ASVAB Study Guide Flashcards

A collection of vocabulary flashcards covering key definitions, formulas, and concepts from the ASVAB Arithmetic Reasoning, Mathematics Knowledge, and Core Sections decks.

Distance Formula

$$Distance = rate \times time$$

Rate Formula

$$Rate = distance \div time$$

Time Formula

$$Time = distance \div rate$$

Per

Indicates a rate or division relationship.

Of (in Percentage Problems)

Indicates operation to multiply.

Difference

The result of subtraction (subtract).

Sum

The result of addition (add).

Product

The result of multiplication (multiply).

Quotient

The result of division (divide).

Percent Change Formula

$$Change \div original \times 100$$

Ratio

A comparison between two quantities.

Proportion

An equation of ratios solved by cross-multiplying, then solving for the unknown.

Average Formula

$$Sum \text{ of values} \div \text{number of values}$$

Probability Formula

$$Favorable \text{ outcomes} \div \text{total possible outcomes}$$

Simple Interest Formula

$Interest = principal \times rate \times time$ ($I = Prt$)

Total Simple-Interest Amount

$$Principal + interest$$

Unit Rate

A rate expressed for one unit.

Work-Rate Formula

$$Work = rate \times time$$

Mixture Principle

$\text{Amount} \times \text{concentration}$ gives pure amount.

Area of a Rectangle

$$Length \times width$$

Perimeter of a Rectangle

$$2(length + width)$$

Area of a Triangle

$$\frac{1}{2} \times base \times height$$

Volume of a Rectangular Prism (Box)

$$Length \times width \times height$$

Circumference of a Circle

$$2\pi r$$

Area of a Circle

$$\pi r^2$$

Pythagorean Theorem

$$a^2 + b^2 = c^2$$

PEMDAS

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Distributive Property

$$a(b + c) = ab + ac$$

Coefficient

The number multiplying a variable.

Variable

A symbol representing an unknown or changing value.

Slope Formula

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Positive Slope

The line rises from left to right.

Negative Slope

The line falls from left to right.

Slope of a Horizontal Line

$$0$$

Slope of a Vertical Line

Undefined.

Area of a Square

$$Side^2$$

Perimeter of a Square

$$4 \times side$$

Area of a Parallelogram

$$Base \times height$$

Area of a Trapezoid

$$\frac{1}{2}(a + b)h$$

Volume of a Cylinder

$$\pi r^2 h$$

Surface Area

The total area of all outside surfaces.

Hypotenuse

The longest side of a right triangle, opposite the right angle.

3-4-5 Right Triangle

A right triangle with side lengths $3$, $4$, and $5$.

5-12-13 Right Triangle

A right triangle with side lengths $5$, $12$, and $13$.

Straight Angle

An angle measuring $180^\circ$.

Right Angle

An angle measuring $90^\circ$.

Full Circle

A circular measurement of $360^\circ$.

Complementary Angles

Two angles that add to $90^\circ$.

Supplementary Angles

Two angles that add to $180^\circ$.

Absolute Value

Distance from zero; always nonnegative.

Prime Numbers

Whole numbers greater than $1$ with exactly two factors.

Least Common Multiple (LCM)

The smallest positive multiple shared by two or more numbers.

Greatest Common Factor (GCF)

The largest factor shared by two or more numbers.

Prefix pre-

Before.

Prefix post-

After.

Prefix anti-

Against.

Prefix bi-

Two.

Prefix tri-

Three.

Prefix sub-

Under or below.

Prefix inter-

Between.

Prefix trans-

Across or beyond.

Prefix mis-

Wrong or badly.

Prefix re-

Again or back.

Atom

The basic unit of an element.

Proton

A subatomic particle that has a positive charge.

Electron

A subatomic particle that has a negative charge.

Neutron

A subatomic particle that has no electrical charge.

Photosynthesis

The process by which plants use light to make chemical energy from $CO_2$ and water.

Gravity

The force that pulls objects toward Earth.

Newton's First Law

An object stays at rest or in motion unless acted on by a force.

Newton's Second Law

$$F = ma$$

Newton's Third Law

Every action has an equal and opposite reaction.

Newton

The unit that force is measured in.

Work (Physics)

$$Force \times distance$$

Power

The rate at which work is done.

Mechanical Advantage

How much a machine multiplies input force.

Lever

A rigid bar rotating around a fulcrum.

Pulley

A simple machine that changes force direction and can provide mechanical advantage.

Torque

A turning force.

Voltage

Electrical potential difference.

Current

The flow of electric charge.

Resistance

Opposition to electrical current.

Ohm's Law

$$V = I \times R$$

Conductor

A material that allows electricity to flow easily.

Insulator

A material that resists electrical flow.

Fuse

An electrical safety component that protects against excessive current.

Engine Oil

Fluid used for lubrication and reducing friction.

Spark Plug

A device that ignites the air-fuel mixture in a gasoline engine.

Wrench

A hand tool that tightens or loosens nuts and bolts.

Screwdriver

A hand tool that tightens or loosens screws.