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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How to convert radians -> degrees? Find 3π/5 radians in degrees.

360⁰ = 2π so, 1 radian = 360/2π 3π/5 x 360/2π = 108⁰

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