Formula sheets for
Mathematics examinations
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TRIM: 2010/5118[V4]
Copyright © Curriculum Council 2011
Formula sheets for examinations
The list of permissible items for use in WACE mathematics examinations no longer includes the
Curriculum Council revised Mathematical formulae and Statistical tables book.
Instead a Formula Sheet will be provided to candidates.
This document includes formula sheets for each pair of units in Mathematics which have a
WACE examination.
Mathematics: Units 2A and 2B
Formula Sheet
Number and algebra
Equation of a line: y = mx + c, where m = gradient; c = y–intercept
Space and measurement
In a right triangle:
sin  
opposite
hypotenuse
cos  
adjacent
hypotenuse
tan  
opposite
adjacent
Pythagoras’ Theorem :
In a right triangle ABC , where a, b are the short sides and c is the hypotenuse
c2  a 2  b2
Circle :
C  2 r   D, where C is the circumference, r is the radius and D is the diameter
A   r 2 , where A is the area
1
Triangle:
A
Parallelogram:
A  bh
Trapezium :
A
2
1
2
b h, where b is the base and h is the perpendicular height
(a  b)h, where a and b are the lengths of the parallel sides
and h is the perpendicular height
Prism:
V  Ah, where V is the volume, A is the area of the base and
h is the perpendicular height
Pyramid:
1
V  Ah
3
Cylinder :
S  2  r h  2  r 2 , where S is the total surface area
V   r 2h
Cone :
S   r s   r 2 , where s is the slant height
V
Sphere :
1
3
 r 2h
S  4 r2
V
4
3
 r3
Gradient of line, m, through the points ( x1 , y1 ) and ( x2 , y2 ) is given by m 
y2  y1
x2  x1
Distance, d , between the points ( x1, y1 ) and ( x2 , y2 ) is given by d  ( y2  y1 )2  ( x2  x1 )2
Note: Any additional formulas identified by the examination panel as necessary will be
included in the body of the particular question
TRIM: 2010/5118[V4]
Copyright © Curriculum Council 2011
Mathematics: Units 2C and 2D
Formula Sheet
Number and algebra
For any numerical value a  0 and integers m and n,
Index laws:
am an  am  n
am  an  am  n
Simple interest :
I  P r t , where P is the principal, r is the rate per year and t is the time in years
Space and measurement
In a right triangle:
sin  
opposite
cos  
hypotenuse
adjacent
hypotenuse
tan  
opposite
adjacent
Pythagoras’ Theorem:
In right triangle ABC , where a, b are the short sides and c is the hypotenuse
c2  a 2  b2
In any triangle ABC :
a
sin A

b
sin B

c
sin C
a 2  b 2  c 2  2 b c cos A
A
Circle :
1
2
cos A 
b2  c2  a 2
2bc
a b sin C , where A is the area
C  2 r   D, where C is the circumference, r is the radius and D is the diameter
A   r 2 , where A is the area
1
Triangle:
A
Parallelogram:
A  bh
Trapezium :
A
2
1
2
b h, where b is the base and h is the perpendicular height
(a  b)h, where a and b are the lengths of the parallel sides
and h is the perpendicular height
Prism:
Pyramid:
TRIM: 2010/5118[V4]
V  Ah, where V is the volume, A is the area of the base and
h is the perpendicular height
1
V  Ah
3
Copyright © Curriculum Council 2011
Cylinder :
S  2  r h  2  r 2 , where S is the total surface area
V   r 2h
Cone :
S   r s   r 2 , where s is the slant height
V
Sphere :
1
3
 r 2h
S  4 r2
V
4
3
 r3
Space and measurement
Gradient of line, m, through the points ( x1, y1 ) and ( x2 , y2 ) is given by m 
y2  y1
x2  x1
Distance d , between the points ( x1, y1 ) and ( x2 , y2 ) is given by d  ( y2  y1 )2  ( x2  x1 )2
Lines are perpendicular if m1 m2  1
Chance and Data
P( A)  P( A)  1
Note: Any additional formulas identified by the examination panel as necessary will be
included in the body of the particular question.
Copyright © Curriculum Council 2011
Mathematics: Units 3A and 3B
Formula Sheet
Number and algebra
Index laws:
For a , b  0 and m ,n real,
am an  am  n
a m b m  ( a b) m
m
an 
Simple interest :
am
 am  n
n
a
1
am
am 
n
am 
 a
n
(a m ) n  a m n
a0  1
m
for m an integer and n a positive integer
I  P r t , where P is the principal, r is the rate per year and t is the time in years
Compound interest :
A  P 1  r  compounded annually
t
r
A  P(1  ) nt compounded n times a year
n
dy
Differentiation:
If f ( x)  y, then f ( x) 
Powers:
If f ( x)  x n , then f ( x)  n x n 1
or
If y  x n , then
Product rule:
If y  f ( x) g ( x)
or
If y  uv
dy du
dv
then

vu
dx
dx dx
dx
then y  f ( x) g ( x)  f ( x) g ( x)
Integration :
x
Antiderivative:
Given
n
dx 
x n 1
n 1
 c, n  1
dy
x n 1
 x n then y =
 c, n   1
dx
n 1
Space and measurement
In any triangle ABC :
a
sin A

b
sin B

c
sin C
a 2  b 2  c 2  2 b c cos A
A
TRIM: 2010/5118[V4]
1
2
cos A 
a b sin C , where A is the area
Copyright © Curriculum Council 2011
b2  c2  a 2
2bc
dy
dx
 n x n 1
Space and measurement
Circle :
C  2 r   D, where C is the circumference, r is the radius and D is the diameter
A   r 2 , where A is the area
1
Triangle:
A
Parallelogram:
A  bh
Trapezium :
A
2
1
2
b h, where b is the base and h is the perpendicular height
(a  b)h, where a and b are the lengths of the parallel sides
and h is the perpendicular height
Prism:
V  Ah, where V is the volume, A is the area of the base and
h is the perpendicular height
Pyramid:
1
V  Ah
3
Cylinder :
S  2  r h  2  r 2 , where S is the total surface area
V   r 2h
Cone :
S   r s   r 2 , where s is the slant height
V
Sphere :
1
3
 r 2h
S  4 r2
V
4
3
 r3
Chance and data
P( A)  P( A)  1
In a normal distribution approximately:
68% of values lie within one (1) standard deviation of the mean
95% of values lie within two (2) standard deviations of the mean
99.7% of values lie within three (3) standard deviations of the mean.
Note: Any additional formulas identified by the examination panel as necessary will be
included in the body of the particular question.
Copyright © Curriculum Council 2011
Mathematics: Units 3C and 3D
Formula sheet
Number and algebra
dy
dx
then f ( x)  e x
then f ( x) 
If f ( x)  y
If f ( x)  e x
Product rule:
If
y  f ( x ) g ( x)
then
then f ( x)  n x n 1
If f ( x)  x n
y  uv
dy du
dv
then

vu
dx
dx dx
or
If
or
If
y   f ( x) g ( x)  f ( x) g ( x)
Quotient rule:
f ( x)
y
If
g ( x)
then y 
u
v
du
f ( x) g ( x )  f ( x ) g ( x )
( g ( x))
y
then
2
dy
 dx
dx
vu
dv
dx
v2
Chain rule:
y  f ( g ( x))
If
or
then y  f ( g ( x)) g ( x)
Powers:
x
n
dx 
x
If
then
y  f (u) and u =g  x 
dy dy du


dx du dx
n 1
n 1
 c, n 1
Fundamental Theorem of Calculus :
d x
f  t  dt  f  x 
and
dx  a
Incremental formula :  y 
dy
dx
Exponentials:  e dx  e x  c
x
 a f   x  dx  f b   f  a 
b
x
Exponential growth and decay :
If
dy
dt
 ky, then y  Aekt
TRIM: 2010/5118[V4]
Copyright © Curriculum Council 2011
Space and measurement
Circle :
C  2 r   D, where C is the circumference, r is the radius and D is the diameter
A   r 2 , where A is the area
1
Triangle:
A
Parallelogram:
A  bh
Trapezium :
A
2
1
2
b h, where b is the base and h is the perpendicular height
(a  b)h, where a and b are the lengths of the parallel sides
and h is the perpendicular height
Prism:
V  Ah, where V is the volume, A is the area of the base and
h is the perpendicular height
Pyramid:
1
V  Ah
3
Cylinder :
S  2  r h  2  r 2 , where S is the total surface area
V   r 2h
Cone :
S   r s   r 2 , where s is the slant height
V
Sphere :
1
3
 r 2h
S  4 r2
V
4
3
 r3
Volume of solids of revolution :
V    y 2 dx rotated about the x  axis
V    x 2 dy, rotated about the y  axis
Chance and data
Probability laws:
P( A)  P( A)  1
P( A  B)  P( A)  P( B)  P( A  B)
P( A  B)  P( A) P( B / A)  P( B) P( A / B)
Binomial distributions :
Mean :   np
and
standard deviation :  
Copyright © Curriculum Council 2011
np (1  p)
A confidence interval for the mean of a population is :
x z

n
 x z

n
where  is the population mean,  is the population standard deviation and
where x is the sample mean, n is the sample size and
z is the cut off value on the standard normal distribution corresponding to the confidence level.
Note: Any additional formulas identified by the examination panel will be included in the body
of the particular question.
Copyright © Curriculum Council 2011