Free USTET Exam Flashcards

Check consecutive differences, ratios, alternating positions, and repeating operations. A sound prediction explains every transition already shown; it is not just a guess that fits the last pair.

First state the relationship in the given pair—for example, tool to function, cause to effect, or part to whole. Choose the option with the same precise relationship, not merely a related word.

A necessary condition must be present, but may not be enough by itself. A sufficient condition guarantees the result. For example, being a square is sufficient for being a rectangle; being a rectangle is necessary for being a square.

For “If P, then Q,” the contrapositive is “If not Q, then not P,” and it is logically equivalent. The converse, “If Q, then P,” does not automatically follow.

The overlap represents members that belong to both sets. A value in only one circle belongs to that set but not the other; a value outside both belongs to neither set.

Translate comparisons into one consistent order. If A is before B and B is before C, then A is before C. Keep only conclusions forced by the clues; do not invent a relation between items with no connecting evidence.

Record constraints, remove impossible choices, and update the remaining possibilities after each deduction. A conclusion is secure only when every other option has been ruled out.

A letter or symbol code may shift positions, reverse order, or substitute by a fixed rule. Verify the proposed rule against every part of the given example before applying it to a new item.

Deduction moves from stated general rules to a conclusion that must follow. If all members of a group have a trait and one person is in that group, that person has the trait. Do not reverse the rule.

Induction uses observations to propose a likely general rule. Its conclusion can be well supported but is not logically certain, because a future observation can be different.

When two variables change together, a third factor may explain both, or the direction may be reversed. A causal claim needs stronger evidence than an observed association.

Members should share the defining feature of the category. In an odd-one-out task, identify the rule uniting most items, then select the item that lacks that defining feature.

A rate compares quantities with units, such as kilometers per hour. Convert time or distance before calculating, then check whether the final unit matches what the question asks for.

Use inverse operations to isolate the variable while doing the same operation to both sides. Check the result by substituting it into the original equation.

a² − b² factors as (a − b)(a + b). This pattern applies only to a subtraction of two perfect squares, not to a sum such as a² + b² over the real numbers.

A rational expression is undefined when its denominator is zero. Find excluded inputs by setting the denominator equal to zero; those values are not in the domain.

Slope is change in y divided by change in x: (y₂ − y₁)/(x₂ − x₁). Use the same point order in both differences. A horizontal line has slope 0; a vertical line has undefined slope.

When multiplying powers with the same nonzero base, add exponents: a^m × a^n = a^(m+n). When dividing, subtract exponents: a^m ÷ a^n = a^(m−n).

A ratio compares quantities; a proportion states that two ratios are equal. Cross-multiplication can solve a proportion after units and corresponding quantities are aligned.

Percent increase = (new value − original value) ÷ original value × 100%. The original value is the reference base, so increasing by 20% and then decreasing by 20% does not return to the starting value.

An arithmetic sequence has a constant difference between consecutive terms. Its nth term can be written aₙ = a₁ + (n − 1)d, where d is the common difference.

A geometric sequence has a constant nonzero ratio between consecutive terms. Its nth term is aₙ = a₁r^(n − 1), where r is the common ratio.

For ax² + bx + c = 0, the discriminant is b² − 4ac. A positive result gives two distinct real roots, zero gives one repeated real root, and a negative result gives no real roots.

For an event A, P(not A) = 1 − P(A). This is especially useful when “at least one” is easier to calculate as 1 minus the probability that none occur.

The mean is the sum of values divided by their number. The median is the middle ordered value. Extreme values can pull the mean strongly while leaving the median unchanged.

The area of a circle is A = πr², where r is the radius. Do not use the diameter directly; if given diameter d, first calculate r = d/2.

The cell membrane regulates movement into and out of a cell. Its phospholipid bilayer and transport proteins allow some substances to pass more readily than others, helping maintain internal conditions.

DNA stores genetic information. Transcription makes an RNA copy of a gene; translation uses messenger RNA at ribosomes to assemble a protein from amino acids.

Individuals with heritable traits that improve survival or reproduction tend to leave more offspring. Across generations, those advantageous traits can become more common in the population.

In a closed system, matter is not created or destroyed during an ordinary chemical reaction. Atoms are rearranged into new substances, so the total mass of reactants equals the total mass of products.

At 25°C, a pH below 7 is acidic, 7 is neutral, and above 7 is basic. The pH scale is logarithmic: a one-unit change represents a tenfold change in hydrogen-ion concentration.

Atomic radius generally decreases from left to right across a period because nuclear attraction increases, and generally increases down a group because additional electron shells are added.

For every force exerted by one object on another, there is an equal-magnitude force in the opposite direction exerted back on the first object. The forces act on different objects, so they do not cancel on one object.

Kinetic energy is energy of motion: KE = ½mv². Because velocity is squared, doubling an object’s speed makes its kinetic energy four times as large when mass stays constant.

Wave speed equals frequency times wavelength: v = fλ. If wave speed stays constant, increasing frequency means wavelength decreases.

Weather is the short-term state of the atmosphere at a place and time. Climate is the long-term pattern of weather in a region, usually described using observations over many years.

At a convergent boundary, plates move toward each other. Collision or subduction can produce mountain ranges, trenches, volcanoes, and strong earthquakes, depending on the plate types involved.

Energy can change form but is conserved in a closed system. For example, a falling object changes gravitational potential energy into kinetic energy; some may also become thermal energy through air resistance.

A thesis states the central claim or controlling idea of an essay. A strong thesis is specific enough to guide the discussion and can be supported with reasons, evidence, or analysis.

A topic sentence states the main point of a paragraph and connects it to the larger argument. The rest of the paragraph should explain, support, or illustrate that point.

The main idea is the passage’s central message; supporting details supply examples, facts, explanations, or evidence. Ask what all major details have in common to identify the main idea.

An inference is a conclusion drawn from textual evidence plus reasoning. It must be supported by clues in the passage, even when the exact conclusion is not stated word for word.

Denotation is a word’s direct dictionary meaning. Connotation is the emotional or cultural association it carries; words with similar denotations can create very different tones.

Items that have the same grammatical role should use the same form. For example: “to read, to write, and to revise” is parallel; mixing infinitives, nouns, and clauses weakens clarity.

A verb agrees with its grammatical subject, not with a nearby noun. Find the main subject first, then choose singular or plural verb form; phrases between them do not change the agreement.

A pronoun should clearly refer to a specific antecedent and agree with it in number. Replace vague references such as “this” or “it” when the reader cannot tell what noun is meant.

Use a comma after an introductory word, phrase, or dependent clause when it helps mark the boundary before the main clause: “After the lecture, the students compared notes.”

Choose a transition that matches the relationship: “however” signals contrast, “therefore” signals result, and “for example” introduces illustration. A polished transition makes the connection explicit.

Use definitions, examples, contrasts, tone, and surrounding events to infer an unfamiliar word’s meaning. Then test the inferred meaning by replacing the word and checking whether the sentence still makes sense.

Prefer precise words and remove repetition without changing the meaning. “Because” is usually clearer than “due to the fact that,” and an active verb often makes a sentence shorter and more direct.