Rate of change 1

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Rate of change (1)

• Understanding Gradient
• new symbology

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Gradient

• Gradient tells us how steep something is.

This child doesnt have a clue about gradient.
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Gradient as Rate of Change
y
Temp. (oc)
15 oc
500m
x
Altitude (m)
gradient change in y 15 0.03 oc per
m change in x 500
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A bit of new symbology
y
x
difference in y difference in x
gradient of line
PRONOUNCED dee-why by dee-ex
Your mathematical life has now changed - this
will be with you for ever
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For these lines..
y 2x 1 y 5x -1 y 0.5x - 27 y 6 - 4x
What is ?
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Other graphs
E.g distance vs. time
s is used to represent displacement (distance
from a point)
s
t
difference in s difference in t
gradient of line
The top letter is always the y-axis and the
bottom letter always the x-axis
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Distance time graphs
40 m
5 sec
What is happening?
What is happening?
Increase in rate of change of distance - speed
increasing - acceleration
Rate of change of distance is constant - speed is
constant
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Distance time graphs
s is used to represent displacement (distance
from a point)
The tangent to the curve gives the gradient at
that point
which is the speed
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Activity sketch these graphs Underneath sketch
graphs of gradient vs time
yax3bx2cxd
yax2bxc
ymxc
t
t
t
yconst.
yax2bxc
ymxc
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Activity

• Turn to page 109 of your text book and follow
• Investigating the slopes of curves