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A Level Maths equations to memorise > ... > Flashcards

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1
Q

area of sector

A

0.5*r(^2)θ

2
Q

area of segment

A

0.5r^2 (θ − sin(θ))

3
Q

arc length

A

4
Q

area of trapezium

A

(a+b)/2 *h

5
Q

cos2A

A

cos(^2)A-sin(^2)A
2cos(^2)A-1
1-2sin(^2)A

6
Q

sin2A

A

2sinAcosA

7
Q

tan2A

A

(2tanA)/(1-tan(^2)A)

8
Q

derivative of a^(kx)

A

a(^kx) k ln a

9
Q

integral of f(AX+B)

A

1/a f(ax+b)

10
Q

prove the sum of the first n terms of an arithmetic series is 1/2n(2a+(n-1)d)

A
  1. Sn= a, a+d, a+2d+…….+ a+(n-2)d + a+(n-1)d
  2. reverse sequence(Sn): a+(n-1)d + a+(n-2)d +………+ a+2d + a+d + a
  3. add the two sequences: 2Sn= n(2a+(n-1)d)
  4. divide by 2: Sn= n/2 (2a+(n-1)d)
11
Q

Proof of geometric series

A

(1) Sn= a+ ar +ar2+ ar3+…..+ar(n-2)+ ar(n-1)
(2) rSn= ar+ ar2+ ar3 +…..+ ar(n-1) + ar(n)
(1)-(2) Sn-rSn = a-ar(n)
Sn(1-r)= a(1-r(n))
Sn= a(1-r(n))/1-r

12
Q

Volume of sphere

A

4/3pi r^2

13
Q

prove the first principles, that the derivative of sin x is cos x

A

f’(x)= (f(x+h)-f(x))/h
(sin(x+h)-sin(x))/h
(sinx cosh + cosx sinh - sin x)/ h
(cos h -1)/h)sinx + (sin h)/h)cosx

cos h-1/ h ——> 0
sin h/h——>1
0sin x +1 cosx
=cos x

14
Q

how to convert degrees to radians

A

multiply value of degrees by pi/180

15
Q

proof of infinite primes

A

Assumption: there are a finite number of prime numbers,
p1, p2, p3, up to pn
. Let X= (p1* p2* p3……Pn)+1
None of the prime numbers are a factor of X as they all leave a remainder of 1 when X is divided by them.
But X must have at least one prime factor.
This is a contradiction

16
Q

area of parrellogram

A

side a* side b* sin((angle between A and B))

17
Q

when a vector has travelled north east what does that mean

A

the I components are equal to the j components