In this paper, each question is fully answered, and all steps taken are explained. In some parts, additional diagrams were added to help the understanding of the method used. Hopefully, this resource will become useful both as revision tool and even as teaching guide.

In this exam, each question is fully solved, including detailed explanations, comments, diagrams, and calculations. It can be useful as a revision tool or as a study guide. Hope it may help!!

In this paper, each question is fully answered, and all steps taken are explained. In some parts, additional diagrams were added to help the understanding of the method used. Hopefully, this resource will become useful both as revision tool or even as teaching guide.

In this paper, each question is fully answered, and all steps taken are explained. In some parts, additional diagrams were added to help the understanding of the method used. Hopefully, this resource will become useful both as revision tool or even as teaching guide.

In this paper, each question is fully answered, and all steps taken are explained. In some parts, additional diagrams were added to help the understanding of the method used. Hopefully, this resource will become useful both as revision tool or even as teaching guide.

In this paper, each question is fully answered, and all steps taken are explained. In some parts, additional diagrams were added to help the understanding of the method used. Hopefully, this resource will become useful both as revision tool or even as teaching guide.

In this paper, each question is fully answered, and all steps taken are explained. In some parts, additional diagrams were added to help the understanding of the method used. Hopefully, this resource will become useful both as revision tool or even as teaching guide.

In this exam, each question is fully solved, including detailed explanations, comments, diagrams, and calculations. It can be useful as a revision tool or as a study guide. Hope it may help!!

In this exam, each question is fully solved, including detailed explanations, comments, diagrams, and calculations. It can be useful as a revision tool or as a study guide. Hope it may help!!

In this exam, each question is fully solved, including detailed explanations, comments, diagrams, and calculations. It can be useful as a revision tool or as a study guide. Hope it may help!!

In this exam, each question is fully solved, including detailed explanations, comments, diagrams, and calculations. It can be useful as a revision tool or as a study guide. Hope it may help!!

In this exam, each question is fully solved, including detailed explanations, comments, diagrams, and calculations. It can be useful as a revision tool or as a study guide. Hope it may help!!

This resource focus on different algebraic methods to differentiate and integrate functions, such as exponentials, logarithmic and trigonometric as well as functions defined parametrically or implicitly. It also covers the “product rule” and the “quotient rule” for differentiation together with the methods of “integration by parts” and "integration with a “substitution”. The last section includes a series of fully solved exam questions related, where each step is carefully described and explained.

We will study the formula for the Binomial expansion, for cases when the index is either negative or fractional. Then, we investigate how to obtain partial fractions from algebraic fractions and how to link these 2 topics as well as how to use them for integration purposes. We finish with a series of fully solved exam questions related, obtained from the CIE examinations.

This ppt introduces differential equations of first degree as well as possible algebraic techniques to solve them. It also contains a series of fully solved exam questions related, all taken from the 9709 CIE exams. Each step is explained, enabling this resource to be used, both as teaching guide and a revision tool.

This ppt introduces all the main computational properties of the roots of polynomial equations, relating them with the coefficients involved. It also contains a series of fully solved exam questions related, all taken from the 9231 CIE exams. Each step is explained, enabling this resource to be used, both as teaching guide and a revision tool.

All questions are solved, trying to show clearly all the steps and deductions made. This includes some diagrams of the “Normal distribution” which were used to help the understanding of some questions. Hope it may be useful!!

This resource presents the recent May 2023 paper for Pure Mathematics 3 (9709/32). Each question is fully solved, and all steps are shown. Hopefully it may be useful, both for students and teachers!