Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Mathematical Methods Formulas Cheat Sheet, Cheat Sheet of Mathematical Methods

Useful formula cheat sheet for your Mathematical Methods exam

Typology: Cheat Sheet

2019/2020

Uploaded on 11/27/2020

yorket
yorket 🇺🇸

4.4

(38)

276 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
MATHMETH EXAM 2
Mathematical Methods Formulas Cheat Sheet
Mensuration
area of a trapezium 1
2
abh+
()
volume of a pyramid
1
3
Ah
curved surface area
of a cylinder 2
π
  rh volume of a sphere 4
3
3
π
r
volume of a cylinder
π
 r 2harea of a triangle
1
2
bc Asin
()
volume of a cone 1
3
2
π
rh
Calculus
d
dx
xnx
nn
()
=1xdx
n
xcn
nn
=
++≠
+
1
1
1
1,
d
dx
ax banaxb
nn
()+
()
=+
()
1() ()
() ,ax bdxan ax bcn
nn
+=
+++≠−
+
1
11
1
d
dx ea
e
ax ax
()
=edxa
ax ax
d
dx
xx
e
log()
()
=
1
1
0
x
dx xcx
e
=+>
log(),
d
dx
ax
aa
xsin( )cos
()
()
= sin( )cos()ax dx aax c=− +
1
d
dx
ax
aa
xcos( )
()
= sin( )cos( )sin ()ax dx aax c
=+
1
d
dx ax
a
ax
aa
xtan( )()
()
==cos sec
()
2
2
product rule
d
dx
uv u
dv
dx
v
du
dx
()
=+
quotient rule d
dx
u
v
v
du
dx u
dv
dx
v
=
2
chain rule
dy
dx
dy
du
du
dx
=
pf2

Partial preview of the text

Download Mathematical Methods Formulas Cheat Sheet and more Cheat Sheet Mathematical Methods in PDF only on Docsity!

MATHMETH EXAM 2

Mathematical Methods Formulas Cheat Sheet

Mensuration

area of a trapezium 1 2

( a^ + b h ) volume of a pyramid 1

Ah

curved surface area of a cylinder 2 π^ rh^ volume of a sphere^

π r^3

volume of a cylinder π r^2 h area of a triangle

bc sin ( A )

volume of a cone

π r h^2

Calculus

d dx

( x^ n^ ) =^ nxn −^1 x dx^

n

n (^) = x n c n

∫ 1 + +^ ≠ −

d dx

( (^ ax^ + b^ ) n^ ) =^ an ax (^^ + b )^ n −^1 (^ )^

ax b dx ( ) , a n

  • n^ = ax b n c n

∫ 1 +^ + +^ ≠ −

d dx

( e^ ax^ ) =^ aeax ∫ e^ ax^ dx^^ =^ a^1 e^ ax + c

d dx

x e x

( log ( )) =^1

∫ x dx^ =^ log ( ) ex^^ +^ c^ , x >

d dx

( sin ( ax^^ )^ ) =^ a^ cos (^ ax ) ∫ sin (^ ax dx )^^ = −^ a^1 cos (^ ax )^ + c

d dx

( cos ( ax )) = − a sin ( ax ) ∫ cos ( ax dx ) = a^1 sin ( ax )+ c

d dx

ax a ax

tan ( ) a ax ( )

cos 2 sec (^2 )

product rule d dx uv u dv dx v du

( ) = dx

  • quotient rule d dx

u v

v du dx u dv dx v

^

2

chain rule dy dx

dy du

du dx

3 MATHMETH EXAM

Probability

Pr( A ) = 1 – Pr( A ′) Pr( AB ) = Pr( A ) + Pr( B ) – Pr( AB )

Pr( A | B ) = Pr Pr

A B

B

mean μ = E( X ) variance var( X ) = σ 2 = E(( X – μ) 2 ) = E( X^2 ) – μ^2

Probability distribution Mean Variance

discrete Pr( X = x ) = p ( x ) μ = ∑ x p ( x ) σ 2 = ∑ ( x – μ)^2 p ( x )

continuous Pr( a X b ) f ( ) x dx a

b

−∞

∫ x f^ ( ) x dx^ σ μ

−∞

∫ (^ x^ )^ f^ ( ) x dx

Sample proportions

P X

n

̂ = mean E( P̂ ) = p

standard deviation sd^ P^

p p n

( ˆ^ ) = (^1 − )

approximate confidence interval

p z , p p n p z p p n

ˆ^1 ˆ ˆ^1 ˆ