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Graphs and Functions Mind Map

An interactive mind map to help you bridge between algebra and calculus (concentrating on functions and graphs) built by the Learning Enhancement Team at the University of East Anglia
by

Learning Enhancement Team

on 21 July 2016

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Transcript of Graphs and Functions Mind Map

Using Functions
Inverse Functions and Graphs
Graphs and Functions
The function is a central idea in mathematics and these resources introduce the basic language and definitions of functions.
These resources explain the idea of an inverse function and, if possible, how they can be found. They also explore the connection between functions and graphs.
These resources expand the idea of a function further. They explain functions in terms of a machine and how the inputs and outputs work.
Even with the advent of computer programs, being able to plot a graph by hand is still an important skill to have. These resources explain all the parts of a graph and give advice about plotting.
Functions
Inverse Functions and Graphs Webcast
Click on the rectangle to open the Inverse Functions and Graphs Study Guide
Using Functions Webcast
Click on the rectangle to open the Using Functions Study Guide
Click on the rectangle to open the Using Functions Model Answers
Click on the rectangle to open the Using Functions Worksheet
Functions Webcast
Click on the rectangle to open the Functions Model Answers
Click on the rectangle to open the Functions
Study Guide
Click on the rectangle to open the Functions Worksheet
Plotting a Graph by Hand Webcast
Plotting a Graph by Hand
Click on the rectangle to open the Plotting a Graph by Hand Study Guide
Using This Mind Map
Click on the rectangle below to open a document to help you get the most out of this Mind Map
https://portal.uea.ac.uk/documents/6207125/8124756/Interactive+mind+map+guide.pdf/0e299529-fe1a-4c31-8675-bb29564d5a99
More Complicated Functions Webcast
Click on the rectangle to open the More Complicated Functions Study Guide
Click on the rectangle to open the More Complicated Functions Worksheet
Click on the rectangle to open the More Complicated Functions
Model Answers
These resources explain how more complicated functions can be created from five basic functions
More Complicated Functions
https://portal.uea.ac.uk/documents/6207125/8198422/bridging+algebra+calculus+more+complicated+functions.pdf
https://portal.uea.ac.uk/documents/6207125/8198422/bridging+algebra+calculus+more+complicated+functions+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8198422/bridging+algebra+calculus+more+complicated+functions+model+answers.pdf
Definition and tips for identifying straight lines. Looking more closely at the gradient, intercepts and common straight lines
What is a Straight Line? Webcast
What is a Straight line?
Click on the rectangle to open the What is a Straight Line?
Study Guide
Resources about sketching different types of straight lines: horizontal, vertical and diagonal. They show two separate methods for sketching a line and discusses the difference between plotting and sketching.
Sketching Straight Lines Webcast
Sketching Straight Lines
Click on the rectangle to open the Sketching Straight Lines Study Guide
A quadratic function is a simple power function (order 2). These resources describe the connection between a general quadratic function and its graph.
Quadratic
Functions
The trigonometric identities (sine, cosine and tangent) are properties of the angles in right-angled triangles. Sine and cosine are basic functions.
Click on the rectangle to open the Trigonometric Ratios
Study Guide
Trigonometric
Ratios Webcast
Click on the rectangle to open the Trigonometric Ratios
Worksheet
Click on the rectangle to open the Trigonometric Ratios
Model Answers
https://portal.uea.ac.uk/documents/6207125/8197337/steps+into+trigonometry+trigonometric+ratios+sine+cosine+and+tangent.pdf
https://portal.uea.ac.uk/documents/6207125/8197337/steps+into+trigonometry+trigonometric+ratios+sine+cosine+and+tangent+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8197337/steps+into+trigonometry+trigonometric+ratios+sine+cosine+and+tangent+model+answers.pdf
Trigonometric Ratios: Sine, Cosine and Tangent
Resources describing how to find the equation of a straight line for various given situations in both mathematics and experiments.

Finding Equations of Straight Lines Webcast
Click on the rectangle to open the Finding Equations of Straight Lines
Study Guide
https://portal.uea.ac.uk/documents/6207125/8194890/steps+into+algebra+quadratic+functions.pdf
Click on the rectangle to open the Sketching a Graph
Study Guide
Sketching a Graph
Sketching a Graph
Webcast
https://portal.uea.ac.uk/documents/6207125/8198428/bridging+algebra+calculus+sketching+a+graph.pdf
Definite
Integrals
Definite integrals involve calculating areas and values of integrals. Visualising the problems by sketching the region you are interested in is important.
Definite
Integrals Webcast
Click on the rectangle to open the Definite
Integrals Study Guide
https://portal.uea.ac.uk/documents/6207125/8199682/steps+into+calculus+definite+integrals.pdf
Stationary Points
These resources look at the stationary points (maximums, minimums and points of inflexion) on graphs.
Stationary Points Webcast
Click on the rectangle to open the Stationary Points Study Guide
The exponential function is well-known in science and economics. It is also a basic function. These resources give some basics definitions and graphs.
Exponential
Functions
Exponential Functions Webcast
Click on the rectangle to open the Exponential Functions
Study Guide
These resources explain the language and mathematics surrounding logarithms, specifically the logarithmic transformation. The logarithm function is a basic function.
Basics of Logarithms
Basics of Logarithms Webcast
Click on the rectangle to open the Basics of Logarithms Worksheet
Click on the rectangle to open the Basics of Logarithms Study Guide
The laws of logarithms are the rules which control the manipulation and simplification of logarithms. As logarithms are very common in mathematics, it is well-worth mastering them.
Laws of Logarithms
Laws of Logarithms Webcast
Click on the rectangle to open the Laws of Logarithms Study Guide
Five Basic Functions
Five Basic Functions
Webcast
Click on the rectangle to open the Five Basic Functions Factsheet
A factsheet with the properties of the five basic functions power, sine, cosine, exponential and logarithm.
https://portal.uea.ac.uk/documents/6207125/8221205/bridging+algebra+calculus+five+basic+functions+factsheet.pdf
https://portal.uea.ac.uk/documents/6207125/8198419/bridging+algebra+calculus+using+functions.pdf
https://portal.uea.ac.uk/documents/6207125/8198419/bridging+algebra+calculus+using+functions+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8198419/bridging+algebra+calculus+using+functions+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8198425/bridging+algebra+calculus+inverse+functions+and+graphs.pdf
Quadratic Functions Webcast
Click on the rectangle to open the Quadratic Functions
Study Guide
https://portal.uea.ac.uk/documents/6207125/8198443/bridging+algebra+calculus+exponential+functions.pdf
https://portal.uea.ac.uk/documents/6207125/8198446/bridging+algebra+calculus+basics+of+logarithms.pdf
https://portal.uea.ac.uk/documents/6207125/8198449/bridging+algebra+calculus+the+laws+of+logarithms.pdf
https://portal.uea.ac.uk/documents/6207125/8203701/other+essential+skills+plotting+a+graph+by+hand.pdf
https://portal.uea.ac.uk/documents/6207125/8198440/bridging+algebra+calculus+simultaneous+equations.pdf
Click on the rectangle to open the Simultaneous Equations Study Guide
Solving and understanding the meaning of simultaneous equations can be very useful. They describe many complicated situations and continue to be relevant in higher mathematics.
Simultaneous Equations
Finding equations of straight lines
Simultaneous Equations Webcast
https://portal.uea.ac.uk/documents/6207125/8198434/bridging+algebra+calculus+finding+equations+of+straight+lines.pdf
https://portal.uea.ac.uk/documents/6207125/8198437/bridging+algebra+calculus+sketching+straight+lines.pdf
Click on the rectangle to open the Sketching Straight Lines Model Answers
Click on the rectangle to open the Sketching Straight Lines Worksheet
https://portal.uea.ac.uk/documents/6207125/8198437/bridging+algebra+calculus+sketching+straight+lines+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8198437/bridging+algebra+calculus+sketching+straight+lines+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8198431/bridging+algebra+calculus+what+is+a+straight+line+worksheet.pdf
Click on the rectangle to open the What is a Straight Line?
Model Answers
Click on the rectangle to open the What is a Straight Line?
Worksheet
https://portal.uea.ac.uk/documents/6207125/8198431/bridging+algebra+calculus+what+is+a+straight+line+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8198431/bridging+algebra+calculus+what+is+a+straight+line.pdf
What is Differentiation? Webcast
https://portal.uea.ac.uk/documents/6207125/8199642/steps+into+calculus+what+is+differentiation.pdf
Resources describing the meaning and language of differentiation. It helps to understand the connection between the gradient of a straight line and the derivative.
What is Differentiation?
Click on the rectangle to find out more about differentiation
Click on the rectangle to open the What is Differentiation? Study Guide
http://prezi.com/7enhnyzgjkov/steps-into-calculus/
Being able to sketch a graph from its equation plays an increasingly important role as mathematics gets more complicated. These resources offer tips to help you do it successfully.
Click on the rectangle for more resources about Trigonometry
http://prezi.com/xx9s9ksxtenl/steps-into-trigonometry/
Click on the rectangle to find out more about integration
https://portal.uea.ac.uk/documents/6207125/8198416/bridging+algebra+calculus+functions.pdf
https://portal.uea.ac.uk/documents/6207125/8198416/bridging+algebra+calculus+functions+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8198416/bridging+algebra+calculus+functions+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8198446/bridging+algebra+calculus+basics+of+logarithms+worksheet.pdf
http://prezi.com/7enhnyzgjkov/steps-into-calculus/
https://portal.uea.ac.uk/documents/6207125/8199660/steps+into+calculus+stationary+points.pdf
Click on the rectangle to open the Basics of Logarithms Model Answers
https://portal.uea.ac.uk/documents/6207125/8198446/bridging+algebra+calculus+basics+of+logarithms+model+answers.pdf
Click on the rectangle to open the Laws of Logarithms Worksheet
Click on the rectangle to open the Laws of Logarithms Model Answers
https://portal.uea.ac.uk/documents/6207125/8198449/bridging+algebra+calculus+the+laws+of+logarithms+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8198449/bridging+algebra+calculus+the+laws+of+logarithms+model+answers.pdf
Click on the rectangle to open the Finding Equations of Straight Lines
Worksheet
https://portal.uea.ac.uk/documents/6207125/8198434/bridging+algebra+calculus+finding+equations+of+straight+lines+worksheet.pdf
Click on the rectangle to open the Simultaneous Equations Worksheet
Click on the rectangle to open the Simultaneous Equations Model Answers
https://portal.uea.ac.uk/documents/6207125/8198440/bridging+algebra+calculus+simultaneous+equations+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8198440/bridging+algebra+calculus+simultaneous+equations+model+answers.pdf
Click on the rectangle to open the Finding Equations of Straight Lines
Model Answers
https://portal.uea.ac.uk/documents/6207125/8198434/bridging+algebra+calculus+finding+equations+of+straight+lines+model+answers.pdf
Full transcript