Functions

Desmos - function notation

Desmos – function notation

Desmos can be used very simply to illustrate function notation and note the use of Desmos as a calculator to evaluate the value of a function for a given input. (Select image to go to the Desmos graph page).


The University of Plymouth have a series of very clear notes with examples, exercises and solutionssee this booklet on Functions.

University of Plymouth Notes

University of Plymouth Notes


Helm Notes - Functions

Helm Notes – Functions

The Helm Project – Basic Functions and One-to-one and inverse functions 


Desmos and Functions

You can use the Desmos graphing calculator to support your study and understanding of functions. Using function notation you can enter composite functions as shown in the next two illustrations. Selecting each image will take you to the relevant Desmos graph page.

Composite Functions with Desmos

Composite Functions with Desmos – select image

Composite functions with Desmos

Composite functions with Desmos – select image

For further exploration of composite functions check the pages in this slideshow.

You can also easily explore transformations of graphs with Desmos.

Simon Singh – The Simpsons and Their Mathematical Secrets

Colleen Young:

Note the daily deal today for Simon’s book on Kindle.

Originally posted on Mathematics, Learning and Technology:

Simposon & Their Mathematical Secrets - Simon Singh

May 14th – get the book as a deal today
on Kindle:  
UK £1.09       USA $1.70

In Simon Singh’s ‘The Simpson’s and Their Mathematical Secrets”, now published in paperback Simon explains how writers have included mathematical jokes throughout the cartoon’s twenty-five year history. Here Simon Singh answers some questions I put to him.

I love the scene with Lisa surrounded by all her books including the one with Euler’s identity! I suppose if I had to pick a favourite mathematics reference in The Simpsons, then it would be that one – do you have a favourite?
It has to be Fermat’s last theorem, which appears in two episodes, namely “Treehouse of Horror VI” and “The Wizard of Evergreen Terrace”. My first book was all about Fermat’s notorious problem, so it is close to my heart and seeing it make cameo appearances in the world’s favorite TV…

View original 676 more words

Simultaneous Equations

MathisFun Easter Puzzle

MathisFun Easter Puzzle

An Easter puzzle from MathisFun – as an excuse for solving simultaneous equations. We could of course use algebra. Using the notation, h, q and t for the egg Horace wants, the egg with the small square pattern and the egg with the stripey pattern respectively.
We have:
h + 2q      =550 (1)
h + q   +t =600 (2)
—-2q  +t =500 (3)
Subtracting equation (3) from equation (2) gives
h−q=100 (4)

(1)−(4) gives 3q=450 so q=150 and h must be 250 ($2.50).

We could check our solution on WolframAlpha of course:

Select image for WolframAlpha query

Did you know that you can easily invert matrices and solve simultaneous equations using Excel?

Excel sim equations & matrices

Select image for Excel file

Select the image or this link for the Excel file. Excel simultaneous equations

To enter the MINVERSE function in the example above, select cells C7:E9, enter the MINVERSE function as shown then press CTRL + SHIFT + ENTER; similarly to enter the MMULT function in this example, select cells H7:H9, enter the MMULT function as shown and then press CTRL + SHIFT + ENTER. (Using formulae like these demonstrates a neat Excel technique, to learn more see MrExcel on Array Formulae).

For notes / examples / tutorials on Simultaneous Equations try the mathcentre resources or this workbook from Plymouth University. For more on solving three equations in three unknowns for older students see Simultaneous Linear Equations from AJ Hobson’s ‘Just the Maths’

Since it’s Easter an updated version of the best Easter Eggs of all – from WolframAlpha.

If you want some more puzzles, MathisFun has plenty more, or try some of the puzzles here.

 

 

 

 

Box Plots

Box&Whisker - WolframAlpha

Box&Whisker – WolframAlpha

Box Plots show summary information for data – the box shows the median and quartiles and the whiskers are extended to all points which are not outliers.

A very clear description for younger students can be found on BBC Bitesize. For A Level Students the Centre for Innovation in Mathematics Teaching includes Box Plots in Chapter 3 of their Statistics text (page 26 of the pdf file, which is page 76 of the text).

Box Plots are particularly useful when comparing one or more distributions;

CIMT notes

CIMT Statistics Text

To help older students think further about about outliers and skew, have a look at this excellent illustration of Nobel Prize data from Plotly. Who is that outlier for the Nobel Peace Prize?!

Plotly - Nobel Prize winners by field

Plotly – Nobel Prize winners by field

Note that it is possible to display points with Box Plots in Plotly, the following data and charts demonstrates skew well:

Data

Box Plots & Skew

You can learn more about Plotly for graphing and sharing your data here: Learn and explore Plotly 

Valentine’s Day is coming…

Desmos Valentine

Click on the image and then on the slider!

Desmos Valentine instructions

Why not send your mathematical friends (or anybody else!) a Desmos ValentineThe wonderful team at Desmos have made their brilliant math-o-grams available earlier this year….and watch out for new designs coming soon.

The math-o-grams are really easy to create; why not give it a try? Just select your design, add your message and share!

 

 

Regression

If you want to check your calculations for a regression line and see the line then Excel and WolframAlpha are both very easy to use. In Excel – just add the data, insert a chart – choose Scatter, then add a trend line.

Regression Excel

…or let WolframAlpha do all the work for you (including a plot)!

WolframAlphaRegression

WolframAlpha Regression

You could also use Desmos. Their video gives clear instructions:

For another example with an A Level question (using the same data as for Excel and WolframAlpha above) check this slideshow.

Try this least squares demonstration on GeoGebra.
GeoGebra least squares

Transum Maths Puzzles

Colleen Young:

Transum Pu Wiang TrophyIf you enjoy puzzles try Pu Wiang from Transum

Update: 19 is the new record!

Originally posted on Mathematics - Games:

Transum Tweet Select Image for Transum’s Pu Wiange puzzle

I couldn’t resist this counter moving challenge – happy to report that I scored 20! Evidence in the image!
Pu Wiang

You can try more puzzles from Transum here.

There are plenty to try, all are attractively presented and easy to use. Fun to do but these puzzles will help students practise a variety of mathematical skills.

Some of these puzzles would make good lesson starters, for example the Magic Square puzzle or Prime Square.

Note – this has been added to the Puzzles page.

View original