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2008 JC1 INTER-CLASS “DESIGNING with the GRAPHICS CALCULATOR” COMPETITION

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Graphics Calculator and Sports Theme of Competition:

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ALL JC1 classes are required to submit at least ONE icon design using GC (must be individual submission). Each design should be related to the given theme. The class with the most entries will receive a hamper consisting of attractive prizes. ONLY designs produced using equations in the GC will be accepted for this competition. Win Attractive Prizes

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Stage 1: Short-listing 15 best designs by judges (to represent the college in the Inter-College GC Competition organised by VJC) Stage 2: Voting for the 15 short-listed designs by all Pioneers through college portal (voting period to be announced later) to decide top 3 winners Competition Format

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Judging Criteria Originality Creativity Difficulty Suitability

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Prizes to be Won… Graphing Calculator Movie Vouchers Book Vouchers GC Accessories Winner

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Submission of Work Deadline for Submission: Thursday 3 July 2008. Please submit the following as attachments via e-mail to maths_stw@yahoo.com.sg :maths_stw@yahoo.com.sg –completed entry form (name it as.doc, example 08S01_Tan Ah Kow.doc) –soft copy of the design (name it as.8xi, example 08S01_Tan Ah Kow.8xi). This can be done after downloading the picture from the graphics calculator onto a computer via USB cable and renaming the file. * Hard copy submissions will not be accepted

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To capture the image of your design Install TI Connect software using the installation CD provided in your GC package Connect your GC to the computer using the TI Connectivity cable provided in your GC package Select the icon on the desktop

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To capture the image of your design Select TI ScreenCapture on Rename your file name as given in the instructions and change the file type to “.8xi” before submitting your work:

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Possible designs using GC

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Refer to the following slides for some guiding steps…

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To draw the shape of the Fish… First, remove the axes by choosing FORMAT then AxesOff Key in Use VARS for y 1, X,T,θ,n for x To shade the different regions with different patterns, you may want to overlap some pattern to create new pattern For the bubbles, use 2nd DRAW, 9:Circle For the eye, 2nd DRAW, A:Pen

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To shade: use 2nd DRAW and choose 7: shade the region above y 2, below y 1, from x = π/4 to π/2, use pattern number 1, shade every 2 pixels for pattern: 1 = vertical line, 2 = horizontal line, 3 = gradient +1 line, 4 = gradient -1 line by default, it is the pattern that is all black

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to restrict domain and to avoid unwanted line, divided the equation by the domain you want instead of multiply Use [WINDOW] to adjust the Xmin, Xmax, Ymin, Ymax to "shift" the picture around the screen Try: Xmin=-10, Xmax=10, Ymin=-10, Ymax=10 (this is ZOOM 6;Zstandard) Store Pic Try: Xmin=-20, Xmax=10, Ymin=-20, Ymax=10

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Use 2nd DRAW, STO, 1:StorePic, key in any number from 0 to 9 to store your picture To recall back the picture number 1: Recall pic1 to display pic1 that you stored To add on another object to the pic1, you need to draw it onto the current pic1, then restore it again as pic1 Each time you add an object to the current pic1, you need to store it

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you may draw two patterns overlapping each other to create a new pattern (eg. pattern 1 and 2 give grid pattern) to erase unwanted portion in your graph, use 2nd DRAW and choose 0:Text and use the blank key (it will act as eraser) to key in text, use 2nd DRAW and choose 0:Text ClrDraw :(DRAW) ClrDraw ZSquare : ZOOM, 5:ZSquare, to set square grids

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You may also draw in polar coordinates. Go to (Mode) to change to polar coordinates first

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The graph will have petals In Polar Coordinates …

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You may want to play around with some polar equations: r = 3 + cos3θ r = 1 – sinθ r = 1 + cosθ r = 3 + 2 cosθ r = √(2 cos2θ – 1) r = 1 + sin2θ r = 2 – cos2θ r = √(cot2 θ cosec2θ) r = 1 – cos(θ/2)

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More about Polar Coordinates… You may refer to the following for more information about polar coordinates: 1.Further Pure Mathematics by Brian and Mark Gaulter: pg 43 – 56(Call No: 510 GAU) 2.http://tutorial.math.lamar.edu/Classes/CalcII/P olarCoordinates.aspx 3.http://www.analyzemath.com/polarcoordinates/g raphing_polar_equations.html 4.http://people.bath.ac.uk/maf20/polarcoords.html

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Another example in the next slide…

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Who will win e or ? draw 9 horizontal lines, y1=0/((x>0)(x<8)) y2=1/((x>0)(x 0)(x<8)) shade the regions accordingly : for example remember to ZOOM, 5:ZSquare key in the texts

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Happy Exploring and hope to see your creative designs soon…! Organised by the Mathematics Department (Jointly sponsored by )

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Polar Form and Complex Numbers. In a rectangular coordinate system, There is an x and a y-axis. In polar coordinates, there is one axis, called the polar.

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