Maths general formula sheet

2014 HIGHER SCHOOL CERTIFIC ATE EXAMINATION

Mathematics General 2
FORMULAE AND DATA SHEET
Financial Mathematics

Data Analysis

Simple interest

Mean of a sample

I = Prn
P
r n 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 approximately 68% of scores have z-scores between –1 and 1 approximately 95% of scores have

z-scores between –2 and 2
•

a decimal is number of periods

–1–

approximately 99.7% of scores have z-scores between –3 and 3

Spherical Geometry
Circumference of a circle

C = 2p r or