Functions

This section of the website focusses on the study of mathematical models. These are key concepts for application of mathematics to real world problems and the activities and resources here will start with explorations of the different function types and then exploration of they are used in context to model and solve real world problems. It is important to cover the key concepts that underpin this notion of exploring how quantities change with respect to each other and then we move in to the diffferent classes and types of functions and their properties before a big focus on the skills involved in modelling real world situations.

What is here?

See the subsections below

SL Scheme - Functions

The new Mathematics: Applications and Interpretation syllabus is out and published on the IB website. Log in to your MyIB account and head to this link . It is a new course with a new name and renewed...

SL Concept & Notation

This page is an introduction to concept of a function in the context of mathematics. The applicatuions course has a strong focus on modelling which depends much on a through understanding of the concept...

SL Linear models

Commonly seen in the form y = f(x) = mx + c where m represents the gradient/rate of change of the function and c is the y-intercept, where x = 0. These models are a fundamental bit of algebra that come...

SL Quadratic models

f(x) = ax2 + bx + cQuadratic functions are those in the form f(x) = ax2 + bx + c, and have fascinated mathematicians for centuries. They have some fundamental properties that will explored in this unit....

SL Exponential models

The exponential function is set apart from other families of functions because of the fundamental impact of having the variable in the exponent. It stops being a multiplier and starts being more 'powerful'...

SL Sinusoidal models

This section is all about sine waves and various transofrmations of them. These stand out from the other functions because they are cyclical in nature. As such, they are good for modelling occurences...

SL Inverse functions

When we create/make something, we almost always want/need to know how to 'undo' it - how to return it to its original parts/pieces.A 'function' relates/converts x-values in to y-values.An inverse function,...

SL Modelling skills

This page differs from the other topic pages because the heading 'modelling skills' referes to a much broader and more general set of skills, knowledge and processes about how, when and why we try to...


HL(SL) Functions

Just as a musician will hear the symphony play in their mind when they read a musical score, so we, by the end of this course, will see the lines and curves, and the physical realities, described by our...

HL Transformations of Functions

It's worth explicitly making the link between transformations of shapes: translation, rotation, reflection and enlargement with which students have a number of years experience, by their last two years...

Concepts

Something about the concepts on which this unit is based

Selected Pages

free

SL Scheme - Functions 16 November 2019

The new Mathematics: Applications and Interpretation syllabus is out and published on the IB website. Log in to your MyIB...
more

free

Sinusoidal functions - practice 12 April 2021

The following questions are designed just to practice some of the fundamentals of working with arithmetic sequences, generatings,...
more

SL Exponential models 2 March 2021

The exponential function is set apart from other families of functions because of the fundamental impact of having the variable...
more

HL(SL) Functions 30 July 2020

Just as a musician will hear the symphony play in their mind when they read a musical score, so we, by the end of this course,...
more

HL Transformations of Functions 17 April 2020

It's worth explicitly making the link between transformations of shapes: translation, rotation, reflection and enlargement...
more

SL Linear models 11 January 2020

Commonly seen in the form y = f(x) = mx + c where m represents the gradient/rate of change of the function and c is the...
more

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