FREE OAR Study Guide 2026: Math, Reading & Mechanical Comprehension

This free OAR study guide teaches to the Officer Aptitude Rating — the U.S. Navy aptitude test used to predict academic success at Officer Candidate School (OCS) and to select candidates for non-aviation officer programs.^[1] The OAR is built from three ASTB-E subtests: the Math Skills Test, the Reading Comprehension Test, and the Mechanical Comprehension Test. This guide covers all three, in that order.

It’s interactive, not a wall of text: every subtest has a built-in checkpoint quiz, hover-able glossary terms, worked math examples, labeled mechanical diagrams, and concept questions, so you learn by doing.

Work through it subtest by subtest, test yourself at each checkpoint, then round out your free OAR prep with our practice questions and flashcards.

OAR Exam Snapshot

The OAR is reported as a single t-score from 20 to 80, so about half of candidates score above 50 and most land between 40 and 60.^[1] There is no universal passing score — each officer program sets its own competitive minimum, and those minimums change with each accession board, so confirm the current target with a recruiter or the relevant officer community manager.^[4]

Spread your study time across all three subtests, but know that Mechanical Comprehensionis the one most candidates have never formally studied — it’s where focused prep pays off most. Math Skills is the largest in raw question volume, and Reading Comprehension rewards a disciplined “answer from the text only” habit:

Because the ASTB-E is computer-adaptive, the exact number of questions and the time per subtest vary from candidate to candidate.^[1] The shares above reflect where your study hours are best spent, not fixed question counts.

1 · Math Skills Test (MST)

The Math Skills Test covers high-school math without a calculator. Expect arithmetic, fractions, decimals, percentages, ratios, algebra, geometry, and word problems. Speed and clean by-hand arithmetic matter as much as knowing the rules.^[1]

Arithmetic, Fractions & Percentages

Start with the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division left to right, then Addition and Subtraction left to right. To find a percent of a number, convert the percent to a decimal and multiply — 35% of 80 is $0.35 \times 80 = 28$.

Algebra & Equations

Solve a linear equation by isolating the variable with inverse operations. For $3x + 7 = 22$, subtract 7 to get $3x = 15$, then divide by 3 to get $x = 5$. The same idea works for inequalities, with one rule: flip the inequality sign when you multiply or divide by a negative number.

Geometry & Measurement

Memorize the workhorses: rectangle area $= lw$, triangle area $= \tfrac{1}{2}bh$, circle area $= \pi r^2$, and circle circumference $= 2\pi r$. A triangle’s interior angles always sum to 180°, and the Pythagorean theorem $a^2 + b^2 = c^2$ gives the sides of a right triangle.

Word Problems

The biggest skill is translation: turn the words into an equation, solve step by step, then re-read the question to make sure you answered what was asked. Remember distance = rate × time, and that “of” means multiply while “is” means equals.

2 · Reading Comprehension Test (RCT)

The Reading Comprehension Test gives you short passages and asks what the text supports. The single most important rule: answer only from the passage — never from outside knowledge or opinion.^[1] This subtest rewards technique more than content.

Main Idea & Supporting Detail

The main idea is the central point the whole passage supports — broader than any one detail, but never beyond what the text says. A supporting detail is a specific fact the passage gives to back that point up. For a main-idea question, pick the choice that fits every paragraph, not just one.

Inferences & Conclusions

An inference is a conclusion the passage implies but does not state outright. The correct inference is the one the text most directly supports — not the most dramatic. If a choice needs information the passage never gives, eliminate it.

Vocabulary in Context & Tone

Vocabulary-in-context questions ask what a word means as used in the passage, which may not be its most common meaning. Substitute each choice back into the sentence and keep the one that preserves the author’s logic and tone(the author’s attitude — neutral, critical, enthusiastic).

3 · Mechanical Comprehension Test (MCT)

The Mechanical Comprehension Test is about how the physical world works— simple machines, forces and motion, energy, and fluids. It’s the subtest most candidates have never formally studied, which makes it the highest-yield place to spend prep time.^[1] The good news: nearly every question reduces to a handful of principles below.

Simple Machines & Mechanical Advantage

There are six simple machines: the lever, wheel and axle, pulley, inclined plane, wedge, and screw. Each provides a mechanical advantage — the number of times it multiplies your input force. The universal trade-off: the more force a machine saves, the farther you must move the input. A machine never gives free energy.

Tell the three lever classes apart by what sits in the middle: the fulcrum (1st class, like a seesaw), the load (2nd class, like a wheelbarrow — always multiplies force), or the effort (3rd class, like tweezers — always multiplies speed). For a lever, mechanical advantage equals the effort-arm length divided by the load-arm length.

For pulleys, count the rope segments that support the load — that number is the mechanical advantage. A single fixed pulley only changes direction (mechanical advantage 1); a movable pulley gives a mechanical advantage of 2. A ramp (inclined plane) works the same way: a longer, gentler slope needs less force but more travel.

Force, Motion & Newton’s Laws

Most motion questions reduce to one of Newton’s three laws. The first (inertia) explains why passengers lurch forward when a car suddenly stops; the second, $F = ma$, says a heavier object accelerates less for the same force; the third pairs every action with an equal and opposite reaction.

Don’t confuse mass and weight: mass is the amount of matter (constant), while weight is the force of gravity on that mass and changes with location. Friction always opposes motion and turns some energy into heat; torque is a turning force equal to force times distance from the pivot, so a longer wrench turns a bolt more easily.

Work, Energy & Power

Work is force times the distance moved in the direction of the force — no motion means no work. Kinetic energy is the energy of motion $(\tfrac{1}{2}mv^2)$, so doubling speed quadruples it; potential energy is stored energy of position $(mgh)$.

Power is the rate of doing work — the same job done faster takes more power. Energy is never created or destroyed, only converted.

Fluids, Pressure & Gases

Pressure is force divided by area, so the same force on a smaller area gives higher pressure — why a sharp blade cuts. Pascal’s principle (pressure in a confined fluid spreads equally) powers hydraulic lifts and brakes, letting a small force on a small piston create a large force on a big one. Bernoulli’s principle says faster-moving fluid has lower pressure, which helps explain how a wing generates lift.

How to Use This Study Guide

A study guide is a map, not the whole territory — use it alongside our free OAR practice questions and flashcards. Because the OAR is adaptive and unforgiving of slow arithmetic, spaced, mixed practice beats one long cram. Give Mechanical Comprehensionextra attention: most candidates start it cold, so it’s where a few focused hours move your score the most.

OAR Glossary

Quick definitions for the terms you’ll see most across the three OAR subtests:

APEX

The web-based, computer-adaptive system used to deliver the ASTB-E. Because it adapts to your answers, exact question counts and timing vary between candidates.

ASTB-E

The Aviation Selection Test Battery (Enhanced) — the full Navy/Marine Corps officer-selection test. The OAR is the non-aviation portion of it; aviation candidates take all of it.

Bernoulli's principle

In a moving fluid, faster flow means lower pressure. It helps explain lift on a wing and why fluid speeds up in a narrow pipe.

First-class lever

A lever with the fulcrum in the middle (effort–fulcrum–load), such as a seesaw or crowbar. It can multiply force or distance.

Friction

A force that opposes motion between surfaces in contact. Static friction holds a still object; kinetic friction acts on a sliding one.

Fulcrum

The fixed pivot point that a lever rotates around.

Gear ratio

The driven gear's teeth divided by the driver gear's teeth. A small gear driving a large one gives more torque but less speed; meshed gears turn in opposite directions.

Inclined plane

A ramp. It lowers the force needed to raise a load by spreading the work over a longer distance — the same total work either way.

Inertia

An object's resistance to a change in its motion. The more mass an object has, the more inertia.

Inference

A conclusion a passage implies but does not state directly. The correct inference is the one the text most strongly supports.

Kinetic energy

The energy of motion, equal to one-half mass times velocity squared. Doubling speed quadruples kinetic energy.

Lever

A rigid bar that pivots on a fulcrum to move a load. Levers are first, second, or third class depending on whether the fulcrum, load, or effort is in the middle.

Main idea

The central point a passage supports — broader than any single detail, but never beyond what the text actually says.

Mass vs weight

Mass is the amount of matter (constant); weight is the force of gravity on that mass (weight = mass × gravity) and changes with location.

Mechanical advantage

How many times a machine multiplies the input force, equal to output force divided by input force. Above 1 multiplies force; below 1 multiplies speed or distance.

Newton's first law

An object stays at rest, or in motion at constant velocity, unless a net force acts on it. Also called the law of inertia.

Newton's second law

Net force equals mass times acceleration (F = ma). For the same force, a heavier object accelerates less.

Newton's third law

For every action there is an equal and opposite reaction, with the two forces acting on different objects.

Officer Aptitude Rating (OAR)

A 20–80 aptitude score the Navy uses to predict academic success at Officer Candidate School. It is built from three ASTB-E subtests: Math Skills, Reading Comprehension, and Mechanical Comprehension.

Pascal's principle

Pressure applied to a confined fluid is transmitted equally in all directions — the basis of hydraulic lifts and brakes.

Potential energy

Stored energy of position, equal to mass times gravity times height for a raised object.

Pressure

Force divided by area. The same force on a smaller area gives higher pressure — why a sharp blade cuts.

Pulley

A wheel with a grooved rim that a rope runs over. A fixed pulley changes direction only; movable pulleys and block-and-tackle systems multiply force.

Second-class lever

A lever with the load in the middle (fulcrum–load–effort), such as a wheelbarrow. It always multiplies force.

T-score

A standardized score scaled to a mean of 50 and a standard deviation of 10. The OAR is reported as a t-score from 20 to 80, so most candidates land between 40 and 60.

Third-class lever

A lever with the effort in the middle (fulcrum–effort–load), such as tweezers or the human forearm. It always multiplies speed and distance.

Torque

A turning force, equal to force times the distance from the pivot. A longer wrench produces more torque for the same push.

Vocabulary in context

Choosing a word's meaning from how it is used in the passage, rather than its most common dictionary definition.

Work (physics)

Force times the distance moved in the direction of the force, measured in joules. No motion means no work.

Free OAR Study Materials & Resources

Everything you need to prepare for the OAR is free here — no paywall, no sign-up. This guide is the foundation; pair it with the rest of our free OAR study materials for active recall, timed practice, and last-minute review:

• OAR Practice Test — exam-style questions across all three subtests, with explanations.
• OAR Flashcards — active-recall decks for the math formulas, reading strategies, and mechanical concepts.
• ASTB Practice Test — for aviation candidates who need the full ASTB-E beyond the OAR.

OAR Study Guide FAQ

References

1. 1.U.S. Navy / Naval Operational Medicine Institute. “Aviation Selection Test Battery (ASTB) Overview.” U.S. Navy. ↑
2. 2.U.S. Navy. “MILPERSMAN 1542-010 — Aviation Selection Test Battery.” MyNavyHR / U.S. Navy. ↑
3. 3.Naval Education and Training Command. “Naval Aviation Schools Command (NASC).” U.S. Navy. ↑
4. 4.MyNavyHR. “Aviation Officer Community Management.” U.S. Navy. ↑

Sources for the concept answers

Every answer in the OAR concept questions above is drawn from an official primary source:

Career Employer

Career Employer is the ultimate resource to help you get started working the job of your dreams. We cover topics from general career information, career searching, exam preparation with free study materials, career interviewing, and becoming successful in your career of choice.

Follow Us:

All Posts