AS A Level 9231 9709 Mathematics MF19 2020
List MF19
List of formulae and statistical tables
Cambridge International AS & A Level Mathematics (9709) and Further Mathematics (9231)
For use from 2020 in all papers for the above syllabuses.
CST319 *2508709701*
PURE MATHEMATICS
Mensuration
Volume of sphere =
4 3
r 3
Surface area of sphere = 4r2
Volume
of
cone
or
pyramid
=
1 3
?
base
area
?
height
Area of curved surface of cone = r ? slant height
Arc length of circle = r ( in radians)
Area
of
sector
of
circle
=
1 2
r
2
( in radians)
Algebra For the quadratic equation ax2 + bx + c = 0 :
For an arithmetic series:
x = -b ? b2 - 4ac 2a
un = a + (n -1)d ,
Sn
=
1 2
n(a
+
l)
=
1 2
n{2a
+
(n
- 1)d }
For a geometric series:
un = ar n-1 ,
Sn
=
a(1 - 1-
rn) r
(r 1) ,
S
=
a 1- r
( r a)
( x < a)
4
FURTHER PURE MATHEMATICS
Algebra Summations:
n
r
=
1 2
n(n
+ 1)
,
r =1
n
r2
=
1 6
n(n
+ 1)(2n
+ 1)
,
r =1
n
r3
=
1 4
n2 (n
+ 1)2
r =1
Maclaurin's series:
f(x) = f(0) + x f (0) + x2 f (0) + K + xr f (r) (0) +K
2!
r!
ex = exp(x) = 1 + x + x2 +K + xr +K
2!
r!
ln(1 + x) = x - x2 + x3 -K + (-1)r+1 xr + K
23
r
sin
x
=
x
-
x3 3!
+
x5 5!
-K+
(-1)r
x 2 r +1 (2r +1)!
+
K
cos x = 1 - x2 + x4 -K + (-1)r x2r + K
2! 4!
(2r)!
tan -1
x
=
x-
x3 3
+
x5 5
-K + (-1)r
x 2 r +1 2r +1
+
K
sinh
x
=
x
+
x3 3!
+
x5 5!
+K+
x 2 r +1 (2r +1)!
+
K
cosh x = 1 + x2 + x4 + K + x2r + K
2! 4!
(2r)!
tanh -1
x
=
x+
x3 3
+
x5 5
+K+
x2 2r
r +1
+1
+
K
(all x) (?1 < x 1)
(all x) (all x) (?1 x 1) (all x) (all x) (?1 < x < 1)
Trigonometry
If
t
=
tan
1 2
x
then:
sin x = 2t 1+ t2
and
cos x = 1 - t2
1+ t2
Hyperbolic functions cosh2 x - sinh2 x 1 ,
sinh 2x 2sinh x cosh x ,
sinh-1 x = ln(x + x2 +1)
cosh 2x cosh2 x + sinh2 x
cosh-1 x = ln(x + x2 -1) (x 1)
tanh -1
x
=
1 2
ln
1 1
+ -
x x
(| x | < 1)
5
................
................
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