Mistake library
Common SAT mistakes
58 write-ups, one trap each: why your brain falls for it, what it looks like under time pressure, and the habit that stops it. Every one of them is an error the question bank can file against you by name.
- Traps written up
- 58Traps written up
- Official categories
- 8Official categories
- Sections of the test
- 2Sections of the test
- Every trap maps to a practice skill
- 1:1Every trap maps to a practice skill
Showing 58 of 58 traps
Algebra
The sign flip that costs SAT points: moving terms across the equals sign
Under time pressure, "move the 7 over" becomes a mechanical token-shuffle and the sign flip gets lost. The −7 must become +7 on the other side.
3x = 14 − 7 = 7 → x = 7/3.
3x = 14 + 7 = 21 → x = 7.
a(b + c) ≠ ab + c: the distribution slip on SAT Algebra
Your eye latches onto the first term, distributes once, and moves on. The parenthesis silently loses its second multiplication.
5x + 2 = 40 → 5x = 38 → x = 7.6.
5x + 10 = 40 → 5x = 30 → x = 6.
Flipping rise over run: the SAT slope inversion
"Rise over run" is verbal, not visual. When both differences are computed, nothing forces the y-difference into the numerator.
(6 − 2)/(11 − 3) = 4/8 = 1/2.
(11 − 3)/(6 − 2) = 8/4 = 2.
(−3)² vs −3²: the parenthesis that changes the sign
Exponents bind tighter than the minus sign. Without parentheses, the square applies to 3 first and the negation comes last.
−3² − 2(−3) = −9 + 6 = −3.
(−3)² − 2(−3) = 9 + 6 = 15.
Forgetting to flip the inequality when dividing by a negative
Flipping feels like an arbitrary bolt-on rule, so it drops out first under pressure. (It isn't arbitrary: multiplying by a negative reverses the number line.)
x < −4.
x > −4 (dividing by −2 flips the inequality).
Substituting into systems without the parentheses
Substitution is mentally 'replace a letter', but algebraically it's 'replace a letter with a wrapped expression'. Skipping the wrapper drops a distribution.
3x − 2·2x − 3 = 12 → −x − 3 = 12 → x = −15.
3x − 2(2x − 3) = 12 → 3x − 4x + 6 = 12 → x = −6.
Stopping at the slope: forgetting to solve for b
Slope is the satisfying computation, so finishing it feels like finishing the problem. The second step (plug a point back in to find b) has no computational 'click' to remind you.
m = (13 − 7)/(4 − 2) = 3. Answer: 3.
m = 3, then 7 = 3(2) + b → b = 1.
SAT word problems: writing the equation is the whole question
English orders words by emphasis; algebra orders them by operation. "Five more than twice a number" and "twice a number more than five" read almost identically and are different expressions. Once the equation is wrong, every step after it is correct and useless.
C = 90h + 45 — the first number met becomes the rate.
C = 45h + 90. The rate is the amount that repeats; the flat fee is paid once.
SAT linear models: what the slope and intercept mean in the story
Interpretation questions strip out the computation and test only the mapping between symbol and situation. Because both numbers in the model appear in the choices, an answer that swaps them looks exactly as plausible as the right one, and there is no arithmetic to catch the swap.
"96 litres are used each hour" — the right number attached to the wrong role.
The paint in the tank before spraying started. 96 is the value at t = 0; −8 is the litres-per-hour rate.
SAT systems of equations: line up the variable before you add
Adding two equations is safe. Subtracting means distributing a minus sign across every term on both sides, and the term that gets forgotten is almost always the constant on the right. The result still looks like a reasonable answer, so nothing warns you.
Multiplying the first by 3 and subtracting, but negating only the left-hand side.
6x + 15y = 93. Subtract the second: 19y = 76, so y = 4 — the minus applied to 17 as well.
Advanced Math
x³·x⁴ vs (x³)⁴: add or multiply the exponents?
Two similar-looking rules stored side by side interfere with each other. Without a quick derivation habit, retrieval is a coin flip.
x³·x⁴ = x¹²; (x³)⁴ = x⁷.
x³·x⁴ = x³⁺⁴ = x⁷; (x³)⁴ = x³ˣ⁴ = x¹².
√(a² + b²) is not a + b: the radical shortcut that fails
Radicals DO distribute over multiplication (√(ab) = √a·√b), and the pattern generalizes in your head to addition, where it's false.
√9 + √16 = 3 + 4 = 7.
√25 = 5.
f(g(x)) means g first: composition order on the SAT
English reads left to right, so f-then-g feels natural. But composition evaluates inside-out, like nested parentheses.
f(3) = 7, then g(7) = 49.
g(3) = 9, then f(9) = 19.
Reading the minimum from vertex form: the sign trap in (x − h)²
Two numbers sit in the formula and the question asks for one number. Without labeling which coordinate is which, the first number wins.
3 (the number inside the parentheses).
5 — the minimum value of f, reached AT x = 3.
SAT functions: f(2) means substitute, then finish the arithmetic
Substitution feels like the hard part, so attention drops the moment it is done. But the exponent and the coefficient still have to be applied in the right order, and the answer choices are built from the plausible wrong orders — cubing after multiplying, or adding before multiplying.
(4 · 3)³ − 9 = 1,719, or 4 · 3 · 3 − 9 = 27 — the coefficient pulled inside the exponent, or the exponent read as a third factor.
3³ = 27 first, then 4 · 27 = 108, then − 9 = 99.
SAT exponential growth and decay: the base is 1 + r, not r
A percent change describes the change; the base of an exponential model describes the whole amount after the change. Writing 0.03 models a population that loses 97% a year. The two forms look so alike that the error survives right through to the answer.
P = 4,500(0.03)^y — the percent inserted directly as the base.
P = 4,500(1.03)^y. Growth adds to 1; decay subtracts from it — a 3% decline would be 0.97, not −0.03.
SAT discriminant: how many solutions, without solving
Questions that say "exactly one", "no real", or "two distinct" are counting solutions, not finding them. The count is decided entirely by b² − 4ac: positive gives two, zero gives one, negative gives none. Solving instead turns a one-line calculation into an algebra problem carrying an unknown constant — and when the numbers are not friendly, into guesswork.
Factoring into (x + ?)(x + ?) and guessing values of c that work.
Exactly one solution means b² − 4ac = 0, so 36 − 4c = 0 and c = 9.
Problem-Solving and Data Analysis
Why +10% then −10% isn't 0% on SAT Math
Percent changes feel like ordinary numbers, so your brain wants to add them. But each change applies to a *different base* — the second 10% is taken from a bigger number than the first.
+10% − 10% = 0% → $200.
200 × 1.10 × 0.90 = $198. The net change is −1%, not 0%.
Grabbing the mean when the SAT asked for the median
Mean has a formula; median has a procedure (sort, then pick). Brains prefer formulas under time pressure, so the formula fires first.
(3 + 9 + 4 + 4 + 10)/5 = 6.
Sort: 3, 4, 4, 9, 10 → middle value = 4.
"150% of" vs "150% more": the phrase that doubles answers
Everyday speech blurs the two phrasings, so both parse to "×1.5" unless you consciously check for the word 'more'.
B = 1.5 × 40 = 60.
B = 40 + 1.5 × 40 = 2.5 × 40 = 100.
AND multiplies, OR adds: the SAT probability mix-up
The words 'and'/'or' read as connectors, not operations. Without a rule anchored to them, addition is the default reflex.
½ + ½ = 1.
½ × ½ = ¼.
Converting square units: why 1 m² is not 100 cm²
The linear conversion is memorized as a number (×100), and numbers don't carry dimensions. The 'squared' in cm² silently applies to the unit, not your factor.
0.5 × 100 = 50 cm².
0.5 × 100² = 5,000 cm².
Setting up proportions upside down
Proportions require consistent placement (miles over hours on BOTH sides). Nothing in the mechanics warns you when one side is flipped.
210/3.5 = 5/x → x ≈ 0.083 miles.
210/3.5 = x/5 → x = 300 miles.
SAT standard deviation: spread, not size
Standard deviation measures how far values sit from their own mean, so sliding the whole set up or down leaves it unchanged. Bigger numbers feel like more variation, and that intuition is wrong in a way the SAT tests directly — usually with two sets whose means differ obviously and whose spreads differ subtly.
B — the numbers are far larger.
Neither. Both are three consecutive integers, so both are spread identically around their own mean.
Geometry and Trigonometry
Using the diameter as the radius: the SAT circle trap
Formulas are memorized in terms of r, but problems love to give d. Under pressure, the number you're handed goes straight into the formula slot.
A = π(10)² = 100π.
r = 10/2 = 5, so A = π(5)² = 25π.
2πr vs πr²: mixing up circumference and area under pressure
The formulas share symbols and live in the same mental drawer. Retrieval under stress grabs the wrong one because nothing anchors them to what they measure.
2π(6) = 12π.
π(6)² = 36π.
Matching the wrong sides in similar triangles
The figures are drawn rotated or reflected, so 'the left side' of one triangle is not the left side of the other. Position, not correspondence, drives the pairing.
Pairing by how the figure looks — AB with EF: 4/8 = EF/6 → EF = 3.
Pair by letter order: AB↔DE and BC↔EF, so 4/8 = 6/EF → EF = 12.
SAT equation of a circle: the number on the right is r², not r
The standard form stores the radius squared, so every circle question has a hidden square root in it. Doubling a radius multiplies the right-hand side by four, not two — which is why "radius twice as large" questions have such convincing wrong answers.
= 75, tripling the number that is written down.
r = 5, so Q has r = 15 and r² = 225. Tripling the radius multiplies the right-hand side by nine.
SAT SOHCAHTOA: naming the sides from the angle you were given
The hypotenuse is the only side that never moves. Opposite and adjacent are defined relative to the angle named in the question, so switching angles swaps them — and the resulting ratio is the reciprocal of the right one, which is always among the choices.
Treating JL as adjacent to K because it is drawn on the left, giving KL = 5.6.
From angle K, JL is opposite and KL is adjacent. So 2/5 = 14 / KL and KL = 35.
Information and Ideas
Command of Evidence: true is not the same as supporting
Verifying a statement against the text is a satisfying, concrete act, and it feels like the work the question asked for. But the question asked which finding supports a particular hypothesis — a relationship between two things, only one of which is in the choice.
"The sites were abandoned in 2019." — true, and consistent with every competing explanation.
"Abandonment occurred only at sites within 200 m of the new runway." — this one distinguishes noise from the alternatives.
Quantitative evidence: reading the graph the question did not ask about
Reading a graph correctly feels like the whole task, so once a choice checks out against the axes it gets accepted. But the question is about a claim in the text, and the chart's other true trends are exactly what the wrong choices report.
"Yields under treatment A rose from 2.1 to 2.4 tonnes." — correctly read, and about the wrong series.
A choice comparing B's increase to A's, because the claim is comparative.
Inferences: the answer you knew before you read the passage
Truth and support feel like the same signal. When a choice matches something you already believe, the belief supplies the confidence the text was supposed to supply, and you stop looking for the sentence that backs it.
"Car ownership in the city subsequently fell." — plausible, widely true, and never stated.
"More people used the expanded routes after they opened." — narrower than you want it to be, and forced by the two facts given.
Central Ideas: picking a true detail instead of the main point
Memory ranks by vividness, not by structural importance. So the choice you recognize is the one built from the most concrete sentence, which is exactly the sentence that was serving as an example.
"The project was delayed by 14 months." — the most memorable fact, offered as evidence.
"The project suffered from poor management." — the claim the delay was cited to support.
Craft and Structure
Words in Context: the hardest word is rarely the answer
Years of vocabulary lists trained the association "harder word = better answer". The digital SAT dropped isolated vocabulary in favor of context, so difficulty of the word carries no information at all — only fit with the sentence does.
"laconic" — impressive, but it means brief, and brevity is not what "avoiding commitment" describes.
"vague" — plain, and exactly what the second half of the sentence defines.
The word you know, in a meaning you did not expect
Recognition is instant and correctness feels immediate, so you never reopen the question. The primary meaning arrives before you have finished reading the sentence that would have overridden it.
Reading "qualifies" as "makes eligible" and rejecting it as nonsense.
"qualifies" here means limits or narrows — the sense the contrast with "overturn" requires.
Text Structure: naming what a sentence says instead of what it does
Restating is easier than analyzing, and the restating choice is verifiable word by word against the text — which feels like exactly the kind of evidence the SAT rewards. Function is a relationship to the rest of the paragraph, which requires reading past the underlined sentence.
"It describes two revisions to the early estimates." — true, and merely a paraphrase.
"It supplies the evidence for the claim made in the previous sentence." That relationship is the sentence's job, and it is only visible if you read the sentence before it.
Cross-Text Connections: answering from one text
Two passages is more than working memory comfortably holds, and the second one is fresher. Every wrong choice is written to be defensible from exactly one text — that is what makes them feel supported.
"Trade route changes explain the settlement's decline." — an accurate statement of Text 2, which never mentions Text 1's claim.
"The drought coincided with the decline but was not its cause." — Text 2's position, applied to the specific claim Text 1 made.
Expression of Ideas
however vs therefore: the SAT transition question in one question
"However" and "therefore" both sound analytical, and both fit smoothly into almost any academic sentence. Fit is not what is tested — direction is. One reverses the previous sentence, the other extends it.
"Therefore" — treating a drawback as a consequence of the advantage.
"However" — the second sentence works against the first, so the transition must reverse.
Reading only the sentence before the transition
The blank's position pulls your attention backwards. And the previous sentence alone is usually compatible with several transitions — the sentence after it is what eliminates all but one.
Reading only the first sentence and picking "Consequently" — plausible until you read on.
"However". The second sentence undercuts the first result rather than following from it, so the transition has to reverse direction.
for example vs in addition: is it a case or a second point?
The contrast/consequence test gets you to a shortlist and then stops working. Every remaining choice fits the direction, so students fall back on which one sounds more academic.
"In addition" — implying a second, separate benefit.
"For example" — the oak is an instance of the claim just made, not a new claim.
Rhetorical Synthesis: the bullet points are not the question
The bullet list is long and the goal is one italicized line above it, so attention goes to the notes. Several choices then look defensible, because they are true statements built from those notes and only the goal rules them out.
A choice that accurately summarizes both techniques' history — true, but it emphasizes no difference.
A choice that puts the two durability figures side by side, because contrast is what the goal asked for.
Synthesis goals that name an audience change the answer
The audience clause sits at the end of a long sentence you have already extracted a verb from, so it gets skimmed. But it eliminates choices that a purely content-based reading would keep.
A choice opening with the alloy's phase-transition temperature — accurate, on topic, and unreadable to the stated audience.
A choice that says what the technique does in plain terms before naming anything technical.
Standard English Conventions
Comma splice: why the SAT never lets a comma join two sentences
Both halves sound like one connected thought, so a comma feels like the right amount of pause. But the SAT tests structure, not pauses: if each side could stand alone as a sentence, a comma alone is never strong enough to hold them together.
"chapter, it now begins" — both sides are full sentences, so the comma cannot join them.
"chapter; it now begins" — or a period, or "chapter, and it now begins". Semicolon, period, or comma + FANBOYS.
Semicolon or comma? The SAT rule that decides it in one test
In everyday reading, semicolons show up in places where the writer wanted a longer beat, so the punctuation gets filed under "style". The SAT never tests style. A semicolon there is a structural claim: complete sentence on the left, complete sentence on the right.
"consistent; across every trial" — the right side is a fragment, so the semicolon is wrong.
"consistent across every trial" — no punctuation at all. Nothing is being joined.
The SAT colon rule: the part that matters is BEFORE the colon
A colon feels like an announcement, so we place it wherever a list is about to start. The SAT's rule ignores what comes after entirely: the words to the left of the colon must form a complete sentence on their own.
"includes: gloves" — "The kit includes" is not a sentence; it is missing its object.
"includes gloves, a pipette, and two slides" — or rewrite as "The kit includes three items: gloves, a pipette, and two slides."
One dash in, one comma out: the SAT's mismatched-pair trap
Each punctuation mark looks individually defensible, so you evaluate them one at a time and both pass. The error only exists in the relationship between them, which is exactly the thing a left-to-right read never checks.
"rover — launched in 2003, transmitted" — a dash opened it and a comma closed it.
"rover, launched in 2003, transmitted" — two commas. Two dashes would also be correct; one of each never is.
The comma that never belongs: splitting a subject from its verb
Long subjects are tiring to read, and a comma feels like permission to rest. But nothing separates a subject from its verb — the longer the subject, the stronger the urge, and the more often the SAT tests it.
"program, received" — the comma cuts the subject off from its own verb.
"program received" — no punctuation. The subject runs straight into the verb.
The comma pair that changes what a sentence means
The commas look decorative, so students add or drop them by ear. They are not decorative — they mark information as removable. If a phrase narrows down which thing you mean, it cannot be removable, and it cannot take commas.
"The novel, she published in 1997, won" — commas mark the phrase as removable, but she wrote four novels, so it is the only thing identifying which one.
"The novel she published in 1997 won the national prize." No commas. Had the paragraph said she published exactly one novel, the date would be a bonus fact and both commas would go in.
The words between the subject and the verb are a decoy
You match the verb to the nearest noun because that is the last one you read. The SAT places a plural noun immediately before the blank precisely so proximity fights grammar — and proximity usually wins.
"manuscripts are housed" — agreeing with the noun inside the prepositional phrase.
"A collection ... is housed" — the subject is singular; "of rare manuscripts" is just a modifier.
When the subject comes after the verb: SAT inverted sentences
Every rule you learned assumes subject-then-verb order. Inverted sentences break that, so the habit of "look left for the subject" quietly returns the wrong word — or no word at all.
"There is several reasons" — matching the verb to "there".
"There are several reasons ... among them was a supply shortage." The subjects are "reasons" and "shortage".
Each, every, either: the words that look plural and are not
The plural noun sits right next to the pronoun ("of the museums"), and the actual antecedent, "each", is further away and does not look plural to the ear. Distance loses to proximity every time you are reading quickly.
"their archive" — a plural pronoun matched to the nearby plural "museums".
"its archive" — the antecedent is "each", which is singular. Note the verb agrees the same way: "has", not "have".
The tense shift you will not hear: SAT verb sequence
You evaluate the blank as its own sentence, where any tense sounds fine. Tense consistency is a property of the passage, and the passage is the thing you stopped reading once you found the blank.
"writes his notes" — a present-tense verb inside a past-tense narrative.
"wrote his notes" — matching "reached" and "photographed".
Dangling modifiers: the SAT sentence that says the wrong thing
You know who did the studying, so your brain supplies Dr. Reyes and the sentence reads fine. The grammar does not care what you know — the opening phrase grabs the first noun after the comma, and that noun is "the conclusion".
"the conclusion was obvious to Dr. Reyes." — the subject is "conclusion", which cannot study.
"Dr. Reyes found the conclusion obvious." — the doer of the opening action is now the subject.
its vs it's: the one possessive with no apostrophe
You generalize correctly from "the dog's collar" and get punished for it. Pronoun possessives (its, hers, theirs, yours, whose) never take an apostrophe; the apostrophe form is always a contraction of two words.
"it's findings ... its clear" — both reversed.
"its findings ... it's clear" — possessive first, then the contraction of "it is".
students / student's / students': picking the right apostrophe
All three forms sound identical when read aloud, so there is no sound to check against. Students then pick by feel, which is a coin flip among three options.
"student's proposals ... teacher's" — singular owner, and a possessive with nothing owned.
"students' proposals ... teachers" — plural students each owning a proposal; plural teachers owning nothing.
Comparing a thing to the wrong thing: SAT faulty comparisons
The intended comparison is obvious, so your brain completes it and moves on. The sentence as written compares whatever noun actually sits on each side of "than" or "unlike" — and one of them is usually a possessive standing in for a person.
"than Nairobi" — a population compared to a city.
"than that of Nairobi" — population to population. For plurals, "those of".
Parallel structure: lists that change grammatical gear mid-sentence
By the third item you are reading for content rather than form, and the change lands past the point where your attention was. It is the same reason the error is almost always planted in the last item.
"she led two workshops" — a clause where the pattern established two -ing phrases.
"leading two workshops" — the third item now matches the first two.
SAT verb forms: when the blank needs -ing and when it needs a real verb
A clause needs a finite verb, and a second one has to be licensed by something — a coordinator ("the report combines data and was published") or a subordinator. When the blank sits inside a modifier set off by commas there is neither, so a finite verb there has nothing to attach to and the blank must be a participle or an infinitive. The choices are written so that both sound fine read aloud, because the ear does not check what licenses a verb.
"combines" — a real verb, and the sentence reads smoothly.
"combining". The subject "report" already has its verb, "was published", so the blank cannot be a second one.