Download 2014 HSC Mathematics General 2 - Formulae

2014 HIGHER SCHOOL CERTIFIC ATE EXAMINATION
Mathematics General 2
FORMULAE AND DATA SHEET
Financial Mathematics
Simple interest
P
r
n
Data Analysis
Mean of a sample
I = Prn
x=
sum of scores
number of scores
is initial amount
is interest rate per period, expressed as
a decimal
is number of periods
z-score
For any score
x,
z=
Compound interest
A = P (1 + r )
A
P
r
n
n
x
s
is final amount
is initial amount
is mean
is standard deviation
Outlier(s)
is interest rate per period, expressed as
a decimal
is number of compounding periods
score(s) less than
r
n
FV
(1 + r )
n
,
score(s) more than
FV = PV (1 + r )
QL
QU
IQR
n
is interest rate per period, expressed as
a decimal
is number of compounding periods
r
x
y
is amount of depreciation per period
is number of periods
standard deviation of y scores
standard deviation of x scores
is correlation coefficient
x scores
is mean of y scores
is mean of
Normal distribution
n
S is salvage value of asset after n periods
V0 is initial value of asset
r is depreciation rate per period, expressed as
3240
is interquartile range
y-intercept = y − (gradient × x )
n periods
Declining-balance method of depreciation
n
is upper quartile
gradient = r ×
is initial value of asset
S = V0 (1 − r )
is lower quartile
y = gradient × x + y-intercept
S = V0 − Dn
is salvage value of asset after
QU + 1.5 × IQR
Least-squares line of best fit
Straight-line method of depreciation
S
V0
D
n
QL − 1.5 × IQR
or
Present value and future value
PV =
x−x
s
a decimal
is number of periods
–1–
•
approximately 68% of scores have
z-scores between –1 and 1
•
approximately 95% of scores have
z-scores between –2 and 2
•
approximately 99.7% of scores have
z-scores between –3 and 3
Spherical Geometry
Circumference of a circle
C = 2p r or C = p D
r
D
Surface Area
Sphere
r
is radius
A = 4p r 2
is radius
is diameter
Closed cylinder
q
2p r
360
Arc length of a circle
l=
r
q
r
h
is radius
is perpendicular height
is radius
Volume
is number of degrees in central angle
Prism or cylinder
Radius of Earth
(taken as)
V = Ah
6400 km
A
h
Time differences
For calculation of time differences using longitude:
15˚
A = 2p r 2 + 2p rh
= 1 hour time difference
is area of base
is perpendicular height
Pyramid or cone
V=
Area
Circle
r
A = pr2
A=
is perpendicular height
Volume and capacity
q
pr2
360
Approximation Using Simpson’s Rule
Area
is number of degrees in central angle
(
A = π R2 − r 2
A≈
)
h
df
dm
dl
is radius of outer circle
is radius of inner circle
h
(a + b )
2
h
AL
AM
AR
Area of land and catchment areas
unit conversion: 1
ha = 10 000 m
2
–2–
)
is first measurement
is middle measurement
is last measurement
V≈
h is perpendicular height
a and b are the lengths of the parallel sides
(
h
d + 4 dm + dl
3 f
is distance between successive measurements
Volume
Trapezium
A=
m3 = 1000 L
unit conversion: 1
is radius
Annulus
R
r
is area of base
is radius
Sector
r
q
A
h
1
Ah
3
{
h
A + 4 AM + AR
3 L
}
is distance between successive measurements
is area of left end
is area of middle
is area of right end
Trigonometric Ratios
Blood Alcohol Content Estimates
BACmale =
hypotenuse
opposite
side
q
adjacent side
sin q =
opposite side
hypotenuse
cos q =
adjacent side
hypotenuse
tan q =
or
BACfemale =
Distance, Speed and Time
opposite side
adjacent side
D = ST, S =
Area of a triangle
In
average speed =
r ABC,
a
b
c
=
=
sin A sin B sin C
The probability of an event where outcomes are equally
likely is given by:
P(event) =
r ABC,
c2 = a2 + b2 − 2ab cos C
or
cos C =
a +b −c
2ab
2
2
Gradient
1 byte = 8 bits
10
bytes
20
bytes
1 megabyte = 2
number of favourable outcomes
total number of outcomes
Straight Lines
m=
2
Units of Memory and File Size
1 kilobyte = 2
total distance travelled
total time taken
Probability of an Event
1
ab sin C
2
Cosine rule
In
D
D
, T=
T
S


 
stopping distance = reaction-time  +  braking 
 distance  distance 
r ABC,
A=
10N − 7.5H
5.5M
N is number of standard drinks consumed
H is number of hours of drinking
M is person’s mass in kilograms
Sine rule
In
10N − 7.5H
6.8M
vertical change in position
horizontal change in position
Gradient–intercept form
y = mx + b
= 1024 bytes
m
b
= 1024 kilobytes
1 gigabyte = 230 bytes = 1024 megabytes
1 terabyte = 240 bytes = 1024 gigabytes
–3–
is gradient
is y-intercept
BLANK PAGE
–4–
© Board of Studies NSW 2014