SAT Repeatable Patterns Reference Guide

1. Linear Systems — No Solution vs. Infinitely Many Solutions

2. The Discriminant Trap

3. Vertex & Parabola Extremes

4. Percent Increase/Decrease & Successive Percentage Changes

5. Exponential Models vs. Linear Word Problems

6. Circle Equation Geometry

7. Similar Triangles & Trigonometric Cofunction Identities

8. Rational Functions & Undefined Values

9. Sum and Product of Roots Shortcuts

10. Margin of Error & Sampling Statistics

Distractor 1 — “Too Extreme / Scope Creep”

Mechanism: Uses absolute language (always, never, all, none, every, proves, completely, only) or stretches the passage’s specific, limited claim into a sweeping general one.

The passage supports a modest, bounded claim; the trap answer swaps in a universal one that sounds like a natural extension but isn’t licensed by the text.

Distractor 2 — “True in the World, Unsupported in the Text”

Mechanism: A factually reasonable statement about the general topic that the specific passage never actually states, implies, or discusses.

The tell: the correct answer always paraphrases something traceable to a specific sentence or detail; the trap answer sounds like something a textbook would say about the topic in general.

Distractor 3 — “Reversal of Polarity / Right Words, Wrong Relationship”

Mechanism: Recycles the exact vocabulary and topic of the passage but flips the actual logical relationship — cause becomes effect, increase becomes decrease, support becomes contradiction.

Passage relationship: Rising ocean temperatures caused coral bleaching.

Because the vocabulary overlap is nearly total, this distractor is the easiest to fall for while skimming — the fix is to explicitly re-state the direction of the relationship in your own words before checking answer choices.

Distractor 4 — “Half-Right, Half-Wrong”

Mechanism: The first clause accurately paraphrases the text; the second clause quietly introduces an unsupported or false extension, betting that the accurate first half earns your trust.

The first clause of the distractor is lifted almost verbatim from the passage; the second clause (“the only factor”) is an overreach the data can’t support. Evaluate every clause of a multi-clause answer choice independently — don’t let an accurate first half vouch for an inaccurate second half.

The 4 Punctuation Equivalencies (Joining Two Independent Clauses)

Non-Essential Clauses: Dash/Comma Symmetry

A non-essential (parenthetical) clause must be bracketed by matching punctuation on both sides: comma…comma, or dash…dash. Mixing comma…dash (mid-sentence) is wrong.

Dangling Modifiers

Fix: "Having finished the report, Maria turned off the printer."

Transitions: 15 High-Frequency Words in 3 Functional Buckets

4 Question Types Trivialized by Desmos

1. 1Line/curve of best fit (regression): Enter the data table’s points directly into Desmos; run a linear, quadratic, or exponential regression to get the equation instantly — no manual slope/intercept calculation.
2. 2Systems of equations (linear-linear or linear-quadratic): Graph both equations exactly as given; read the intersection point(s) directly off the graph — no substitution or elimination required.
3. 3Root-finding / zeros of a function: Graph the function; Desmos marks the x-intercepts directly, skipping factoring or the quadratic formula entirely.
4. 4“For what value of k…” slider problems: Define k as a slider, drag it until the stated visual condition is met (tangency, single intersection, a specific point falling on the curve), then read the slider’s value.

4 Anti-Desmos Adaptations in Modern Test Items

1. 1Exact symbolic answers instead of decimals: Choices are given as radicals or fractions (e.g., (3 + √5)/2) rather than decimal approximations, so a decimal graphing solution doesn’t cleanly match any answer choice without further algebraic simplification.
2. 2Embedded unknown constants (k, a, b) in the function itself: A function like f(x) = ax² + kx − 3 can’t be graphed meaningfully without first assigning numeric test values to the unknowns — forcing symbolic manipulation (discriminant, vertex formula) instead of pure graphing.
3. 3Answer choices as equivalent expressions/equations, not numbers: Questions asking “which equation is equivalent to…” require checking algebraic equivalence; graphing all four choices to compare is slower than factoring/expanding directly, and choices can look visually identical at a given zoom level while differing at extreme values or having different domains (holes).
4. 4Requirements to justify a rule “for all x” or “for any k”: A graph only confirms behavior within the visible window — it can’t prove a general algebraic identity or that a relationship holds for every possible input. These items force a return to symbolic proof (factoring, identity manipulation) since visual confirmation in one window isn’t a valid substitute for generality.