Free OAR Exam Flashcards

Resolve in order: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Multiplication and division share a tier; do whichever appears first reading left to right. A single misordered step is the most common avoidable MST error.

Fraction to decimal: divide top by bottom. Decimal to percent: move the point two places right (0.35 = 35%). Percent to fraction: put it over 100 and reduce (25% = 1/4). Memorizing 1/8 = 0.125, 1/3 ≈ 0.333, 3/4 = 0.75 saves time when no calculator is allowed.

Same signs multiplied/divided give a positive; different signs give a negative. Adding numbers with the same sign: add and keep the sign. Different signs: subtract the smaller absolute value from the larger and keep the sign of the larger. Subtracting a negative is the same as adding a positive.

Round each value to an easy benchmark, compute a rough answer, and discard choices that are not close. Because answer choices are usually spread apart, a good estimate often isolates one option without exact computation — a key tactic with no calculator and tight time.

Isolate the variable by undoing operations in reverse order: clear parentheses, combine like terms, move variable terms to one side and constants to the other, then divide by the coefficient. Whatever you do to one side you must do to the other.

Solve an inequality like an equation, with one exception: when you multiply or divide both sides by a negative number, reverse the inequality direction (≤ becomes ≥). Forgetting this flip is the classic inequality trap.

Multiplying same base: add exponents (x^a · x^b = x^(a+b)). Dividing: subtract (x^a / x^b = x^(a−b)). Power of a power: multiply (x^a)^b = x^(ab). Anything to the 0 power = 1. Negative exponent means reciprocal: x^(−n) = 1/x^n.

For ax² + bx + c = 0, x = [−b ± √(b² − 4ac)] / 2a. Try factoring first; use the formula when factoring is not obvious. The discriminant (b² − 4ac) sign tells you whether there are two, one, or no real solutions.

(a + b)(c + d) = ac + ad + bc + bd — multiply First, Outer, Inner, Last terms, then combine like terms. Recognize the shortcut: (a + b)(a − b) = a² − b² (difference of squares).

Assign a variable to each unknown, write one equation per stated relationship, then solve by substitution (isolate one variable and plug in) or elimination (add/subtract equations to cancel a variable). Two unknowns require two independent equations.

The three interior angles of any triangle always sum to 180°. Angles on a straight line also sum to 180°, and angles around a point sum to 360°. These let you find a missing angle by subtraction.

For a right triangle, a² + b² = c², where c is the hypotenuse (opposite the right angle). Recognizing the 3-4-5 and 5-12-13 triples (and their multiples like 6-8-10) lets you skip the square root entirely.

Rectangle: length × width. Triangle: ½ × base × height. Circle: πr². Parallelogram: base × height. Trapezoid: ½ × (b₁ + b₂) × height. Height must be perpendicular to the base, not a slanted side.

Circumference = 2πr = πd. Area = πr². The radius is half the diameter — a frequent OAR trap is being given the diameter and using it directly as r. Always check which one the problem provides.

Rectangular solid (box): length × width × height. Cylinder: πr² × height (base area times height). Volume scales with three dimensions, so doubling every side multiplies volume by 8.

Similar figures have equal corresponding angles and proportional corresponding sides. If sides scale by factor k, perimeter scales by k, but area scales by k² and volume by k³. Set up a proportion of corresponding sides to find a missing length.

Perimeter is the total distance around a shape (a length, added once around). Area is the space inside (a length squared). Fencing a yard uses perimeter; sodding it uses area. Misreading which is asked is a common word-problem error.

Distance = Rate × Time. Rearrange as Rate = D/T and Time = D/R. For two objects moving toward each other, add their speeds; moving apart or one catching another, the closing/gap speed is the difference. Keep units consistent (mph with hours).

Express each worker's rate as job-per-unit-time (1/time). Add individual rates to get a combined rate, then time = 1 ÷ combined rate. Example: 1/4 + 1/6 = 5/12 of the job per hour, so the job takes 12/5 hours together.

Percent change = (new − old) / old × 100. A successive increase then equal-percent decrease does NOT return to the start (a +20% then −20% leaves you below the original). 'Percent of' multiplies; 'percent change' compares to the original base.

Track the amount of the pure component, not just total volume. (concentration × amount) summed across all parts equals (final concentration × final total). Solving for an unknown volume usually means writing one equation in that variable.

A ratio a:b can be scaled by a common multiplier x, so the parts are ax and bx and the total is (a+b)x. Set the cross products of a proportion equal (a/b = c/d → ad = bc) to solve for one missing term.

Mean = sum ÷ count. Median = middle value when ordered (average of the two middle values if the count is even). Mode = most frequent value. The median is far less affected by extreme outliers than the mean.

Multiply the desired average by the total number of items to get the required total sum, then subtract the sum of the known values. The remainder is the value (or values) you still need.

Probability = favorable outcomes ÷ total equally likely outcomes, always between 0 and 1. For independent events both occurring, multiply their probabilities. The probability of an event NOT happening is 1 minus the probability that it does.

Every correct Reading Comprehension answer must be provable using the text itself, not outside knowledge or assumptions. If you cannot point to the supporting sentence, it is not the answer — even if it is true in real life.

The main idea is the single point the whole passage supports; a detail is one piece of evidence inside it. A main-idea answer that is too narrow (one detail) or too broad (beyond the passage scope) is wrong. Test it: does every paragraph relate to that statement?

An inference must follow logically from stated text with minimal assumption — it is the smallest reasonable step beyond what is written, not a creative leap. Eliminate choices that require information the passage never provides.

Determine the word's meaning from how it is used in the sentence, not its most common dictionary definition. Substitute each answer choice back into the sentence; the right one preserves the author's intended meaning and logic.

Answer choices with absolute words (always, never, all, none, only) are frequently wrong because passages rarely support absolute claims. Moderate, qualified statements (often, may, generally) are more defensible against the text.

Tone is the author's attitude (neutral, critical, persuasive, informative); purpose is why the passage was written (to inform, argue, describe, or analyze). Use word choice and emphasis as evidence, and pick the least extreme tone the text actually supports.

An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net external force. More mass means more inertia and greater resistance to a change in motion.

Net force = mass × acceleration (F = ma). For a fixed force, more mass means less acceleration. Acceleration is always in the direction of the net force, not necessarily the direction of motion.

For every action force there is an equal and opposite reaction force. The two forces act on different objects, so they do not cancel each other — a rocket pushes gas down and the gas pushes the rocket up.

Mass is the amount of matter and is constant everywhere. Weight is the force of gravity on that mass (W = m × g) and changes with gravitational field — the same object weighs less on the Moon but has the same mass.

Static friction must be overcome to start motion and is generally larger than kinetic (sliding) friction. Friction opposes motion and increases with the normal force pressing surfaces together. Lubrication, smoother surfaces, or rollers/bearings reduce it.

Work = Force × distance moved in the direction of the force (W = F × d). If an object does not move, or the force is perpendicular to the motion, zero work is done — holding a weight still does no physics work.

Power = Work ÷ time. Doing the same work faster requires more power. Two engines that lift the same load the same height do equal work, but the faster one is more powerful.

Kinetic energy is energy of motion (depends on mass and speed); gravitational potential energy is stored by height (PE = mgh). In an ideal system energy converts between forms but the total is conserved — a falling object trades PE for KE.

Mechanical advantage = output (resistance) force ÷ input (effort) force, or equivalently effort distance ÷ resistance distance. A machine multiplies force at the cost of distance (or speed); it does not create energy.

A lever balances when effort × effort arm = resistance × resistance arm. Torque = force × perpendicular distance from the pivot. Moving the effort farther from the fulcrum increases its turning effect, so a longer lever arm needs less force.

First class: fulcrum between effort and load (seesaw). Second class: load between fulcrum and effort, always multiplies force (wheelbarrow). Third class: effort between fulcrum and load, multiplies distance/speed not force (tweezers, forearm).

An inclined plane lets you raise a load with less force over a longer distance; a longer, gentler ramp gives greater mechanical advantage. A wedge is essentially a moving inclined plane that converts a pushing force into splitting/lifting forces.

A screw is an inclined plane wrapped around a cylinder. Threads that are closer together (finer pitch) require more turns but less force per turn, giving greater mechanical advantage than a coarse-threaded screw.

A single fixed pulley only changes the direction of force (MA = 1). A movable pulley multiplies force. In a block-and-tackle, the ideal mechanical advantage equals the number of rope strands directly supporting the load.

A small gear driving a large gear turns the large gear slower but with more torque; a large gear driving a small gear gives more speed and less torque. Two meshed gears always rotate in opposite directions.

A belt over two pulleys makes both turn the same direction; a crossed belt reverses direction. A smaller driven pulley spins faster than the driver; a larger driven pulley spins slower with more torque. A chain (like gears) does not slip.

Pressure applied to a confined fluid transmits equally in all directions. In a hydraulic system, a small force on a small piston produces a large force on a large piston, scaled by the ratio of piston areas — the basis of mechanical advantage in jacks and brakes.

Pressure = Force ÷ Area, so the same force over a smaller area gives greater pressure. In a fluid, pressure increases with depth and does not depend on the container's shape — only on depth, fluid density, and gravity.

The upward buoyant force on a submerged or floating object equals the weight of the fluid it displaces. An object floats if it is less dense than the fluid and sinks if it is denser; it floats at the depth where displaced fluid weight equals its own weight.