Math Formulas: Percentages, Interest, Algebra, Geometry & Statistics
Percentages
% of whole amount: part of whole / whole amount
% increase or decrease: (New / original x 100) – 100
Find % of amount: A x % / 100
% profit/loss amount: profit or loss / cost price x 100
GST Example
(GST = Amount / 11)
The total amount already includes the GST. The GST is 10% of the total excluding GST.
If we divide the total excluding GST into 10 equal amounts then:
- one of these amounts is equal to the GST and
- 11 of these amounts gives us the total including GST
Amount / 11
Simple and Compound Interest
Simple Interest: I = ART
I = Interest, P = A + I
A = Original Amount, I = ART / D
R = Rate (decimal)
T = Time
P = Principal
D = Time Divider
For Example: 8 days, 3% P/A, A = $11000
I = (11000 x 0.03 x 8) / 365 = $7.23
P = 11000 + 7.23
Minimum Monthly Balance uses the smallest amount in the account for the month when calculating interest for the month.
Daily balance uses the amount in the account daily when calculating interest.
Compound Interest: I = A(1 + R/D)^n
P = Principal
A = Original amount
R = Rate
N = number of compounds (T x D)
D = divider
T = time (in years)
I = Interest earned, I = P – A
Example: 10000, 3 years, 3.5% p/a, compounded monthly
P = 10000 (1 + 0.035 / 12) ^ (3×12)
P = $11106.73
Future cost (compound interest)
Depreciation: I = A(1 – R)^N
Appreciation: I = A(1 + R)^N
Consumer Mathematics
Inflation: process in which value increases in a compounded manner
Depreciation: process in which value decreases in a compounded manner
Wage: payment per hour for time spent working
Salary: fixed amount of money earned in a year
Commission: money made per sales
Price per 1 quantity: Price / quantity
Exchange Rates
When 1x = y of other currency
x by y > Y
X Y
Example:
1aud = 0.7 usd
50aud = ?usd
50 x 0.7 = 35 usd
Price to earning ratio: share price / earning from last year
Share price: value
Earning = dividend
Dividend earned = total share x dividend per share
Algebra and Matrices
Times rows by column
Can only add or subtract matrices if both matrices are of the same size
Can only multiply same sized matrices in this way
(A) 2×2 (B) 4×2
AB will not work
BA will work (4 x 2) (2 x 2)
Pythagoras Theorem and Measurement
C^2 = A^2 + B^2
A = [C^2 – B^2]
B = [C^2 – A^2]
Area of a circle: = πr^2 (x degrees / 360) for sector
Circumference: = 2πr (x degrees / 360) for a sector
Inverse Example:
2πr = 72
R = 72 / 2π
Surface Area
Cone Curved area
Cone Total Area
Sphere
1/2 Sphere
1/4 Sphere
Cylinder = 2πr^2 + 2πxrxL
Similar Figures and Scale Factors
Scale Factor
Length 1:K
Area 1^2 : K^2
Volume 1^3 : K^3
Two shapes are similar if:
- all sides are proportional
- all angles are the same
Similarity In Triangles
AAA
SAS
SSS
Algebra
Data and Statistics
Standard Deviation
Mean, Median, Mode, Range, Quartiles
Describe and compare different data sets using location, spread shape + approach
Z – Score (Standardised score)
simplifies normal distribution to a mean of 0 and a SD of 1
Z = (raw score – average) / SD
standard score
standard score = 0 = at mean
standard score > 0 = above mean
Normal distribution
Linear Equations
Straight Line Equation
Y = MX + C
Gradient
Rise / run
y2 – y1
x2 – x1