Victorian Certificate of Education
Year
MATHEMATICAL METHODS
Written examinations 1 and 2
FORMULA SHEET
Instructions
This formula sheet is provided for your reference.
A question and answer book is provided with this formula sheet.
Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic
devices into the examination room.
© VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 2023
Version 2 – July 2023
MM FORMULA SHEET
2
Mathematical Methods formulas
Mensuration
area of a trapezium
1 ab 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
d
n 1
(ax b) n an ax b dx
(ax b) dx a(n 1) (ax b)
d ax
e ae ax
dx
e dx a e c
1
d
log e ( x) x
dx
d
sin (ax) a cos (ax)
dx
sin (ax)dx a cos (ax) c
d
cos (ax) = a sin (ax)
dx
cos (ax)dx a sin (ax) c
1
n
n 1
1
n
ax
1
c, n 1
n 1
c, n 1
ax
1
dx log e ( x) c, x 0
x
1
1
d
a
a sec 2 (ax)
tan (ax) = 2
dx
cos (ax)
product rule
d
dv
du
uv u v
dx
dx
dx
quotient rule
du
dv
u
d u
dx
dx
2
dx v v
chain rule
dy dy du
=
dx du dx
Newton’s
method
xn 1 xn trapezium rule
approximation
Area xn x0
2n
v
f xn f xn f ( x ) 2 f ( x ) 2 f ( x ) 2 f ( x ) 2 f ( x ) f ( x )
0
1
2
n2
n 1
n 3
MM FORMULA SHEET
Probability
Pr(A) = 1 – Pr(A′)
Pr(A|B) =
Pr(A ∪ B) = Pr(A) + Pr(B) – Pr(A ∩ B)
Pr A B Pr B mean
µ = E(X)
binomial
coefficient
n!
n
x x !(n x)!
var(X) = σ 2 = E((X – µ)2) = E(X 2) – µ2
variance
Probability distribution
Mean
Variance
discrete
Pr(X = x) = p(x)
µ = ∑ x p(x)
σ 2 = ∑ (x – µ)2 p(x)
binomial
n
Pr( X x) p x (1 p ) n x
x
μ = np
σ 2 = np (1 − p)
continuous
Pr(a X b) b
a
f ( x)dx
x f ( x)dx
2 ( x ) f ( x)dx
2
Sample proportions
P̂ =
X
n
standard
deviation
ˆ) =
sd ( P
p (1 − p )
n
mean
E(P̂ ) = p
approximate
confidence
interval
ˆp (1 − ˆp ) , p + z ˆp (1 − ˆp )
ˆp − z
ˆ
n
n
END OF FORMULA SHEET
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