In this PowerPoint, we begin by introducing the new set of formulae involving the 3 “new” trigonometric functions: secant, cosecant and cotangent. We explore the formulas for the addition/subtraction of two angles as well as formulas for the “double angle”. Additionally, we also study how to express certain algebraic expressions containing trigonometric functions in a way which facilitates important calculations related. Afterwards, we investigate the process of differentiating and integrating trigonometric functions, by exploring different scenarios and appropriate algebraic techniques. For each case, there are worked examples, guided steps and clear explanations. 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 PowerPoint, we explore different forms of differentiating and integrating functions. We include the study of trigonometric, exponential and logarithmic functions, whether we wish to differentiate or integrate them. Additionally, we also take a close look on how to differentiate functions which are defined parametrically or implicitly, including the “product rule” and “quotient rule” for differentiation. In the section of “Integration”, apart from the already mentioned functions, we also include slides where we study the methods of “integration by parts” and the method of “integration with a substitution”. For all these cases, there are worked examples with explanations and tips for similar cases. Finally, the last section of this resource includes a series of solved exam-style questions, where we go over some of the typical questions related, by explaining each step taken as well as relevant comments to help understand the rational used in each of those questions. Hopefully, this resource can help students in their preparation for examinations which require differentiation and integration techniques and can also be used as a complementary teaching tool, when delivering these topics.

In this PowerPoint, we explore the topic of “1st order differential equations”. We present different approaches to solve these equations, with worked examples related. The integration skills are important to solve these equations and care must be taken when trying to integrate different types of functions, especially when it comes to exponential, logarithmic and trigonometric functions. The methods of “integration by parts” or using “substitutions” are also explored throughout the different examples. The last section contains a few examples of solved exam style questions which can be useful as preparation for future assessments. Hopefully, this resource can help students in their preparation for future exams but also as a backup teaching tool, when delivering this topic.

In this PowerPoint, we explore the topic of “Vectors”. 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 PowerPoint, we explore all the key features of complex numbers, expressed either in algebraic, polar or exponential forms. There are multiple explained examples of operations between complex numbers, complemented with diagrams and relevant information related to each situation studied. It also contains a few examples of solved exam style questions which can be useful as preparation for future assessments.

In this PowerPoint, we begin by deriving the formula for the binomial expansion for cases when the power is not a positive integer. We then explore different examples where the coefficient for a specific power of the variable is requested, including detailed explanations and relevant comments. Afterwards, we explore different algebraic manipulation to decompose rational fractions into specific types of partial fractions, by introducing related worked examples. 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 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.