USTET cheat sheet

Number series: test constant differences first, then constant ratios, then alternating or two interleaved sequences (odd-position and even-position terms).

Alphabet positions: A=1 through Z=26; letters opposite each other sum to 27 (A-Z, B-Y, C-X), which solves most coding and reverse-alphabet items.

Syllogism rule: 'All A are B' plus 'All B are C' gives 'All A are C'; a conclusion beginning with 'All' can never be drawn from premises containing only 'Some'.

Deductive validity depends on form, not on whether the premises are factually true; a conclusion must follow necessarily from the given statements.

Set counting: for two overlapping groups, total = (group A) + (group B) - (both), which prevents double-counting members in both categories.

Clock angle: angle between hour and minute hands = |30H - 5.5M| degrees; if the result exceeds 180, subtract it from 360.

Paper folding and punching: each fold acts as a mirror line, so holes repeat as mirror images across every crease when the paper is unfolded.

Odd-one-out: name the attribute shared by all but one item (shape, function, category, material), then select the item that lacks it.

Rotation preserves shape and size but reverses nothing; reflection reverses orientation, so a rotated figure can never be a mirror image.

Subject-verb agreement: a prepositional phrase between subject and verb does not change the subject's number ('The box of pens is heavy').

Each, every, either, neither, everyone, everybody, someone, nobody are grammatically singular and take singular verbs.

With either...or and neither...nor, the verb agrees with the subject nearer to it ('Neither the boys nor the teacher was ready').

Pronoun after a preposition takes the object case: 'between you and me', 'for him and her'.

Introductory participial phrase must modify the subject of the main clause; otherwise the modifier is dangling ('Walking home, I saw the rain' not 'Walking home, the rain fell').

Two items take the comparative (-er / more); three or more take the superlative (-est / most).

Items in a list or series must be parallel: same grammatical form (all nouns, all gerunds, or all infinitives).

Semicolon joins two independent clauses; a colon follows a complete clause and introduces a list, explanation, or quotation.

Fewer for countable plurals (fewer chairs); less for mass nouns (less water); affect is normally a verb, effect normally a noun.

Quadratic formula: for ax^2 + bx + c = 0, x = (-b +/- sqrt(b^2 - 4ac)) / (2a).

Discriminant b^2 - 4ac: positive gives two distinct real roots, zero gives one repeated root, negative gives no real roots.

Slope m = (y2 - y1)/(x2 - x1); parallel lines have equal slopes, perpendicular lines have slopes whose product is -1.

Distance between points = sqrt((x2-x1)^2 + (y2-y1)^2); midpoint coordinates are the averages of the x-values and of the y-values.

Special right triangles: 45-45-90 sides are in ratio 1:1:sqrt(2); 30-60-90 sides are in ratio 1:sqrt(3):2.

Interior angles of an n-sided polygon sum to (n - 2) x 180 degrees; a triangle totals 180 and a quadrilateral 360.

Percent change = (new - old)/old x 100; a negative result indicates a decrease.

Exponent rules: a^m x a^n = a^(m+n); (a^m)^n = a^(mn); a^(-n) = 1/a^n; a^0 = 1 for a not equal to 0.

Circle: area = pi r^2, circumference = 2 pi r; triangle area = 1/2 x base x height; average = sum of terms / number of terms.

Newton's second law: F = ma; weight is W = mg with g approximately 9.8 m/s^2 near Earth's surface.

Speed = distance/time; acceleration = change in velocity/time; velocity includes direction, speed does not.

Density = mass/volume; an object floats in a fluid when its density is less than the fluid's density.

Photosynthesis: 6CO2 + 6H2O + light energy -> C6H12O6 + 6O2, carried out in chloroplasts using chlorophyll.

Organelles: mitochondria release energy as ATP, ribosomes synthesize proteins, nucleus stores DNA, cell membrane controls entry and exit.

pH scale: below 7 acidic, 7 neutral, above 7 basic; each whole unit is a tenfold change in hydrogen ion concentration.

Atomic number = number of protons; mass number = protons + neutrons; isotopes differ in neutrons only.

In a balanced chemical equation, the number of atoms of each element is equal on both sides (law of conservation of mass).

DNA base pairing: adenine pairs with thymine, guanine pairs with cytosine.

Main idea = topic + the author's central point about it; it is often stated in the first or last sentence of the passage.

An inference is valid only if it is supported by details in the passage, not by outside knowledge or personal opinion.

Context clues signal meaning through synonyms, examples, contrasts (antonyms), and cause-effect links in surrounding sentences.

Tone is revealed by word choice: 'lament' suggests sorrow, 'chide' suggests mild criticism, 'jest' suggests humor.

Fact statements can be verified; opinion statements contain value judgments signaled by words like should, best, beautiful, ought.

Author's purpose is usually to inform, persuade, entertain, or describe; the purpose determines which answer choice fits.

Common passage structures: chronological, cause-effect, compare-contrast, problem-solution; structure signals where key details sit.

The correct answer must match the passage's scope: choices that are too broad or too narrow than the passage are wrong.