Your FREE OAR Flashcards 2026 – 200+ Cards

Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Convert the percent to a decimal and multiply. 35% of 80 = 0.35 × 80 = 28.

Percent change = (change ÷ original) × 100. Always divide by the starting value, not the new one.

Divide the numerator by the denominator. 7/8 = 7 ÷ 8 = 0.875.

Write it over 100 and simplify. 25% = 25/100 = 1/4.

Divide the top and bottom by their greatest common factor. 18/24 = 3/4 (both ÷ 6).

Find a common denominator, add the numerators, keep the denominator, then simplify. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

Multiply the numerators and the denominators straight across, then simplify. 2/3 × 3/4 = 6/12 = 1/2.

Multiply by the reciprocal of the second fraction (flip and multiply). 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.

Isolate the variable using inverse operations. For 3x + 7 = 22: subtract 7 (3x = 15), divide by 3 (x = 5).

Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁). It measures steepness; positive rises left to right.

y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).

Cross-multiply: a/b = c/d means a × d = b × c, then solve for the unknown.

A comparison of two quantities. A 3:2 ratio means 3 parts to 2 parts, for 5 parts total.

Add all the values and divide by how many there are. The average of 14, 18, 22 is 54 ÷ 3 = 18.

The middle value of a data set in order. With an even count, average the two middle values.

The value that appears most often in a data set.

Repeated multiplication. 4² = 4 × 4 = 16; 3³ = 3 × 3 × 3 = 27.

Add the exponents: xᵃ × xᵇ = xᵃ⁺ᵇ.

Subtract the exponents: xᵃ ÷ xᵇ = xᵃ⁻ᵇ.

Multiply the exponents: (xᵃ)ᵇ = xᵃᵇ.

A negative exponent means reciprocal: x⁻ⁿ = 1 ÷ xⁿ.

The number that, multiplied by itself, gives the value. √64 = 8 because 8 × 8 = 64.

Area = length × width.

Area = ½ × base × height.

Area = π × radius². Use π ≈ 3.14.

Circumference = 2 × π × radius = π × diameter.

The total distance around a shape — add the lengths of all sides.

Volume = length × width × height.

For a right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle).

They always add up to 180°.

They always add up to 360°.

Two angles that add up to 180° (a straight line).

Two angles that add up to 90° (a right angle).

Distance = rate × time. A car at 60 mph for 4 hours travels 240 miles.

Total distance ÷ total time. 240 miles in 4 hours = 60 mph.

Favorable outcomes ÷ total outcomes, a value from 0 to 1. One head on a coin flip = 1/2.

The smallest number both values divide into evenly. LCM of 6 and 8 is 24.

The largest number that divides both values evenly. GCF of 18 and 24 is 6.

A whole number greater than 1 with exactly two factors: 1 and itself (2, 3, 5, 7, 11, ...).

The distance of a number from zero, always non-negative. |−7| = 7.

Add or subtract terms with the same variable. 3x + 5x = 8x; you can't combine 3x and 5.

Multiply a term across a sum: a(b + c) = ab + ac. 3(x + 4) = 3x + 12.

Solve like an equation, but flip the inequality sign when you multiply or divide by a negative number.

Multiply two binomials: First, Outer, Inner, Last. (x + 2)(x + 3) = x² + 5x + 6.

a² − b² = (a + b)(a − b).

Multiply by 100 and add a percent sign. 0.875 = 87.5%.

Look at the digit to the right of the place you're rounding to: 5 or more rounds up, 4 or less rounds down.

A number written as a value between 1 and 10 times a power of 10. 4,500 = 4.5 × 10³.

Interest = principal × rate × time (I = P × r × t).

A 25% markup multiplies the price by 1.25; a 25% discount multiplies it by 0.75.

Multiply the whole number by the denominator, add the numerator, keep the denominator. 2 1/3 = 7/3.

The number you multiply by to get 1 — flip a fraction. The reciprocal of 3/4 is 4/3.

Use inverse operations to isolate the wanted variable, treating the others as constants.

Translate words to an equation, solve step by step, then check the answer against the question asked.

Multiply by a conversion factor so unwanted units cancel. 5 feet × 12 in/ft = 60 inches.

Round numbers to estimate the result; if your exact answer is far from the estimate, recheck your work.

150% of a number is 1.5 times it. Percents above 100 mean more than the whole.

ax² + bx + c = 0. Solve by factoring, completing the square, or the quadratic formula.

A whole number and its negatives, including zero: ..., −2, −1, 0, 1, 2, ... (no fractions or decimals).

A number that divides another evenly. The factors of 12 are 1, 2, 3, 4, 6, and 12.

The product of a number and an integer. Multiples of 4 are 4, 8, 12, 16, ...

The number multiplying a variable. In 7x, the coefficient is 7.

A letter that stands for an unknown or changing value, like x or y.

Undo addition/subtraction first, then multiplication/division. For 2x − 3 = 7: add 3 (2x = 10), divide by 2 (x = 5).

From 80 to 100: change is 20, so increase is 20 ÷ 80 = 25%.

From 100 to 80: change is 20, so decrease is 20 ÷ 100 = 20%.

To compare or solve fractions, multiply each numerator by the other's denominator. a/b = c/d gives ad = bc.

A shared multiple of two denominators, needed to add or subtract fractions.

A fraction whose numerator is at least as large as its denominator, like 7/4.

Digits after the point are tenths, hundredths, thousandths, ... 0.25 is 2 tenths + 5 hundredths.

Multiply as whole numbers, then place the decimal point so the answer has as many decimal places as both factors combined.

Move the decimal point in the divisor to make it whole, move it the same in the dividend, then divide.

A negative times a negative is positive; a negative times a positive is negative.

Multiply the number by itself. 9² = 81.

Multiply the number by itself three times. 2³ = 8.

A number that is the square of an integer: 1, 4, 9, 16, 25, 36, ...

Find the perfect squares it falls between. √50 is between √49 (7) and √64 (8), so about 7.1.

The total area of all the faces of a 3-D shape, measured in square units.

Volume = π × radius² × height.

The diameter is twice the radius; the radius runs from the center to the edge of a circle.

An angle of exactly 90°, marked with a small square.

Acute angles are less than 90°; obtuse angles are between 90° and 180°.

Parallel lines never meet (equal slopes); perpendicular lines cross at 90° (slopes are negative reciprocals).

Solve one equation for a variable, plug it into the other, then solve for the remaining variable.

The difference between the largest and smallest values.

60 minutes = 1 hour. 90 minutes = 1.5 hours; 2.25 hours = 2 hours 15 minutes.

If one worker finishes in a hours and another in b hours, together they do 1/a + 1/b of the job per hour.

Track the amount of the key ingredient: amount = concentration × total, and set the parts equal to the whole.

In percent word problems, 'of' means multiply and 'is' means equals: 'what is 20% of 50' = 0.20 × 50.

Substitute your answer back into the original equation to confirm both sides are equal.

Consecutive integers differ by 1: n, n+1, n+2. Their sum is 3n + 3 for three of them.

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

A specific fact, example, or statement the passage gives to back up the main idea.

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

Answer only from the passage. The correct choice is supported by the text — never by your own outside knowledge or opinion.

Why the author wrote the passage — to inform, persuade, describe, or entertain. Look at tone and word choice.

The author's attitude toward the subject (neutral, critical, enthusiastic, skeptical), revealed by word choice.

Choosing the meaning of a word based on how it is used in the sentence — not its most common dictionary definition.

Combining stated facts in the passage to reach a logical end point the text supports.

A fact can be verified; an opinion expresses a belief or judgment (often signaled by words like 'best' or 'should').

Cross out choices that are too extreme, off-topic, contradicted by the text, or true in the world but not in the passage.

Be cautious of answer choices with absolute words like 'always,' 'never,' or 'all' — passages rarely support them.

A choice that brings in information the passage never mentions. If you can't point to support in the text, eliminate it.

A restatement repeats what the passage directly says; an inference goes one logical step beyond what is stated.

Note the main idea and the structure as you read so you can find support quickly — passages are short, so read for the point.

When two choices seem possible, pick the one with the most direct textual support, not the most interesting one.

The topic is what the passage is about (one phrase); the main idea is the point the passage makes about that topic (a full claim).

What the author suggests without saying directly — read between the lines, but stay anchored to the text.

Surrounding words and sentences that hint at the meaning of an unfamiliar word or the answer to a question.

Form your own answer before reading the choices, then match it to the closest option — it guards against trap answers.

Capturing the main idea and key support in a sentence or two — a check that you grasped the point.

Transitions like 'however,' 'therefore,' and 'for example' that show how ideas relate — contrast, cause, or example.

Identifying what made something happen (cause) and the result (effect), often linked by words like 'because' or 'so.'

Finding how two ideas in a passage are alike and how they differ.

Asks for an exact fact stated in the passage — scan back to the relevant line rather than relying on memory.

Roughly 20 questions in about 30 minutes — read efficiently, don't reread the whole passage, and don't dwell on one question.

Restating an idea from the passage in your own words while keeping its exact meaning.

The order in which events or steps occur in a passage — watch for time or order signal words (first, then, finally).

Since OAR passages are short, read to grasp the author's main claim quickly rather than memorizing every detail.

If you can't underline support for a choice in the passage, it's wrong — even if it sounds true.

Loaded or emotional language can reveal the author leans toward one side of an issue.

Asks why the passage as a whole was written — the answer should fit every paragraph, not just one.

A strengthening fact supports the author's claim; a weakening fact undermines it.

An implication follows from what's said; an assumption is something the author takes for granted without stating.

For detail questions, find a distinctive word from the question in the passage and read around it.

Ask which choice is NOT supported — eliminate the three that ARE supported and pick the leftover.

Often the first or last sentence of a paragraph; it usually states that paragraph's main point.

Correct answers often paraphrase the passage rather than repeat it word for word.

Don't reread the whole passage for each question; locate the relevant lines and move on.

An inference is firmly supported by the text; a guess adds information the passage never provides.

Look for the claim the rest of the passage is built to support — often signaled by 'therefore' or 'thus.'

Don't pick an answer because you personally agree with it; pick the one the passage supports.

When a passage weighs two views, note where they agree and disagree before answering.

Inertia: an object stays at rest, or in motion at constant velocity, unless a net force acts on it. (Why riders lurch forward when a car brakes.)

F = ma — net force equals mass times acceleration. For the same force, more mass means less acceleration.

For every action there is an equal and opposite reaction. A rocket pushes gas down; the gas pushes the rocket up.

Lever, wheel and axle, pulley, inclined plane, wedge, and screw. Every complex machine is built from these.

How many times a machine multiplies your input force: MA = output force ÷ input force. MA > 1 multiplies force; MA < 1 multiplies speed/distance.

Fulcrum in the middle (effort–fulcrum–load). Examples: seesaw, crowbar, scissors. Can multiply force or distance.

Load in the middle (fulcrum–load–effort). Always multiplies force (MA > 1). Examples: wheelbarrow, bottle opener, nutcracker.

Effort in the middle (fulcrum–effort–load). Always multiplies distance/speed (MA < 1). Examples: tweezers, fishing rod, human forearm.

The fixed pivot point a lever rotates around.

Effort × effort arm = load × load arm. A longer effort arm lets a small force lift a large load.

Equals the number of rope segments that support the load. One fixed pulley = MA 1 (changes direction only); two supporting ropes = MA 2.

A pulley attached to a fixed point. It changes the direction of the force but gives no mechanical advantage (MA = 1).

A pulley that moves with the load. It gives a mechanical advantage of 2 but you must pull twice the rope length.

A machine never gives free energy: the more it multiplies force, the more distance you must move the input. Work in ≈ work out.

A ramp. It reduces the force needed to raise a load by spreading the work over a longer distance. A longer, gentler ramp needs less force.

Two inclined planes back to back. It converts a downward force into sideways splitting force. Examples: axe, knife, chisel.

An inclined plane wrapped around a cylinder. Closer threads (finer pitch) give more mechanical advantage.

A large wheel fixed to a smaller axle. A small force on the large wheel produces a large force at the axle. Examples: doorknob, steering wheel.

Driven gear teeth ÷ driver gear teeth. Meshed gears turn in opposite directions.

The large (driven) gear turns slower but with more torque. Speed is traded for force.

The small (driven) gear turns faster but with less torque. Force is traded for speed.

A turning force: torque = force × distance from the pivot. A longer wrench gives more torque for the same push.

Work = force × distance, when the force acts in the direction of motion. Measured in joules. No motion means no work.

The rate of doing work: power = work ÷ time. The same job done faster requires more power.

Energy of motion: KE = ½ × mass × velocity². Doubling speed quadruples kinetic energy.

Stored energy of position: PE = mass × gravity × height. Lifting an object higher stores more energy.

Energy is never created or destroyed, only converted. A falling object trades potential energy for kinetic energy.

A force that opposes motion between surfaces in contact. It always acts opposite to the direction of motion and produces heat.

Static friction holds a still object in place and is usually larger; kinetic (sliding) friction acts on a moving object and is usually smaller.

The force that pulls masses together. Near Earth it accelerates falling objects at about 9.8 m/s² regardless of their mass (ignoring air resistance).

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

Speed is how fast (magnitude only). Velocity is speed with a direction.

The rate of change of velocity. A change in speed OR direction is acceleration. Units: m/s².

Force per unit area: pressure = force ÷ area. The same force on a smaller area gives higher pressure (why a sharp knife cuts).

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

In a hydraulic system, a small force on a small piston creates a large force on a large piston, in proportion to the piston areas.

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

When a pipe narrows, the fluid speeds up; when it widens, the fluid slows down. The flow rate stays the same.

An object in a fluid is pushed up by a force equal to the weight of the fluid it displaces. It floats if that force ≥ its weight.

Mass per unit volume: density = mass ÷ volume. Less-dense objects float on denser fluids.

Transfer of heat through a material by direct contact. Metals are good conductors; wood, air, and plastic are insulators.

Conductors (copper, most metals) let current flow easily; insulators (rubber, glass, wood) resist it.

Voltage = current × resistance (V = I × R). For a fixed voltage, higher resistance means lower current.

Components on one path. The same current flows through all; if one breaks, the whole circuit stops.

Components on separate branches. Each gets the full voltage; if one branch breaks, the others keep working.

The force a spring exerts is proportional to how far it is stretched or compressed: F = k × x.

The point where an object's weight is balanced. A lower, more central center of gravity makes an object more stable.

Mass in motion: momentum = mass × velocity. A heavier or faster object has more momentum and is harder to stop.

A state of balanced forces — no net force and no net torque, so the object stays at rest or moves at constant velocity.

Tension is a pulling force that stretches; compression is a pushing force that squeezes. Cables carry tension; columns carry compression.

Putting effort far from the fulcrum multiplies force; putting it close multiplies speed and distance.

The time for one swing depends on the pendulum's length and gravity — not on the mass of the bob or (for small swings) the size of the swing.

Most materials expand when heated and contract when cooled. Why bridges and rails have expansion gaps.

A push or pull that can change an object's motion or shape. Measured in newtons; it has both size and direction.

The single combined force from all forces acting on an object. A nonzero net force causes acceleration.

It trades force for distance: raising a load over a longer, gentler slope needs less force but more travel — the same total work.

On a lever, the effort arm is the distance from the fulcrum to the effort; the load arm is from the fulcrum to the load. Longer effort arm = more force advantage.

A gear placed between two others that changes the direction of rotation without changing the overall gear ratio.

To balance, the lighter child sits farther from the fulcrum so weight × distance is equal on both sides.

Energy transferred because of a temperature difference, always flowing from hotter to colder objects.

Reduces friction between surfaces, lowering heat and wear and making machines more efficient.

A small edge area concentrates force into high pressure (pressure = force ÷ area).

Stable: an object returns to position after a small push. Unstable: a small push topples it. A wide base and low center of gravity add stability.

The constant speed a falling object reaches when air resistance balances gravity, so net force becomes zero.

A pulley system combining fixed and movable pulleys to multiply force. The mechanical advantage equals the number of supporting rope segments.

Ideal MA assumes no friction; actual MA is always lower because friction wastes some input force as heat.

Useful work output ÷ work input, as a percent. Friction makes real machines less than 100% efficient.

Two or more simple machines working together, like scissors (two levers + two wedges) or a bicycle (gears, levers, wheels).

A first-class lever: you push down on one end (effort), the fulcrum is the bend, and the load is lifted at the other end.

A second-class lever: the wheel is the fulcrum, the load sits in the middle, and you lift the handles (effort).

A third-class lever: the elbow is the fulcrum, the biceps applies effort in the middle, and the hand holds the load.

The distance between threads. A smaller pitch (threads closer together) gives a greater mechanical advantage.

It lubricates contacting surfaces, lowering friction so less force is lost to heat and parts last longer.

A number describing how much two surfaces resist sliding. Rougher surfaces have a higher coefficient.

Motion under gravity alone. All objects fall at the same rate (about 9.8 m/s²) when air resistance is ignored.

Horizontal and vertical motion act independently: gravity pulls the object down while it keeps moving forward.

The more mass an object has, the more inertia — and the harder it is to start, stop, or turn it.

Forces always come in pairs that are equal in size and opposite in direction, acting on two different objects.

The inward force that keeps an object moving in a circle, directed toward the center of the curve.

MA = effort arm length ÷ load arm length. A longer effort arm lets a small effort move a large load.

Two meshed gears turn in opposite directions. An odd number of gears reverses direction; an even number keeps it.

Meshed gears have the same speed at their teeth, so a smaller gear must spin faster than a larger one.

The sum of kinetic and potential energy. In an ideal system it stays constant as one converts to the other.

Lifting a load does work equal to weight × height — independent of the path taken to raise it.

A single fixed pulley lets you pull down to lift up; it gives no force advantage but is easier to use.

Uses Pascal's principle: a small force on a small piston produces a large force on a large piston.

Air moving faster over the curved top of a wing has lower pressure (Bernoulli), and the wing deflects air downward.

At constant temperature, a gas's pressure and volume are inversely related: squeeze the volume and pressure rises.

At constant pressure, a gas's volume increases as its temperature rises.

The weight of the air above us pressing down, about 14.7 pounds per square inch at sea level.

In a vacuum all objects accelerate equally under gravity; air resistance, not weight, makes some fall slower.

A wide base and a low center of gravity resist tipping — that's why race cars are low and wide.

The three ways heat moves: direct contact (conduction), fluid currents (convection), and waves (radiation).

Its rotating mass has rotational inertia, so it keeps spinning and smooths out changes in speed.