Welcome back to the start of the winter term! We hope you have had a restful break and been able to read a few non-mathematical books. I have been trying to read the 2^{nd} book in the series by Stieg Larsson (died 2004) and get it finished before the movie of the 3^{rd} book hits the cinemas! We hope you enjoy the read in this newsletter.

What’s in here!

Included in this terms newsletter are:

Calculator activities for the Classpad 330+ and Casio graphic calculator

Worksheet for the Classpad 330 +: Differential equations and Geometrical construction and loci

Worksheet for the FX9750GII and similar models: Tangents and Normals on the FX9750Gii model

Term 3, 2010 pricing list.

N.B. The Graphic Technologies Catalogue is available on request. Please email us @ graph.tech@xtra.co.nz, to receive your free copy.

GST rising to 15%.

The 1^{st} October (term 4) signals a rise in pricing. Make the most of GST being 12.5% during term 3. That is a 20% increase in government revenue that we need to adjust our pricing for. We still intend to have the lowest pricing to support schools and provide opportunities to access great Casio products.

Workshop opportunities.

Workshop opportunities: These were run in June, and we will be heading back to Christchurch for a workshop early in September. Please register ASAP. 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 and the ClassPad330+, to look at how the graphic calculator and CAS could impact on and be integrated into your classroom practices. With the new features of the FX9750Giiillustrated later in this newsletter, an opportune time to consider booking a session.

Worksheets downloaded offthe web.

Visit Monaco Corporation or Graphic Technologies website to view and download worksheets. There are links to other informative mathematics education websites too. For teachers we currently offer a large number of ‘classroom ready’ resources available and are designedprimarily for the CASIO_{®} FX9750Gii, FX9750G, FX9750G+, CFX9850GB, CFX9850GB+, CFX9850GC+FX9750GA+ models of graphical calculators and the ALGEBRA 2.0. There is also a variety of activity sheets designed for the ClassPad300, 300+, 330A and 330A+ models. All of the activities and worksheets are designed for beginners to advanced users of the GC and CAS. More have been added to the website since the last newsletter.

We are pleased to have two NEW products added to our range of Casio products. These are Casio projectors models, namely the XJA130 and XJA145 models. These have been included on the term 3 pricing list.

Data projector XJA130New product!

$1900.00

Data projector XJA145New product!

$2500.00

Features Include

·Ecologically sound and energy saving.

·NEW mercury-free light source

·2 x optical zoom

·Lamp-free technology with up to 20,000 hours continuous performance

·USB 2.0 for PC-free presentations [XJA145]

·WLAN capability

·The size of a ream of A4 paper!See the flyer with this mailout for our introductory offer:

The Differences Between the FX9750GII and the FX9750GA+, the Facts!

Specification of NEW fx-9860GII and NEW fx-9750GII

FX9750GII

FX9750GA+

Probability Function (ex : NormPD( )

X

Advanced STAT functionTest, Interval, Distribution, Probability

X

X

Numeric Derivative

X

X

Numeric Integration

X

X

Solve Integral function (in EQUA mode)

X

Solve Probability function in EQUA mode

X

REF/RREF function

X

Xc < (Inequality) Graphing in GRAPH Mode

X

Reduction (Simp.)

X

Division with remainder (Int /)

X

mod function (Remainder)

X

MOD2 (for special calculus)

X

Incorrect French Translation (in EQUA mode (simultaneous))

X

Integral Graphing (in GRAPH mode)

X

Complex number

X

X

View Window Setting (same as G85/G35)

X

X

Setting the Graph Type (Rectangle/Inequality)

X

X

Graph solve function (in GRAPH mode)/(Root, Min, Max, YICPT, YCAL, XCAL)

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 theY2 space.

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

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

Solve x^{4} + 2x^{3} – 3x^{2 }= 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 x^{4} + x^{3} + x^{2} + 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.

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 SENSOREA200 CASIO DATA LOGGER

Emits Ultrasonic pulses Data Analyser

Detects Pulses returned Includes Temperature, Optical and Voltage Probe

Can connect to EA200Data collection at up to 50,000 points per second

Product

EA-200 Data Logger

EA- 2 Motion Sensor

Both units

Price (exclusive GST) per unit

$300.00

$300.00

$500.00

A problem to finish on!

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.

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.

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 . . . ]

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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 offthe 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 designedprimarily 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/

The quality analyst’s supervisor tells her that when she is estimating μ_{1} – μ_{2} (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 μ_{1} – μ_{2} 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:

‘Power’

‘Super’

Sample size

40

40

Sample mean (lifetime in hours)

10.73

9.35

Sample standard deviation (hours)

1.09

0.65

Let μ_{1} be the mean lifetime of all ‘power’ batteries and let μ_{2} be the mean lifetime of all ‘super’ batteries.

This question looks at the analyse estimates of population parameters.

Here z = 2.576

By table:

np

ns

SE

width

40

40

0.201

1.036

50

30

0.194

1.004

60

20

0.202

1.044

70

10

0.243

1.256

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(1.09^{2}/_{x}+0.65^{2}/_{(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(1.09^{2}/_{x}+0.65^{2}/_{(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(1.09^{2}/_{x}+0.65^{2}/_{(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