ASVAB Math: Formula Memorization

A set of vocabulary flashcards covering key mathematical formulas, geometric rules, and algebraic principles from the ASVAB Math formula memorization lecture notes.

Volume of a Cylinder

The formula given by $\pi r^2 h$, where $r$ represents the radius and $h$ represents the height.

Volume of a Rectangular Prism

The formula calculated by multiplying length, width, and height: $L \times W \times H$.

Area of a Rectangle

The formula calculated as $L \times W$, multiplying the length by the width.

Area of a Triangle

The formula given by $\frac{b \times h}{2}$ or $(b \times h) / 2$, representing half the base times the height.

Area of a Circle

The formula given by $\pi r^2$, where $r$ is the radius of the circle.

Circumference of a Circle

The linear distance around a circle, given by the formula $2\pi r$.

Perimeter of a Rectangle

The total distance around a rectangle, given by the formula $2(L + W)$.

Volume of a Cube

The formula calculated as $s^3$, where $s$ is the side length.

Pythagorean Theorem

The geometric formula for right triangles relating sides $a$ and $b$ to hypotenuse $c$: $a^2 + b^2 = c^2$.

Distance Formula

The relationship found by multiplying speed and time: $\text{Speed} \times \text{time}$.

Speed Formula

The rate of travel determined by the formula $\text{Distance} / \text{time}$.

Travel Time Formula

The duration of travel determined by the formula $\text{Distance} / \text{speed}$.

Average Speed Formula

The overall rate of motion found by the formula $\text{Total distance} / \text{total time}$.

Simple Interest Formula

The formula calculated as $P \times r \times t$, representing principal times rate times time.

Percent Change Formula

The formula given by

$\frac{\text{Change}}{\text{original}} \times 100$.

Discount Amount Formula

The monetary deduction found using the formula $\text{Price} \times \text{discount rate}$.

Price After a 20% Discount

The resulting reduced price calculated by multiplying the original price by $0.80$: $\text{Price} \times 0.80$.

Price After a 15% Increase

The resulting increased price calculated by multiplying the original price by $1.15$: $\text{Price} \times 1.15$.

Combined Worker Equation

The work-rate equation used to find the total time $T$ when two workers combine efforts:

$\frac{1}{T} = \frac{1}{A} + \frac{1}{B}$.

Daily Work Rate

The fraction of a total job completed in one day; if a worker completes a job in $4$ days, the daily work rate is $\frac{1}{4}$.

Fraction Division Rule

The rule where dividing by a fraction is converted into multiplication by flipping the divisor to its reciprocal

Gallon to Quarts Conversion

A liquid unit conversion stating that $1\text{ gallon} = 4\text{ quarts}$, solved by multiplying the number of gallons by $4$.

Radius

The measurement denoted by the variable $r$ in circle and cylinder formulas, equal to half of the diameter (e.g., a diameter of $10$ gives a radius of $5$).

Product Rule for Exponents

The algebraic rule stating that multiplying powers with the same base adds their exponents: $x^2 \times x^3 = x^5$.

Quotient Rule for Exponents

The algebraic rule stating that dividing powers with the same base subtracts the bottom exponent from the top exponent: $x^5 / x^2 = x^3$.

Scientific Notation

A standard format for writing numbers using powers of $10$, where $4{,}500{,}000$ is expressed as $4.5 \times 10^6$.

Difference of Two Squares

A factoring pattern for expressions in the form of $a^2 - b^2$, such as factoring $x^2 - 9$ into $(x - 3)(x + 3)$.

Simplifying Algebraic Fractions

The mathematical procedure of factoring the numerator and denominator completely and canceling matching common factors.

Exterior Angle Formula of a Regular Polygon

The formula used to find the measure of one exterior angle by dividing $360^\circ$ by the number of sides: $\frac{360^\circ}{\text{sides}}$.

Sum of Exterior Angles

The total sum of all exterior angles for any convex polygon, which always equals $360^\circ$.

Supplementary Relationship of Polygon Angles

The geometric principle that an interior angle and its exterior angle sum to $180^\circ$ (for example, an interior angle of $140^\circ$ gives an exterior angle of $40^\circ$).

Distributive Property

The algebraic property of multiplying a monomial by each term inside parentheses: $3(x + 4) = 3x + 12$.

Percentage Decrease Amount Formula

The calculation to determine the amount lost in a decrease: $\text{Original} \times \text{rate}$.