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Using Graphical Calculators in the Classroom Richard Tarry Sept 2004

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

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Getting Started Press AC/ ON to switch onPress AC/ ON to switch on The calculator uses a menu systemThe calculator uses a menu system Let’s go into GRAPHLet’s go into GRAPH Either press the menu number (4) or navigate with the cursor to the GRPH icon and push EXEEither 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 screenPush MENU to get back to the home screen Press QUIT to return to an earlier screenPress QUIT to return to an earlier screen

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

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

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

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

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Learning the keys EXEcute is like = it gives the answerEXEcute is like = it gives the answer Find out how to add, subtract, multiply, divide, square, square root, raise to a power (such as 5 3 ), find sine & cosineFind out how to add, subtract, multiply, divide, square, square root, raise to a power (such as 5 3 ), find sine & cosine Find out the difference between the – and (-) keysFind out the difference between the – and (-) keys Find out what SHIFT and ALPHA doFind out what SHIFT and ALPHA do Find out how you can use the cursor to edit a calculationFind out how you can use the cursor to edit a calculation Find out how to use DELete & INSertFind out how to use DELete & INSert Clear the screenClear the screen

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Some easy calculations 1.4.1 x 3.8 2.6.5 0.175 … then edit to 6.5 0.185 2.6.5 0.175 … then edit to 6.5 0.185 3.sin30 + cos45 4. 40 + 20 …. then edit to 4.4 + 2.1 5.(2.35 + 1.82) 0.9 5.(2.35 + 1.82) 0.9 6.4.1 5 (-2.5) 3 6.4.1 5 (-2.5) 3 7.3.5x10 8 X 7 000 000 8.16 π Answers are on the next slide Do the following calculations and write down your answers to 3 sf.

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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 10 15 8.50.3

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Variables & Memories Results of calculations are stored automatically and manuallyResults of calculations are stored automatically and manually Ans automatically stores the last answerAns automatically stores the last answer X,T is an easy access storage and also acts as the variable xX,T is an easy access storage and also acts as the variable x The stores a value into a memoryThe stores a value into a memory A, B, C, D, …. Z are all memoriesA, B, C, D, …. Z are all memories

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Using variables and memories – the Ans key Calculate 2 x 1.4Calculate 2 x 1.4 Then type – 1 EXE and explain what has happenedThen type – 1 EXE and explain what has happened Now calculate 3 x 1.4, followed by 5 – Ans.Now calculate 3 x 1.4, followed by 5 – Ans. Now type 2 x Ans.Now type 2 x Ans. Describe in your notes how ANS can be usedDescribe in your notes how ANS can be used

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Using the X,T key and replay Clear the screenClear the screen Type 2 X EXE, then 3x 2 –5x + 12 EXE. Check the answer and explain what the calculator has done.Type 2 X EXE, then 3x 2 –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/ ONNow type 5 X EXE, and then clear the screen with AC/ ON Press the cursor twice – you should now see 3x 2 –5x + 12 on the screenPress the cursor twice – you should now see 3x 2 –5x + 12 on the screen Press EXEPress EXE Explain the result.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 lineGradient of a straight line PythagorasPythagoras Area of a circleArea of a circle Volume of a cylinderVolume of a cylinder The quadratic formulaThe quadratic formula Distance between 2 pointsDistance between 2 points

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Finding a gradient… Write down the gradient formulaWrite down the gradient formula Write down a mathematical expression to find the gradient of the line joining the points (2,5) and (10,41)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 goUse 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 4.5You 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)Now find the gradient of the line joining (-3,15) to (17,-35) Challenge: Find the equation of each line.

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Volume of a cylinder Write down the volume formulaWrite down the volume formula Write down a mathematical expression to find the volume of a cylinder with radius 6.5 cm and height 13cm.Write down a mathematical expression to find the volume of a cylinder with radius 6.5 cm and height 13cm. Use the π key and find this volumeUse the π key and find this volume You should get an answer of 1726 cm 3You should get an answer of 1726 cm 3

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More volume calculations… Find the volume of a cylinder with radius 2.5cm and height 18 cm.Find the volume of a cylinder with radius 2.5cm and height 18 cm. Rearrange the formula to make height the subjectRearrange 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 5.5cmWrite 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.Find the height correct to 1 dp.

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Volumes … You should have written h=500÷(πx5.5 2 ) EXE and got an answer of 5.3cmYou should have written h=500÷(πx5.5 2 ) EXE and got an answer of 5.3cm What height is a cylinder holding 1 litre, with radius 7.5cm?What height is a cylinder holding 1 litre, with radius 7.5cm?Challenge: Make radius the subjectMake radius the subject Write down a mathematical expression to find the radius of a cylinder holding 600 ml of height 11cmWrite down a mathematical expression to find the radius of a cylinder holding 600 ml of height 11cm Now find the radius (in one go!)Now find the radius (in one go!)

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The quadratic formula.. Use the quadratic formula to solve 3x 2 + 5x – 17 = 0. Save both answers.Use the quadratic formula to solve 3x 2 + 5x – 17 = 0. Save both answers. Remember to use brackets!Remember to use brackets! Use the edit function to get the 2 nd solution by changing a plus to a minus.Use the edit function to get the 2 nd solution by changing a plus to a minus. You should get answers of -3.36 and 1.69 You should have typed (-5+ (5 2 -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 u n+1 = 1.05U n – 20 with u 0 = 1500Write down the first 4 terms of the sequence u n+1 = 1.05U n – 20 with u 0 = 1500 First type 1500 EXE (This stores 1500 in Ans)First type 1500 EXE (This stores 1500 in Ans) Type 1.05Ans-20 EXEType 1.05Ans-20 EXE Press EXE again, and again… Describe a situation that this sequence could model.Press EXE again, and again… Describe a situation that this sequence could model. You should get answers 1555, 1612.75, 1673…, 1737…You should get answers 1555, 1612.75, 1673…, 1737…

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Challenge… From an AS Using Maths paper T w = 33 – (33 – T)[0.47 + 0.3 v – 0.02v] T w = 33 – (33 – T)[0.47 + 0.3 v – 0.02v] T w is windchill temperature ( o C)T w is windchill temperature ( o C) T is temperature out of the wind ( o C)T is temperature out of the wind ( o C) V is the wind speed (mph)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 8 o C… 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 10 o C, but in the wind it was 2 o C. 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 compartmentReset the calculator by pressing a pen into the little hole above the battery compartment Press YES (F1) below the screen, then press MENUPress YES (F1) below the screen, then press MENU

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STAT mode Enter STATEnter STAT Data can be stored in Lists 1 – 6Data can be stored in Lists 1 – 6 You can navigate around the lists with the cursorYou can navigate around the lists with the cursor You can simply overtype existing data or delete an entire listYou 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, 1510, 9, 9, 12, 15 You need to push EXE after each numberYou need to push EXE after each number The top row of function keys are used in conjunction with the screenThe 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, INSUse 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?Move the cursor onto the 12 in the list, press F1 (DEL) – what happens? Now press F3 (INS) – what happens?Now press F3 (INS) – what happens? Overtype the 0 with 8.Overtype the 0 with 8. Move the cursor to any position in List 1. Then press F2 (DEL-A). What happens? Press F1 (YES).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, 17Enter the following data into List 1 : 10, 8, 9, 12, 15, 8, 3, 17 Press CALC (F2 ), then 1 VAR (F1)Press CALC (F2 ), then 1 VAR (F1) Use the cursor to scroll downUse the cursor to scroll down Check that n=8 (this this a good way to check you haven’t missed any data)Check that n=8 (this this a good way to check you haven’t missed any data) Write down the mean and standard deviation, and the median and quartiles (Q1 & Q3).Write down the mean and standard deviation, and the median and quartiles (Q1 & Q3). What is the range of the data?What is the range of the data? Press QUIT when you have finishedPress QUIT when you have finished

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Statistical graphs Press GRPH (F1 )Press GRPH (F1 ) Use to obtain SEL(ect) & SETUse to obtain SEL(ect) & SET Press SET (F4 )Press SET (F4 ) Use the cursor to move down the settings listUse the cursor to move down the settings list Notice how a new set of choices appears at the bottom of the screen for each settingNotice 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 : PieG-Type : Pie Data : List1Data : List1 Display : DataDisplay : Data Set up StatGraph2 with G-Type : Box (you will need to use )G-Type : Box (you will need to use ) XList : List1XList : List1 Freq : 1Freq : 1 Now press QUIT

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Draw your statistical graphs and use Trace (F1) Press GRPH (F1), then GPH1Press GRPH (F1), then GPH1 QUIT and press GRPH then GPH2QUIT and press GRPH then GPH2 Now press SHIFT followed by TraceNow press SHIFT followed by Trace Use the horizontal cursor to locate points on the box chartUse the horizontal cursor to locate points on the box chart Sketch the box chart labelling the 5 points that Trace shows you.Sketch the box chart labelling the 5 points that Trace shows you. Use G T to return to the statistics screen and then QUITUse G T to return to the statistics screen and then QUIT Explain what the box plot shows.Explain what the box plot shows.

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Analysing grouped data AgeFrequency 155 1628 1759 1844 1923 2013 214 Delete any previous dataDelete any previous data Enter data opposite into Lists 1 & 2Enter data opposite into Lists 1 & 2 Discuss in your group what this data meansDiscuss 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 – e nter CALC & press SETThe SET function assigns statistical variables to your data lists – e nter CALC & press SET Assign List1 to 1Var X and List2 to 1Var F (Discuss what this means – why not 2Var?)Assign List1 to 1Var X and List2 to 1Var F (Discuss what this means – why not 2Var?) QUIT to return to the List screenQUIT to return to the List screen Enter CALC, 1VAR and scroll down the resultsEnter 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 surveyedFind the number of students who were surveyed Find the mean ageFind the mean age Find the median age & the quartilesFind the median age & the quartiles Make a boxplot & copy it – show the position of the mean on your sketchMake a boxplot & copy it – show the position of the mean on your sketch QUITQUIT

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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)Enter the data in List 1 (Age) & List 2 (Height) Use CALC and SET to to set up 2Var X: List1 2Var Y: List2 2Var F: 1Use CALC and SET to to set up 2Var X: List1 2Var Y: List2 2Var F: 1 QUIT, press CALC and 2VARQUIT, press CALC and 2VAR

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Data showing the ages and heights of some children Age in months 18192021222324 Height in cm 76.177.078.278.278.879.779.9

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

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

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Advanced analysis Here’s some more data to add to your listsHere’s some more data to add to your lists Draw a scattergram but this time choose x^2Draw a scattergram but this time choose x^2 Write down the equationWrite down the equation Compare the x and x^2 graphs and explain what this showsCompare the x and x^2 graphs and explain what this shows Age28323640 Height83.087.390.695.5

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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 redrawnIf 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 dataAfter 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 useYou can COPY the equation into the Graph Functions list for later use

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End of Statistics section

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

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Working with Graphs From the menu, enter the GRPH modeFrom the menu, enter the GRPH mode Type 2X+3 (use the X,T key) next to Y1 then EXEType 2X+3 (use the X,T key) next to Y1 then EXE Press EXE again (or DRAW)Press EXE again (or DRAW) Use Zoom (F2) OUT to display both interceptsUse Zoom (F2) OUT to display both intercepts Use Trace (SHIFT F1) to find the coordinates of the interceptsUse Trace (SHIFT F1) to find the coordinates of the intercepts Make a rough sketch of the graph labelling the interceptsMake a rough sketch of the graph labelling the intercepts

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Adjusting the view Press GT a few times and see what happens.Press G T a few times and see what happens. Press SHIFT F3 to obtain the V(iew) Window.Press SHIFT F3 to obtain the V(iew) Window. Use the cursor to move down the settings – discuss what they all do.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.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.Redraw the graph.

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Investigating graphs Press GT to return to the Graph Function screenPress G T to return to the Graph Function screen At Y2 type in 5 – X and draw the graphsAt Y2 type in 5 – X and draw the graphs Adjust the View to show all intercepts – add the new graph to your sketchAdjust 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) Press Trace (SHIFT F1) Use the left-right cursor to move along a graphUse the left-right cursor to move along a graph The up-down cursor enables you to jump to the other graphThe up-down cursor enables you to jump to the other graph Find the coordinates of the intersection as accurately as you canFind 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.Now use Zoom and Trace to improve your accuracy – write down your answer to 3 dp.

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Check with algebra Here are the two equations again y = 2x + 3 and y = 5 – xHere are the two equations again y = 2x + 3 and y = 5 – x Solve them algebraically in your groups.Solve them algebraically in your groups. Compare your answers to what you got for the graphical solution.Compare your answers to what you got for the graphical solution.

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Moving on … Quadratic transformations Delete all previous graph functionsDelete all previous graph functions Draw Y1= X 2 and set the View to INIT(ial)Draw Y1= X 2 and set the View to INIT(ial) Draw Y2= (X–3) 2 and Y3= (X+2) 2Draw Y2= (X–3) 2 and Y3= (X+2) 2 Return to the Graph Functions - investigate how to select and deselect functions.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.Make a labelled sketch showing all 3 graphs, their equations and x-intercepts.

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What’s the rule? Make a table like the one aboveMake a table like the one above What do you think the rule is? Make up another equation and predict the transformation.What do you think the rule is? Make up another equation and predict the transformation. Verify your prediction using the calculatorVerify your prediction using the calculator Equation Description of the transformation from x 2

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More transformations… Delete or deselect functions Y2 & Y3Delete or deselect functions Y2 & Y3 Draw Y= X 2, Y= X 2 + 2 and Y= X 2 – 3Draw Y= X 2, Y= X 2 + 2 and Y= X 2 – 3 Adjust the View to show all the y-intercepts and copy a sketchAdjust the View to show all the y-intercepts and copy a sketch Make a new table showing the transformationsMake a new table showing the transformations Predict, verify and formulate the rule as before.Predict, verify and formulate the rule as before. What’s the difference between the rules?What’s the difference between the rules?

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Combining transformations On the next slide are some quadratic functionsOn the next slide are some quadratic functions Each is a double transformation from Y= X 2 – describe both transformations fully.Each is a double transformation from Y= X 2 – describe both transformations fully. Predict what the graphs will look like and sketch them.Predict what the graphs will look like and sketch them. Verify using the calculator.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 functionsDelete all previous functions Press SET UP (SHIFT MENU)Press SET UP (SHIFT MENU) Change Angle to Deg(rees)Change Angle to Deg(rees) QUIT and enter Y1= sin XQUIT and enter Y1= sin X Set the View to TRIG & draw the graphSet the View to TRIG & draw the graph Make a rough labelled sketchMake a rough labelled sketch Show the coordinates of all intercepts and the maximum & minimum pointsShow the coordinates of all intercepts and the maximum & minimum points

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Solve a trig equation Return to Graph FunctionsReturn to Graph Functions Enter another equation Y2 = 0.5Enter another equation Y2 = 0.5 Draw the graphs and use them to solve sin x = 0.5Draw 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.Use Trace (and Zoom) to find four solutions to this equation as accurately as you can. Sketch and label your graphsSketch and label your graphs How are the solutions related to each other?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 UPEnter RUN mode, then SET UP Change F-Type to ParametricChange F-Type to Parametric QUIT and enter GRAPH modeQUIT and enter GRAPH mode DELete existing functionsDELete existing functions

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Demonstrate projectile motion QUIT RUN mode and enter GRAPHQUIT RUN mode and enter GRAPH Set up the V-Window to Xmin: 0, max: 280, scl:20 Ymin: -20, max: 70, scl: 10 Tmin: 0, max: 8, ptch: 0.1Set up the V-Window to Xmin: 0, max: 280, scl:20 Ymin: -20, max: 70, scl: 10 Tmin: 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 20 0 to the horizontal.A projectile is fired at a speed of 50 m/s, and an angle of 20 0 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 firingWrite 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 = ….Enter these equations as Xt1= … and Yt1 = ….

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Projectile task You should have written Xt1 = 50Tcos20 and Yt1 = 50Tsin20 – 4.9T 2You should have written Xt1 = 50Tcos20 and Yt1 = 50Tsin20 – 4.9T 2 If you did NOT write this, show on paper that these are correctIf 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 projectilePress 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 angleBy 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 chooseWrite 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 CoursesYou can find it on the Shared Drive (U:) in Maths – Advanced Level Courses You can also find it on CurWebYou can also find it on CurWeb

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