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Welcome to Möbius
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We’ve compiled a lesson for you that demonstrates the different types of content, questions, and methods that we use to deliver course materials to students. This is by no means our full content offering but it will give you an idea of what our platform looks like and the varied levels of interaction on each page.
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Algebra & Trigonometry
It's time to do some math. This lesson will combine a larger number of subtle, technical issues than many of the lectures that will follow. Like most of the lessons in this course, we will introduce some definitions, state and prove some results, and do quite a number of examples.
Introduction to Inverses
In this lesson, the concept of the inverse of a function is introduced. Inverses are constructed and analyzed for functions described using tables, mapping diagrams, or graphs. We also take a first look at inverses of functions described algebraically.
A scatter plot is a graph consisting of points which are formed using the values of two variable quantities. Scatter plots are used to display a relationship between the two variables in question. In this lesson, we discuss the features of a scatter plot and practise creating scatter plots from paired data sets. We discuss the roles that the two variables play in a scatter plot and explore what information might be revealed when we consider the shape formed by the data points as a whole.
Curve Sketching and the First Derivative
In this lesson, we explore turning points of functions and introduce the first derivative test. More precisely, we will learn how to use the first derivative to find the intervals of increase and decrease of a given function.
Modelling With Derivatives
In this lesson, we will consider mathematical models that involve quantities and their rates of change (expressed as functions) and their derivatives. These models are typically expressed as differential equations (i.e., equations that involve an unknown function and one or more of its derivatives).
Sums and Differences of Functions
Graphs of functions, \( y=f(x) \pm g(x) \), formed by the addition or subtraction of two functions, will be investigated. Key properties of the functions will be discussed and factors influencing the behaviour of the graphs will be identified. Connections will be made to real-world applications to model and solve problems.
Pascal's Triangle and Binomial Expansions
In this lesson, we will be introduced to a famous pattern of numbers known as Pascal’s triangle. Patterns within Pascal’s triangle will be investigated, including those that assist in expanding powers of binomials, \((a+b)^n\). The Binomial Theorem will be used to expand binomials of the form \((a+b)^n\) and to find specific terms within a binomial expansion.
Average and Instantaneous Acceleration
By the end of this lesson, you will be able to calculate the average acceleration between two points in time, calculate the instantaneous acceleration given the functional form of velocity, explain the vector nature of instantaneous acceleration and velocity, explain the difference between average acceleration and instantaneous acceleration, and find instantaneous acceleration at a specified time on a graph of velocity versus time.