OAR flashcards
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32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Order of operations
- Evaluate expressions in this order: parentheses or grouping symbols, exponents or roots, multiplication and division from left to right, then addition and subtraction from left to right.
- Common denominator
- A shared multiple of two or more denominators. Rewrite each fraction with this denominator before adding or subtracting so the numerators can be combined directly.
- Percent change formula
- Percent change equals the difference between new and old values divided by the old value, multiplied by 100. A positive result is an increase; a negative result is a decrease.
- Cross-multiplication
- A method for solving a proportion a/b = c/d by multiplying ad and bc to get ad = bc. It works because multiplying both sides by bd clears the denominators.
- Mean vs median
- The mean is the sum of values divided by their count. The median is the middle value in an ordered list, or the average of the two middle values for an even count.
- Distance-rate-time formula
- Distance equals rate multiplied by time, written d = rt. Rearranged, rate equals distance divided by time, and time equals distance divided by rate.
- Area of a circle
- The area of a circle is π times the radius squared, A = πr². If the diameter is given, first divide it by two to find the radius.
- Volume of rectangular solid
- The volume of a rectangular solid is length times width times height, V = lwh. Volume is expressed in cubic units such as cubic inches or cubic meters.
- Feet-to-inches conversion
- One foot equals 12 inches, so multiply a number of feet by 12 to convert to inches. Divide inches by 12 to convert back to feet.
- Exponent product rule
- When multiplying powers with the same base, add the exponents: x^a · x^b = x^(a+b). For example, x^3 · x^4 = x^7.
- Reciprocal
- The reciprocal of a nonzero number is 1 divided by that number; for a fraction, swap numerator and denominator. Dividing by a fraction is the same as multiplying by its reciprocal.
- Main idea
- The central point the passage develops and supports. It is broader than a single detail but more specific than the general topic.
- Supporting detail
- A fact, example, reason, or statistic that explains or proves the main idea. It can be located in the passage and should not be confused with the central claim.
- Inference
- A conclusion that follows logically from stated information plus ordinary knowledge. A valid inference is strongly supported by the text, not merely possible.
- Tone
- The author’s attitude toward the subject, revealed through word choice, connotations, and emphasis. Tone differs from mood, which is the feeling created in the reader.
- Author's purpose
- The reason the author writes the passage, commonly to inform, explain, persuade, or entertain. The overall purpose shapes which details and language the author selects.
- Context clue
- Information in nearby words or sentences that helps define an unfamiliar word. Types include definitions, examples, contrasts, and cause-effect relationships.
- Passage structure
- The organizational pattern of a passage, such as compare-contrast, cause-effect, problem-solution, chronological, or description. Recognizing it helps locate main ideas and supporting details.
- Exception question
- A question asking which answer choice is NOT supported by the passage. Verify each choice against the text; the correct answer is the one contradicted or absent.
- Extreme language
- Words such as always, never, all, or only that make a statement absolute. Answer choices containing them are usually wrong unless the passage explicitly supports the absolute claim.
- Transition word
- A word or phrase such as however, therefore, or for example that signals a logical relationship between ideas. It can indicate contrast, cause, result, addition, or illustration.
- Work formula
- Work equals force multiplied by the distance an object moves in the direction of the force, W = Fd. The unit is the joule, equal to one newton-meter.
- Power formula
- Power equals work divided by time, P = W/t. The unit is the watt, equal to one joule per second; more power means work is done faster.
- Mechanical advantage
- The ratio of output force to input force, or output distance to input distance, in a machine. A mechanical advantage greater than one multiplies force.
- First-class lever
- A lever with the fulcrum between the effort and the load, like a seesaw. It can multiply force or speed depending on the relative distances from the fulcrum.
- Second-class lever
- A lever with the load between the fulcrum and the effort, like a wheelbarrow. It always multiplies force because the effort arm is longer than the load arm.
- Third-class lever
- A lever with the effort between the fulcrum and the load, like a pair of tweezers. It increases speed and distance rather than multiplying force.
- Pulley mechanical advantage
- For an ideal movable pulley system, mechanical advantage equals the number of rope segments supporting the moving load. Friction reduces the actual advantage.
- Gear ratio
- The number of teeth on the driven gear divided by the number on the driving gear. A larger driven gear turns more slowly but delivers greater torque.
- Pressure formula
- Pressure equals force divided by the area over which it acts, P = F/A. For the same force, a smaller area produces greater pressure.
- Density
- Density equals mass divided by volume, d = m/V. An object with greater density than the surrounding fluid sinks; lower density floats.
- Friction
- A force that opposes sliding or rolling between surfaces in contact. It acts along the surfaces and increases with normal force or surface roughness.