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Applied Mathematics and Statistics Formulas

30 flashcards covering essential applied mathematics formulas, commercial arithmetic methods, and statistical concepts for the vocational matura. Study material written for practice, not an official test.

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Value-Added Tax (DDV) gross price calculation from net price

N

at standard rate

22%

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Value-Added Tax (DDV) gross price calculation from net price

N

at standard rate

22%

Gross = N \times 1.22

Net price

N

calculation from gross price

G

with

22%

VAT

N = \frac{G}{1.22}

Simple interest formula for principal

P

, annual rate

r

, and time

t

in years

I = P \cdot r \cdot t

Compound interest formula with annual compounding over

n

years

A = P (1 + r)^{n}

Straight-line annual depreciation formula with cost

C

, salvage value

S

, and useful life

n

D = \frac{C - S}{n}

Declining-balance book value after

n

years at depreciation rate

d

B V_{n} = C (1 - d)^{n}

Commercial markup percentage based on cost

C

with selling price

P

Markup % = \frac{P - C}{C} \times 100%

Gross margin percentage based on selling price

P

and cost

C

Margin % = \frac{P - C}{P} \times 100%

Break-even volume formula with fixed costs

F C

, price

P

, and variable cost per unit

V C

Q_{B E} = \frac{F C}{P - V C}

Linear equation slope formula passing through points

(x_{1}, y_{1})

and

(x_{2}, y_{2})

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

Condition for two straight lines with slopes

m_{1}

and

m_{2}

to be perpendicular

m_{1} \cdot m_{2} = - 1

(negative reciprocal)

Coordinates of the vertex of parabola

y = a x^{2} + b x + c

x_{v} = - \frac{b}{2 a}

, then

y_{v} = c - \frac{b ^{2}}{4 a}

Pythagorean theorem in a right triangle with legs

a, b

and hypotenuse

c

a^{2} + b^{2} = c^{2}

Area of a trapezoid with parallel bases

a, c

and height

h

A = \frac{a + c}{2} \cdot h

Volume of a cylinder with base radius

r

and height

h

V = π r^{2} h

Total surface area of a closed cylinder

A = 2 π r^{2} + 2 π r h = 2 π r (r + h)

Volume of a cone with radius

r

and height

h

V = \frac{1}{3} π r^{2} h

Lateral surface area of a cone with slant height

s

A_{l a t} = π r s

where

s = r^{2} + h^{2}

Volume of a sphere with radius

r

V = \frac{4}{3} π r^{3}

Trigonometric tangent definition in a right triangle

tan α = \frac{Opposite leg}{Adjacent leg}

Law of cosines for side

c

with opposite angle

γ

c^{2} = a^{2} + b^{2} - 2 ab cos γ

Arithmetic mean of sample values

x_{1}, x_{2}, \dots, x_{n}

\overset{x}{ˉ} = \frac{1}{n} \sum_{i = 1}^{n} x_{i}

Median of an ordered numerical dataset

The middle value if

n

is odd, or the average of the two middle values if

n

is even.

Sample variance formula

s^{2}

s^{2} = \frac{1}{n - 1} \sum_{i = 1}^{n} (x_{i} - \overset{x}{ˉ})^{2}

Standard deviation relationship to variance

s = s^{2}

(the positive square root of variance)

Probability of the union of two mutually exclusive events

A

and

B

P (A \cup B) = P (A) + P (B)

Probability of two independent events

A

and

B

both occurring

P (A \cap B) = P (A) \cdot P (B)

Conditional probability of event

A

given event

B

P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )}

Empirical rule for a normal distribution: percentage within one standard deviation

μ \pm σ

Approximately

68.2%

of observations.

Empirical rule for a normal distribution: percentage within two standard deviations

μ \pm 2 σ

Approximately

95.4%

of observations.

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