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In this PowerPoint, we begin by introducing the concept of exponential function and, by exploring its inverse, we introduce the logarithmic function. We then investigate key features of these functions, including domain, range, graphs, algebraic expressions as well as the most important algebraic properties related with logarithms. Afterwards, we investigate the process of differentiating and integrating, both logarithmic and exponential functions, alerting for the need to use relevant operational rules, like the “product and quotient rules” for differentiation or the technique of “integration by parts”. For each case, there are worked examples, guided steps and clear explanations. Additionally, 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.

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 explore the topic of “Vectors”. Despite the fact that the concept of plane was removed from the syllabus of the Pure Mathematics (A2 Level) since 2020, this PPT contains references to it as it seems an important feature to learn, and relates with possible continuation of this topic in the curriculum of “Further Mathematics”. We begin with some considerations about the concept of a vector as well as some basic operations between vectors, including the “scalar product” and the “vector product”. The next section includes examples of solved exam style questions, which describe the following situations: • possible intersections between lines and planes • angles between lines and planes • distances between points, lines and planes~ In each example, we can find detailed explanations complemented with key diagrams and tips for similar cases. Hopefully, this resource can help students when revising for their examinations as well as teachers, who can use it a complement to their explanations in lessons.

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 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.

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 “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 “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 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 “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 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 “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 “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.