Calculus 1 Differentiation and Integration: Curves and Lines

The course was created for students of Mathematics from Cambridge (IGCSE) Ordinary level, IGCSE AS level, Grade 12 for those doing the Matric system, IGCSE A level up to University level students of Applied mathematics, Actuarial Sciences, Operations Research, Pure mathematics, and Engineering mathematics as well as those doing Economics and Econometrics both of which require a level of understanding of Calculus 1.

The objective is to help students practice for examinations by working out solutions of past examination questions and interesting questions in set books used by schools. The questions are answered live in the video to simulate what students will be going through during an examination session, so mistakes are made and corrected as we go along and if there are any mistakes that are not picked during recording please highlight them.

This video is a combination of seven videos from 4 separate questions which were recorded as:

1. The application of Calculus 1 Differentiation;

2. a three part video: The Application of Calculus 2 Differentiation Parts:

· 1,

· 2, and

· 3;

3. a two part video:

· The Application of Calculus 5: Differentiation First Principles Part 1 and

· The Application of Calculus 5: Differentiation of Differences of functions Part2 and

4. The application of Calculus 1 & 2 Differentiation and Integration

The first two questions appeared in the 2012 Grade 12 Matric paper in South Africa. They were question 6.3 and question 7.1 respectively.

The first question 6.3, deals with a quadratic function and a line at a given point of tangency. The quadratic function has two unknowns a and b that you are required to determine. It was an 8 marks question.

The second question of the first two questions 7.1, has 6 sub-questions from 7.1.1 to 7.1.1.6 that varied in the level of difficultness starting with the first question worth only 1 mark. The medium questions were worth 2 to 3 marks each, the difficult ones were worth 4 marks each and the very difficult and challenging ones were worth 5 marks each. The total marks were 20.

The third question was sent by a Grade 12 Matric student and it had 3 questions, but we just did question 1 which had two parts 1.1 and 1.2. Question 1.1 required as to find the differential of a given function from first principles and the second question 1.2, required us to find the differential of a difference of two functions.

The last and fourth question was posted on our Maths WhatsApp group by a colleague and the question appeared in the Cambridge IGCSE AS level June/July examinations of the year 2020. The question had a diagram of a cubic function and a line that intersected at the origin O and the maximum point of the cubic function at A. The question had 4 part questions a, b, c and d which required the application of both differentiation and integration to find the area bounded by curves. It had two constants a and b and did not have much numbers. Very interesting question.

In this combined video we answer question 6.3 and the 6 part questions of question 7.1 as well as the 2 part questions to question 1 in combinations of 2, bridged by an interlude otherwise all the questions are answered in this single video for the convenience of the learner.

Let’s do mathematics.