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Who am I?
Peter Hayes –
I teach Mathematics at Ellesmere College an independent school in Shropshire, part of the Woodard corporation.
I have taught Maths at all levels from Year 7 to Further Mathematics in the Upper Sixth.
Currently I am teaching Higher Level IB Maths and A level Core, Statistics and Mechanics.
Also have a passionate interest in Cricket i/c school cricket and yesterday I captained the Shropshire over 50 cricket side
TI‐nspire cx
MEI Summer 2012
P J Hayes ‐ MEI 2012
Who am I?
Today
Peter Hayes –
Students in our IB classes all have a nspire‐cx.
I also have a passionate interest in Cricket being master i/c of school cricket and yesterday I captained the Shropshire over 50 cricket side.
P J Hayes ‐ MEI 2012
Share some of the ways my students use the TI‐nspire cx to explore and solve problems using some of the special features of the calculator:
Sliders
Spreadsheet
Interactive notes
Data capture
The analytic window 3
Linking notes and spreadsheet
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Sliders
Add a geometry application below the notes application on the same page:
Dynamic notes and spreadsheets
In a new problem open a spreadsheet page and a notes page.
Insert a Maths Box into the Notes pages and enter nCr(5,2)
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Sliders
Pascal’s triangle
Add a slider using the variable n and rewrite nCr(5,2) as nCr(n,2)
P J Hayes ‐ MEI 2012
Name column A pascal
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Pascal’s triangle
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seq() function
Name column A pascal
Name column A pascal
Use the seq function in the formula row of column A to enter: =seq(nCr(n,r),r,0,n)
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Pascal’s triangle
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Dynamic notes page
Define n = 5
Enter seq(ncr(n,r),r,0,n)
• Enter pascal inside a Maths Box:
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Dynamic notes page
Using nsolve
Use the slider to change the value of n
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nSolve(equation, variable, min value)
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Solving triangles
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Sine rule
In the triangle below find angle C.
In the triangle below find angle C.
58o
58o
C = 91.3o
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Multiple lines
Multiple lines
Open new problem with graph page and notes page.
Name the sequence {1,2,3} →a in a notes page.
Enter f1(x) = a.x on the graphs page:
Open new problem with graph page and notes page.
Name the sequence {1,2,3} → a in a notes page.
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Envelope of straight lines
Envelope of straight lines
Define two sequences on a notes page:
seq(n,n,‐1,1,0.2) →e
seq(n,n,‐4,4,1) →d
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Finding the equation
Envelope of straight lines
The lines appear to have an envelope with equation y2 = ‐ax
New problem with graphs page and notes page
Draw graph f1(x) = b.x – 1/b and on notes page define 2→b
Draw graph f1(x) = (b+h).x – 1/(b+h) and on notes page define 0.01→h
The lines appear to have an envelope with equation y2 = ‐ax
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Finding the equation
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Finding the equation
Find point of intersection of two lines
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Finding the equation
Capture data to spreadsheet
Store coordinates of point of intersection as (x1,y1)
Calculate the value of the text expression ‐(yc)2/xc
Store coordinates of point of intersection as (x1,y1)
Calculate the value of the text expression ‐(yc)2/xc
Equation of curve y2 = – 4x
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Method 2 – Show that the equation of the tangent is of the form y = b.x – 1/b
Open new problem with a geometry page. This time open an analytic window:
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Calculate equation of tangent
Calculate equation of tangent
Adjust analytic window to a suitable size and scale.
New operating system allows us to enter, using text, the equation x = – y2/4
Drag to either axis and curve will appear:
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Calculate equation of tangent
Check calculation
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Draw tangent to curve.
Find equation of tangent.
Find the coordinates of the point where tangent touches curve.
Find the gradient of the tangent (using point of contact).
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Calculate equation of tangent
Equation of tangent with slope m at point (x1,y1)
y – y1 = m(x – x1)
or y = mx + (y1 – mx1)
Using text calculate the value of m(y1 – mx1).
Expect value of ‐1.
P J Hayes ‐ MEI 2012
THE END
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