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Victorian Certificate of Education
Year
MATHEMATICAL METHODS
Written examinations 1 and 2
FORMULA SHEET
Instructions
This formula sheet is provided for your reference.
Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic
devices into the examination room.
© VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 2016
Version 2 – April 2016
MATHMETH EXAM
2
Mathematical Methods formulas
Mensuration
area of a trapezium
1 a+b h
(
)
2
volume of a pyramid
1
Ah
3
curved surface area
of a cylinder
2π rh
volume of a sphere
4 3
πr
3
volume of a cylinder
π r 2h
area of a triangle
1
bc sin ( A )
2
volume of a cone
1 2
πr h
3
Calculus
d n
x = nx n − 1
dx
∫ x dx = n + 1 x
n +1
d
n −1
(ax + b) n = an ( ax + b )
dx
∫
1
(ax + b) n + 1 + c, n ≠ − 1
a (n + 1)
d ax
e = ae ax
dx
∫e
( )
(
1
n
)
( )
(ax + b) n dx =
ax
dx =
+ c, n ≠ −1
1 ax
e +c
a
∫
1
dx = log e ( x) + c, x > 0
x
d
( sin (ax) ) = a cos (ax)
dx
∫
1
sin (ax)dx = − cos (ax) + c
a
d
( cos (ax) ) = − a sin (ax)
dx
∫ cos (ax)dx = a sin (ax) + c
d
1
( log e ( x) ) = x
dx
1
d
a
= a sec 2 (ax)
( tan (ax) ) = 2
dx
cos (ax)
product rule
d
dv
du
( uv ) = u + v
dx
dx
dx
chain rule
dy dy du
=
dx du dx
quotient rule
du
dv
−u
v
d u
dx
dx
 =
dx  v 
v2
3
MATHMETH EXAM
Probability
Pr(A ∪ B) = Pr(A) + Pr(B) – Pr(A ∩ B)
Pr(A) = 1 – Pr(A′)
Pr(A|B) =
Pr ( A ∩ B )
Pr ( B )
µ = E(X)
mean
var(X) = σ 2 = E((X – µ)2) = E(X 2) – µ2
variance
Probability distribution
discrete
Pr(X = x) = p(x)
continuous
Pr(a < X < b) =
Mean
Variance
σ 2 = ∑ (x – µ)2 p(x)
µ = ∑ x p(x)
∫
b
a
f ( x)dx
µ=
∫
∞
−∞
x f ( x)dx
σ2 =
∫
∞
( x − µ ) 2 f ( x)dx
−∞
Sample proportions
P̂ =
X
n
standard
deviation
mean
ˆ) =
sd ( P
p (1 − p )
n
approximate
confidence
interval
E(P̂ ) = p

ˆp (1 − ˆp ) , p + z ˆp (1 − ˆp ) 
 ˆp − z
ˆ


n
n


END OF FORMULA SHEET