Digital SAT flashcards

The central idea (or main idea) is the overarching message or point that the author is trying to convey. It is the core concept around which all other details revolve.

• Look for recurring themes and dominant messages.
• Distinguish between main ideas and supporting details.
• Consider the author's purpose in conveying the information.

Memory trick: Main Message Makes Most Meaning.

The rate at which a population is changing at a specific moment in time within a logistic growth model. It is highest when the population is half of the carrying capacity (K/2).

• Calculated using the derivative: dP/dt = kP(1 - P/K).
• k is the growth rate constant from the model P(t) = K / (1 + Ae^(-kt)).
• Maximum rate of change occurs when P = K/2.

Memory trick: Rate is fastest when population is 'halfway up the hill'!

The area of a region bounded by two radii and the intercepted arc of a circle.

• Formula (degrees): A = (θ/360°) * πr²
• Formula (radians): A = (1/2)r²θ
• Represents a 'slice' of the circle.

Memory trick: A sector is a pizza slice – its area is a fraction of the whole pizza.

A straight line that touches a circle at exactly one point.

• The tangent line is always perpendicular to the radius at the point of tangency.
• Forms a right angle, useful for Pythagorean theorem and trigonometry.
• Important concept in geometry and calculus.

Memory trick: Tangent means 'touching just once,' and it's always 'right' with the radius.

Inferring quality of life involves drawing conclusions about the well-being and characteristics of an environment or population based on demographic, infrastructural, and social indicators, rather than direct statements.

• Connect observed characteristics to common implications for daily living.
• Consider how different elements of an environment interact.
• Avoid making subjective judgments not supported by objective indicators.

Memory trick: Details Describe Daily Delights, Distinguishing Different Dwellings.

For a quadratic function f(x) = ax^2 + bx + c, the x-coordinate of the vertex, given by -b/(2a), represents the time or input value at which the function reaches its maximum or minimum output.

• If 'a' is positive, the vertex is a minimum point.
• If 'a' is negative, the vertex is a maximum point.
• The formula -b/(2a) finds the input (e.g., time) for the extremum.

Memory trick: Time to find the 'tip-top' or 'bottom-out' of the curve!

The Pythagorean theorem (a^2 + b^2 = c^2) is used to find an unknown side of a right-angled triangle when two sides are known.

• Applies only to right-angled triangles.
• c always represents the hypotenuse (the longest side, opposite the right angle).
• a and b represent the other two sides (legs).

Memory trick: Right angle, right answer, sides squared, sum it up!

Rates describe how one quantity changes in relation to another, often requiring conversion of units to ensure consistency for calculations.

• Ensure units are consistent (e.g., all in minutes or hours).
• A rate is a ratio of two quantities with different units.
• Multiply the rate by the quantity of the independent variable to find the total.

Memory trick: Match units, find rate, then multiply for the new total time.

Binomial probability calculates the likelihood of getting exactly 'k' successes in 'n' independent Bernoulli trials, where each trial has only two possible outcomes (success/failure).

• Requires fixed number of trials (n).
• Each trial has only two outcomes (success/failure).
• Probability of success (p) is constant for each trial.
• Trials are independent.

Memory trick: How many ways to get successes, times probability of one way.

A proportional relationship exists between two quantities when their ratio is constant. This means as one quantity changes, the other changes by a constant multiple.

• Can be expressed as a/b = c/d
• Graph is a straight line through the origin
• Constant of proportionality is the ratio y/x

Memory trick: Ratios Remain Equal, Always Balanced.

Relative frequency is the proportion or fraction of times an event occurs in a dataset, calculated by dividing the frequency of the specific event by the total number of observations.

• Expressed as a decimal, fraction, or percentage.
• Sum of all relative frequencies for all categories is 1 (or 100%).
• Used to understand the distribution of data.

Memory trick: Part over Whole, always a fraction of the total.

The deeper, often abstract meaning or representation a concrete object, character, or event holds within a text.

• Symbols often recur and evolve in meaning.
• Requires interpretation beyond the literal meaning.
• Connects to the text's themes or character development.

Memory trick: Object, Observe, Outcome: What's the 'O'verarching message?

Reconciling contradictory data involves finding a plausible explanation that accounts for all observed facts, even when they initially appear to conflict. It often requires considering external factors or nuanced interpretations.

• Identify the conflicting pieces of information.
• Look for a single explanation that can logically bridge the gap between them.
• Consider external variables or contextual factors that might influence the outcomes.

Memory trick: Conflicting Clues Call for Clever Contextual Connections.

Drawing conclusions based on numerical data, statistics, or measurements, often by comparing different data points or trends.

• Requires careful interpretation of percentages, rates, or counts.
• Must be directly supported by the provided numbers.
• Focuses on what the numbers *imply* rather than explicitly state.

Memory trick: Data, Discrepancy, Deduction: What do the 'D'igits truly mean?

Synthesizing diverse perspectives involves combining information from different sources, which may offer contrasting views or focus on different aspects, to form a comprehensive and nuanced understanding of a topic or event.

• Identify the central claim or focus of each perspective.
• Look for areas of agreement and disagreement.
• Formulate a summary that integrates all relevant information, acknowledging complexity.

Memory trick: Voices Vary, Viewpoints Validate, Vexing Verdicts Vanish.

Explaining discrepancies involves identifying an underlying reason or factor that accounts for an apparent contradiction or unexpected outcome between two pieces of information or observations.

• Pinpoint the exact contradiction or unexpected result.
• Look for a missing piece of information or an unstated assumption.
• The explanation should logically bridge the gap between the conflicting observations.

Memory trick: Conflicting Clues Call for Clever Contextual Connections.

The percentage of a whole represents a part of a total quantity expressed as a fraction of 100.

• All percentages of parts must sum to 100% for the whole.
• To find the quantity, multiply the percentage (as a decimal) by the total.
• Useful for breaking down populations or distributions.

Memory trick: Total is 100%, subtract what you know to find the rest.

These problems involve using percentages to find a part of a whole, and then applying a ratio to further divide that part into sub-components.

• Calculate the absolute number from the percentage first.
• Ratios represent parts of a whole; sum the ratio parts to find the total parts.
• Divide the absolute number by the total ratio parts to find the value of one part.

Memory trick: First percentage, then ratio, then the specific part.

Inferring societal characteristics involves drawing conclusions about a society's structure, values, and daily life based on archaeological, historical, or cultural evidence. It requires synthesizing multiple clues.

• Look for patterns in artifacts and structures.
• Consider what the presence or absence of certain evidence implies.
• Synthesize disparate clues to form a holistic picture.

Memory trick: Artifacts Announce Ancient Attributes Astutely.

In a right-angled triangle, the tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

• Formula: tan(θ) = Opposite / Adjacent
• Used to find unknown side lengths or angles in right triangles.
• Part of the SOH CAH TOA mnemonic.

Memory trick: SOH CAH TOA helps you pick the right ratio for sides and angles.

Analyzing rhetorical strategy involves identifying the deliberate choices an author or creator makes in language, imagery, and appeals to persuade an audience, evoke emotion, or convey a specific message.

• Identify specific rhetorical devices (metaphors, appeals, imagery).
• Consider the intended effect on the audience.
• Determine the underlying message or purpose being conveyed.

Memory trick: Words Wield Willful Weapons, Winning Worthy Ways.

Combining various details and findings from a text into a concise statement that captures the main point or overarching message.

• Requires identifying both positive and negative, or multiple perspectives.
• Goes beyond simply listing details to form a cohesive conclusion.
• Must be comprehensive without overstating or understating any aspect.

Memory trick: Pieces, Pattern, Point: What's the 'P'rimary message?

A constant rate of change means that a quantity increases or decreases by the same amount over equal intervals of time or other independent variable.

• Can be represented by a linear function.
• The slope of the line represents the rate of change.
• Often involves calculating total change over a period.

Memory trick: Rate times Time equals Total Change, then add to Start.

Drawing quantitative inferences involves interpreting numerical data to identify patterns, relationships, and conclusions that are not explicitly stated but are strongly implied by the numbers and comparisons.

• Look for correlations and consistent trends in the numbers.
• Identify factors that consistently override or modify other trends.
• Avoid making causal claims unless directly supported by the data's design.

Memory trick: Numbers Narrate Nuanced Nudges to New Understandings.

Complex inference and synthesis involve integrating multiple, sometimes nuanced or seemingly contradictory, pieces of information to draw a comprehensive conclusion about a system or phenomenon. It often requires understanding interactions and conditional relationships.

• Identify all contributing factors and their observed effects.
• Note any conditions or exceptions to observed correlations.
• Formulate a conclusion that accounts for all nuances and interactions.

Memory trick: Many Movers Make Major Messes, Marking Multi-faceted Models.

The maximum or minimum value of a quadratic function f(x) = ax^2 + bx + c is the y-coordinate of its vertex, found by evaluating f(-b/(2a)).

• If a > 0, the vertex is a minimum.
• If a < 0, the vertex is a maximum.
• The x-coordinate of the vertex is -b/(2a).

Memory trick: Find the peak's x, then find the peak's y.

Unit conversion is the process of changing a quantity from one unit of measurement to another using conversion factors, such as converting hours to minutes.

• 1 hour = 60 minutes
• 1 minute = 60 seconds
• Use conversion factors to cancel out unwanted units

Memory trick: Distance equals Speed Times Time, always.

The sum of the measures of the interior angles of any triangle is always 180 degrees.

• Applies to all types of triangles (equilateral, isosceles, scalene).
• Used to find an unknown angle if two are known.
• Fundamental concept in Euclidean geometry.

Memory trick: Triangles always have angles that add to a straight line (180).

Triangles can be classified as acute, right, or obtuse by comparing the square of the longest side (c^2) to the sum of the squares of the other two sides (a^2 + b^2).

• If c^2 < a^2 + b^2, the triangle is acute (all angles < 90°).
• If c^2 = a^2 + b^2, the triangle is right (one angle = 90°).
• If c^2 > a^2 + b^2, the triangle is obtuse (one angle > 90°).

Memory trick: Longest side squared, compare to others' sum, angles revealed!

For a quadratic function f(x) = ax^2 + bx + c, if a < 0, the parabola opens downwards and has a maximum value at its vertex. If a > 0, the parabola opens upwards and has a minimum value at its vertex.

• The x-coordinate of the vertex is always -b/(2a).
• The maximum or minimum value is the y-coordinate of the vertex, f(-b/(2a)).
• This concept is crucial for optimization problems.

Memory trick: Vertex's 'y' gives the peak, for the function's highest streak!

The reason an author writes a text, often categorized as to inform, persuade, or entertain.

• Determines the text's tone, structure, and content.
• Requires careful analysis of the main idea and supporting details.
• Can be explicit or implicit.

Memory trick: PIE: Persuade, Inform, Entertain.

The general character or attitude of a piece of writing, often conveyed through word choice and style.

• Reflects the author's attitude towards the subject or audience.
• Can be formal, informal, serious, humorous, objective, subjective, etc.
• Identified by analyzing diction, syntax, imagery, and rhetorical devices.

Memory trick: An author's tone colors the text like a painter's palette.

A historical term for a citizen of a borough or town, particularly one with specific rights and privileges.

• Urban resident, not rural.
• Often possessed legal or economic rights.
• Formed an important part of the early modern European middle class.

Memory trick: Town's best citizen, not a rural peasant.

Perspective refers to the viewpoint from which a story or account is told; tone refers to the author's attitude toward the subject matter.

• Perspective is influenced by the author's background, role, and experiences.
• Tone is conveyed through word choice, sentence structure, and imagery.
• Both significantly shape how an event or topic is presented.

Memory trick: Accounts reveal truth, but also who, why, and how.

A text structure that explains how one event or circumstance (the cause) leads to another (the effect).

• Often uses transition words like 'because,' 'as a result,' 'consequently,' 'therefore.'
• Can have a single cause with multiple effects, or multiple causes leading to one effect.
• Helps readers understand relationships between events or phenomena.

Memory trick: Text structures organize ideas like building blocks in a story or report.

A sentence that expresses the main idea of a research paper or essay. It is often found in the introduction.

• States the essay's purpose.
• Provides a roadmap for the reader.
• Is typically arguable and specific.

Memory trick: Introductions set the stage, Body builds the house, Conclusions wrap it up.

A rhetorical strategy where one acknowledges an opposing point of view (concession) and then argues against its validity or importance (refutation).

• Strengthens an argument by demonstrating fair-mindedness.
• Builds credibility with the audience.
• Often uses phrases like 'While it is true that...' or 'Opponents may argue, however...'

Memory trick: To win the debate, use strategies that make your points resonate.

Demonstrating that one text or idea has had a specific and identifiable impact on another text or thinker.

• Requires identifying specific parallels or references.
• Goes beyond general thematic similarity.
• Often involves direct quotations or explicit acknowledgments.

Memory trick: Relationships between texts can be direct or indirect.

The author's reason for writing and the attitude conveyed towards the subject and audience.

• Purpose drives content and structure.
• Tone is communicated through word choice and sentence structure.
• Different purposes and tones evoke different reader responses.

Memory trick: What's the goal? What's the feeling?

Information, facts, or examples that directly support or prove a claim or argument.

• Must directly relate to the topic sentence or thesis.
• Strengthens the credibility of the argument.
• Can be statistics, examples, expert testimony, or anecdotes.

Memory trick: Evidence builds your argument, brick by convincing brick.

A recurring element, image, or idea that has symbolic significance in a story.

• Helps to develop the main theme.
• Can be an object, idea, sound, or figure of speech.
• Adds depth and meaning to the narrative.

Memory trick: Imagery paints pictures with words for deeper meaning.

The process of weaving external information and ideas into one's own writing to support or develop an argument.

• Requires synthesis, not just summary.
• Should clearly explain the relevance of the source material.
• Must advance the essay's main thesis or purpose.

Memory trick: Blend the voices, make them sing your tune.

Descriptive or figurative language used to create sensory experiences or mental pictures for the reader.

• Appeals to the five senses (sight, sound, smell, taste, touch).
• Helps to create mood and atmosphere.
• Makes writing more vivid and engaging.

Memory trick: Devices make stories shine and chime.

A text structure that presents events or steps in the order in which they happened or should happen.

• Uses time-order words (first, next, then, finally).
• Often found in historical accounts, instructions, or scientific processes.
• Helps readers understand a series of events over time.

Memory trick: Organization helps readers follow the plot.

A direct or natural consequence or result.

• Implies a logical or inevitable connection.
• Often used in scientific or academic contexts.
• Suggests a relationship where one thing follows directly from another.

Memory trick: Precise words pierce the ambiguity.

Different or opposing opinions, perspectives, or arguments on the same subject.

• Focus on the same topic.
• Present conflicting conclusions or interpretations.
• Often found in debates or analyses of complex issues.

Memory trick: Connect the dots, see how texts relate.

Strong and healthy; able to withstand or overcome adverse conditions.

• Implies strength and resilience.
• Often used to describe materials or systems.
• Suggests resistance to damage or failure.

Memory trick: Strong materials Resist Breakage.

The final section of a text that restates the thesis, summarizes main points, and offers a final thought or call to action.

• Provides a sense of closure.
• Reinforces the main argument.
• Can suggest implications or future directions.

Memory trick: Close the door, review the path, leave a lasting thought.

When an author aims to convince the reader to agree with a particular viewpoint, take action, or change their beliefs.

• Often uses emotional language and strong imagery.
• Frequently found in editorials, advertisements, and political cartoons.
• Seeks to influence the reader's opinion or behavior.

Memory trick: Authors PIE their purpose: Persuade, Inform, Entertain.

Deviating from what is standard, normal, or expected.

• Implies a deviation from a pattern or norm.
• Often used in scientific or technical contexts.
• Suggests something out of place or irregular.

Memory trick: Look around the word, the context is your guide.

The opening section of a text that hooks the reader, provides background, and states the main purpose or thesis.

• Establishes context for the topic.
• Signals the scope and direction of the argument/discussion.
• Engages the reader's interest.

Memory trick: Open the door, show the path, light the way.

An organizational pattern that presents a cause and then its resulting effects, or vice versa, to demonstrate relationships.

• Clearly links actions or events to their outcomes.
• Often used in historical or scientific explanations.
• Requires evidence for both the cause and the effect.

Memory trick: Structure guides the reader, making your point clear.

The unspoken or unwritten meanings, emotions, or intentions conveyed by a text, often through tone, context, or subtle cues.

• Requires inference beyond literal interpretation.
• Influenced by word choice, punctuation, and character actions.
• Adds depth and complexity to a text.

Memory trick: Peel back the layers to find the true meaning.

A literary device where human qualities or actions are attributed to inanimate objects, animals, or abstract ideas.

• Used to create vivid imagery and atmosphere.
• Helps readers connect emotionally with non-human elements.
• Often involves verbs and adjectives typically associated with human behavior.

Memory trick: Figurative language paints pictures with words beyond their literal meaning.

Relating to or believing in the principle that all people are equal and deserve equal rights and opportunities.

• Focuses on equality among individuals.
• Often characterizes societies with shared resources and decision-making.
• Opposite of hierarchical or authoritarian.

Memory trick: Societies organize around power, wealth, or equality.

A text structure used in comparison and contrast essays where similarities and differences are discussed item by item for all subjects, rather than discussing all aspects of one subject then all aspects of another.

• Also known as the 'alternating method'.
• Effective for detailed comparisons of multiple subjects.
• Each paragraph or section focuses on a single point of comparison across all subjects.

Memory trick: Compare and contrast: either block all or point-by-point each.

An argument or set of reasons put forward to oppose an idea or theory developed in another argument.

• Acknowledges opposing viewpoints.
• Strengthens one's own argument by addressing and refuting objections.
• Often introduced with phrases like 'Some may argue,' 'Critics contend,' or 'However'.

Memory trick: Arguments need claims, evidence, and counter-moves.

A text structure that highlights differences between two or more subjects, often concluding with a way to overcome or cope with the presented conflict.

• Presents opposing ideas or situations.
• Often uses 'but,' 'however,' 'on the other hand' keywords.
• May end with a sense of hope, compromise, or ongoing struggle.

Memory trick: Structures help stories stand tall and clear.

Of vital importance; crucial.

• Indicates extreme necessity or urgency.
• Often used in formal or serious contexts.
• Suggests that something must be done.

Memory trick: Words wield power, shaping the message.

A set of two or more linear inequalities involving the same variables. The solution to a system of linear inequalities is the region where the solutions of all inequalities overlap.

• Used to model real-world constraints or boundaries.
• Each inequality represents a boundary line and a shaded region.
• The solution set is typically a feasible region in a graph.

Memory trick: Constraints are like fences: know what's allowed and what's restricted.