ASTB-E cheat sheet

Order of operations: parentheses, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

Percent change = (new value − old value) ÷ old value × 100. A 20% increase followed by a 20% decrease leaves 96% of the original amount, a net 4% loss.

Distance = rate × time. For two equal-distance legs flown at speeds a and b, average speed = 2ab ÷ (a + b), which is always less than the simple mean.

Combined work rate: add individual rates. Two workers alone take t₁ and t₂ hours, together they take 1 ÷ (1/t₁ + 1/t₂) hours.

Area: rectangle lw, triangle ½bh, circle πr², trapezoid ½(b₁ + b₂)h. Volume of a cylinder = πr²h.

Memorize triples 3-4-5, 5-12-13, 8-15-17. A 30-60-90 triangle has sides x : x√3 : 2x; a 45-45-90 triangle has x : x : x√2.

Average = sum ÷ count, so sum = average × count; this rearrangement solves most missing-value average problems.

Exponent rules: xᵃ·xᵇ = xᵃ⁺ᵇ, (xᵃ)ᵇ = xᵃᵇ, x⁻ᵃ = 1/xᵃ, x⁰ = 1 for any nonzero x.

Compound interest A = P(1 + r/n)^(nt); simple interest A = P(1 + rt).

A main-idea answer must cover the whole passage; a choice describing one paragraph or one detail is too narrow.

An inference answer must be supported by statements in the passage; a real-world fact the author never implies is wrong even if true.

Transition words signal logic: however, although, yet, nevertheless = contrast; therefore, thus, consequently = cause-effect conclusion; moreover, additionally = continuation.

For EXCEPT or NOT questions, three choices are supported by the passage and the remaining one is the answer.

Extreme qualifiers (always, never, all, none, impossible) are usually wrong; hedged wording (some, may, often, tends to) is more often correct.

Tone and purpose questions: decide whether the author informs, persuades, criticizes, or narrates, then match the verb in the answer choice to that purpose.

Vocabulary in context: substitute each option into the original sentence and check whether the sentence's logic still holds.

Statements containing should, ought, better than, or value judgments are opinions rather than facts.

Lever balance: F₁d₁ = F₂d₂, where d is distance from the fulcrum. A longer effort arm reduces the force required.

First-class lever has the fulcrum between load and effort; second-class has the load between (wheelbarrow); third-class has the effort between (tongs) and never multiplies force.

Pulley mechanical advantage equals the number of rope segments supporting the movable block; a single fixed pulley only changes direction.

Inclined plane: mechanical advantage = length of slope ÷ height. A longer, gentler ramp reduces force but increases the distance pushed.

Meshed gears rotate in opposite directions; the smaller gear turns faster, with speed ratio equal to the inverse ratio of tooth counts.

Pressure = force ÷ area. In a hydraulic system pressure is transmitted undiminished (Pascal), so a larger output piston yields greater force but shorter travel.

Buoyant force equals the weight of fluid displaced; an object floats when its density is less than the fluid's and sinks when greater.

Ohm's law V = I × R and power P = V × I. Work = force × distance moved in the direction of the force; energy is conserved in simple machines.

The instrument shows attitude from the pilot's seat: a fixed miniature aircraft symbol stays still while the horizon bar and sky-ground background move.

Bank left: the horizon appears tilted with its left end raised, which reads as a clockwise rotation of the horizon line.

Bank right: the horizon appears tilted with its right end raised, a counterclockwise rotation of the horizon line.

Nose-up attitude pushes the horizon line down toward the bottom of the instrument; nose-down attitude raises the horizon toward the top.

The tilt angle of the horizon corresponds to the bank angle; straight-and-level shows a horizontal horizon centered in the window.

Combine cues: a climbing left turn shows the horizon low and tilted with the left end high; a descending right turn shows it high and tilted with the right end high.

Standard rate turn = 3 degrees per second, so 180 degrees of heading change takes 30 seconds and a full 360 takes two minutes.

The display shows attitude only; a wing-low, wings-level-heading condition still registers as a bank, and the instrument never indicates airspeed or heading.

Four forces of flight: lift upward, weight downward, thrust forward, drag rearward; in unaccelerated level flight lift equals weight and thrust equals drag.

Control surfaces: ailerons control roll about the longitudinal axis, elevator controls pitch about the lateral axis, rudder controls yaw about the vertical axis.

A wing stalls when angle of attack exceeds the critical angle, which can occur at any airspeed and in any attitude, including a climb or a descent.

Port is the left side facing forward and shows a red sidelight; starboard is the right side and shows a green sidelight; bow is forward, stern is aft.

One nautical mile = 6,076 feet ≈ 1.15 statute miles; one knot = one nautical mile per hour.

Right-of-way: the more maneuverable vessel generally gives way; a sailing vessel usually has right of way over a power-driven vessel, but not over one not under command.

Red right returning: when entering a US harbor from seaward, keep red buoys and marks to starboard and green marks to port.

Relative bearing is measured clockwise from the bow, from 000° through 360°; the NATO phonetic alphabet (Alpha, Bravo, Charlie) is used to spell letters by radio.

UAV tracking: keep the crosshair on the target using small, continuous corrections; large delayed inputs overshoot and cost more than steady micro-adjustments.

Lead a moving target by aiming slightly ahead of it along its direction of travel, then correct as its course changes.

In the tracking task the horizontal stick and throttle act on separate axes, so vertical and lateral corrections can be made independently and simultaneously.

Dichotic listening: repeat aloud the cues arriving in the designated ear while still monitoring the other channel for the specified target cue.

Multi-task battery: allocate attention on a fixed cycle among tracking, monitoring, and response tasks; fixating on one lets penalties accumulate on the others.

Errors are penalized, so when speed and accuracy conflict, favor the accurate response.

Performance improves across repeated trials, so the battery reflects learning rate and adaptability as well as initial skill.

Items ask about school, work, activities, honors, and accomplishments; there is no correct answer, only an accurate one.

Similar items are repeated in different wording, and contradictory responses are detected and can reduce the validity of the whole record.

Endorsing nearly every item, or choosing the same option for long runs of questions, triggers a response-set flag.

Many items ask for frequency or quantity of verifiable activities, so overstatement is detectable through cross-referenced questions.

Answer from actual history rather than from what seems most desirable; the inventory is scored for pattern and consistency, not for virtue.

Items tapping leadership roles, team participation, and academic recognition are scored as evidence of background experience, not as pass/fail criteria.

The aviation interest inventory measures enjoyment of flying, ships, and mechanical work; it reflects preference, not knowledge or aptitude.

Officer trait items ask for self-ratings on leadership, integrity, decisiveness, teamwork, judgment, initiative, and stress tolerance.

Responses use Likert-type scales; extreme answers are acceptable when accurate, but a uniform pattern across unrelated items suggests careless responding.

Interest items have no right answer, so choosing the option that sounds most officer-like rather than most personally true weakens the profile.

Answers should describe long-standing preferences and typical behavior rather than a single recent event or current mood.

Trait scores are interpreted alongside the biographical inventory and cognitive tests, so consistency across instruments matters more than any single answer.