A. Some basic operations
(i) Entering an equation in ‘GRAPH’ mode
Example:
(ii) Zooming or changing the viewing window
- Axis ranges:
- Or use ‘ ZOOM ’ menu via [F2]
(iii) Deleting a function
Highlight the equation using cursor
Then use [F2] to delete and [F1] to confirm
(iv) Exploring the effect of gradient in
(a) ‘ GRAPH ’ mode
with
(b) ‘ DYNA ’ mode
with in increments of
Activity: Explore the effect of changing the variable in using the two modes above.
Question: Which calculator mode did you find gave you greatest insight into what was happening?
Why? Which do you think would students find most useful?
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B: Intersection of two lines
Example: Enter the following equations in ‘ GRAPH ’ mode
,
Question: Find the point of intersection of the two lines using G-SOLVE
[F5] function.
C: Intersection of Lines and Parabolas
Example:
Enter the following equations in ‘
GRAPH
’ mode
,
Note that when using G-SOLVE to find more than one point of intersection, enables you to move to different solutions.
Exercise:
Q1. Find the point(s) of intersection for the following pairs of functions
(i) and .
(ii) and
(iii) and
(iv) and
(v) and
Q2. The three lines , and form a triangle.
Find the coordinates of the vertices of the triangle.
Hint: You will need to select 2 of the three lines at a time using and
Q3. Change one coefficient of or so that
(a) there are two points of intersection and
(b) there is one point of intersection.
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A. ‘CONICS’ mode
(i) Using the equation form
( ) ( )
.
Enter the following values:
Using G-SOLVE [F5] function, find the centre and radius of the circle.
Activity: Complete the table below for your choice of values for :
( ) ( )
Centre
Question: Why does it state that ?
(ii) Using the equation form
Enter the following values:
Using G-SOLVE [F5] function, find the centre and radius of the circle.
Activity: Complete the table below for your choice of values for :
Question: Why does it state that ?
Centre
Radius
Radius
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B: ‘GRAPH’ mode
(i) Equations of circles
In ‘ GRAPH ’ mode equations have to be entered in the form
With some algebraic manipulation the equation of a circle with centre
( )
and radius can be written in the usual form as
( ) ( ) and then rearranged to give √ ( )
This has to be entered as two separate equations on the graphics calculator:
Note: Equations can be copied and pasted by highlighting the equation and then using the ‘CLIP’, ‘COPY’ and ‘PASTE’ operations:
(ii) Intersection of circles & lines
Example: Find the points where the line meets the circle
( ) ( )
and find the length of the chord that is formed.
Exercise:
Q1. Find the points of intersection
( ) ( )
and
( ) ( )
.
Q2. Find the point of intersection of and and describe the geometrical situation.
Q3. Find an equation of a circle that …
…has a radius of ;
…doesn’t cross either axis;
…passes through the origin;
…has as a diameter.
Q4. Find the equation of a circle with centre
( )
which has the point
( )
on its circumference.
Does the point
( )
lie on the circle?
Q5. For each equation either give the centre and radius of the circle or a reason why it is not a circle.
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Some Circles Activities:
Q1. Can you create the following diagrams on your graphics calculator?
Circles touching the origin Concentric circles
Straight line and circle 4 large and one small circle
Q2. Draw all the possible ways in which two circles can be arranged in relation to one another. Try to produce a diagram of each arrangement on your calculator and write down the equations of circles you used.
Q3. Window challenge
This is a photo of a window in a church building in
Stratford-on-Avon, Warwickshire.
Can you re-create the outline of it on your graphical calculator?
5 of 5 Aug 2013 © MEI