Finding turning points in the RUN-MAT icon.

FMin( equation, lower bound, upper bound) and FMax( equation, lower bound, upper bound)

                                     [OPTN]                                               [F4]                                      [F6]  [F1]

Find the maximum(s) and minimum(s) of y = x⁴ + 2x³ – 3x²

Fmax(x^4 + 2x^3 – 3x²,-0.5,0.5)                                                         Fmin(x^4 + 2x^3 – 3x²,-1,1)

Fmin(x^4 + 2x^3 – 3x²,0,1)

Graphing Inequalities in the GRAPH icon.

Graph the intersection of y ≥ (x – 3)² – 2 and y ≤ x – 2 and x ≤ 4

Select ‘Type’ [F3] [F6],select Y≥ [F3]. Type in the expression (x – 3)² – 2 in the Y1 space.

Repeat the process for ‘Type and select Y≤ [F4]. Type in the expression x – 2 in the Y2 space.

Make sure the V-Window is appropriate.                                 Select DRAW [F6].

Solving Polynomial Equations without and with Complex Roots in the EQUA icon.

Solve x⁴ + 2x³ – 3x² = 0

Enter Polynomial [F2]                          Select degree = 4 [F3].

Enter the coefficients of this quartic: 1 [EXE] 2 [EXE] -3 [EXE] 0 [EXE] 0 [EXE] then [F1] solve.

Note that the roots at x = 0 has been indicated to be a double root with the ‘×2’

[SHIFT] [MENU] for SETUP.

Solve x⁴ + x³ + x² + x+ 1 = 0

Arrow down to the Complex mode, press [F2] for ‘a+bi’ format, then [EXIT].

Press [F1] to SOLVe.

Results are displayed in the rectangular format [(x + yi)].

[SHIFT] [MENU] for SETUP.

Arrow down to the Complex mode, press [F3] for ‘r∠θ’ format, then [EXIT].

Press [F1] to SOLVe.

Results are displayed in the polar format. [r×cisθ]

Table entries and features in the TABLE icon.

Enter the function in the Y1 space, e.g. y = 2x + 5.     Enter SET [F5] to select the Start, End and Step values.

[EXIT] then [F6] for display of the table values.        You can overtype an x-value the press [EXE] to activate the new calculation.

New values can be inserted without                             Press the down arrow to where you want

overwriting pre-determined x-values.                          to insert a new x-value, press [F3] for ROW and the

              [F2] for INSert. This creates a duplicate of the current row.

              Alter the x-value as desired.

[Note: Entering fractions using the [a^b/_c] button will be displayed as decimals in the x-value column BUT displayed as fractions on the RHS display area of the screen.]

You are able to plot the points that you have generated in the Table format. Make sure that you have an appropriate domain and range in the V-Window. Press [F6] for G-PloT.

Enter [SHIFT] [MENU] for SETUP. And scroll down to ‘Dual Screen’ and select [F1] T+G [EXIT].

[F6] for TABLe and [F6] for G-PloT to display both formats.

You can display a mixture of rectangular, parametric and polar equations in both the TABLE and GRAPH icons.

Inverse Binomial and Poisson calculations in the STAT icon.

A new feature to the FX9750Gii model.

Explore and enjoy!

An interesting discovery!

^d/_dx(x^r) = (e^(rlnx)), = e^(rlnx))(e^(rlnx))’ = x^r (^r/_x) = rx^(r-1)

For some videos on UTube form MIT visit:

http://www.youtube.com/watch?v=jbIQW0gkgxo&feature=channel

http://www.youtube.com/watch?v=eHJuAByQf5A&feature=related

EA-200 Data logger and EA-2 Motion Sensor.

These have been very popular and we have only 6 of each left. These can connect to the graphic calculator (or ClassPad) and we are offering a 63% saving purchasing these accessories singularly or a huge 69% discount on these two accessories when purchased together (While stocks last, so be quick!). The EA200 can connect up to 7 graphic calculators (or ClassPad) for data transfer from probes and motion sensor.

[N.B. Both of these models have a RRP of $799.00 each.]

EA-2 CASIO MOTION SENSOR                 EA200 CASIO DATA LOGGER

Emits Ultrasonic pulses                                                Data Analyser

Detects Pulses returned                                                Includes Temperature, Optical and Voltage Probe

Can connect to EA200                                     Data collection at up to 50,000 points per second                                          

Players 1, 2, 3, …, n are seated around a table and each has a single coin. Player 1 passes a coin to Player 2, who then passes two coins to Player 3. Player 3 then passes one coin to Player 4, who passes two coins to Player 5, and so on, players alternately passing one coin or two to the next player who still has some coins. A player who runs out of coins drops out of the game and leaves the table. Find the set of numbers n for which the n^th player ends up with all n coins.

A last word!

Well again, that’s all I can fit onto the 4 pages! Enjoy the ‘Winter’ term! Hope to see you at some workshops or hear from you via this newsletter or otherwise! If you would like to contribute or have suggestions as to what you would like to have discussed via this medium, please do not hesitate to contact us either by snail - mail, email, website, telephone, text or fax.

Graphical Times term 3 2010

Graphical Times term 2 2010



Graphical Times term 1 2010



Graphical Times term 4 2009



Graphical Times term 3 2009 



Graphical Times term 1 2009

Graphical Times.
Volume 7, Issue 27, 2008.

Welcome back to term 3!

Hope that you have had an enjoyable break and managed to read a novel or two in between pleasant walks between the cold southerly blasts that have rattled the walls of the house!

Due to the popularity of the calculator promotion started last term we are continuing this until the end of the month. This gives you just on 2 weeks to stock up for the remainder of the year or taking advantage of this savings offer to get ready for 2009.

Included in this terms newsletter are:

Calculator activities –

Worksheets for:         Graphic calculator       - Benford's Law Statistical graphing

ClassPad 300              - Circles, polygons and chords

Term 3 pricing list – is also included in this newsletter and mail-out.

Specials for Term 3 continue due to their popularity.

1.  The RM9000SET, RMClassPad SET, VI9850GSET, EA 200, EA2, SB-62 and SB-87 specials.

RM9000SET - $500 + GST (5 only available) RRP: $1,100 + GST

RMCLASSPADSET - $500 + GST (5 only available) RRP: $850 + GST

VI9850GSET - $500 + GST (1 only available) RRP: $850.00 + GST

EA200 data logger – Promotion special, see below.

EA200 data logger – Promotion special, see below.

SB-62 Cable (Calculator to calculator) - $15 + GST (10 only available) RRP: $30.00 + GST

SB-87 Cable (Calculator to computer) - $60 + GST (5 only available) RRP: $110.00 + GST

2. We are continuing the graphics calculator promotion. Buy 50 FX9750G+ graphic calculators and get 10 free plus a free data analysis system.

THE PACKAGE OFFER TO SCHOOLS: 1st May to 31st July 2008 (or while stocks last)

See the Flyer sent out in term two’s mailout.Or emailgraph.ech@xtra.co.nz to have it resent to you.

Another promotion on the CFX9850GC + [with 64kB memory].

The CFX-9850GCPlus has over 900 functions and 64KB total memory. E.g. List editor creates, edits and manages 36 separate data lists.  Special price for term 3, 2008 - $98+GST [RRP $189.00]

Is there a new teacher in the Mathematics Department? Or one for yourself or the entire mathematics department members - treat them to the NEW CFX9850GCplus model, a colour graphic with 64KB memory – a saving of over 40%. Or alternatively, buy 19 FX9750G+ and 1 CFX9850GC+ for the pricing of 20 FX9750G+ in bulk orders.

[Note: Please indicate the 19+1 deal on your order form and cannot be used in conjunction with the ‘Package offer to schools’ graphic calculator promotion’, see above.]

Mathematics Department Cycle [Pass it on to . . . ]

Workshop opportunities.

Workshop opportunities, if you would like to have a workshop for teachers and or students then please make contact with Graphic Technologies. A large number of schools are taking up this opportunity either singularly or as a cluster of schools with both the graphic calculator or with the ClassPad300, to look at how the graphic calculator and CAS could impact on and be integrated into your classroom practices.

Some basic functions on the ClassPad300.

A Problem: Can you solve this problem using the ClassPad300+?

What is the equation of the ellipse that passes through the four extreme points of this approximation to an ellipse?

Replacement parts:

Stylus:                 Part No: 1010 4597 $4.00 + GST
Protective Sheet: Part No: 1011 7012 $4.00 + GST
Hard Cover:        Part No: 1011 4575  $4.00 + GST

Visit: http://edu.casio.com/use/ for assistance with video support to operating your Classpad300 in the Main and Geometry icon, guidance in e-Activities.

Worksheets downloaded off  the web.

Visit Monaco Corporation’s website to view and download the worksheets. There are links to other informative mathematics education websites too. For teachers we currently offer a large number of ‘classroom ready’ resources available are designed primarily for the CASIO_® FX9750G, FX9750G+, CFX9850GB, CFX9850GB+, CFX9850GC+  models of graphical calculators and the ALGEBRA 2.0. There is also a variety of activity sheets designed for the ClassPad 300 models. All of the activities and worksheets are designed for beginners to advanced users of the G.C. and C.A.S. all useful for all secondary year levels. More have been added to the website since the last newsletter. www.monacocorp.co.nz/casio

Websites of mathematical interest.

Are you familiar with this? If not you should check out Maxima. It is a free GPL computer algebra
system which you can install. Visit: http://maxima.sourceforge.net/

Check out this world clock! Fascinating WORLD CLOCK http://www.chippynews.com:80/worldclock.htm Note the numbers of oil pumped, goes faster than any of the others!

Conferences on technology in mathematics education (with a search engine) can be found at http://b.kutzler.com .

Census@school website has been considerable updated http://www.censusatschool.org.nz/ along with some statistical links via http://www.censusatschool.org.nz/2008/informal-inference/

CASIO Support Classroom E-mail News, What's New.
Download the latest resources: Manager PLUS for fx-9860G series software updater. The latest version of Software updaters for Manager PLUS for fx-9860G series can be downloaded  by going through the following CASIO Educational website.
(A) CASIO Educational website/ CASIO Online Service (Downloads) page: http://edu.casio.com/dl/
(B) [Enter] [Accept]  [Log in] You need to use your ID (E-mail address) and your password.
If you have not registered any of CASIO products to this service, please push the [Registration] button first.
If you have registered some of CASIO products to this service, and have not registered your Manager PLUS for fx-9860G series, please push [ Update/ modify ] button first.
(C) Select the following items which you need, and then click [NEXT].
Update for fx-9860G Slim Ver.1, or Update for fx-9860G(SD) Ver.1, or Update for GRAPH85(SD) Ver.1.
(D) Click underlined items to download the file.
        http://edu.casio.com/confe/icme11session_7_8_9.html
        http://edu.casio.com/confe/icme11session_11_12.html
Please visit the Worldwide Education Website to get the latest information.
Education HOME: http://edu.casio.com

Hot products list: http://edu.casio.com/products/
FX-9860G Slim: http://edu.casio.com/products/graphic/fx9860gslim/
FX-9860G: http://edu.casio.com/products/graphic/fx9860g/
Manager PLUS for fx-9860G series: http://edu.casio.com/products/peripheral/9860slim-mgr/
The latest Updater for classpad manager: http://edu.casio.com/products/classpad/cp_v303/probability.html
Advanced NATURAL V.P.A.M: <ES PLUS series> http://www.casio-intl.com/calc/ntd/ and http://edu.casio.com/products/

Useful movie contents: http://edu.casio.com/use/
Information about the ClassPad: http://edu.casio.com/products/classpad/

Some Light Entertainment!

ASTRONOMER: When you rearrange the letters: MOON STARER
THE EYES: When you rearrange the letters: THEY SEE

THE MORSE CODE: When you rearrange the letters: HERE COME DOTS

SLOT MACHINES: When you rearrange the letters: CASH LOST IN ME
ELECTION RESULTS: When you rearrange the letters: LIES, LET'S RECOUNT

SNOOZE ALARMS: When you rearrange the letters: ALAS! NO MORE Z 'S

A DECIMAL POINT: When you rearrange the letters: I’M A DOT IN PLACE

THE EARTHQUAKES: When you rearrange the letters: THAT QUEER SHAKE

ELEVEN PLUS TWO: When you rearrange the letters: TWELVE PLUS ONE

Classroom  Activities.  

http://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2005/90642-exm-05.pdf

QUESTION FIVE

The quality analyst’s supervisor tells her that when she is estimating μ₁ – μ₂ (the difference in the mean lifetimes for the two models of battery) in her 2006 survey:

• she can use standard deviations obtained in 2005 as estimates of population standard deviations (see the table of data in Question Four)

• that, rather than taking a random sample of 40 of each type of battery, she might be able to reduce the width of the confidence interval by taking a larger sample from one model of battery and a smaller sample from the other model

• that the total number of batteries sampled (both ‘super’ and ‘power’ combined) must still be 80

• that, for each model, the number of batteries sampled must be a multiple of 10.

Perform calculations to establish the number of each model of battery that the quality analyst should sample (when she calculates her 99% confidence interval for μ₁ – μ₂ in order to obtain a minimum width for the interval.

Justify your answer.

This question draws on previous information that was supplied in the previous question, this was:

QUESTION FOUR

The quality analyst is asked if there is a significant difference between the lifetimes of ‘power’ batteries and ‘super’ batteries when they are used in torches.

In order to answer this question, she collects data from a random sample of each model. The results

are shown in the following table:

Let μ₁ be the mean lifetime of all ‘power’ batteries and let μ₂ be the mean lifetime of all ‘super’ batteries.

This question looks at the analyse estimates of population parameters.

Here z = 2.576

By table:

Minimum width is given by sampling 50 ‘power’ batteries and 30 ‘super’ batteries.

Or by using calculus and finding the minimum point on the graph:

By graphic calculator:

Y1 = Ö(1.09²/_x+0.65²/_(80-x)) and using the fact that x £ 80 to find an optimum domain for the graph and then using G-Solve to find the minimum point

By CAS:

Differentiate Ö(1.09²/_x+0.65²/_(80-x)) with respect to x and set the answer to zero for max/min, the graph confirms that the minimum occurs at x = 50.1149 (4d.p.)

Y1=Ö(1.09²/_x+0.65²/_(80-x))

Giving two solutions with x = 50.1149 (4d.p.) the result required.

Establishing, with reasoning, that a 50/30 split gives a minimum interval width required.

Updating the email list.

To be placed back onto the email list and receive this mail-out and future mail-outs electronically then please send a return email to graph.tech@xtra.co.nz stating that you wish to be reactivated on to the Graphic Technologies email list. If you do not want to receive any more newsletters via email, then please send a return email to graph.tech@xtra.co.nz stating that you wish to be removed from the email list. To update your preferences, please send a return email to graph.tech@xtra.co.nz stating your preferred contact email address.

A last word!  

Well again, that’s all I can fit onto the 4 pages! Have a great term 3! Hope to see you at some workshops or next term via this newsletter or otherwise! If you would like to contribute or have suggestions as to what you would like to have discussed via this medium, please do not hesitate to contact either by snail - mail, email, telephone, text or fax.

Would you like to receive this mailout electronically? Please email your request to: graph.tech@xtra.co.nz

2008 Activity sheets

Estimating Pi                   Radial Survey          

Random Walk Art          Summing to infinity and beyond 

Circlespolygons and chords