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Arithmetic Sequences!
Where;
A = first number
n = number of terms
D = difference
Generalizing Arithmetic
Sequences
a , (a+d) , (a +2d) , (a + 3d) .... And so
the last term must be (a+ (n-1) d)
If we pair up all the terms in the
sequence we can easily find the
sum of all the terms. Eg with the
sequence 1, 2, 3 ...+ ...+ 10
Generalizing the sum of all n terms 1+9 8+2 7+3 4+6 and 5
Pair up; a + (a+(n-1)d) = 2a + (n-1)d 2nd Pair; (a+2d) + (a+(n-2)d = 2a + (n-1) d
They all equal 2a + (n-1)d! So we simply have to times this by the number of pairs we
have which is n/2. So we have come to n/2 (2a +(n-1)d…read more

Slide 3

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Differentiation!
Differentiation is finding the GRADIENT of a tangent at the point on the
curves
Finding the equation of the tangent;
Find the equation to the tangent of
the curve y=3x^2 + 2 at x =1
1) Differenciate the equation of curve
2) Substitute X =1 into the Differention to
find the gradient of the tangent
3) Substitute X = 1 into the original
equation of the curve to find a Y value
Handy Tip for 4) Plug all the values into y-y1 = M (x-x1)
remembering; Where M is the gradient
In Diffentiation we
Decrease the power
Finding the equation to the normal
In Integration we
We use the same method However;
Increase the power
Once we have differenciated and found the gradient
we then take the negative reciprocal of the gradient.…read more

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Integration!
Integration is the opposite of differentiation
Particular solutions a.k.a
finding C
·For example integrating (f)' 2x +
4
Gives us y = x^2 + 4x + c (the
general solution)
·If we are told that our curve
passes through the point (1,9)
Handy Tip for ·Then f(1) = 9 and so we
remembering; substitute 1 in;
In Diffentiation we 1 ^2 + 4(1) + C = 9
Decrease the power
In Integration we
Increase the power ·Therefore C must equal 4 and
so the equation of our curve is
Y = x^ 2 + 4x + 4 (the particular
solution)…read more

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Coordinate Geometry!
When you see intersecting
lines think of
Simultaneous equations!
·If two lines are
parallel they have the
same gradient.
·A perpendicular line
has a negative
reciprocal of the…read more

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Transforming
Graphs!
f(x)+a moves the graph up by a
f(x) -a moves the graph down by a
f(x+a) moves the graph to the left
f(x-a) moves the graph to the right
af(x) stretches the graph in the y axis by the scale of a
f(ax) stretches the graph in the x axis by a scale of 1/a…read more

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