Using Graphical
Calculators in the
Classroom
Richard Tarry
Sept 2004
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
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
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
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
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!
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
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
Some easy calculations
Do the following calculations and
write down your answers to 3 sf.
1.
2.
3.
4.
5.
6.
7.
8.
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 π
Answers are on the next slide
Answers (all to 3 sf)
1.
2.
3.
4.
5.
6.
7.
8.
15.6
37.1, 35.1
1.21
10.8, 3.55
4.63
-74.1
2.45 x 1015
50.3
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
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
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
Now start the RUN
tasks…
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
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
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.
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
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.
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!)
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
Generating a sequence
• 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, 1612.75, 1673…, 1737…
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)
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?
End of RUN mode
exercises
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
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
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
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).
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 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
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
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
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.
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
16
17
18
19
20
21
5
28
59
44
23
13
4
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
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
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
Data showing the ages and
heights of some children
Age in
18
months
Height
in cm
19
20
21
22
23
24
76.1 77.0 78.2 78.2 78.8 79.7 79.9
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.
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.
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
Height 83.0
32
36
40
87.3
90.6
95.5
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
End of Statistics
section
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
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
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.
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
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.
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.
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.
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
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?
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.
Transformations….
Here they are…
Y
Y
Y
Y
Y
=
=
=
=
=
(x
(x
(x
(x
(x
- 5)2 + 3
+ 3)2 – 1
– 10)2 – 50
+ 100)2 + 500
– 200)2 - 80
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
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?
End of GRAPHING
sessions !!
Advanced stuff – for
A2
More advanced graphing
- parametrics
•
•
•
•
Enter RUN mode, then SET UP
Change F-Type to Parametric
QUIT and enter GRAPH mode
DELete existing functions
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
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 = ….
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
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
THE END
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