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
Let’s 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 2 STAT 4 GRAPH 5 TABLE 8 CONT
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

6. 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!

7. 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

8. 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

9. Some easy calculations
Do the following calculations and write down your answers to 3 sf.
4.1 x 3.8
6.5  … then edit to 6.5  0.185
sin30 + cos45
40 + 20 …. then edit to 4.4 + 2.1
( )  0.9
4.15  (-2.5)3
3.5x108 X
16 π
Answers are on the next slide

10. Answers (all to 3 sf)
15.6
37.1, 35.1
1.21
10.8, 3.55
4.63
-74.1
2.45 x 1015
50.3

11. 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

12. 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

13. 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.

14. Now start the RUN tasks…

15. 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

17. 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)
Challenge: Find the equation of each line.

18. 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 π key and find this volume
You should get an answer of 1726 cm3

19. 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.

20. Volumes …
You should have written h=500÷(πx5.52) 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!)

21. 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 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

22. Generating a sequence Type 1.05Ans-20 EXE
Write down the first 4 terms of the sequence un+1 = 1.05Un – 20 with u0 = 1500
First type 1500 EXE (This stores 1500 in Ans)
Type 1.05Ans-20 EXE
Press EXE again, and again… Describe a situation that this sequence could model.
You should get answers 1555, , 1673…, 1737…

23. Challenge… From an AS Using Maths paper
Tw = 33 – (33 – T)[ v – 0.02v]
Tw is windchill temperature (oC)
T is temperature out of the wind (oC)
V is the wind speed (mph)

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

25. End of RUN mode exercises

26. 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

27. 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

28. 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

29. 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).

30. Working with some data
Enter the following data into List 1 : , 8, 9, 12, 15, 8, 3, 17
Press CALC (F2 ), then 1 VAR (F1)
Use the cursor to scroll down
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).
What is the range of the data?
Press QUIT when you have finished

31. 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

32. 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

33. 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.

34. Analysing grouped data
Delete any previous data
Enter data opposite into Lists 1 & 2
Discuss in your group what this data means
Age
Frequency 15 5 16 28 17 59 18 44 19 23 20 13 21 4

35. 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

36. 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

37. 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: List1 2Var Y: List2 2Var F: 1
QUIT, press CALC and 2VAR

38. 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
78.8
79.7
79.9

39. 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.

40. 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.

41. Advanced analysis Here’s some more data to add to your lists
Draw a scattergram but this time choose x^2
Write down the equation
Compare the x and x^2 graphs and explain what this shows
Age 28 32 36 40
Height
83.0
87.3
90.6
95.5

42. 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

43. 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

45. Working with Graphs From the menu, enter the GRPH mode
Type 2X+3 (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

46. 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.

47. 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

48. 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.

50. Moving on … Quadratic transformations
Delete all previous graph functions
Draw Y1= X2 and set the View to INIT(ial)
Draw Y2= (X–3)2 and Y3= (X+2)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. What’s 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

52. 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.
What’s the difference between the rules?

53. 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.

54. Transformations…. Here they are… Y = (x - 5)2 + 3 Y = (x + 3)2 – 1

55. 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

56. 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?

57. End of GRAPHING sessions !!

58. Advanced stuff – for A2

59. More advanced graphing - parametrics
Enter RUN mode, then SET UP
Change F-Type to Parametric
QUIT and enter GRAPH mode
DELete existing functions

60. Demonstrate projectile motion
QUIT 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: 0.1

61. 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 = ….

62. Projectile task
You should have written Xt1 = 50Tcos20 and Yt1 = 50Tsin20 – 4.9T2
If you did NOT write this, show on paper that these are correct

63. 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

64. THE END

65. 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