Comprehensive Mathematics Review Flashcards

Vocabulary flashcards reviewing core topics from mathematics including financial formulas, unit conversions, surface area and volume of 3D objects, map scaling, currency conversion, function graphs, and order of operations.

Percentage Increase Formula

$$\text{Percentage Increase} = \left(\frac{\text{Increase}}{\text{Original Value}}\right) \times 100$$

Value Added Tax (VAT)

Calculated as $\text{VAT} = \text{Original Price} \times \text{VAT Rate}$, with final price equal to $\text{Final Price} = \text{Original Price} + \text{VAT}$.

Discount and Sale Price

Calculated as $\text{Discount} = \text{Original Price} \times \text{Discount Rate}$ and $\text{Sale Price} = \text{Original Price} - \text{Discount}$.

Profit Percentage

Calculated as $\text{Profit \%} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100$, where $\text{Profit} = \text{Selling Price} - \text{Cost Price}$.

Purchasing Power and Inflation

If prices increase faster than salary, real purchasing power decreases.

Simple Interest Formula

$I = Prt$, where $I$ is interest, $P$ is principal, $r$ is annual interest rate in decimal, and $t$ is time in years.

Maturity Value (Simple Interest)

The total amount including principal and interest, calculated as $MV = \text{Principal} + \text{Interest}$.

Simple Interest Rearranged Formulas

Rearrangements of $I = Prt$: $\text{rate} = \frac{I}{Pt}$, $\text{time} = \frac{I}{Pr}$, and $\text{Principal} = \frac{I}{rt}$.

Compound Interest Formula

$A = P\left(1 + \frac{r}{n}\right)^{nt}$, where $A$ is maturity value, $P$ is principal, $r$ is annual rate in decimal, $n$ is compounding periods per year, and $t$ is time in years.

Compound Interest Amount

Calculated as $CI = A - P$, representing the interest accumulated over time.

Compounding Frequency ($n$)

The number of periods per year: Annually ($n = 1$), Semi-annually ($n = 2$), Quarterly ($n = 4$), and Monthly ($n = 12$).

Customary and Metric Conversions

Unit equivalents: $1\, \text{foot} = 12\, \text{inches}$, $1\, \text{pound} = 16\, \text{ounces}$, $1\, \text{pound} = 453.592\, \text{grams}$, and $1\, \text{mile} = 1\,609.344\, \text{meters}$.

Surface Area of 3D Objects

Formulas in square units: Rectangular Prism ($SA = 2(lw + lh + wh)$), Cube ($SA = 6s^2$), Cylinder ($SA = 2\pi r^2 + 2\pi rh$), Sphere ($SA = 4\pi r^2$), Square Pyramid ($SA = s^2 + 2sl$), and Cone ($SA = \pi r^2 + \pi rl$).

Volume of 3D Objects

Formulas in cubic units: Rectangular Prism ($V = lwh$), Cube ($V = s^3$), Cylinder ($V = \pi r^2 h$), Cone ($V = \frac{1}{3}\pi r^2 h$), Sphere ($V = \frac{4}{3}\pi r^3$), and Square Pyramid ($V = \frac{1}{3}Bh$).

Map Scale Formula

$$\text{Scale} = \frac{\text{Map Distance}}{\text{Actual Distance}}$$

Currency Exchange Rates

Base rates: $US\$1 = \text{₱}60$, $€1 = \text{₱}70$, $£1 = \text{₱}80$, and $AU\$1 = \text{₱}40$.

Currency Conversion Formulas

Foreign to Pesos: $\text{Pesos} = \text{Foreign Currency} \times \text{Exchange Rate}$; Pesos to Foreign: $\text{Foreign Currency} = \frac{\text{Pesos}}{\text{Exchange Rate}}$.

Linear Function

General form $y = mx + b$, producing a straight-line graph with slope $m$ and y-intercept $b$.

Quadratic Function

General form $y = ax^2 + bx + c$, producing a parabola graph shape.

Absolute Value Function

General form $y = |x|$, producing a V-shaped graph.

Square Root Function

General form $y = \sqrt{x}$, producing a curve beginning at the origin and extending to the right.

Cubic Function

General form $y = x^3$, producing an S-shaped graph.

Function Graph Reference Table

Reference chart summarizing equations and graph shapes for Quadratic, Absolute Value, Square Root, and Cubic functions.

PEMDAS

Order of operations rule for evaluating algebraic expressions: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.