        Spotting the patterns!

This resource was written by Derek Smith with the support of CASIO New Zealand. It may be freely distributed but remains the intellectual property of the author and CASIO.

Select GRAPH icon (press 5) from the

main menu or by using the arrow keys to

highlight and then press EXE. Turning a 2-D image into 3-D will have an awesome effect in enhancing the learning and understanding of graphing, along with the students having fun making them!

Once entered in the Graph icon, go into SETUP [SHIFT] [MENU]. Here you can alter a range of settings for the calculator, we want the Grid ON. Scroll down to Grid being highlighted and then press [F1] then EXIT to return to the graph entry screen. Enter the function y = x2 into the Y1 space then press [EXE] to store this. Set up the V-Window: [SHIFT] [F3] to the settings illustrated in the

screensnap on the right. Then [EXIT] and [F6] to draw the graph.  OR

Enter in the Table icon from the MAIN MENU. Go into [RANG]e, [F5] and set up the domain (x) values as shown in

 } }à×.è }  }@  }n on the right.

Then [EXIT] and [TABL]e [F6] to create the table of co-ordinates then [F5] to draw the graph of y = x2. This is the template for making the parabolaoid.

You need 14 of these made either by using the CASIO FA122 or FA123 software to capture the graph and then copy 14 times into a word document and print or by making a template on some card and copying this.

See the finished product on the right. To create the 3-D effect using scissors and the

wide to ½ way marks, as illustrated. Repeat the same, as illustrated here. Now trim four of your templates to this size. Then using

1 mm wide to ½ way marks. Trim another four of your templates to this size. Then using

1 mm wide to ½ way marks. With the remaining four of your templates. Then using

1 mm wide to ½ way marks, as illustrated. Now, fit them all together to make the 3-D parabolaloid. Once constructed it should flatten as shown below. Questions:

What is the equation of the parabolae that passes through the midpoints of the 4 template sizes that you have made?

[Hint: You only need 3 co-ordinate points to generate the equation vai the STAT icon from the MAIN MENU.]

What is the volume that this shape holds when symmetric?

[Hint: Use integration and solids of revolution in the RUN icon from the MAIN MENU.]

What is the equation of the 3-D shape that would cover this shape?

[Hint: z = f(x,y).] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

# Hidden Keys

This resource was written by Derek Smith with the support of CASIO New Zealand. It may be freely distributed but remains the intellectual property of the author and CASIO.

 } }à×.è }  }@  }eight">

Select RUN (press 1) from the Main Menu or by

using the arrow keys to highlight and then press EXE. Some of the functions available as keys are not immediately obvious on a graphics calculator. All can be found via the OPTN key. Below is a table of some commonly used functions and where to found them on the FX9750G+ and CFX9850GC+ graphics calculator models.  An example for each is shown.

 Function Key Location Example Factorials x! OPTN, F6►, F3 (PROB), F1 Permutations nPr OPTN, F6►, F3 (PROB), F2 Combinations nCr OPTN, F6►, F3 (PROB), F3 Random Numbers Ran# OPTN, F6►, F3 (PROB), F4 Absolute Value OPTN, F6►, F4 (NUMB), F1 Integer Part of Answer Int OPTN, F6►, F4 (NUMB), F2 Fractional Part of Answer Frac OPTN, F6►, F4 (NUMB), F3 Rectangular Coordinates to Polar Coordinates Pol( OPTN, F6►, F5 (ANGL), F6, F1 Polar Coordinates to Rectangular Rec( OPTN, F6►, F5 (ANGL), F6, F2 Radians to Degrees r OPTN, F6►, F5 (ANGL), F2      (Ensure angle set to degrees) º OPTN, F6►, F5 (ANGL), F1    (Ensure angle set to radians) www.monacocorp.co.nz/casio

For teachers we currently offer, a large number of classroom ready, resources available are designed primarily for the CASIO® FX9750G, FX9750G+, CFX9850GB, CFX9850GB+, CFX9850GC+  and FX9750GA+ 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 GC and CAS. More have been added to the website since the last newsletter.

SEE BELOW

Algebraic substitution

Algebraic substitution-numeric

A line-multiple representations for y=x+c, part 1

A line-multiple representations for y=mx, part 2

An introduction to the FX9750G+

An M & M worksheet

A parabola-multiple representations for y=ax2

A parabola-multiple representations for y=x2+c

A simulation of n-sided dice

Basic Algebra

Binomial and Poisson Distributions Calculations

Binomial Distribution Calculation in STAT mode

Combinations and Permutations-Calculations

Complex Numbers

Confidence Intervals

Confidence Intervals 1-P type

Confidence Intervals 1-S type

Confidence Intervals 2-P type

ConfidenceIntervals 2-S type

Confidence intervals how big does n need to be

Confidence interval to be halved does what to the sample size

Conic sections

Curve fitting

Curve fits to a line parabola etc

Differentiation

Differentiation checking

Dynamic graphing

Equation Solver

Expectation algebra and Lists

Exploring inequalities

Factorisation checking

Factorising in run mode-factor theorem

Finding sample sizes for confidence intervals

Finding the derivative function in STAT mode

Getting in the know with the CFX9750GII Calculator

Graphing  Rational Functions

Graph and text window

Graph drawing  Zooming in and out

Graphic calculator screen

Graphing and calculating unknown x-values

Graphing and calculating unknown y-values

Graphing and intercepts

Graphing and the maximum or minimum point

Graphing-Screen Snaps

Graphing two equations and finding the intersection point

Hidden Keys

Integration

Integration with a Graph

Introducing Calculus-PART 1

Introducing Calculus-PART 2

Inverse Normal Distribution Calculations  with and without the mean

Inverse Normal Distribution Calculations

Laws of Exponents

Le Hopitals Rule

Linear programming with vertical lines

Making use of the syntax

Mathematical modelling

Multiple representations for the derivative

Multiple representations for the line

Newton-Raphson Method Part 1

Newton-Raphson Method Part 2

Nth roots of a Complex Number

Pascals Triangle Calculations 2

Pick and match

Piecewise Functions

Plotting points in STAT and transferring to GRAPH mode

Poisson distribution calculations in STAT mode

Polar - rectangular form

Programmes  Normal distribution.

Recursive Formulas type 1

Recursive Formulas type 2

Recursive Formulas type 2A

Recursive Formulas type 3

Right angled triangles and trigonometry

Rolling a dice simulation using a tally table part 1

Rolling a dice simulation using a tally table part 2

Sampling-using random numbers

Sequence and series

Setting up the graphic calculator before use

Sigma notation

Simpsons Rule - 1

Simpsons Rule - 2

Simpsons Rule - 3

Simulations

Simultaneous equations

Solving equations on the GC

Solving Polynomial Equations

Solving Simultaneous Equations 2 unknowns

Solving Simultaneous Equations 3 unknowns

Solving trigonometric equations

Statistical graphs-an overview

Statistical graphs-bivariate part 1

Statistical graphs-bivariate part 2

Statistical graphs-univariate part 1

Statistical graphs-univariate part 2

Statistical graphs-univariate part 3

Statistical simulations -1

Statistical simulations -2

Statistical simulations -3

Statistical simulations -4

Statistics and probability

Summing up rows of Pascals Triangle

Table of values

The [F-D] key

The Dam Busters

The Function Keys

The Viewing-Window

The V-Window settings in Graph Mode

Trapezium Rule-1

Trapezium Rule-2

Trapezium Rule-3

Trapezium rule using LIST mode

Trigonometric Identities

Understanding Normal Distribution

Understanding the Central Limit Theorem

Using the EA-100 Data logger and the Graphic Calculator

Vertical and horizontal lines

Volume of revolution

Volume of revolution  part 1

Zooming in and zooming out                