# Core 2 (C2)

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What is the formula for the arc length of a sector?
l = r x θ
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What is the formula for the area of a sector?
½ x r^2 x θ
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How do you use the trapezium rule?
h=(b-a)/n to find width of strips. These are what X values increase by to get to b. (The first value is y0) Substitute x values into the formula to find y. Sub into trapezium rule formula (in formula book)
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LogaA = ?
1. -The logarithm of a number to the same base is always 1
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How to find x when N=a^x
X=logaN a is the base.
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log1 = ?
0. -The logarithm of 1 to any base is always 0
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log N^k
klogN
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logaX-logaY = ?
loga(X/Y)
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logaX + logaY = ?
loga(XY)
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Differentiate y=5x - 4/(3x^2) +15
dy/dx = 5 + 8/3 x^ -3
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How do you integrate?
Increase the power by one, divide by the new power
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When do you integrate?
To find the area under a curve or to find y
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what does y=af(x) do to the graph y=f(x)?
Stretch in the Y direction of scale factor a
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what does a translation of [a, b] do to the graph y=f(x) ?
y-b = f(x-a) or y=(f(x-a)+b
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What does a translation of y=f(2x) do to y=f(x)?
Stretched scale factor 1/2 in x direction. Opposite happens in X
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What does a translation of y=f(x/a) do to y=f(x)?
Stretch in x direction, scale factor a.
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what turns y=f(x) into y=f(-x)?
Reflection in the y axis (x=0)
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What turns y=f(x) into y=-f(x)
Reflected in the x axis, (y=0)
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What has happened to the graph y=f(x) to turn it into y=f(x-a)
Has been translated by the vector [a 0], moved right by a.
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How to find the nth term in geometric series?
Un = ar^(n-1)
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What form is a geometric series in?
a + ar + ar^2 + ar^3...
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How to find r? (common ratio)
divide the second term by the first term (ar/a)
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How to find the nth term in a geometric series? (Don't have to know this, it is in the formula book)
ar^(n-1) a = the first term, r= the common ratio, n= the term
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How do you convert 20⁰ into radians?
360⁰ = 2π so, 1⁰ =2π/360 20⁰ -> (20 x 2π)/360 = 40π/360 = π/9 radians
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360⁰ = 2π so, 1 radian = 360/2π 3π/5 x 360/2π = 108⁰
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What are the trigonometric identities?
cos^2 θ + sin^2 θ = 1 and tanθ = sinθ/cosθ (Remember: sin(gerine)/cos(gerine) = Tan(gerine))
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## Other cards in this set

### Card 2

#### Front

What is the formula for the area of a sector?

½ x r^2 x θ

### Card 3

#### Front

How do you use the trapezium rule?

LogaA = ?

### Card 5

#### Front

How to find x when N=a^x

#### Back

Report

For integration you raise the power by one then divide by the new power, 11/26 decrease needs to be increase.

Report

Oops thanks for noticing!

Report

Gd stuff...:)

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