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Mathematics A & B Revision Bundle II
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Formulae 
© OCR 2023 H230/01 Jun23 
x 
2 
2 
2 
h"0 h 
AS Level Mathematics A (H230) 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2 +f+ 
nCr 
a 
n-r 
b 
r +f+b 
n 
n e N , 
where 
nC = C = c 
n 
m = 
n! 
r n r r r!^n -rh! 
Differentiation from first principles 
fl^xh =...
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Formulae 
© OCR 2023 H230/01 Jun23 
x 
2 
2 
2 
h"0 h 
AS Level Mathematics A (H230) 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2 +f+ 
nCr 
a 
n-r 
b 
r +f+b 
n 
n e N , 
where 
nC = C = c 
n 
m = 
n! 
r n r r r!^n -rh! 
Differentiation from first principles 
fl^xh =...
1x sold
2 
© OCR 2023 H230/02 Jun23 
x 
2 
2 
Formulae 
AS Level Mathematics A (H230) 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2 +f+ 
nCr 
a 
n-r 
b 
r +f+ b 
n ^n e Nh, 
where nC = C = c 
n 
m = 
n! 
r n r r r!^n-rh! 
Differentiation from first principles 
fl^xh = lim f^x+hh-...
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© OCR 2023 H230/02 Jun23 
x 
2 
2 
Formulae 
AS Level Mathematics A (H230) 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2 +f+ 
nCr 
a 
n-r 
b 
r +f+ b 
n ^n e Nh, 
where nC = C = c 
n 
m = 
n! 
r n r r r!^n-rh! 
Differentiation from first principles 
fl^xh = lim f^x+hh-...
2 
© OCR 2023 H240/01 Jun23 
^ h 
= 
n+1 
2 
n 2 2 
L P 
2! r! 
dx dx 
Formulae 
A Level Mathematics A (H240) 
Arithmetic series 
S = 
1 
n^a + lh = 
1 
n"2a +^n - 1hd, 
Geometric series 
Sn 
= 
a 1-r 
n 
1 -r 
 a 
3 1-r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2...
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© OCR 2023 H240/01 Jun23 
^ h 
= 
n+1 
2 
n 2 2 
L P 
2! r! 
dx dx 
Formulae 
A Level Mathematics A (H240) 
Arithmetic series 
S = 
1 
n^a + lh = 
1 
n"2a +^n - 1hd, 
Geometric series 
Sn 
= 
a 1-r 
n 
1 -r 
 a 
3 1-r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2...
1x sold
2 
© OCR 2023 H240/02 Jun23 
^ h 
= 
n+1 
2 
n 2 2 
L P 
2! r! 
dx dx 
Formulae 
A Level Mathematics A (H240) 
Arithmetic series 
S = 
1 
n^a + lh = 
1 
n"2a +^n - 1hd, 
Geometric series 
Sn 
= 
a 1-r 
n 
1 -r 
 a 
3 1-r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2...
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© OCR 2023 H240/02 Jun23 
^ h 
= 
n+1 
2 
n 2 2 
L P 
2! r! 
dx dx 
Formulae 
A Level Mathematics A (H240) 
Arithmetic series 
S = 
1 
n^a + lh = 
1 
n"2a +^n - 1hd, 
Geometric series 
Sn 
= 
a 1-r 
n 
1 -r 
 a 
3 1-r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2...
1x sold
2 
© OCR 2023 H240/03 Jun23 
^ h 
= 
n+1 
2 
n 2 2 
2! r! 
dx dx 
Formulae 
A Level Mathematics A (H240) 
Arithmetic series 
S = 
1 
n^a + lh = 
1 
n"2a +^n - 1hd, 
Geometric series 
Sn 
= 
a 1-r 
n 
1 -r 
 a 
3 1-r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
...
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© OCR 2023 H240/03 Jun23 
^ h 
= 
n+1 
2 
n 2 2 
2! r! 
dx dx 
Formulae 
A Level Mathematics A (H240) 
Arithmetic series 
S = 
1 
n^a + lh = 
1 
n"2a +^n - 1hd, 
Geometric series 
Sn 
= 
a 1-r 
n 
1 -r 
 a 
3 1-r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
...
2 
© OCR 2023 H630/01 Jun23 
-1 
2 
2 
2 
L P 
2! r! 
Formulae AS Level Mathematics B (MEI) (H630) 
Binomial series 
(a + b) 
n = a 
n + 
nC1 
a 
n–1 
b + 
nC2 
a 
n–2 
b 
2 + ... + 
nCr 
a 
n–r 
b 
r + ... +bn n e N , 
n 
Jn 
N n! 
where Cr 
= n 
Cr 
= K 
r 
O = 
r!^n -rh! 
^1+xh 
n 
= 1+nx+...
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© OCR 2023 H630/01 Jun23 
-1 
2 
2 
2 
L P 
2! r! 
Formulae AS Level Mathematics B (MEI) (H630) 
Binomial series 
(a + b) 
n = a 
n + 
nC1 
a 
n–1 
b + 
nC2 
a 
n–2 
b 
2 + ... + 
nCr 
a 
n–r 
b 
r + ... +bn n e N , 
n 
Jn 
N n! 
where Cr 
= n 
Cr 
= K 
r 
O = 
r!^n -rh! 
^1+xh 
n 
= 1+nx+...
2 
© OCR 2023 H630/02 Jun23 
-1 
2 
2 
2 
L P 
2! r! 
Formulae AS Level Mathematics B (MEI) (H630) 
Binomial series 
(a + b) 
n = a 
n + 
nC1 
a 
n–1 
b + 
nC2 
a 
n–2 
b 
2 + ... + 
nCr 
a 
n–r 
b 
r + ... +bn n e N , 
n 
Jn 
N n! 
where Cr 
= n 
Cr 
= K 
r 
O = 
r!^n -rh! 
^1 + xh 
n 
= 1 +...
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© OCR 2023 H630/02 Jun23 
-1 
2 
2 
2 
L P 
2! r! 
Formulae AS Level Mathematics B (MEI) (H630) 
Binomial series 
(a + b) 
n = a 
n + 
nC1 
a 
n–1 
b + 
nC2 
a 
n–2 
b 
2 + ... + 
nCr 
a 
n–r 
b 
r + ... +bn n e N , 
n 
Jn 
N n! 
where Cr 
= n 
Cr 
= K 
r 
O = 
r!^n -rh! 
^1 + xh 
n 
= 1 +...
2 
© OCR 2023 H640/01 Jun23 
= 
r n r Kr 
O 
e 
n+1 
2 
Formulae A Level Mathematics B (MEI) (H640) 
Arithmetic series 
S = 
1 
n^a+lh = 
1 
n"2a+^n-1hd, 
n 2 2 
Geometric series 
Sn 
= 
a^1-r 
nh 
1 -r 
 a 
3 1 -r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2...
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© OCR 2023 H640/01 Jun23 
= 
r n r Kr 
O 
e 
n+1 
2 
Formulae A Level Mathematics B (MEI) (H640) 
Arithmetic series 
S = 
1 
n^a+lh = 
1 
n"2a+^n-1hd, 
n 2 2 
Geometric series 
Sn 
= 
a^1-r 
nh 
1 -r 
 a 
3 1 -r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2...
2 
© OCR 2023 H640/02 Jun23 
^ h 
= 
e 
n+1 
2 
n 2 2 
L P 
Formulae A Level Mathematics B (MEI) (H640) 
Arithmetic series 
S = 
1 
n^a + lh = 
1 
n"2a +^n - 1hd, 
Geometric series 
Sn 
= 
a 1-r 
n 
1 -r 
 a 
3 1-r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2...
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© OCR 2023 H640/02 Jun23 
^ h 
= 
e 
n+1 
2 
n 2 2 
L P 
Formulae A Level Mathematics B (MEI) (H640) 
Arithmetic series 
S = 
1 
n^a + lh = 
1 
n"2a +^n - 1hd, 
Geometric series 
Sn 
= 
a 1-r 
n 
1 -r 
 a 
3 1-r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2...
2 
© OCR 2023 H640/03 Jun23 
= 
e 
n+1 
2 
Formulae A Level Mathematics B (MEI) (H640) 
Arithmetic series 
S = 
1 
n^a+lh = 
1 
n"2a+^n-1hd, 
n 2 2 
Geometric series 
Sn 
= 
a^1-r 
nh 
1 -r 
 a 
3 1 -r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2 +f+ 
nCr 
a ...
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© OCR 2023 H640/03 Jun23 
= 
e 
n+1 
2 
Formulae A Level Mathematics B (MEI) (H640) 
Arithmetic series 
S = 
1 
n^a+lh = 
1 
n"2a+^n-1hd, 
n 2 2 
Geometric series 
Sn 
= 
a^1-r 
nh 
1 -r 
 a 
3 1 -r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2 +f+ 
nCr 
a ...
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