Free OAR Exam Flashcards

Evaluate grouping symbols first, then exponents, then multiplication and division from left to right, followed by addition and subtraction from left to right. Multiplication and division share a level.

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 values to convenient benchmarks and estimate the result. Use the estimate to rule out incompatible choices. If two choices are close to the estimate, calculate the exact result.

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.

For like bases, add exponents when multiplying and subtract them when dividing. For a power of a power, multiply exponents. For x ≠ 0, x⁰ = 1 and x⁻ⁿ = 1/xⁿ. A quotient also requires a nonzero denominator.

For ax² + bx + c = 0 with a ≠ 0, x = (−b ± √(b² − 4ac))/(2a). A positive discriminant gives two real roots, zero gives one repeated real root, and a negative discriminant gives no real roots.

(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.

In plane geometry, a triangle’s interior angles sum to 180°. Adjacent angles that form a straight line also sum to 180°, and angles around a point sum to 360°.

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.

For constant speed, distance = speed × time. For motion along one line, opposite directions give a relative speed equal to the sum of the speeds. The relative speed for travel in the same direction is the absolute difference. Keep distance and time units consistent.

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.

Use only the information in the passage. Support your choice with a specific sentence or with a conclusion that follows from several statements in the text.

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.

Check whether the passage supports the full scope of absolute terms such as always, never, all, none, and only. A qualified answer is appropriate when the passage itself limits the claim.

Tone is the author’s attitude, such as neutral, skeptical, or approving. Purpose is the effect the author aims for, such as informing, persuading, or explaining. Use wording and emphasis to support the choice.

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 adjusts up to a maximum to oppose the tendency to slip. Once the surfaces slide, kinetic friction opposes their relative sliding and is often below the maximum static friction. In the dry-friction model, both limits scale with the normal force. Bearings can replace sliding with rolling.

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 ½mv². Near Earth, gravitational potential energy relative to a chosen height is mgh. During a fall with negligible air resistance, gravitational potential energy decreases by the same amount that kinetic energy increases.

Mechanical advantage is output force divided by input force. In an ideal lossless machine, that equals input distance divided by output distance. A force gain requires a corresponding increase in input travel.

A lever balances when opposing torques are equal. Torque magnitude is force times the perpendicular distance from the pivot to the force’s line of action. Increasing that perpendicular arm increases torque for the same 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).

A frictionless ramp reduces the force needed to raise a load by increasing the distance traveled. For a fixed rise, a longer ramp provides greater ideal mechanical advantage. A wedge redirects an applied force to separate or lift material.

A screw turns rotary motion into linear motion. For screws with the same handle radius and negligible friction, less axial advance per turn gives more mechanical advantage and takes more turns for the same travel. On a single-start screw, advance per turn equals thread pitch.

An ideal single fixed pulley changes the pull direction and has mechanical advantage 1. An ideal movable pulley arrangement can multiply force. With vertical supporting strands of equal tension, the ideal mechanical advantage is the number supporting the moving load.

In a directly meshed external gear pair, the gears turn in opposite directions and speed is inversely proportional to tooth count. A small driver turning a large driven gear reduces speed and increases ideal output torque.

An open belt or ordinary chain drive makes both shafts turn in the same direction. A crossed belt reverses direction. With no slip, a smaller driven pulley spins faster. A chain engages sprocket teeth to maintain the speed ratio.

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 is normal force divided by area. In a stationary liquid of uniform density, gauge pressure increases with depth according to ρgh. Absolute pressure also includes the pressure at the surface.

Buoyant force equals the weight of displaced fluid. For a freely floating object at rest, buoyant force balances its weight. An object denser on average than the fluid sinks, while equal density allows neutral buoyancy when fully submerged.