# C2 Hit List of Revision

A brief outline of the key things you need to remember for Core 2.

• Integration, Trigonometry, Sequences, Remainder Theorem, Logs

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• Created by: Rhi_
• Created on: 18-04-14 16:52

## Integration

1. Integrate to find the area under curves.

2. ∫ x^n dx = x^(n+1) / n+1 + c

3. If you cannot integrate, use the trapezium rule:

1/2xh[y0 + 2(y1 + y2 + y3) + y4] {etc.}

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## Trigonometry

1. Make sure you know the three curves, sin, cos and tan.

2. tan = sin/cos

3. sin^2 = 1 - cos^2 and cos^2 = 1 - sin^2

4. The sine and cosine rules:

Sine rule: sinA/a = sinB/b = sinC/c

Cosine rule: a^2 = b^2+c^2-2bc(cosA)

5. The area of a triangle: 1/2absinC

π radians = 180 degrees, L = rθ, A = 1/2r^2θ

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## Sequences

All of these sequences are in the formula book, but make sure you know how to use them.

These may look complicated at first, so make sure you understand them and can use them.

Arithmetic Progressions

1. nth term: Un = a + (n-1)d

2. the sum of: Sn = n/2[2a + (n-1)d]

Geometric Progressions

1. nth term: Un = ar^n-1 (= a x r^n-1 NOT (ar)^n-1)

2. the sum of: Sn = a(1-r^n)/(1-r)

3. sum to infinity: a/(1-r) ........... (ONLY if -1<r<1)

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## Binomial Theorem

Here's an example, make sure you understand it. (C = button on calucator)

(1+X)^4

1^4 + 1^3 x 4C1 x X + 1^2 x 4C2 x X^2 + 1^1 x 4C3 x X^3 + X^4

Explanation if (1+X)^4 = (a+X)^b:

a^b x bC0 x X^0 + a^(b-1) x bC1 x X^1 + a^(b-2) x bC2 x X^2 + a^(b-3) x bC3 x X^3 + a^(b-4) x bC4 x X^4

Patterns:  a's power, b, is decreasing

X's power is increasing

C is increasing

However, it cancels down as bC0, X^0, a(b-4) and bC4 (in bold) all equal 1 in (1+X)^4, as they equal 4C0, X^0, 1(4-4), and 4C4, and so would not make a difference.

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## Remainder Theorem

If f(x) is divided by x-a, then R=f(a) (R = remainder)

For example:

f(x) = x^2 + 2x + 2, divided by (x-4)

Remainder = f(4)

So replace all of the 'x' with the 4, and work it out.

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## Logarithms

a^x = b --> x = log(↓a)b

log a + log b = log ab

log a - log b = log a/b

log a^n = n log a

Help:

log(↓a)b = means the a is lower down than the log and the b, to make it clear that a is not multiplyed by b

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