Free PSAT 8/9 Exam Flashcards

Read the whole short passage and predict the word's meaning in context. Contrast markers, reasons and examples can guide you, but no signal word determines the answer alone. Check each choice against the sentence: 'credit' can mean accept as true rather than lend money, and 'reserved' can mean quiet rather than booked.

The chosen word or phrase must: (1) match the logical direction set by the sentence's hinge words (agreement vs. contrast), (2) fit the exact grammatical part of speech required by the slot, and (3) match the passage's register and tone without introducing unsupported intensity or slang.

The topic is merely the subject matter (e.g., 'tardigrades' or '1930s tree planting'). The main purpose is the author's rhetorical action verb—such as to explain a process, illustrate a general claim with an example, describe features, argue a disputed claim, or qualify an earlier statement. Eliminate choices whose introductory verb ('argue', 'warn', 'refute') is not supported by the text.

Examples include cause and effect ('because', 'as a result'), comparison or contrast ('similarly', 'whereas'), claim and illustration ('for example'), problem and solution ('to address this obstacle'), and qualification ('only when', 'however'). These are useful reading patterns, not a ranked list of the test's most frequent structures; confirm the relationship in the whole passage.

Mentally delete the underlined sentence and ask what job the passage loses without it—such as defining a key term, providing a concrete example of the preceding claim, introducing a limitation, or stating the study's result. Do not confuse the purpose of the whole passage with the specific role of the underlined sentence.

1. Summarize Text 1's core claim in one short clause. 2. Summarize Text 2's core claim in one short clause. 3. Name the exact relationship: does Text 2 support, challenge, illustrate with a specific case, explain a mechanism for, or qualify Text 1's claim? Remember that sharing a topic does not automatically mean the two authors agree.

To qualify a claim is to accept its basic observation while adding a condition, boundary, or limitation (often signaled by 'only if', 'unless', or 'not by itself'). A qualifying response neither fully endorses Text 1 without reservation nor completely refutes Text 1.

Track evaluative adjectives, verbs, and concession words that reveal attitude. In informational texts, distinguish the author's own conclusion from third-party views introduced with attribution ('some critics contend', 'early observers assumed') that the author subsequently tests or revises.

A valid central idea must: (1) cover the primary point of the entire short passage rather than a single supporting detail, (2) stay strictly within the scope of the text without adding outside facts, and (3) preserve the passage's qualifiers rather than overstating the claim with extreme words like 'always' or 'completely'.

Identify the exact claim or character judgment in the question stem first (e.g., that a character feels reluctant despite outward calm). Then select the quotation that directly demonstrates both parts of that claim, eliminating quotes that merely mention the setting or require unstated assumptions.

Identify the proposed relationship and compare the finding with its prediction. A result consistent with the prediction may support the hypothesis; a contrary result may weaken it. Check comparison groups, alternative explanations and qualifiers. Observing X together with Y can support a relationship without proving that X causes Y; removing X need not eliminate Y if other causes exist.

An answer choice must pass two gates: (1) Data accuracy—the numbers, units, categories, and trend direction must match the table, bar graph, or line graph; and (2) Rhetorical relevance—that accurate statistic must actually support or complete the specific claim in the passage's final sentence. Eliminate choices that cite true data from the wrong row or column.

Choose the completion most strongly supported by the stated and implied information. Track the passage’s evidence, comparisons and qualifiers, and reject choices requiring an unsupported assumption. A justified scientific inference can be probable rather than deductively necessary; do not change a cautious conclusion into certainty.

1. Extreme absolutes ('all', 'never', 'only', 'proves') when the passage uses hedged language ('may', 'often', 'some'). 2. Reversed cause and effect. 3. True-for-the-wrong-group comparisons (swapping two species, time periods, or experimental groups). 4. Half-right choices where the second clause introduces an unmentioned concept.

Locate the stated detail or a supported paraphrase, matching its subject, time and scope. The answer need not summarize the whole passage. If a text says “Sampling occurred in spring, and analysis began in autumn,” a question about when samples were collected is answered spring, not autumn. Choose the requested detail rather than a broad main-idea statement or an outside assumption.

Separate independent clauses with a period or semicolon, or join them with a comma plus a coordinating conjunction (for, and, nor, but, or, yet, so). A colon or single dash can introduce an explanation after a complete clause. A comma alone does not join two independent clauses. Thus 'The result changed; however, the method did not' and 'The result changed. However, the method did not' work; a comma before however cannot do that joining job.

A colon introducing a list or explanation normally follows a complete independent clause. A single dash can also introduce an explanation after a complete clause. What follows may be a list, phrase or clause. Do not insert a colon between a verb or preposition and its object: write “The kit included gloves and goggles,” or “The kit included two items: gloves and goggles.”

A nonessential element adds information without identifying which person or thing is meant. In the middle of a sentence, set it off with matching commas, dashes or parentheses; at the end, the sentence-ending punctuation closes it. An essential modifier identifies the referent and is not set off as an aside. Decide from meaning and sentence structure rather than treating every which or that as a complete rule.

Locate the head of the subject rather than agreeing with a noun inside an intervening phrase: “The box of samples is sealed.” In an inverted sentence such as “Beyond the ridge stand two towers,” find the subject after the verb. Each, every and neither used as singular subjects take singular agreement; neither...nor constructions need their own agreement check. In standard American usage, a collective noun acting as one unit takes a singular verb.

For an introductory participial phrase describing the subject, the subject after the comma must be the person or thing performing the action or having the described trait. In “Walking across the stage, Maya reached for the trophy,” Maya is walking. Writing “Walking across the stage, the trophy caught Maya’s eye” incorrectly makes the trophy the walker.

Possessive pronouns have no apostrophe: its, their and whose. It's means it is or it has; they're means they are; who's means who is or who has. For nouns, add ’s to a singular owner ('the student’s lab') and to an irregular plural not ending in s ('the children’s lab'). Add only an apostrophe to a regular plural ending in s ('the students’ lab'). Ordinary plurals have no possessive apostrophe.

Use time markers and surrounding context to choose verb tense: “In 1934, crews planted...” describes a past event, while a general scientific fact commonly uses present tense. Coordinate corresponding grammatical forms in a list or comparison, such as “measured rainfall, recorded totals, and graphed results.” Parallel structure concerns grammatical roles, not identical words or a ban on every justified tense change.

Read the question stem's exact rhetorical goal before reading the bulleted notes. Break the goal into its required parts (e.g., 'introduce the researcher's method AND state the main finding'), then eliminate any choice that fails to perform every part of that instruction—even if the choice is grammatically correct and uses true facts from the notes.

For a difference or similarity, the answer must establish the requested comparison clearly; the names can be implicit if the sentence already identifies them. For an unfamiliar audience, include enough background to identify the subject before explaining the requested feature. In every case, satisfy the exact rhetorical goal using supported notes; extra true information cannot repair a missing goal.

Use a contrast transition when the second sentence opposes, limits, or reverses an expectation set by the first sentence. Use 'however' or 'by contrast' for direct opposition between two claims or groups, and 'nevertheless' or 'still' when an outcome occurs despite an obstacle stated in the first sentence.

Result or inference transitions such as 'therefore', 'thus' and 'consequently' connect a conclusion or outcome to its supporting reason; the relationship need not be a physical cause. Addition transitions such as 'moreover' add related support, and 'similarly' highlights a resemblance. Sequence markers such as 'previously' and 'subsequently' establish time order. Choose the relationship supported by both sentences.

'For instance' introduces an example; 'specifically' narrows a general statement to a particular detail. 'In other words' and 'that is' restate or clarify. 'In short' and 'overall' summarize. 'Ultimately' can mark a final outcome or an eventual development, so its role depends on the passage. Read the complete relationship rather than assigning every transition one unchanging label.

Cover the blank and describe the relationship between the surrounding ideas, then test every choice in that context. Two apparent synonyms can differ in emphasis, reference or placement. Check syntax and punctuation as well as logic; do not automatically eliminate both choices because they look interchangeable, or assume every option is already punctuated correctly.

After simplifying both sides to ax + b = cx + d: (1) One solution when the x-coefficients differ (a ≠ c). (2) No solution when the x-coefficients match (a = c) but the constants differ (b ≠ d), leaving a false statement like 4 = −2. (3) Infinitely many solutions (an identity) when both the x-coefficients and constants match (a = c and b = d), leaving 0 = 0.

For two distinct points with x₂ ≠ x₁, m = (y₂ − y₁)/(x₂ − x₁). It is the change in output per unit increase in input in y = mx + b. A positive slope means y increases as x increases; a negative slope means it decreases. If x₂ = x₁ for distinct points, the line is vertical and its slope is undefined.

For a nonvertical line, y = mx + b has slope m and y-intercept (0,b); y − y₁ = m(x − x₁) passes through (x₁,y₁). In Ax + By = C, A and B cannot both be zero. If B ≠ 0, slope is −A/B and the y-intercept is (0,C/B). If A ≠ 0, the x-intercept is (C/A,0). When a denominator is zero, inspect the horizontal or vertical line directly rather than dividing by zero.

Distinct nonvertical parallel lines have equal slopes and different y-intercepts. Distinct vertical lines x = h are also parallel. For two nonvertical lines, perpendicularity means m₁m₂ = −1; the negative-reciprocal rule applies when both slopes exist. A horizontal line has slope 0 and is perpendicular to a vertical line, whose slope is undefined.

To evaluate f(4), use input x = 4 to find the output, provided 4 belongs to the domain. To solve f(x) = 4, find all allowed inputs whose output is 4; there may be none, one or several. If 0 belongs to the domain, (0,f(0)) is the y-intercept. In a model, it represents an initial value only when x = 0 has that contextual meaning.

Substitution is convenient when one variable is already isolated. Elimination combines equations so a variable cancels, possibly after scaling one or both equations. If the question asks for a combined expression, check whether an appropriate linear combination gives that expression directly; adding or subtracting works only when the coefficients produce the needed combination.

For A₁x + B₁y = C₁ and A₂x + B₂y = C₂, assume each equation represents a genuine line. If A₁B₂ − A₂B₁ ≠ 0, the lines intersect once. If it equals 0, eliminate or compare the complete equations: an identity means the same line and infinitely many solutions; a contradiction means distinct parallel lines and no solution. Coefficient ratios are safe only when their denominators are nonzero.

Reverse the inequality sign when multiplying or dividing both sides by a negative number. For a two-variable linear inequality, use a dashed boundary for < or > and a solid boundary for ≤ or ≥. With y isolated, y greater than the boundary means shade above; y less means below. A test point must be off the boundary: (0,0) is convenient only when it is not on that line.

Substitute the solved input into the expression for the quantity actually requested. If T = 2x + 3 counts tickets from x packages, and solving the given conditions gives x = 5, then T = 2(5) + 3 = 13 tickets. Enter 13 when asked for T, not the input 5. Keep units and contextual restrictions, such as nonnegative whole-number counts, separate from the algebraic calculation.

Expand, factor and combine like terms using valid algebraic identities. For example, 3x(2x − 5) + 4x = 6x² − 15x + 4x = 6x² − 11x for every real x. Substituting one value can expose a counterexample but cannot prove a polynomial identity; justify the transformations or compare all coefficients. Terms such as x² and x are unlike terms and cannot be added as though they had the same power.

For a ≠ 0, f(x) = a(x − h)² + k has vertex (h,k) and axis x = h. In f(x) = ax² + bx + c, h = −b/(2a) and k = f(h). For the unrestricted real-input quadratic, a > 0 gives minimum k and a < 0 gives maximum k. If a context restricts the domain, also check whether the vertex is allowed and whether endpoints determine the contextual extreme.

For ax² + bx + c = 0 (a ≠ 0), the solutions are x = (−b ± √(b² − 4ac)) / (2a). The discriminant D = b² − 4ac tells how many real solutions (and x-intercepts) exist: if D > 0, there are 2 distinct real solutions; if D = 0, there is exactly 1 real solution (the vertex touches the x-axis); if D < 0, there are 0 real solutions.

A linear model has a constant additive change per equal input interval. A positive-quantity exponential model f(t) = a·b^t has a > 0 and b > 0: b > 1 gives growth, while 0 < b < 1 gives decay. Write b = 1 + r for growth or b = 1 − r for decay, with r a decimal rate. Thus b = 0.85 means a 15% decrease each period. If b = 1, the model is constant rather than growing or decaying.

For two disjoint groups making up the whole with ratio A:B = a:b, A represents a/(a+b), not a/b, of the total. For example, if a club consists only of 8th and 9th graders in ratio 2:5, the 8th graders are 2/7 of the club. If other groups are present, a+b is not automatically the whole-club denominator.

Use conversion factors equal to 1 so units cancel: 8 m/s × (1 km/1000 m) × (3600 s/1 h) = 28.8 km/h. Two hours 15 minutes is 2.25 hours. Overall average speed is total distance/total positive elapsed time. For two positive-duration legs, the simple mean of their speeds equals the overall average when the durations are equal or the speeds are equal; otherwise use the time-weighted average.

If New = Original × (1+p) after an increase, or ×(1−p) after a decrease, recover Original by dividing by that nonzero factor; p is a decimal rate. A price of $48 after 20% off came from 48/0.8 = $60. Multiplying 48 by 1.2 gives 57.6, not 60. Successive 20% discounts multiply: 0.8×0.8 = 0.64, so the net discount is 36%, not 40%. A 100% decrease cannot be reversed from the final value alone.

Mean is sum/count for a nonempty data set; median is the sorted middle value, or the mean of the two middle values for an even count. Modes are values of greatest frequency; there may be several. Range is maximum minus minimum. An extreme value can strongly affect the mean and range. The median resists the magnitude of extremes, but adding an observation can change which values occupy the middle: it is not guaranteed to stay unchanged or change only a little.

In a scatterplot, a line of best fit y = mx + b gives the predicted value for a given input x. The residual for a data point (x, y) is actual y − predicted y (positive if the data point sits above the line, negative if below). A positive or negative association on a scatterplot shows only that two variables move together; it does not by itself prove that changing x causes y to change.

For a conditioning group B with positive count, P(A|B) = count(A and B)/count(B). Use the given group’s total rather than the grand total unless B is the whole population. With P(B) > 0, independence means P(A|B) = P(A). More generally, the definition P(A and B) = P(A)P(B) also applies when a conditioning probability would be zero.

Rectangle area is lw, triangle area is bh/2 with perpendicular height, and rectangular-prism volume is lwh. For a prism or cylinder, V = Bh uses base area B and perpendicular height h. When all lengths of similar figures scale by positive factor k, areas scale by k² and volumes by k³. PSAT 8/9 Geometry covers area, volume, lines, angles and right triangles. Standalone circle theorems and trigonometry are outside its published scope; circular-solid volume questions can still occur.

Complementary angles sum to 90°; supplementary angles (linear pairs on a straight line) sum to 180°; vertical angles across an intersection are equal. When a transversal crosses parallel lines, corresponding angles and alternate interior angles are equal, while consecutive (same-side) interior angles sum to 180°. The interior angles of any triangle sum to 180°, and an exterior angle of a triangle equals the sum of the two remote interior angles.

For a right triangle with legs a,b and hypotenuse c, a²+b²=c². Examples include 3-4-5, 5-12-13 and 8-15-17; scaled versions also work. A 45°-45°-90° triangle has side ratio 1:1:√2, and a 30°-60°-90° triangle has ratio 1:√3:2, with 2 opposite 90°. Match sides to angles before substituting. PSAT 8/9 assesses right-triangle geometry; sine, cosine and tangent are outside its published scope.