NTS NAT cheat sheet

A verb agrees with its subject in number; a prepositional phrase between them never changes it, so write 'The box of pens is on the table.'

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

A comma alone cannot join two independent clauses; use a period, a semicolon, or a coordinating conjunction (and, but, or, nor, for, so, yet).

Form the possessive of a singular noun by adding 's (the child's book) and of a regular plural noun by adding only an apostrophe (the students' essays).

'Its' shows possession; 'it's' is only a contraction of 'it is' or 'it has'. The same distinction separates 'whose' (possessive) from 'who's' (who is).

An introductory participial phrase must describe the subject of the main clause; otherwise the modifier is dangling ('Walking home, the rain began' is wrong).

A colon follows an independent clause and introduces a list, example, or explanation; it never separates a verb from its object.

Items in a series or on either side of a correlative pair must share grammatical form: 'hiking, swimming, and cycling', not 'hiking, swimming, and to cycle'.

'Between' governs two items; 'among' governs three or more. 'Fewer' counts things, 'less' measures quantity.

Use the bridge-sentence method for analogies: write a precise sentence relating the first pair, then test each option against that same sentence.

Contrast signals (although, despite, however, yet, on the contrary) tell you the blank takes a word opposite in meaning to the clue in the sentence.

Cause and result signals (because, therefore, since, thus, consequently) tell you the blank moves in the same direction as the clue.

Common roots: cred- (believe), dict- (say), ject- (throw), spec- (look), vert- (turn), bene- (good), mal- (bad), voc- (call).

Common prefixes: circum- (around), trans- (across), sub- (under), hyper- (over), anti- (against), auto- (self), ambi- (both).

Common suffixes: -ology (study of), -phobia (fear of), -cide (killing of), -ous (full of), -ify (to make), -ism (doctrine or practice).

Negating prefixes in-, im-, il-, ir-, un-, dis-, and non- usually build a word's antonym, so an antonym answer often shares the base word.

Denotation is the dictionary meaning; connotation is the emotional charge, which shifts along a scale (thrifty is positive, frugal neutral, stingy negative).

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

Mean = sum / n, so sum = mean x n; this identity finds a missing value or a total when the average is known.

Speed = distance / time; for combined work, the rate together is 1/a + 1/b of the job per hour.

Slope m = (y2 - y1) / (x2 - x1); the line y = mx + b has slope m and y-intercept b, and parallel lines share m.

Areas: triangle = bh/2; circle = pi r^2; trapezoid = (b1 + b2)h/2. Volumes: cylinder = pi r^2 h; rectangular solid = lwh.

Pythagorean theorem a^2 + b^2 = c^2; memorized triples 3-4-5, 5-12-13, 8-15-17 and their multiples avoid square roots.

Simple interest I = Prt; compound amount A = P(1 + r/n)^(nt), where n is the number of compounding periods per year.

Probability = favorable outcomes / total outcomes; for independent events multiply the separate probabilities.

When a ratio a:b is given, write the quantities as ax and bx, then solve for x using the stated total or difference.

A conditional 'If P then Q' is equivalent to its contrapositive 'If not Q then not P'; the converse and inverse are not equivalent to it.

Valid form modus ponens: P implies Q, P is true, therefore Q is true. Valid form modus tollens: P implies Q, Q is false, therefore P is false.

Invalid form affirming the consequent: P implies Q, Q is true, therefore P. Invalid form denying the antecedent: P implies Q, P is false, therefore Q is false.

'All A are B' never licenses the reversal 'All B are A'; it supports 'Some B are A' only when A is known to be non-empty.

'P unless Q' means 'if not Q then P'; 'P only if Q' means 'if P then Q', so Q is necessary for P.

Validity depends on the form of the argument, not on whether its premises happen to be true in the real world.

A necessary condition must be present for the outcome; a sufficient condition guarantees it. Being a mammal is necessary but not sufficient for being a dog.

In ordering puzzles, fix the positions that are given absolutely first, then place relative clues; draw a numbered line rather than holding positions in memory.

Physics: F = ma for net force; weight w = mg; kinematics v = u + at and v^2 = u^2 + 2as; kinetic energy = (1/2)mv^2.

Physics: Ohm's law V = IR; electrical power P = VI = I^2R; resistors in series add, in parallel their reciprocals add.

Chemistry: moles = mass / molar mass; one mole contains 6.02 x 10^23 particles; acid + base -> salt + water (neutralization).

Chemistry: pH = -log[H+]; pH below 7 is acidic, above 7 basic; oxidation is loss of electrons, reduction is gain.

Biology: photosynthesis is 6CO2 + 6H2O -> C6H12O6 + 6O2; mitochondria release ATP by respiration; DNA pairs A with T and G with C.

Computer Science: binary place values from the right are 1, 2, 4, 8, 16, 32, 64, 128; 1 byte = 8 bits; 1 KB = 1024 bytes.

Commerce: Assets = Liabilities + Owner's Equity; in double-entry bookkeeping every transaction debits one account and credits another by an equal amount.

Arts: match an artwork or idea to its period by date markers - Renaissance roughly 1400-1600, Baroque roughly 1600-1750, Romanticism roughly 1800-1850.