Business Math & Sequences Lecture Flashcards

Comprehensive vocabulary flashcards covering basic retail business mathematics and mathematical sequences including Fibonacci, Arithmetic, and Geometric patterns.

Mark-up

The amount added to the cost price of goods to cover overhead expenses and generate profit.

Mark-up Amount Formula

$$\text{Mark-up Amount} = \text{Cost Price} \times \text{Mark-up Rate}$$

Mark-up Rate Formula

$$\text{Mark-up Rate} = \frac{\text{Mark-up Amount}}{\text{Cost Price}} \times 100$$

Selling Price (Mark-up)

$$\text{Selling Price} = \text{Cost Price} + \text{Mark-up Amount}$$

Discount

A reduction from the original selling price used as a marketing strategy.

Discount Amount Formula

$$\text{Discount Amount} = \text{Selling Price} \times \text{Discount Rate}$$

Discount Rate Formula

$$\text{Discount Rate} = \frac{\text{Discount Amount}}{\text{Selling Price}} \times 100$$

Sale Price

$$\text{Sale Price} = \text{Original Price} - \text{Discount Amount}$$

Value-Added Tax (VAT)

A $12\%$ consumption tax mandated by the Bureau of Internal Revenue (BIR) in the Philippines.

VAT Zero-Rated (0%)

A classification subject to $0\%$ VAT that allows for input VAT credit claims.

VAT Exempt

Goods or services not subject to VAT where no input VAT credit claims are allowed.

VAT-Inclusive Total Price Formula

$$\text{Total Price} = \text{Base Price} \times 1.12$$

VAT Amount Formula (from Inclusive Price)

$$\text{VAT Amount} = \frac{\text{Selling Price}}{1.12} \times 0.12$$

Base Price Formula (VAT-exclusive)

$$\text{Base Price} = \frac{\text{Selling Price}}{1.12}$$

Cost Price (CP)

The acquisition or production cost of a product.

Selling Price (SP)

The revenue generated from sales.

Profit

The positive difference between Selling Price and Cost Price.

Loss

The negative difference when Cost Price exceeds Selling Price.

Break-Even

The point where total revenue equals total cost.

Percentage Profit Formula

$$\% \text{Profit} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\%$$

Percentage Loss Formula

$$\% \text{Loss} = \frac{\text{Loss}}{\text{Cost Price}} \times 100\%$$

Pattern Descriptor: Shape

A systematic descriptor identifying motifs such as circles, squares, spirals, or triangles.

Pattern Descriptor: Arrangement

A descriptor indicating if a pattern is alternate, symmetrical, or random.

Fibonacci Sequence

A sequence where each term is the sum of the two preceding terms, starting with $1, 1$, defined by $F_n = F_{n-1} + F_{n-2}$.

Binet's Closed Form

$$F_n = \frac{1}{\sqrt{5}} \left[ \left( \frac{1+\sqrt{5}}{2} \right)^n - \left( \frac{1-\sqrt{5}}{2} \right)^n \right]$$

Sum of first n Fibonacci numbers

$$\sum_{k=1}^{n} F_k = F_{n+2} - 1$$

Sum of squares of first n Fibonacci numbers

$$\sum_{k=1}^{n} F_k^2 = F_n \times F_{n+1}$$

Arithmetic Sequence

A number pattern where every term after the first is generated by adding a constant value to the preceding term.

Common Difference (d)

The constant value added to each term in an arithmetic sequence, calculated as $d = a_2 - a_1$.

Arithmetic Sequence nth Term Formula

$$a_n = a_1 + (n - 1)d$$

Geometric Sequence

A sequence where each term after the first is obtained by multiplying the preceding term by a fixed non-zero number.

Common Ratio (r)

The fixed multiplier used to generate successive terms in a geometric sequence, calculated as $r = \frac{a_2}{a_1}$.

Geometric Sequence nth Term Formula

$$a_n = a_1 \times r^{(n-1)}$$