives of sums and multiples of functions;
- calculate derivatives of polynomials and trigonometric functions;
- apply the chain rule in the differentiation of composite functions;
- differentiate products and quotients of simple polynomials and trigonometric functions;
- use the concept of the derivative as a rate of change;
- use the concept of stationary points;
- locate stationary points, maxima and minima, by considering sign changes of the derivative;
- calculate the second derivative, ;
- interpret the significance of the sign of the second derivatives;
- use the sign of the second derivative to determine the nature of stationary points;
- obtain equations of tangents and normal to curves.

INTEGRATION

At the end of this course, students should be able to

- recognise integration as the reverse process of differentiation;
- use the notation ;
- show that the indefinite integral represents a family of functions which differ by constants;
- use simple integration rules;
- integrate functions of the form where are real numbers and ;
- find the indefinite integrals using formulae and integration theorems;
- integrate simple trigonometric functions;
- compute definite integrals;
- formulate the equation of a curve given its gradient function and a point on the curve;
- apply integration to:

1. find the area of the region in the first quadrant bounded by a curve and the lines parallel to the axis;

2. find volumes of revolution about the axis, for polynomials up to and including degree

## Your Instructor

Sean Hunte, Your Passionate Mathematics Teacher

I was once a student just like you. I struggled with Mathematics for the first two (2) years of my secondary school life. In third form my teacher, Dr Sargeant, taught Mathematics in a unique way which allowed me to successfully learn the subject which I was passionate about. Her teaching enabled me to thrive in an area which I would eventually pursue as a career.

Therefore, I have successfully completed CXC's CSEC General Mathematics and CAPE Pure Mathematics Units 1 and 2 before obtaining a degree in Economics and Mathematics.

I have ten (10) years of experience teaching Mathematics at the secondary level in Barbados. During this time I have taught hundreds of students who have successfully completed the following courses:

- CSEC GENERAL MATHEMATICS
- CSEC ADDITIONAL MATHEMATICS
- CAPE PURE MATHEMATICS UNIT 1
- CAPE PURE MATHEMATICS UNIT 2
- SAT MATHEMATICS

Your story will be different from mine but both of us desire the same result. SUCCESS!

I know that for many students Mathematics can be a struggle. I am therefore here to offer assistance in making the learning of Mathematics easier.