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In this paper of “Pure Mathematics 3”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. When using specific algebraic techniques for integration or differentiation, such as “integration by parts” or “integration with a substitution” or “product/quotient rule for differentiation”, amongst other, there were comments to the steps taken to maintain a smooth line of thinking throughout the exercises.

In this paper of “Further Pure Mathematics 1”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. Attention was given to the specific requirements of all the topics involved, namely “Vectors”, “Properties of the roots of polynomials”, “Proof by induction”, “Method of differences”, “Matrices and geometric transformations”, “Polar coordinates” and “Rational functions and their graphs”. Additionally, there were also algebraic techniques which were used and are part of the regular A-Level syllabus for mathematics.

In this paper of “Pure Mathematics 1”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. In question 3, involving the “Binomial expansion”, there is a straightforward method leading to the final answer and then there is also an alternative technique which can become interesting for those who wish to explore further algebraic paths. Hopefully, it will be useful when revising for examinations in this area.

In this paper of “Statistics 1”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. There are mentions to specific actions taken, namely when using the table of the Normal distribution or when applying certain deductions. When possible, there are also detailed listings of cases allocated with the specific requirements of the question, namely when it involves permutations and/or combinations. Hopefully, it may contribute to help students when preparing for their examinations in this subject.

In this paper of “Statistics 2”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. There is some emphasis given to the use of the normal curve as guideline for questions involving confidence intervals or hypothesis tests, which, hopefully, can lead to a deeper understanding of the objectives of the questions.

In this paper of “Pure Mathematics 1”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. Hopefully, it will be useful when revising for examinations in this area.

In this paper of “Statistics 2”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. There are mentions to specific actions taken, namely when applying certain deductions related with the use of the Normal distribution. Hopefully, it may contribute to help students when preparing for their examinations in this subject.

In this paper of “Statistics 1”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. There are mentions to specific actions taken, namely when using the table of the Normal distribution or when applying certain deductions. Hopefully, it may contribute to help students when preparing for their examinations in this subject.

In this paper of “Pure Mathematics 3”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. In some cases, there was the need to use algebraic techniques of differentiation or integration, such as “integration by parts” and specific notes were made to alert for those situations. Hopefully, all the deductions and steps taken are clear and can contribute to a better understanding of all exercises.

In this paper of “Pure Mathematics 1”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams.

In this PowerPoint, we introduce two different types of numerical sequences (arithmetic progression and geometric progression) as part of the syllabus for Pure Mathematics (AS Level). We begin by detailing the main features for each of these sequences, showing examples as well as the rationale for the algebraic expression which provides the nth term. Additionally, we also show how to find the algebraic expressions for the sum of the first n terms, for both cases. It is important to note that these formulas are provided in most examinations and available to students, hence the way to derive them consists on additional skills for students to acquire. In the last section, we explore different examples of worked exam-style questions, where all steps are clear and detailed. Hopefully, this resource can assist students when preparing for their examinations but also as a complementary teaching tool.

In this PowerPoint, we introduce the Binomial theorem as part of the syllabus for Pure Mathematics (AS Level). In the first section, there are mentions to specific details to use the formula correctly as well as different approaches to calculate the coefficient for a specific power of the variable. In the last section, we explore different examples of worked exam-style questions, where all steps are clear and detailed. Hopefully, this resource can assist students when preparing for their examinations but also as a complementary teaching tool.

This resource includes a series of PowerPoints, based on previous resources from the same author, covering all the syllabus for the Pure Mathematics 3 course (A2 Level), each containing theoretical background, detailed explanations, worked examples, relevant diagrams and tips to consider. Some of these 11 PowerPoints approach specific areas such as “Vectors”, “Complex numbers”, “Differential equations”, “Polynomials”, “Exponentials and logarithms”, amongst other. Others have a broader intention, namely the one on “Differentiation and integration methods”, where there is a transversal look at different algebraic techniques across the other topics. Additionally, there is a section in each of the PowerPoints containing fully solved exam-style questions, where attention is given to detail in the explanations and, at the same time, tries not to become too heavy in terms of the visual approach. Hopefully, this can serve as a complete study guide for A-Level students who wish to prepare for their exams but it can also become a useful teaching tool, when delivering this course.

In this PowerPoint, we introduce an alternative way of describing the coordinates of the points on the graph of a curve. We explain the relation between the parametric equations of a curve and the corresponding Cartesian equation, also showing how to transition from one to the other. We then approach the concept of differentiation of a curve which is defined parametrically, by showing how to find the gradient in any point, using the information available. In the last section, we explore different examples of worked exam-style questions, where all steps are clear and detailed.

In this PowerPoint, we begin by recalling some of the most common algebraic techniques used to solve equations and inequalities. Then, we show that, for some cases, those methods won’t solve the problem, hence requiring for alternative techniques. We then introduce the “Sign-change rule” which can be used, either to prove the existence of a root of an equation in a given interval as to actually determine such root. Afterwards, we introduce the method of iterations, where we develop a full method to gradually obtain approximations to the root of a given equation. In the last section, we explore different examples of worked exam-style questions, where all steps are clear and detailed. Hopefully, this resource can help students in their preparation for examinations and can also be used as a complementary teaching tool, when delivering these topics.

In this paper of “Further Pure Mathematics 2”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. Attention was given to the specific requirements of all the topics involved, namely “Complex numbers”, “Hyperbolic functions”, “Properties of matrices”, “Differentiation”, “Integration” and “Differential equations”. Additionally, there were also algebraic techniques which were used and are part of the regular A-Level syllabus for mathematics.

In this paper of “Further Pure Mathematics 1”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams. Attention was given to the specific requirements of all the topics involved, namely “Vectors”, “Properties of the roots of polynomials”, “Proof by induction”, “Method of differences”, “Matrices and geometric transformations”, “Polar coordinates” and “Rational functions and their graphs”. Additionally, there were also algebraic techniques which were used and are part of the regular A-Level syllabus for mathematics.

In this paper of “Statistics 2”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams.

In this paper of “Pure Mathematics 3”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams.

In this paper of “Statistics 1”, each question is fully solved, and all the steps are explained with relevant calculations and/or comments and diagrams.