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
Sean Hunte

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.


Courses Included with Purchase



DIFFERENTIATION - Additional Mathematics
Learn how to Differentiate.
Sean Hunte
$10
INTEGRATION For Additional Mathematics
Integration techniques for Additional Mathematics
Sean Hunte
$10

Original Price: $20


Frequently Asked Questions


When does the course start and finish?
The course starts now and never ends! It is a completely self-paced online course - you decide when you start and when you finish.
How long do I have access to the course?
How does lifetime access sound? After enrolling, you have unlimited access to this course for as long as you like - across any and all devices you own.
What if I am unhappy with the course?
We would never want you to be unhappy! If you are unsatisfied with your purchase, contact us in the first 30 days and we will give you a full refund.

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