Using Graphical Calculators in the Classroom

1
Using Graphical Calculators in the Classroom

• Richard Tarry
• Sept 2004

2
Setting up the calculator

• If necessary insert the 2 batteries supplied
• After you have inserted the batteries, pull out
  the protection strip
• All users reset the calculator by pressing a
  pen into the little hole above the battery
  compartment
• Press YES (F1) below the screen, then press MENU

3
Getting Started

• Press AC/ON to switch on
• The calculator uses a menu system
• Lets go into GRAPH
• Either press the menu number (4) or navigate with
  the cursor to the GRPH icon and push EXE
• Push MENU to get back to the home screen
• Press QUIT to return to an earlier screen

4
Useful Modes
1 RUN Powerful scientific calculator
2 STAT Single paired variable statistical calculation graphs
4 GRAPH Graph sketching
5 TABLE Generates tables of values from a formula
8 CONT Screen contrast adjustment
5

• Using RUN mode
• Reset the calculator by pressing a pen into the
  little hole above the battery compartment
• Press YES (F1) below the screen, then press MENU

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SET UP for RUN

• Enter RUN
• Enter SET UP
• Use the cursor and the function keys to set Angle
  to Deg(rees)
• Use QUIT to return to a blank screen
• This is the most common setup change!

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RUN Mode

• RUN mode features
• On-screen display algebraic order
• You should use brackets
• You can work with fractions
• You can edit (before and after AC)
• Ans stores the last answer
• You can store results in ALPHA memories

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Learning the keys

• EXEcute is like it gives the answer
• Find out how to add, subtract, multiply, divide,
  square, square root, raise to a power (such as
  53), find sine cosine
• Find out the difference between the and (-)
  keys
• Find out what SHIFT and ALPHA do
• Find out how you can use the cursor to edit a
  calculation
• Find out how to use DELete INSert
• Clear the screen

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Some easy calculations
Do the following calculations and write down your
answers to 3 sf.

• 4.1 x 3.8
• 6.5 ? 0.175 then edit to 6.5 ? 0.185
• sin30 cos45
• ?40 ?20 . then edit to ?4.4 ?2.1
• (2.35 1.82) ? 0.9
• 4.15 ? (-2.5)3
• 3.5x108 X 7 000 000
• 16 p
• Answers are on the next slide

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Answers (all to 3 sf)

1. 15.6
2. 37.1, 35.1
3. 1.21
4. 10.8, 3.55
5. 4.63
6. -74.1
7. 2.45 x 1015
8. 50.3

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Variables Memories

• Results of calculations are stored automatically
  and manually
• Ans automatically stores the last answer
• X,T is an easy access storage and also acts as
  the variable x
• The ? stores a value into a memory
• A, B, C, D, . Z are all memories

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Using variables and memories the Ans key

• Calculate 2 x 1.4
• Then type 1 EXE and explain what has happened
• Now calculate 3 x 1.4 , followed by 5 Ans.
• Now type 2 x Ans.
• Describe in your notes how ANS can be used

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Using the X,T key and replay

• Clear the screen
• Type 2 ?X EXE, then 3x2 5x 12 EXE. Check the
  answer and explain what the calculator has done.
• Now type 5 ? X EXE, and then clear the screen
  with AC/ON
• Press the ? cursor twice you should now see 3x2
  5x 12 on the screen
• Press EXE
• Explain the result.

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Now start the RUN tasks
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In your groups, find and write down the following
formulas

• Gradient of a straight line
• Pythagoras
• Area of a circle
• Volume of a cylinder
• The quadratic formula
• Distance between 2 points

16
Finding a gradient

• Write down the gradient formula
• Write down a mathematical expression to find the
  gradient of the line joining the points (2,5) and
  (10,41)
• Use the brackets function of the calculator to
  find the gradient in one go

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More gradients

• You should have typed (41-5)(10-2) EXE and
  obtained a gradient of 4.5
• Now find the gradient of the line joining (-3,15)
  to (17,-35)
• ChallengeFind the equation of each line.

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Volume of a cylinder

• Write down the volume formula
• Write down a mathematical expression to find the
  volume of a cylinder with radius 6.5 cm and
  height 13cm.
• Use the p key and find this volume
• You should get an answer of 1726 cm3

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More volume calculations

• Find the volume of a cylinder with radius 2.5cm
  and height 18 cm.
• Rearrange the formula to make height the subject
• Write down a mathematical expression (using
  brackets) to find the height of a cylinder of
  capacity 500 ml, and radius 5.5cm
• Find the height correct to 1 dp.

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Volumes

• You should have written h500(px5.52) EXE and
  got an answer of 5.3cm
• What height is a cylinder holding 1 litre, with
  radius 7.5cm?
• Challenge
• Make radius the subject
• Write down a mathematical expression to find the
  radius of a cylinder holding 600 ml of height
  11cm
• Now find the radius (in one go!)

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The quadratic formula..

• Use the quadratic formula to solve 3x2 5x 17
  0. Save both answers.
• Remember to use brackets!
• Use the edit function to get the 2nd solution by
  changing a plus to a minus.
• You should get answers of -3.36 and 1.69
• You should have typed (-5?(52-4x3x-17))?(2x3)
  EXE but there are other methods using a memory
  rather than a single calculation

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Generating a sequence

• Write down the first 4 terms of the sequence un1
  1.05Un 20with u0 1500
• First type 1500 EXE (This stores 1500 in Ans)
• Type 1.05Ans-20 EXE
• Press EXE again, and againDescribe a situation
  that this sequence could model.
• You should get answers 1555, 1612.75, 1673, 1737

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Challenge

• From an AS Using Maths paper
• Tw 33 (33 T)0.47 0.3?v 0.02v
• Tw is windchill temperature (oC)
• T is temperature out of the wind (oC)
• V is the wind speed (mph)

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Harder problems

1. Find the windchill temperature if the temperature
   out of the wind is 8oC when the wind is blowing
   at 5 mph.
2. What is the temperature if the wind speed
   increases 4 times.
3. One day the temperature out of the wind was 10oC,
   but in the wind it was 2oC. What was the wind
   speed?

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• End of RUN mode exercises

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• Using the Statistics mode
• Reset the calculator by pressing a pen into the
  little hole above the battery compartment
• Press YES (F1) below the screen, then press MENU

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STAT mode

• Enter STAT
• Data can be stored in Lists 1 6
• You can navigate around the lists with the cursor
• You can simply overtype existing data or delete
  an entire list

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Entering data

• Enter the following data into List 1
• 10, 9, 9, 12, 15
• You need to push EXE after each number
• The top row of function keys are used in
  conjunction with the screen

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Deleting and inserting data

• Use ?in the top row just below the screen to
  obtain DEL, DEL-A, INS
• Move the cursor onto the 12 in the list, press F1
  (DEL) what happens?
• Now press F3 (INS) what happens?
• Overtype the 0 with 8.
• Move the cursor to any position in List 1. Then
  press F2 (DEL-A). What happens? Press F1 (YES).

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Working with some data

• Enter the following data into List 1 10,
  8, 9, 12, 15, 8, 3, 17
• Press CALC (F2 ), then 1 VAR (F1)
• Use the cursor to scroll down
• Check that n8 (this this a good way to check you
  havent missed any data)
• Write down the mean and standard deviation, and
  the median and quartiles (Q1 Q3).
• What is the range of the data?
• Press QUIT when you have finished

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Statistical graphs

• Press GRPH (F1 )
• Use?to obtain SEL(ect) SET
• Press SET (F4 )
• Use the cursor to move down the settings list
• Notice how a new set of choices appears at the
  bottom of the screen for each setting

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Set up some graphs

• Set up StatGraph1 with
• G-Type Pie
• Data List1
• Display Data
• Set up StatGraph2 with
• G-Type Box (you will need to use ?)
• XList List1
• Freq 1
• Now press QUIT

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Draw your statistical graphs and use Trace (F1)

• Press GRPH (F1), then GPH1
• QUIT and press GRPH then GPH2
• Now press SHIFT followed by Trace
• Use the horizontal cursor to locate points on the
  box chart
• Sketch the box chart labelling the 5 points that
  Trace shows you.
• Use G?T to return to the statistics screen and
  then QUIT
• Explain what the box plot shows.

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Analysing grouped data
Age Frequency
15 5
16 28
17 59
18 44
19 23
20 13
21 4

• Delete any previous data
• Enter data oppositeinto Lists 1 2
• Discuss in your group what this data means

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Set up the calculator

• The SET function assigns statistical variables to
  your data lists enter CALC press SET
• Assign List1 to 1Var X and List2 to 1Var F
  (Discuss what this means why not 2Var?)
• QUIT to return to the List screen
• Enter CALC, 1VAR and scroll down the results

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Analysis of the data

• Write down the answers to all these questions
  and make sure you understand them check if
  possible.
• Find the number of students who were surveyed
• Find the mean age
• Find the median age the quartiles
• Make a boxplot copy it show the position of
  the mean on your sketch
• QUIT

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Another problem this time with two variables

• The data is on the next slide
• Enter the data in List 1 (Age) List 2 (Height)
• Use CALC and SET to to set up 2Var X
  List12Var Y List22Var F 1
• QUIT, press CALC and 2VAR

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Data showing the ages and heights of some children
Age in months 18 19 20 21 22 23 24
Height in cm 76.1 77.0 78.2 78.2 78.8 79.7 79.9
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Questions

• What is the mean age of the children?
• What is their mean height?
• Press REG, then F1 (X)
• Copy down the values for a, b, r and write down
  the equation.
• Substitute a b into the equation and discuss
  what it means.

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Further analysis

• Press GRPH then?then SET
• Set up StatGraph1 to draw a scattergram with
  Xlist set to List1, Ylist set to List2, Freq as 1
• QUIT and use GRPH to draw the scattergram
• Press x what do you notice?
• Then press DRAW. Copy what you see and relate it
  to your equation.

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Advanced analysis

• Heres some more data to add to your lists
• Draw a scattergram but this time choose x2
• Write down the equation
• Compare the x and x2 graphs and explain what
  this shows

Age 28 32 36 40
Height 83.0 87.3 90.6 95.5
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Useful tips

• If you want to clear the screen, press SHIFT,
  Sketch, then Cls (F1 ) the last graph only will
  be redrawn
• After you have drawn a graph, press G?T to return
  to the screen showing data
• You can COPY the equation into the Graph
  Functions list for later use

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• End of Statistics section

44

• Using the Graphs mode
• Reset the calculator by pressing a pen into the
  little hole above the battery compartment
• Press YES (F1) below the screen, then press MENU

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Working with Graphs

• From the menu, enter the GRPH mode
• Type 2X3 (use the X,T key) next to Y1 then EXE
• Press EXE again (or DRAW)
• Use Zoom (F2) OUT to display both intercepts
• Use Trace (SHIFT F1) to find the coordinates of
  the intercepts
• Make a rough sketch of the graph labelling the
  intercepts

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Adjusting the view

• Press G?T a few times and see what happens.
• Press SHIFT F3 to obtain the V(iew) Window.
• Use the cursor to move down the settings
  discuss what they all do.
• Reset to Xmin to (-)4, max to 4, Ymin to (-)2,
  max to 6. You need to use EXE to store each
  setting you change.
• Redraw the graph.

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Investigating graphs

• Press G?T to return to the Graph Function screen
• At Y2 type in 5 X and draw the graphs
• Adjust the View to show all intercepts add the
  new graph to your sketch

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Using the Trace to solve equations simultaneously

• Press Trace (SHIFT F1)
• Use the left-right cursor to move along a graph
• The up-down cursor enables you to jump to the
  other graph
• Find the coordinates of the intersection as
  accurately as you can
• Now use Zoom and Trace to improve your accuracy
  write down your answer to 3 dp.

49
Check with algebra

• Here are the two equations again y 2x 3 and
  y 5 x
• Solve them algebraically in your groups.
• Compare your answers to what you got for the
  graphical solution.

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Moving on Quadratic transformations

• Delete all previous graph functions
• Draw Y1 X2 and set the View to INIT(ial)
• Draw Y2 (X3)2 and Y3 (X2)2
• Return to the Graph Functions - investigate how
  to select and deselect functions.
• Make a labelled sketch showing all 3 graphs,
  their equations and x-intercepts.

51
Whats the rule?
Equation Description of the transformation from x2

• Make a table like the one above
• What do you think the rule is? Make up another
  equation and predict the transformation.
• Verify your prediction using the calculator

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More transformations

• Delete or deselect functions Y2 Y3
• Draw Y X2, Y X2 2 and Y X2 3
• Adjust the View to show all the y-intercepts and
  copy a sketch
• Make a new table showing the transformations
• Predict, verify and formulate the rule as before.
  
• Whats the difference between the rules?

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Combining transformations

• On the next slide are some quadratic functions
• Each is a double transformation from Y X2
  describe both transformations fully.
• Predict what the graphs will look like and sketch
  them.
• Verify using the calculator.

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Transformations.

• Here they are
• Y (x - 5)2 3
• Y (x 3)2 1
• Y (x 10)2 50
• Y (x 100)2 500
• Y (x 200)2 - 80

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Drawing a simple trig graph

• Delete all previous functions
• Press SET UP (SHIFT MENU)
• Change Angle to Deg(rees)
• QUIT and enter Y1 sin X
• Set the View to TRIG draw the graph
• Make a rough labelled sketch
• Show the coordinates of all intercepts and the
  maximum minimum points

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Solve a trig equation

• Return to Graph Functions
• Enter another equation Y2 0.5
• Draw the graphs and use them to solve sin x
  0.5
• Use Trace (and Zoom) to find four solutions to
  this equation as accurately as you can.
• Sketch and label your graphs
• How are the solutions related to each other?

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• End of GRAPHING sessions !!

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• Advanced stuff for A2

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More advanced graphing- parametrics

• Enter RUN mode, then SET UP
• Change F-Type to Parametric
• QUIT and enter GRAPH mode
• DELete existing functions

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Demonstrate projectile motion

• QUIT RUN mode and enter GRAPH
• Set up the V-Window to Xmin 0, max 280,
  scl20Ymin -20, max 70, scl 10Tmin 0, max
  8, ptch 0.1

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Projectile motion task

• A projectile is fired at a speed of 50 m/s, and
  an angle of 200 to the horizontal.
• Write down the equations of motion which will
  give the horizontal and vertical position of the
  projectile at time t s after firing
• Enter these equations as Xt1 and Yt1 .

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Projectile task

• You should have writtenXt1 50Tcos20 andYt1
  50Tsin20 4.9T2
• If you did NOT write this, show on paper that
  these are correct

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Modelling projectile motion

• Press DRAW, and use Trace to find the maximum
  height and the range of the projectile
• By changing the angle, find the maximum range
  that could be achieved, and the height at this
  angle
• Write down the range height at each angle you
  choose

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• THE END

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• PS - This presentation can be viewed online
• You can find it on the Shared Drive (U) in Maths
  Advanced Level Courses
• You can also find it on CurWeb